%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE128+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:13:03 AM UTC 2025
% Result : Theorem 5.83s 6.03s
% Output : Proof 5.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE128+1 : TPTP v9.0.0. Released v4.0.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.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 19:01:33 EDT 2025
% 0.12/0.33 % CPUTime :
% 5.83/6.03 % SZS status Theorem
% 5.83/6.03 % SZS output start Proof
% 5.83/6.03 tff(zero_type, type, (
% 5.83/6.03 zero: $i)).
% 5.83/6.03 tff(addition_type, type, (
% 5.83/6.03 addition: ( $i * $i ) > $i)).
% 5.83/6.03 tff(antidomain_type, type, (
% 5.83/6.03 antidomain: $i > $i)).
% 5.83/6.03 tff(tptp_fun_X1_1_type, type, (
% 5.83/6.03 tptp_fun_X1_1: $i)).
% 5.83/6.03 tff(divergence_type, type, (
% 5.83/6.03 divergence: $i > $i)).
% 5.83/6.03 tff(tptp_fun_X0_0_type, type, (
% 5.83/6.03 tptp_fun_X0_0: $i)).
% 5.83/6.03 tff(domain_type, type, (
% 5.83/6.03 domain: $i > $i)).
% 5.83/6.03 tff(forward_diamond_type, type, (
% 5.83/6.03 forward_diamond: ( $i * $i ) > $i)).
% 5.83/6.03 tff(multiplication_type, type, (
% 5.83/6.03 multiplication: ( $i * $i ) > $i)).
% 5.83/6.03 tff(one_type, type, (
% 5.83/6.03 one: $i)).
% 5.83/6.03 tff(star_type, type, (
% 5.83/6.03 star: $i > $i)).
% 5.83/6.03 tff(1,plain,
% 5.83/6.03 ((~![X0: $i] : ((~(divergence(X0) = zero)) | ![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero)))) <=> (~![X0: $i] : ((~(divergence(X0) = zero)) | ![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero))))),
% 5.83/6.03 inference(rewrite,[status(thm)],[])).
% 5.83/6.03 tff(2,plain,
% 5.83/6.03 ((~![X0: $i] : ((divergence(X0) = zero) => ![X1: $i] : ((addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1))) => (domain(X1) = zero)))) <=> (~![X0: $i] : ((~(divergence(X0) = zero)) | ![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero))))),
% 5.83/6.03 inference(rewrite,[status(thm)],[])).
% 5.83/6.03 tff(3,axiom,(~![X0: $i] : ((divergence(X0) = zero) => ![X1: $i] : ((addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1))) => (domain(X1) = zero)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 5.83/6.03 tff(4,plain,
% 5.83/6.03 (~![X0: $i] : ((~(divergence(X0) = zero)) | ![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero)))),
% 5.83/6.03 inference(modus_ponens,[status(thm)],[3, 2])).
% 5.83/6.03 tff(5,plain,
% 5.83/6.03 (~![X0: $i] : ((~(divergence(X0) = zero)) | ![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero)))),
% 5.83/6.03 inference(modus_ponens,[status(thm)],[4, 1])).
% 5.83/6.03 tff(6,plain,
% 5.83/6.03 (~![X0: $i] : ((~(divergence(X0) = zero)) | ![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero)))),
% 5.83/6.03 inference(modus_ponens,[status(thm)],[5, 1])).
% 5.83/6.03 tff(7,plain,
% 5.83/6.03 (~![X0: $i] : ((~(divergence(X0) = zero)) | ![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero)))),
% 5.83/6.03 inference(modus_ponens,[status(thm)],[6, 1])).
% 5.83/6.03 tff(8,plain,
% 5.83/6.03 (divergence(X0!0) = zero),
% 5.83/6.03 inference(and_elim,[status(thm)],[7])).
% 5.83/6.03 tff(9,plain,
% 5.83/6.03 (^[X0: $i] : refl((forward_diamond(X0, divergence(X0)) = divergence(X0)) <=> (forward_diamond(X0, divergence(X0)) = divergence(X0)))),
% 5.83/6.03 inference(bind,[status(th)],[])).
% 5.83/6.03 tff(10,plain,
% 5.83/6.03 (![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0)) <=> ![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0))),
% 5.83/6.04 inference(quant_intro,[status(thm)],[9])).
% 5.83/6.04 tff(11,plain,
% 5.83/6.04 (![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0)) <=> ![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0))),
% 5.83/6.04 inference(rewrite,[status(thm)],[])).
% 5.83/6.04 tff(12,axiom,(![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+7.ax','divergence1')).
% 5.83/6.04 tff(13,plain,
% 5.83/6.04 (![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0))),
% 5.83/6.04 inference(modus_ponens,[status(thm)],[12, 11])).
% 5.83/6.04 tff(14,plain,(
% 5.83/6.04 ![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0))),
% 5.83/6.04 inference(skolemize,[status(sab)],[13])).
% 5.83/6.04 tff(15,plain,
% 5.83/6.04 (![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0))),
% 5.83/6.04 inference(modus_ponens,[status(thm)],[14, 10])).
% 5.83/6.04 tff(16,plain,
% 5.83/6.04 ((~![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0))) | (forward_diamond(X0!0, divergence(X0!0)) = divergence(X0!0))),
% 5.83/6.04 inference(quant_inst,[status(thm)],[])).
% 5.83/6.04 tff(17,plain,
% 5.83/6.04 (forward_diamond(X0!0, divergence(X0!0)) = divergence(X0!0)),
% 5.83/6.04 inference(unit_resolution,[status(thm)],[16, 15])).
% 5.83/6.04 tff(18,plain,
% 5.83/6.04 (zero = divergence(X0!0)),
% 5.83/6.04 inference(symmetry,[status(thm)],[8])).
% 5.83/6.04 tff(19,plain,
% 5.83/6.04 (forward_diamond(X0!0, zero) = forward_diamond(X0!0, divergence(X0!0))),
% 5.83/6.04 inference(monotonicity,[status(thm)],[18])).
% 5.83/6.04 tff(20,plain,
% 5.83/6.04 (^[X0: $i, X1: $i] : refl((forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1)))) <=> (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1)))))),
% 5.83/6.04 inference(bind,[status(th)],[])).
% 5.83/6.04 tff(21,plain,
% 5.83/6.04 (![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1)))) <=> ![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))),
% 5.83/6.04 inference(quant_intro,[status(thm)],[20])).
% 5.83/6.04 tff(22,plain,
% 5.83/6.04 (![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1)))) <=> ![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))),
% 5.83/6.04 inference(rewrite,[status(thm)],[])).
% 5.83/6.04 tff(23,axiom,(![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax','forward_diamond')).
% 5.83/6.04 tff(24,plain,
% 5.83/6.04 (![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))),
% 5.83/6.04 inference(modus_ponens,[status(thm)],[23, 22])).
% 5.83/6.04 tff(25,plain,(
% 5.83/6.04 ![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))),
% 5.83/6.04 inference(skolemize,[status(sab)],[24])).
% 5.83/6.04 tff(26,plain,
% 5.83/6.04 (![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))),
% 5.83/6.04 inference(modus_ponens,[status(thm)],[25, 21])).
% 5.83/6.04 tff(27,plain,
% 5.83/6.04 ((~![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))) | (forward_diamond(X0!0, zero) = domain(multiplication(X0!0, domain(zero))))),
% 5.83/6.04 inference(quant_inst,[status(thm)],[])).
% 5.83/6.04 tff(28,plain,
% 5.83/6.04 (forward_diamond(X0!0, zero) = domain(multiplication(X0!0, domain(zero)))),
% 5.83/6.04 inference(unit_resolution,[status(thm)],[27, 26])).
% 5.83/6.04 tff(29,plain,
% 5.83/6.04 (domain(multiplication(X0!0, domain(zero))) = forward_diamond(X0!0, zero)),
% 5.83/6.04 inference(symmetry,[status(thm)],[28])).
% 5.83/6.04 tff(30,plain,
% 5.83/6.04 (^[X0: $i] : refl((domain(X0) = antidomain(antidomain(X0))) <=> (domain(X0) = antidomain(antidomain(X0))))),
% 5.83/6.04 inference(bind,[status(th)],[])).
% 5.83/6.04 tff(31,plain,
% 5.83/6.04 (![X0: $i] : (domain(X0) = antidomain(antidomain(X0))) <=> ![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 5.83/6.04 inference(quant_intro,[status(thm)],[30])).
% 5.83/6.04 tff(32,plain,
% 5.83/6.04 (![X0: $i] : (domain(X0) = antidomain(antidomain(X0))) <=> ![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 5.83/6.04 inference(rewrite,[status(thm)],[])).
% 5.83/6.04 tff(33,axiom,(![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax','domain4')).
% 5.83/6.04 tff(34,plain,
% 5.83/6.04 (![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 5.83/6.04 inference(modus_ponens,[status(thm)],[33, 32])).
% 5.83/6.04 tff(35,plain,(
% 5.83/6.04 ![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 5.83/6.04 inference(skolemize,[status(sab)],[34])).
% 5.83/6.04 tff(36,plain,
% 5.83/6.04 (![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 5.83/6.04 inference(modus_ponens,[status(thm)],[35, 31])).
% 5.83/6.04 tff(37,plain,
% 5.83/6.04 ((~![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))) | (domain(multiplication(X0!0, domain(zero))) = antidomain(antidomain(multiplication(X0!0, domain(zero)))))),
% 5.83/6.04 inference(quant_inst,[status(thm)],[])).
% 5.83/6.04 tff(38,plain,
% 5.83/6.04 (domain(multiplication(X0!0, domain(zero))) = antidomain(antidomain(multiplication(X0!0, domain(zero))))),
% 5.83/6.04 inference(unit_resolution,[status(thm)],[37, 36])).
% 5.83/6.04 tff(39,plain,
% 5.83/6.04 (antidomain(antidomain(multiplication(X0!0, domain(zero)))) = domain(multiplication(X0!0, domain(zero)))),
% 5.83/6.04 inference(symmetry,[status(thm)],[38])).
% 5.83/6.04 tff(40,plain,
% 5.83/6.04 ((~![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))) | (domain(zero) = antidomain(antidomain(zero)))),
% 5.83/6.04 inference(quant_inst,[status(thm)],[])).
% 5.83/6.04 tff(41,plain,
% 5.83/6.04 (domain(zero) = antidomain(antidomain(zero))),
% 5.83/6.04 inference(unit_resolution,[status(thm)],[40, 36])).
% 5.83/6.04 tff(42,plain,
% 5.83/6.04 (antidomain(antidomain(zero)) = domain(zero)),
% 5.83/6.04 inference(symmetry,[status(thm)],[41])).
% 5.83/6.04 tff(43,plain,
% 5.83/6.04 (multiplication(X0!0, antidomain(antidomain(zero))) = multiplication(X0!0, domain(zero))),
% 5.83/6.04 inference(monotonicity,[status(thm)],[42])).
% 5.83/6.04 tff(44,plain,
% 5.83/6.04 (multiplication(X0!0, domain(zero)) = multiplication(X0!0, antidomain(antidomain(zero)))),
% 5.83/6.04 inference(symmetry,[status(thm)],[43])).
% 5.83/6.04 tff(45,plain,
% 5.83/6.04 (antidomain(multiplication(X0!0, domain(zero))) = antidomain(multiplication(X0!0, antidomain(antidomain(zero))))),
% 5.83/6.04 inference(monotonicity,[status(thm)],[44])).
% 5.83/6.04 tff(46,plain,
% 5.83/6.04 (antidomain(multiplication(X0!0, antidomain(antidomain(zero)))) = antidomain(multiplication(X0!0, domain(zero)))),
% 5.83/6.04 inference(symmetry,[status(thm)],[45])).
% 5.83/6.04 tff(47,plain,
% 5.83/6.04 (^[X0: $i, X1: $i] : refl((addition(antidomain(multiplication(X0, X1)), antidomain(multiplication(X0, antidomain(antidomain(X1))))) = antidomain(multiplication(X0, antidomain(antidomain(X1))))) <=> (addition(antidomain(multiplication(X0, X1)), antidomain(multiplication(X0, antidomain(antidomain(X1))))) = antidomain(multiplication(X0, antidomain(antidomain(X1))))))),
% 5.83/6.04 inference(bind,[status(th)],[])).
% 5.83/6.04 tff(48,plain,
% 5.83/6.04 (![X0: $i, X1: $i] : (addition(antidomain(multiplication(X0, X1)), antidomain(multiplication(X0, antidomain(antidomain(X1))))) = antidomain(multiplication(X0, antidomain(antidomain(X1))))) <=> ![X0: $i, X1: $i] : (addition(antidomain(multiplication(X0, X1)), antidomain(multiplication(X0, antidomain(antidomain(X1))))) = antidomain(multiplication(X0, antidomain(antidomain(X1)))))),
% 5.83/6.04 inference(quant_intro,[status(thm)],[47])).
% 5.83/6.04 tff(49,plain,
% 5.83/6.04 (![X0: $i, X1: $i] : (addition(antidomain(multiplication(X0, X1)), antidomain(multiplication(X0, antidomain(antidomain(X1))))) = antidomain(multiplication(X0, antidomain(antidomain(X1))))) <=> ![X0: $i, X1: $i] : (addition(antidomain(multiplication(X0, X1)), antidomain(multiplication(X0, antidomain(antidomain(X1))))) = antidomain(multiplication(X0, antidomain(antidomain(X1)))))),
% 5.83/6.04 inference(rewrite,[status(thm)],[])).
% 5.83/6.04 tff(50,axiom,(![X0: $i, X1: $i] : (addition(antidomain(multiplication(X0, X1)), antidomain(multiplication(X0, antidomain(antidomain(X1))))) = antidomain(multiplication(X0, antidomain(antidomain(X1)))))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax','domain2')).
% 5.83/6.04 tff(51,plain,
% 5.83/6.04 (![X0: $i, X1: $i] : (addition(antidomain(multiplication(X0, X1)), antidomain(multiplication(X0, antidomain(antidomain(X1))))) = antidomain(multiplication(X0, antidomain(antidomain(X1)))))),
% 5.83/6.04 inference(modus_ponens,[status(thm)],[50, 49])).
% 5.83/6.04 tff(52,plain,(
% 5.83/6.04 ![X0: $i, X1: $i] : (addition(antidomain(multiplication(X0, X1)), antidomain(multiplication(X0, antidomain(antidomain(X1))))) = antidomain(multiplication(X0, antidomain(antidomain(X1)))))),
% 5.83/6.04 inference(skolemize,[status(sab)],[51])).
% 5.83/6.04 tff(53,plain,
% 5.83/6.04 (![X0: $i, X1: $i] : (addition(antidomain(multiplication(X0, X1)), antidomain(multiplication(X0, antidomain(antidomain(X1))))) = antidomain(multiplication(X0, antidomain(antidomain(X1)))))),
% 5.83/6.04 inference(modus_ponens,[status(thm)],[52, 48])).
% 5.83/6.04 tff(54,plain,
% 5.83/6.04 ((~![X0: $i, X1: $i] : (addition(antidomain(multiplication(X0, X1)), antidomain(multiplication(X0, antidomain(antidomain(X1))))) = antidomain(multiplication(X0, antidomain(antidomain(X1)))))) | (addition(antidomain(multiplication(X0!0, zero)), antidomain(multiplication(X0!0, antidomain(antidomain(zero))))) = antidomain(multiplication(X0!0, antidomain(antidomain(zero)))))),
% 5.83/6.04 inference(quant_inst,[status(thm)],[])).
% 5.83/6.04 tff(55,plain,
% 5.83/6.04 (addition(antidomain(multiplication(X0!0, zero)), antidomain(multiplication(X0!0, antidomain(antidomain(zero))))) = antidomain(multiplication(X0!0, antidomain(antidomain(zero))))),
% 5.83/6.04 inference(unit_resolution,[status(thm)],[54, 53])).
% 5.83/6.04 tff(56,plain,
% 5.83/6.04 (^[X0: $i] : refl((addition(antidomain(antidomain(X0)), antidomain(X0)) = one) <=> (addition(antidomain(antidomain(X0)), antidomain(X0)) = one))),
% 5.83/6.04 inference(bind,[status(th)],[])).
% 5.83/6.04 tff(57,plain,
% 5.83/6.04 (![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one) <=> ![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)),
% 5.83/6.04 inference(quant_intro,[status(thm)],[56])).
% 5.83/6.04 tff(58,plain,
% 5.83/6.04 (![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one) <=> ![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)),
% 5.83/6.04 inference(rewrite,[status(thm)],[])).
% 5.83/6.04 tff(59,axiom,(![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax','domain3')).
% 5.83/6.04 tff(60,plain,
% 5.83/6.04 (![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)),
% 5.83/6.04 inference(modus_ponens,[status(thm)],[59, 58])).
% 5.83/6.04 tff(61,plain,(
% 5.83/6.04 ![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)),
% 5.83/6.04 inference(skolemize,[status(sab)],[60])).
% 5.83/6.04 tff(62,plain,
% 5.83/6.04 (![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)),
% 5.83/6.04 inference(modus_ponens,[status(thm)],[61, 57])).
% 5.83/6.04 tff(63,plain,
% 5.83/6.04 ((~![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)) | (addition(antidomain(antidomain(X1!1)), antidomain(X1!1)) = one)),
% 5.83/6.04 inference(quant_inst,[status(thm)],[])).
% 5.83/6.04 tff(64,plain,
% 5.83/6.04 (addition(antidomain(antidomain(X1!1)), antidomain(X1!1)) = one),
% 5.83/6.04 inference(unit_resolution,[status(thm)],[63, 62])).
% 5.83/6.04 tff(65,plain,
% 5.83/6.04 (one = addition(antidomain(antidomain(X1!1)), antidomain(X1!1))),
% 5.83/6.04 inference(symmetry,[status(thm)],[64])).
% 5.83/6.04 tff(66,plain,
% 5.83/6.04 ((~![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)) | (addition(antidomain(antidomain(antidomain(multiplication(X0!0, domain(zero))))), antidomain(antidomain(multiplication(X0!0, domain(zero))))) = one)),
% 5.83/6.04 inference(quant_inst,[status(thm)],[])).
% 5.83/6.04 tff(67,plain,
% 5.83/6.04 (addition(antidomain(antidomain(antidomain(multiplication(X0!0, domain(zero))))), antidomain(antidomain(multiplication(X0!0, domain(zero))))) = one),
% 5.83/6.04 inference(unit_resolution,[status(thm)],[66, 62])).
% 5.83/6.04 tff(68,plain,
% 5.83/6.04 (forward_diamond(X0!0, divergence(X0!0)) = forward_diamond(X0!0, zero)),
% 5.83/6.04 inference(symmetry,[status(thm)],[19])).
% 5.83/6.04 tff(69,plain,
% 5.83/6.04 (divergence(X0!0) = forward_diamond(X0!0, divergence(X0!0))),
% 5.83/6.04 inference(symmetry,[status(thm)],[17])).
% 5.83/6.04 tff(70,plain,
% 5.83/6.04 (zero = antidomain(antidomain(multiplication(X0!0, domain(zero))))),
% 5.83/6.04 inference(transitivity,[status(thm)],[18, 69, 68, 28, 38])).
% 5.83/6.04 tff(71,plain,
% 5.83/6.04 (antidomain(antidomain(antidomain(multiplication(X0!0, domain(zero))))) = antidomain(domain(multiplication(X0!0, domain(zero))))),
% 5.83/6.04 inference(monotonicity,[status(thm)],[39])).
% 5.83/6.04 tff(72,plain,
% 5.83/6.04 (antidomain(domain(multiplication(X0!0, domain(zero)))) = antidomain(antidomain(antidomain(multiplication(X0!0, domain(zero)))))),
% 5.83/6.04 inference(symmetry,[status(thm)],[71])).
% 5.83/6.04 tff(73,plain,
% 5.83/6.04 (addition(antidomain(domain(multiplication(X0!0, domain(zero)))), zero) = addition(antidomain(antidomain(antidomain(multiplication(X0!0, domain(zero))))), antidomain(antidomain(multiplication(X0!0, domain(zero)))))),
% 5.83/6.04 inference(monotonicity,[status(thm)],[72, 70])).
% 5.83/6.04 tff(74,plain,
% 5.83/6.04 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 5.83/6.04 inference(bind,[status(th)],[])).
% 5.83/6.04 tff(75,plain,
% 5.83/6.04 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 5.83/6.04 inference(quant_intro,[status(thm)],[74])).
% 5.83/6.04 tff(76,plain,
% 5.83/6.04 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 5.83/6.04 inference(rewrite,[status(thm)],[])).
% 5.83/6.04 tff(77,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_identity')).
% 5.83/6.04 tff(78,plain,
% 5.83/6.04 (![A: $i] : (addition(A, zero) = A)),
% 5.83/6.04 inference(modus_ponens,[status(thm)],[77, 76])).
% 5.83/6.04 tff(79,plain,(
% 5.83/6.04 ![A: $i] : (addition(A, zero) = A)),
% 5.83/6.04 inference(skolemize,[status(sab)],[78])).
% 5.83/6.04 tff(80,plain,
% 5.83/6.04 (![A: $i] : (addition(A, zero) = A)),
% 5.83/6.04 inference(modus_ponens,[status(thm)],[79, 75])).
% 5.83/6.04 tff(81,plain,
% 5.83/6.04 ((~![A: $i] : (addition(A, zero) = A)) | (addition(antidomain(domain(multiplication(X0!0, domain(zero)))), zero) = antidomain(domain(multiplication(X0!0, domain(zero)))))),
% 5.83/6.04 inference(quant_inst,[status(thm)],[])).
% 5.83/6.04 tff(82,plain,
% 5.83/6.04 (addition(antidomain(domain(multiplication(X0!0, domain(zero)))), zero) = antidomain(domain(multiplication(X0!0, domain(zero))))),
% 5.83/6.04 inference(unit_resolution,[status(thm)],[81, 80])).
% 5.83/6.04 tff(83,plain,
% 5.83/6.04 (antidomain(domain(multiplication(X0!0, domain(zero)))) = addition(antidomain(domain(multiplication(X0!0, domain(zero)))), zero)),
% 5.83/6.04 inference(symmetry,[status(thm)],[82])).
% 5.83/6.04 tff(84,plain,
% 5.83/6.04 (^[A: $i] : refl((multiplication(A, zero) = zero) <=> (multiplication(A, zero) = zero))),
% 5.83/6.04 inference(bind,[status(th)],[])).
% 5.83/6.04 tff(85,plain,
% 5.83/6.04 (![A: $i] : (multiplication(A, zero) = zero) <=> ![A: $i] : (multiplication(A, zero) = zero)),
% 5.83/6.04 inference(quant_intro,[status(thm)],[84])).
% 5.83/6.04 tff(86,plain,
% 5.83/6.04 (![A: $i] : (multiplication(A, zero) = zero) <=> ![A: $i] : (multiplication(A, zero) = zero)),
% 5.83/6.04 inference(rewrite,[status(thm)],[])).
% 5.83/6.04 tff(87,axiom,(![A: $i] : (multiplication(A, zero) = zero)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','right_annihilation')).
% 5.83/6.04 tff(88,plain,
% 5.83/6.04 (![A: $i] : (multiplication(A, zero) = zero)),
% 5.83/6.04 inference(modus_ponens,[status(thm)],[87, 86])).
% 5.83/6.04 tff(89,plain,(
% 5.83/6.04 ![A: $i] : (multiplication(A, zero) = zero)),
% 5.83/6.04 inference(skolemize,[status(sab)],[88])).
% 5.83/6.04 tff(90,plain,
% 5.83/6.04 (![A: $i] : (multiplication(A, zero) = zero)),
% 5.83/6.04 inference(modus_ponens,[status(thm)],[89, 85])).
% 5.83/6.04 tff(91,plain,
% 5.83/6.04 ((~![A: $i] : (multiplication(A, zero) = zero)) | (multiplication(X0!0, zero) = zero)),
% 5.83/6.04 inference(quant_inst,[status(thm)],[])).
% 5.83/6.04 tff(92,plain,
% 5.83/6.04 (multiplication(X0!0, zero) = zero),
% 5.83/6.04 inference(unit_resolution,[status(thm)],[91, 90])).
% 5.83/6.04 tff(93,plain,
% 5.83/6.04 (multiplication(X0!0, zero) = domain(multiplication(X0!0, domain(zero)))),
% 5.83/6.04 inference(transitivity,[status(thm)],[92, 18, 69, 68, 28])).
% 5.83/6.04 tff(94,plain,
% 5.83/6.04 (antidomain(multiplication(X0!0, zero)) = antidomain(domain(multiplication(X0!0, domain(zero))))),
% 5.83/6.04 inference(monotonicity,[status(thm)],[93])).
% 5.83/6.04 tff(95,plain,
% 5.83/6.04 (antidomain(multiplication(X0!0, zero)) = addition(antidomain(antidomain(X1!1)), antidomain(X1!1))),
% 5.83/6.04 inference(transitivity,[status(thm)],[94, 83, 73, 67, 65])).
% 5.83/6.04 tff(96,plain,
% 5.83/6.04 (addition(zero, antidomain(multiplication(X0!0, zero))) = addition(zero, addition(antidomain(antidomain(X1!1)), antidomain(X1!1)))),
% 5.83/6.04 inference(monotonicity,[status(thm)],[95])).
% 5.83/6.04 tff(97,plain,
% 5.83/6.04 (addition(zero, addition(antidomain(antidomain(X1!1)), antidomain(X1!1))) = addition(zero, antidomain(multiplication(X0!0, zero)))),
% 5.83/6.04 inference(symmetry,[status(thm)],[96])).
% 5.83/6.04 tff(98,plain,
% 5.83/6.04 (^[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)))),
% 5.83/6.04 inference(bind,[status(th)],[])).
% 5.83/6.04 tff(99,plain,
% 5.83/6.04 (![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))),
% 5.83/6.04 inference(quant_intro,[status(thm)],[98])).
% 5.83/6.04 tff(100,plain,
% 5.83/6.04 (![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))),
% 5.83/6.04 inference(rewrite,[status(thm)],[])).
% 5.83/6.04 tff(101,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')).
% 5.83/6.04 tff(102,plain,
% 5.83/6.04 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 5.83/6.04 inference(modus_ponens,[status(thm)],[101, 100])).
% 5.83/6.04 tff(103,plain,(
% 5.83/6.04 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 5.83/6.04 inference(skolemize,[status(sab)],[102])).
% 5.83/6.04 tff(104,plain,
% 5.83/6.04 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 5.83/6.04 inference(modus_ponens,[status(thm)],[103, 99])).
% 5.83/6.04 tff(105,plain,
% 5.83/6.04 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(zero, addition(antidomain(antidomain(X1!1)), antidomain(X1!1))) = addition(addition(zero, antidomain(antidomain(X1!1))), antidomain(X1!1)))),
% 5.83/6.04 inference(quant_inst,[status(thm)],[])).
% 5.83/6.04 tff(106,plain,
% 5.83/6.04 (addition(zero, addition(antidomain(antidomain(X1!1)), antidomain(X1!1))) = addition(addition(zero, antidomain(antidomain(X1!1))), antidomain(X1!1))),
% 5.83/6.04 inference(unit_resolution,[status(thm)],[105, 104])).
% 5.83/6.04 tff(107,plain,
% 5.83/6.04 (addition(addition(zero, antidomain(antidomain(X1!1))), antidomain(X1!1)) = addition(zero, addition(antidomain(antidomain(X1!1)), antidomain(X1!1)))),
% 5.83/6.04 inference(symmetry,[status(thm)],[106])).
% 5.83/6.04 tff(108,plain,
% 5.83/6.04 ((~![A: $i] : (addition(A, zero) = A)) | (addition(antidomain(antidomain(X1!1)), zero) = antidomain(antidomain(X1!1)))),
% 5.83/6.04 inference(quant_inst,[status(thm)],[])).
% 5.83/6.04 tff(109,plain,
% 5.83/6.04 (addition(antidomain(antidomain(X1!1)), zero) = antidomain(antidomain(X1!1))),
% 5.83/6.04 inference(unit_resolution,[status(thm)],[108, 80])).
% 5.83/6.04 tff(110,plain,
% 5.83/6.04 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 5.83/6.04 inference(bind,[status(th)],[])).
% 5.83/6.04 tff(111,plain,
% 5.83/6.04 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 5.83/6.04 inference(quant_intro,[status(thm)],[110])).
% 5.83/6.04 tff(112,plain,
% 5.83/6.04 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 5.83/6.04 inference(rewrite,[status(thm)],[])).
% 5.83/6.04 tff(113,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 5.83/6.04 tff(114,plain,
% 5.83/6.04 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 5.83/6.04 inference(modus_ponens,[status(thm)],[113, 112])).
% 5.83/6.04 tff(115,plain,(
% 5.83/6.04 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 5.83/6.04 inference(skolemize,[status(sab)],[114])).
% 5.83/6.04 tff(116,plain,
% 5.83/6.04 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 5.83/6.04 inference(modus_ponens,[status(thm)],[115, 111])).
% 5.83/6.04 tff(117,plain,
% 5.83/6.04 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(antidomain(antidomain(X1!1)), zero) = addition(zero, antidomain(antidomain(X1!1))))),
% 5.83/6.04 inference(quant_inst,[status(thm)],[])).
% 5.83/6.04 tff(118,plain,
% 5.83/6.04 (addition(antidomain(antidomain(X1!1)), zero) = addition(zero, antidomain(antidomain(X1!1)))),
% 5.83/6.04 inference(unit_resolution,[status(thm)],[117, 116])).
% 5.83/6.04 tff(119,plain,
% 5.83/6.04 (addition(zero, antidomain(antidomain(X1!1))) = addition(antidomain(antidomain(X1!1)), zero)),
% 5.83/6.04 inference(symmetry,[status(thm)],[118])).
% 5.83/6.04 tff(120,plain,
% 5.83/6.04 (addition(zero, antidomain(antidomain(X1!1))) = antidomain(antidomain(X1!1))),
% 5.83/6.04 inference(transitivity,[status(thm)],[119, 109])).
% 5.83/6.04 tff(121,plain,
% 5.83/6.04 (addition(addition(zero, antidomain(antidomain(X1!1))), antidomain(X1!1)) = addition(antidomain(antidomain(X1!1)), antidomain(X1!1))),
% 5.83/6.04 inference(monotonicity,[status(thm)],[120])).
% 5.83/6.04 tff(122,plain,
% 5.83/6.04 (addition(antidomain(antidomain(X1!1)), antidomain(X1!1)) = addition(addition(zero, antidomain(antidomain(X1!1))), antidomain(X1!1))),
% 5.83/6.04 inference(symmetry,[status(thm)],[121])).
% 5.83/6.04 tff(123,plain,
% 5.83/6.04 (antidomain(multiplication(X0!0, zero)) = addition(zero, antidomain(multiplication(X0!0, zero)))),
% 5.83/6.04 inference(transitivity,[status(thm)],[94, 83, 73, 67, 65, 122, 107, 97])).
% 5.83/6.04 tff(124,plain,
% 5.83/6.04 (addition(antidomain(multiplication(X0!0, zero)), antidomain(multiplication(X0!0, antidomain(antidomain(zero))))) = addition(addition(zero, antidomain(multiplication(X0!0, zero))), antidomain(multiplication(X0!0, antidomain(antidomain(zero)))))),
% 5.83/6.04 inference(monotonicity,[status(thm)],[123])).
% 5.83/6.04 tff(125,plain,
% 5.83/6.04 (addition(addition(zero, antidomain(multiplication(X0!0, zero))), antidomain(multiplication(X0!0, antidomain(antidomain(zero))))) = addition(antidomain(multiplication(X0!0, zero)), antidomain(multiplication(X0!0, antidomain(antidomain(zero)))))),
% 5.83/6.04 inference(symmetry,[status(thm)],[124])).
% 5.83/6.04 tff(126,plain,
% 5.83/6.04 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(zero, addition(antidomain(multiplication(X0!0, zero)), antidomain(multiplication(X0!0, antidomain(antidomain(zero)))))) = addition(addition(zero, antidomain(multiplication(X0!0, zero))), antidomain(multiplication(X0!0, antidomain(antidomain(zero))))))),
% 5.83/6.04 inference(quant_inst,[status(thm)],[])).
% 5.83/6.04 tff(127,plain,
% 5.83/6.04 (addition(zero, addition(antidomain(multiplication(X0!0, zero)), antidomain(multiplication(X0!0, antidomain(antidomain(zero)))))) = addition(addition(zero, antidomain(multiplication(X0!0, zero))), antidomain(multiplication(X0!0, antidomain(antidomain(zero)))))),
% 5.83/6.04 inference(unit_resolution,[status(thm)],[126, 104])).
% 5.83/6.04 tff(128,plain,
% 5.83/6.04 (addition(antidomain(multiplication(X0!0, zero)), antidomain(multiplication(X0!0, antidomain(antidomain(zero))))) = antidomain(multiplication(X0!0, domain(zero)))),
% 5.83/6.04 inference(transitivity,[status(thm)],[55, 46])).
% 5.83/6.04 tff(129,plain,
% 5.83/6.04 (addition(zero, addition(antidomain(multiplication(X0!0, zero)), antidomain(multiplication(X0!0, antidomain(antidomain(zero)))))) = addition(antidomain(antidomain(multiplication(X0!0, domain(zero)))), antidomain(multiplication(X0!0, domain(zero))))),
% 5.83/6.04 inference(monotonicity,[status(thm)],[70, 128])).
% 5.83/6.04 tff(130,plain,
% 5.83/6.04 (addition(antidomain(antidomain(multiplication(X0!0, domain(zero)))), antidomain(multiplication(X0!0, domain(zero)))) = addition(zero, addition(antidomain(multiplication(X0!0, zero)), antidomain(multiplication(X0!0, antidomain(antidomain(zero))))))),
% 5.83/6.04 inference(symmetry,[status(thm)],[129])).
% 5.83/6.04 tff(131,plain,
% 5.83/6.04 ((~![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)) | (addition(antidomain(antidomain(multiplication(X0!0, domain(zero)))), antidomain(multiplication(X0!0, domain(zero)))) = one)),
% 5.83/6.04 inference(quant_inst,[status(thm)],[])).
% 5.83/6.04 tff(132,plain,
% 5.83/6.04 (addition(antidomain(antidomain(multiplication(X0!0, domain(zero)))), antidomain(multiplication(X0!0, domain(zero)))) = one),
% 5.83/6.04 inference(unit_resolution,[status(thm)],[131, 62])).
% 5.83/6.04 tff(133,plain,
% 5.83/6.04 (one = addition(antidomain(antidomain(multiplication(X0!0, domain(zero)))), antidomain(multiplication(X0!0, domain(zero))))),
% 5.83/6.04 inference(symmetry,[status(thm)],[132])).
% 5.83/6.04 tff(134,plain,
% 5.83/6.04 (zero = domain(multiplication(X0!0, domain(zero)))),
% 5.83/6.04 inference(transitivity,[status(thm)],[18, 69, 68, 28])).
% 5.83/6.04 tff(135,plain,
% 5.83/6.04 (antidomain(zero) = antidomain(domain(multiplication(X0!0, domain(zero))))),
% 5.83/6.04 inference(monotonicity,[status(thm)],[134])).
% 5.83/6.04 tff(136,plain,
% 5.83/6.04 (antidomain(zero) = antidomain(multiplication(X0!0, domain(zero)))),
% 5.83/6.04 inference(transitivity,[status(thm)],[135, 83, 73, 67, 133, 130, 127, 125, 55, 46])).
% 5.83/6.04 tff(137,plain,
% 5.83/6.04 (antidomain(antidomain(zero)) = antidomain(antidomain(multiplication(X0!0, domain(zero))))),
% 5.83/6.04 inference(monotonicity,[status(thm)],[136])).
% 5.83/6.04 tff(138,plain,
% 5.83/6.04 ((~![A: $i] : (multiplication(A, zero) = zero)) | (multiplication(star(X0!0), zero) = zero)),
% 5.83/6.04 inference(quant_inst,[status(thm)],[])).
% 5.83/6.04 tff(139,plain,
% 5.83/6.04 (multiplication(star(X0!0), zero) = zero),
% 5.83/6.04 inference(unit_resolution,[status(thm)],[138, 90])).
% 5.83/6.04 tff(140,plain,
% 5.83/6.04 (domain(zero) = zero),
% 5.83/6.04 inference(transitivity,[status(thm)],[41, 137, 39, 29, 19, 17, 8])).
% 5.83/6.04 tff(141,plain,
% 5.83/6.04 (multiplication(star(X0!0), domain(zero)) = multiplication(star(X0!0), zero)),
% 5.83/6.04 inference(monotonicity,[status(thm)],[140])).
% 5.83/6.04 tff(142,plain,
% 5.83/6.04 (multiplication(star(X0!0), domain(zero)) = zero),
% 5.83/6.04 inference(transitivity,[status(thm)],[141, 139])).
% 5.83/6.04 tff(143,plain,
% 5.83/6.04 (domain(multiplication(star(X0!0), domain(zero))) = domain(zero)),
% 5.83/6.04 inference(monotonicity,[status(thm)],[142])).
% 5.83/6.04 tff(144,plain,
% 5.83/6.04 ((~![A: $i] : (addition(A, zero) = A)) | (addition(domain(multiplication(star(X0!0), domain(zero))), zero) = domain(multiplication(star(X0!0), domain(zero))))),
% 5.83/6.04 inference(quant_inst,[status(thm)],[])).
% 5.83/6.04 tff(145,plain,
% 5.83/6.04 (addition(domain(multiplication(star(X0!0), domain(zero))), zero) = domain(multiplication(star(X0!0), domain(zero)))),
% 5.83/6.04 inference(unit_resolution,[status(thm)],[144, 80])).
% 5.83/6.04 tff(146,plain,
% 5.83/6.04 ((~![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))) | (forward_diamond(star(X0!0), zero) = domain(multiplication(star(X0!0), domain(zero))))),
% 5.83/6.04 inference(quant_inst,[status(thm)],[])).
% 5.83/6.04 tff(147,plain,
% 5.83/6.04 (forward_diamond(star(X0!0), zero) = domain(multiplication(star(X0!0), domain(zero)))),
% 5.83/6.04 inference(unit_resolution,[status(thm)],[146, 26])).
% 5.83/6.04 tff(148,plain,
% 5.83/6.04 (domain(multiplication(X0!0, domain(zero))) = zero),
% 5.83/6.04 inference(transitivity,[status(thm)],[29, 19, 17, 8])).
% 5.83/6.04 tff(149,plain,
% 5.83/6.04 (forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))) = forward_diamond(star(X0!0), zero)),
% 5.83/6.04 inference(monotonicity,[status(thm)],[148])).
% 5.83/6.04 tff(150,plain,
% 5.83/6.04 (forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))) = domain(multiplication(star(X0!0), domain(zero)))),
% 5.83/6.04 inference(transitivity,[status(thm)],[149, 147])).
% 5.83/6.04 tff(151,plain,
% 5.83/6.04 (addition(forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))), zero) = addition(domain(multiplication(star(X0!0), domain(zero))), zero)),
% 5.83/6.04 inference(monotonicity,[status(thm)],[150])).
% 5.83/6.04 tff(152,plain,
% 5.83/6.04 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(zero, forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero))))) = addition(forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))), zero))),
% 5.83/6.04 inference(quant_inst,[status(thm)],[])).
% 5.83/6.04 tff(153,plain,
% 5.83/6.04 (addition(zero, forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero))))) = addition(forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))), zero)),
% 5.83/6.04 inference(unit_resolution,[status(thm)],[152, 116])).
% 5.83/6.04 tff(154,plain,
% 5.83/6.04 (addition(divergence(X0!0), forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero))))) = addition(zero, forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))))),
% 5.83/6.04 inference(monotonicity,[status(thm)],[8])).
% 5.83/6.04 tff(155,plain,
% 5.83/6.04 ((~![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))) | (domain(X1!1) = antidomain(antidomain(X1!1)))),
% 5.83/6.04 inference(quant_inst,[status(thm)],[])).
% 5.83/6.04 tff(156,plain,
% 5.83/6.04 (domain(X1!1) = antidomain(antidomain(X1!1))),
% 5.83/6.04 inference(unit_resolution,[status(thm)],[155, 36])).
% 5.83/6.04 tff(157,plain,
% 5.83/6.04 (antidomain(antidomain(X1!1)) = domain(X1!1)),
% 5.83/6.04 inference(symmetry,[status(thm)],[156])).
% 5.83/6.04 tff(158,plain,
% 5.83/6.04 (addition(forward_diamond(X0!0, domain(X1!1)), antidomain(antidomain(X1!1))) = addition(forward_diamond(X0!0, domain(X1!1)), domain(X1!1))),
% 5.83/6.04 inference(monotonicity,[status(thm)],[157])).
% 5.83/6.04 tff(159,plain,
% 5.83/6.04 (addition(forward_diamond(X0!0, domain(X1!1)), domain(X1!1)) = addition(forward_diamond(X0!0, domain(X1!1)), antidomain(antidomain(X1!1)))),
% 5.83/6.04 inference(symmetry,[status(thm)],[158])).
% 5.83/6.04 tff(160,plain,
% 5.83/6.04 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(domain(X1!1), forward_diamond(X0!0, domain(X1!1))) = addition(forward_diamond(X0!0, domain(X1!1)), domain(X1!1)))),
% 5.83/6.04 inference(quant_inst,[status(thm)],[])).
% 5.83/6.04 tff(161,plain,
% 5.83/6.04 (addition(domain(X1!1), forward_diamond(X0!0, domain(X1!1))) = addition(forward_diamond(X0!0, domain(X1!1)), domain(X1!1))),
% 5.83/6.04 inference(unit_resolution,[status(thm)],[160, 116])).
% 5.83/6.04 tff(162,plain,
% 5.83/6.04 (~((~(addition(domain(X1!1), forward_diamond(X0!0, domain(X1!1))) = forward_diamond(X0!0, domain(X1!1)))) | (domain(X1!1) = zero))),
% 5.83/6.04 inference(and_elim,[status(thm)],[7])).
% 5.83/6.04 tff(163,plain,
% 5.83/6.04 (addition(domain(X1!1), forward_diamond(X0!0, domain(X1!1))) = forward_diamond(X0!0, domain(X1!1))),
% 5.83/6.04 inference(or_elim,[status(thm)],[162])).
% 5.83/6.04 tff(164,plain,
% 5.83/6.04 (forward_diamond(X0!0, domain(X1!1)) = addition(domain(X1!1), forward_diamond(X0!0, domain(X1!1)))),
% 5.83/6.04 inference(symmetry,[status(thm)],[163])).
% 5.83/6.04 tff(165,plain,
% 5.83/6.04 (forward_diamond(X0!0, domain(X1!1)) = addition(forward_diamond(X0!0, domain(X1!1)), antidomain(antidomain(X1!1)))),
% 5.83/6.04 inference(transitivity,[status(thm)],[164, 161, 159])).
% 5.83/6.04 tff(166,plain,
% 5.83/6.04 (addition(forward_diamond(X0!0, domain(X1!1)), domain(multiplication(X0!0, domain(zero)))) = addition(addition(forward_diamond(X0!0, domain(X1!1)), antidomain(antidomain(X1!1))), zero)),
% 5.83/6.04 inference(monotonicity,[status(thm)],[165, 148])).
% 5.83/6.04 tff(167,plain,
% 5.83/6.04 (addition(addition(forward_diamond(X0!0, domain(X1!1)), antidomain(antidomain(X1!1))), zero) = addition(forward_diamond(X0!0, domain(X1!1)), domain(multiplication(X0!0, domain(zero))))),
% 5.83/6.04 inference(symmetry,[status(thm)],[166])).
% 5.83/6.04 tff(168,plain,
% 5.83/6.04 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(forward_diamond(X0!0, domain(X1!1)), addition(antidomain(antidomain(X1!1)), zero)) = addition(addition(forward_diamond(X0!0, domain(X1!1)), antidomain(antidomain(X1!1))), zero))),
% 5.83/6.04 inference(quant_inst,[status(thm)],[])).
% 5.83/6.04 tff(169,plain,
% 5.83/6.04 (addition(forward_diamond(X0!0, domain(X1!1)), addition(antidomain(antidomain(X1!1)), zero)) = addition(addition(forward_diamond(X0!0, domain(X1!1)), antidomain(antidomain(X1!1))), zero)),
% 5.83/6.04 inference(unit_resolution,[status(thm)],[168, 104])).
% 5.83/6.04 tff(170,plain,
% 5.83/6.04 (addition(antidomain(antidomain(X1!1)), zero) = domain(X1!1)),
% 5.83/6.04 inference(transitivity,[status(thm)],[109, 157])).
% 5.83/6.04 tff(171,plain,
% 5.83/6.04 (addition(forward_diamond(X0!0, domain(X1!1)), addition(antidomain(antidomain(X1!1)), zero)) = addition(forward_diamond(X0!0, domain(X1!1)), domain(X1!1))),
% 5.83/6.04 inference(monotonicity,[status(thm)],[170])).
% 5.83/6.04 tff(172,plain,
% 5.83/6.04 (addition(forward_diamond(X0!0, domain(X1!1)), domain(X1!1)) = addition(forward_diamond(X0!0, domain(X1!1)), addition(antidomain(antidomain(X1!1)), zero))),
% 5.83/6.04 inference(symmetry,[status(thm)],[171])).
% 5.83/6.04 tff(173,plain,
% 5.83/6.04 (addition(forward_diamond(X0!0, domain(X1!1)), domain(X1!1)) = addition(domain(X1!1), forward_diamond(X0!0, domain(X1!1)))),
% 5.83/6.04 inference(symmetry,[status(thm)],[161])).
% 5.83/6.04 tff(174,plain,
% 5.83/6.04 (addition(addition(forward_diamond(X0!0, domain(X1!1)), antidomain(antidomain(X1!1))), zero) = addition(forward_diamond(X0!0, domain(X1!1)), addition(antidomain(antidomain(X1!1)), zero))),
% 5.83/6.04 inference(symmetry,[status(thm)],[169])).
% 5.83/6.04 tff(175,plain,
% 5.83/6.04 (addition(forward_diamond(X0!0, domain(X1!1)), domain(multiplication(X0!0, domain(zero)))) = forward_diamond(X0!0, domain(X1!1))),
% 5.83/6.04 inference(transitivity,[status(thm)],[166, 174, 171, 173, 163])).
% 5.83/6.04 tff(176,plain,
% 5.83/6.04 (addition(domain(X1!1), addition(forward_diamond(X0!0, domain(X1!1)), domain(multiplication(X0!0, domain(zero))))) = addition(domain(X1!1), forward_diamond(X0!0, domain(X1!1)))),
% 5.83/6.04 inference(monotonicity,[status(thm)],[175])).
% 5.83/6.04 tff(177,plain,
% 5.83/6.04 (addition(domain(X1!1), addition(forward_diamond(X0!0, domain(X1!1)), domain(multiplication(X0!0, domain(zero))))) = addition(forward_diamond(X0!0, domain(X1!1)), domain(multiplication(X0!0, domain(zero))))),
% 5.83/6.04 inference(transitivity,[status(thm)],[176, 161, 172, 169, 167])).
% 5.83/6.04 tff(178,plain,
% 5.83/6.04 (^[X0: $i, X1: $i, X2: $i] : refl(((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2))))) <=> ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2))))))),
% 5.83/6.04 inference(bind,[status(th)],[])).
% 5.83/6.04 tff(179,plain,
% 5.83/6.04 (![X0: $i, X1: $i, X2: $i] : ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2))))) <=> ![X0: $i, X1: $i, X2: $i] : ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2)))))),
% 5.83/6.04 inference(quant_intro,[status(thm)],[178])).
% 5.83/6.04 tff(180,plain,
% 5.83/6.04 (![X0: $i, X1: $i, X2: $i] : ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2))))) <=> ![X0: $i, X1: $i, X2: $i] : ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2)))))),
% 5.83/6.04 inference(rewrite,[status(thm)],[])).
% 5.83/6.04 tff(181,plain,
% 5.83/6.04 (^[X0: $i, X1: $i, X2: $i] : rewrite(((addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2))) => (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2))))) <=> ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2))))))),
% 5.83/6.04 inference(bind,[status(th)],[])).
% 5.83/6.04 tff(182,plain,
% 5.83/6.04 (![X0: $i, X1: $i, X2: $i] : ((addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2))) => (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2))))) <=> ![X0: $i, X1: $i, X2: $i] : ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2)))))),
% 5.83/6.04 inference(quant_intro,[status(thm)],[181])).
% 5.83/6.04 tff(183,axiom,(![X0: $i, X1: $i, X2: $i] : ((addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2))) => (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2)))))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+7.ax','divergence2')).
% 5.83/6.04 tff(184,plain,
% 5.83/6.04 (![X0: $i, X1: $i, X2: $i] : ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2)))))),
% 5.83/6.04 inference(modus_ponens,[status(thm)],[183, 182])).
% 5.83/6.04 tff(185,plain,
% 5.83/6.04 (![X0: $i, X1: $i, X2: $i] : ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2)))))),
% 5.83/6.04 inference(modus_ponens,[status(thm)],[184, 180])).
% 5.83/6.04 tff(186,plain,(
% 5.83/6.04 ![X0: $i, X1: $i, X2: $i] : ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2)))))),
% 5.83/6.04 inference(skolemize,[status(sab)],[185])).
% 5.83/6.04 tff(187,plain,
% 5.83/6.04 (![X0: $i, X1: $i, X2: $i] : ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2)))))),
% 5.83/6.04 inference(modus_ponens,[status(thm)],[186, 179])).
% 5.83/6.04 tff(188,plain,
% 5.83/6.04 (((~![X0: $i, X1: $i, X2: $i] : ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2)))))) | ((~(addition(domain(X1!1), addition(forward_diamond(X0!0, domain(X1!1)), domain(multiplication(X0!0, domain(zero))))) = addition(forward_diamond(X0!0, domain(X1!1)), domain(multiplication(X0!0, domain(zero)))))) | (addition(domain(X1!1), addition(divergence(X0!0), forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))))) = addition(divergence(X0!0), forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2)))))) | (~(addition(domain(X1!1), addition(forward_diamond(X0!0, domain(X1!1)), domain(multiplication(X0!0, domain(zero))))) = addition(forward_diamond(X0!0, domain(X1!1)), domain(multiplication(X0!0, domain(zero)))))) | (addition(domain(X1!1), addition(divergence(X0!0), forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))))) = addition(divergence(X0!0), forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))))))),
% 5.83/6.04 inference(rewrite,[status(thm)],[])).
% 5.83/6.04 tff(189,plain,
% 5.83/6.04 ((~![X0: $i, X1: $i, X2: $i] : ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2)))))) | ((~(addition(domain(X1!1), addition(forward_diamond(X0!0, domain(X1!1)), domain(multiplication(X0!0, domain(zero))))) = addition(forward_diamond(X0!0, domain(X1!1)), domain(multiplication(X0!0, domain(zero)))))) | (addition(domain(X1!1), addition(divergence(X0!0), forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))))) = addition(divergence(X0!0), forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))))))),
% 5.83/6.04 inference(quant_inst,[status(thm)],[])).
% 5.83/6.04 tff(190,plain,
% 5.83/6.04 ((~![X0: $i, X1: $i, X2: $i] : ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2)))))) | (~(addition(domain(X1!1), addition(forward_diamond(X0!0, domain(X1!1)), domain(multiplication(X0!0, domain(zero))))) = addition(forward_diamond(X0!0, domain(X1!1)), domain(multiplication(X0!0, domain(zero)))))) | (addition(domain(X1!1), addition(divergence(X0!0), forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))))) = addition(divergence(X0!0), forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero))))))),
% 5.83/6.04 inference(modus_ponens,[status(thm)],[189, 188])).
% 5.83/6.04 tff(191,plain,
% 5.83/6.04 ((~(addition(domain(X1!1), addition(forward_diamond(X0!0, domain(X1!1)), domain(multiplication(X0!0, domain(zero))))) = addition(forward_diamond(X0!0, domain(X1!1)), domain(multiplication(X0!0, domain(zero)))))) | (addition(domain(X1!1), addition(divergence(X0!0), forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))))) = addition(divergence(X0!0), forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero))))))),
% 5.83/6.04 inference(unit_resolution,[status(thm)],[190, 187])).
% 5.83/6.04 tff(192,plain,
% 5.83/6.04 (addition(domain(X1!1), addition(divergence(X0!0), forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))))) = addition(divergence(X0!0), forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))))),
% 5.83/6.04 inference(unit_resolution,[status(thm)],[191, 177])).
% 5.83/6.04 tff(193,plain,
% 5.83/6.04 (addition(zero, forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero))))) = addition(divergence(X0!0), forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))))),
% 5.83/6.04 inference(symmetry,[status(thm)],[154])).
% 5.83/6.04 tff(194,plain,
% 5.83/6.04 (addition(forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))), zero) = addition(zero, forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))))),
% 5.83/6.04 inference(symmetry,[status(thm)],[153])).
% 5.83/6.04 tff(195,plain,
% 5.83/6.04 (addition(domain(multiplication(star(X0!0), domain(zero))), zero) = addition(forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))), zero)),
% 5.83/6.04 inference(symmetry,[status(thm)],[151])).
% 5.83/6.04 tff(196,plain,
% 5.83/6.04 (domain(multiplication(star(X0!0), domain(zero))) = addition(domain(multiplication(star(X0!0), domain(zero))), zero)),
% 5.83/6.04 inference(symmetry,[status(thm)],[145])).
% 5.83/6.04 tff(197,plain,
% 5.83/6.04 (domain(zero) = domain(multiplication(star(X0!0), domain(zero)))),
% 5.83/6.04 inference(symmetry,[status(thm)],[143])).
% 5.83/6.04 tff(198,plain,
% 5.83/6.04 (antidomain(antidomain(multiplication(X0!0, domain(zero)))) = antidomain(antidomain(zero))),
% 5.83/6.04 inference(symmetry,[status(thm)],[137])).
% 5.83/6.04 tff(199,plain,
% 5.83/6.04 (zero = addition(divergence(X0!0), forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))))),
% 5.83/6.04 inference(transitivity,[status(thm)],[18, 69, 68, 28, 38, 198, 42, 197, 196, 195, 194, 193])).
% 5.83/6.04 tff(200,plain,
% 5.83/6.04 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 5.83/6.04 inference(bind,[status(th)],[])).
% 5.83/6.04 tff(201,plain,
% 5.83/6.04 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 5.83/6.04 inference(quant_intro,[status(thm)],[200])).
% 5.83/6.04 tff(202,plain,
% 5.83/6.04 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 5.83/6.04 inference(rewrite,[status(thm)],[])).
% 5.83/6.04 tff(203,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_left_identity')).
% 5.83/6.04 tff(204,plain,
% 5.83/6.04 (![A: $i] : (multiplication(one, A) = A)),
% 5.83/6.04 inference(modus_ponens,[status(thm)],[203, 202])).
% 5.83/6.04 tff(205,plain,(
% 5.83/6.04 ![A: $i] : (multiplication(one, A) = A)),
% 5.83/6.04 inference(skolemize,[status(sab)],[204])).
% 5.83/6.04 tff(206,plain,
% 5.83/6.04 (![A: $i] : (multiplication(one, A) = A)),
% 5.83/6.04 inference(modus_ponens,[status(thm)],[205, 201])).
% 5.83/6.04 tff(207,plain,
% 5.83/6.04 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, antidomain(antidomain(X1!1))) = antidomain(antidomain(X1!1)))),
% 5.83/6.04 inference(quant_inst,[status(thm)],[])).
% 5.83/6.04 tff(208,plain,
% 5.83/6.04 (multiplication(one, antidomain(antidomain(X1!1))) = antidomain(antidomain(X1!1))),
% 5.83/6.04 inference(unit_resolution,[status(thm)],[207, 206])).
% 5.83/6.04 tff(209,plain,
% 5.83/6.04 (addition(antidomain(antidomain(antidomain(multiplication(X0!0, domain(zero))))), antidomain(antidomain(multiplication(X0!0, domain(zero))))) = addition(antidomain(domain(multiplication(X0!0, domain(zero)))), zero)),
% 5.83/6.04 inference(symmetry,[status(thm)],[73])).
% 5.83/6.04 tff(210,plain,
% 5.83/6.04 (one = addition(antidomain(antidomain(antidomain(multiplication(X0!0, domain(zero))))), antidomain(antidomain(multiplication(X0!0, domain(zero)))))),
% 5.83/6.04 inference(symmetry,[status(thm)],[67])).
% 5.83/6.04 tff(211,plain,
% 5.83/6.04 (one = antidomain(domain(multiplication(X0!0, domain(zero))))),
% 5.83/6.04 inference(transitivity,[status(thm)],[210, 209, 82])).
% 5.83/6.04 tff(212,plain,
% 5.83/6.04 (multiplication(one, antidomain(antidomain(X1!1))) = multiplication(antidomain(domain(multiplication(X0!0, domain(zero)))), antidomain(antidomain(X1!1)))),
% 5.83/6.04 inference(monotonicity,[status(thm)],[211])).
% 5.83/6.04 tff(213,plain,
% 5.83/6.04 (multiplication(antidomain(domain(multiplication(X0!0, domain(zero)))), antidomain(antidomain(X1!1))) = multiplication(one, antidomain(antidomain(X1!1)))),
% 5.83/6.04 inference(symmetry,[status(thm)],[212])).
% 5.83/6.04 tff(214,plain,
% 5.83/6.04 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(domain(X1!1))) = addition(antidomain(domain(X1!1)), antidomain(antidomain(antidomain(antidomain(X1!1))))))),
% 5.83/6.05 inference(quant_inst,[status(thm)],[])).
% 5.83/6.05 tff(215,plain,
% 5.83/6.05 (addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(domain(X1!1))) = addition(antidomain(domain(X1!1)), antidomain(antidomain(antidomain(antidomain(X1!1)))))),
% 5.83/6.05 inference(unit_resolution,[status(thm)],[214, 116])).
% 5.83/6.05 tff(216,plain,
% 5.83/6.05 (antidomain(antidomain(antidomain(X1!1))) = antidomain(domain(X1!1))),
% 5.83/6.05 inference(monotonicity,[status(thm)],[157])).
% 5.83/6.05 tff(217,plain,
% 5.83/6.05 (antidomain(domain(X1!1)) = antidomain(antidomain(antidomain(X1!1)))),
% 5.83/6.05 inference(symmetry,[status(thm)],[216])).
% 5.83/6.05 tff(218,plain,
% 5.83/6.05 (addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(domain(X1!1))) = addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(antidomain(antidomain(X1!1))))),
% 5.83/6.05 inference(monotonicity,[status(thm)],[217])).
% 5.83/6.05 tff(219,plain,
% 5.83/6.05 (addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(antidomain(antidomain(X1!1)))) = addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(domain(X1!1)))),
% 5.83/6.05 inference(symmetry,[status(thm)],[218])).
% 5.83/6.05 tff(220,plain,
% 5.83/6.05 ((~![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)) | (addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(antidomain(antidomain(X1!1)))) = one)),
% 5.83/6.05 inference(quant_inst,[status(thm)],[])).
% 5.83/6.05 tff(221,plain,
% 5.83/6.05 (addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(antidomain(antidomain(X1!1)))) = one),
% 5.83/6.05 inference(unit_resolution,[status(thm)],[220, 62])).
% 5.83/6.05 tff(222,plain,
% 5.83/6.05 (one = addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(antidomain(antidomain(X1!1))))),
% 5.83/6.05 inference(symmetry,[status(thm)],[221])).
% 5.83/6.05 tff(223,plain,
% 5.83/6.05 (antidomain(domain(multiplication(X0!0, domain(zero)))) = addition(antidomain(domain(X1!1)), antidomain(antidomain(antidomain(antidomain(X1!1)))))),
% 5.83/6.05 inference(transitivity,[status(thm)],[83, 73, 67, 222, 219, 215])).
% 5.83/6.05 tff(224,plain,
% 5.83/6.05 (multiplication(antidomain(domain(multiplication(X0!0, domain(zero)))), antidomain(antidomain(X1!1))) = multiplication(addition(antidomain(domain(X1!1)), antidomain(antidomain(antidomain(antidomain(X1!1))))), antidomain(antidomain(X1!1)))),
% 5.83/6.05 inference(monotonicity,[status(thm)],[223])).
% 5.83/6.05 tff(225,plain,
% 5.83/6.05 (multiplication(addition(antidomain(domain(X1!1)), antidomain(antidomain(antidomain(antidomain(X1!1))))), antidomain(antidomain(X1!1))) = multiplication(antidomain(domain(multiplication(X0!0, domain(zero)))), antidomain(antidomain(X1!1)))),
% 5.83/6.05 inference(symmetry,[status(thm)],[224])).
% 5.83/6.05 tff(226,plain,
% 5.83/6.05 (^[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))))),
% 5.83/6.05 inference(bind,[status(th)],[])).
% 5.83/6.05 tff(227,plain,
% 5.83/6.05 (![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)))),
% 5.83/6.05 inference(quant_intro,[status(thm)],[226])).
% 5.83/6.05 tff(228,plain,
% 5.83/6.05 (![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)))),
% 5.83/6.05 inference(rewrite,[status(thm)],[])).
% 5.83/6.05 tff(229,axiom,(![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','left_distributivity')).
% 5.83/6.05 tff(230,plain,
% 5.83/6.05 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 5.83/6.05 inference(modus_ponens,[status(thm)],[229, 228])).
% 5.83/6.05 tff(231,plain,(
% 5.83/6.05 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 5.83/6.05 inference(skolemize,[status(sab)],[230])).
% 5.83/6.05 tff(232,plain,
% 5.83/6.05 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 5.83/6.05 inference(modus_ponens,[status(thm)],[231, 227])).
% 5.83/6.05 tff(233,plain,
% 5.83/6.05 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(antidomain(domain(X1!1)), antidomain(antidomain(antidomain(antidomain(X1!1))))), antidomain(antidomain(X1!1))) = addition(multiplication(antidomain(domain(X1!1)), antidomain(antidomain(X1!1))), multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(antidomain(X1!1)))))),
% 5.83/6.05 inference(quant_inst,[status(thm)],[])).
% 5.83/6.05 tff(234,plain,
% 5.83/6.05 (multiplication(addition(antidomain(domain(X1!1)), antidomain(antidomain(antidomain(antidomain(X1!1))))), antidomain(antidomain(X1!1))) = addition(multiplication(antidomain(domain(X1!1)), antidomain(antidomain(X1!1))), multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(antidomain(X1!1))))),
% 5.83/6.05 inference(unit_resolution,[status(thm)],[233, 232])).
% 5.83/6.05 tff(235,plain,
% 5.83/6.05 (addition(multiplication(antidomain(domain(X1!1)), antidomain(antidomain(X1!1))), multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(antidomain(X1!1)))) = multiplication(addition(antidomain(domain(X1!1)), antidomain(antidomain(antidomain(antidomain(X1!1))))), antidomain(antidomain(X1!1)))),
% 5.83/6.05 inference(symmetry,[status(thm)],[234])).
% 5.83/6.05 tff(236,plain,
% 5.83/6.05 (antidomain(antidomain(domain(X1!1))) = antidomain(antidomain(antidomain(antidomain(X1!1))))),
% 5.83/6.05 inference(monotonicity,[status(thm)],[217])).
% 5.83/6.05 tff(237,plain,
% 5.83/6.05 (antidomain(antidomain(antidomain(antidomain(X1!1)))) = antidomain(antidomain(domain(X1!1)))),
% 5.83/6.05 inference(symmetry,[status(thm)],[236])).
% 5.83/6.05 tff(238,plain,
% 5.83/6.05 (multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(domain(X1!1))) = multiplication(antidomain(antidomain(domain(X1!1))), antidomain(domain(X1!1)))),
% 5.83/6.05 inference(monotonicity,[status(thm)],[237])).
% 5.83/6.05 tff(239,plain,
% 5.83/6.05 (multiplication(antidomain(antidomain(domain(X1!1))), antidomain(domain(X1!1))) = multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(domain(X1!1)))),
% 5.83/6.05 inference(symmetry,[status(thm)],[238])).
% 5.83/6.05 tff(240,plain,
% 5.83/6.05 (^[X0: $i] : refl((multiplication(antidomain(X0), X0) = zero) <=> (multiplication(antidomain(X0), X0) = zero))),
% 5.83/6.05 inference(bind,[status(th)],[])).
% 5.83/6.05 tff(241,plain,
% 5.83/6.05 (![X0: $i] : (multiplication(antidomain(X0), X0) = zero) <=> ![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 5.83/6.05 inference(quant_intro,[status(thm)],[240])).
% 5.83/6.05 tff(242,plain,
% 5.83/6.05 (![X0: $i] : (multiplication(antidomain(X0), X0) = zero) <=> ![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 5.83/6.05 inference(rewrite,[status(thm)],[])).
% 5.83/6.05 tff(243,axiom,(![X0: $i] : (multiplication(antidomain(X0), X0) = zero)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax','domain1')).
% 5.83/6.05 tff(244,plain,
% 5.83/6.05 (![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 5.83/6.05 inference(modus_ponens,[status(thm)],[243, 242])).
% 5.83/6.05 tff(245,plain,(
% 5.83/6.05 ![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 5.83/6.05 inference(skolemize,[status(sab)],[244])).
% 5.83/6.05 tff(246,plain,
% 5.83/6.05 (![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 5.83/6.05 inference(modus_ponens,[status(thm)],[245, 241])).
% 5.83/6.05 tff(247,plain,
% 5.83/6.05 ((~![X0: $i] : (multiplication(antidomain(X0), X0) = zero)) | (multiplication(antidomain(antidomain(domain(X1!1))), antidomain(domain(X1!1))) = zero)),
% 5.83/6.05 inference(quant_inst,[status(thm)],[])).
% 5.83/6.05 tff(248,plain,
% 5.83/6.05 (multiplication(antidomain(antidomain(domain(X1!1))), antidomain(domain(X1!1))) = zero),
% 5.83/6.05 inference(unit_resolution,[status(thm)],[247, 246])).
% 5.83/6.05 tff(249,plain,
% 5.83/6.05 (zero = multiplication(antidomain(antidomain(domain(X1!1))), antidomain(domain(X1!1)))),
% 5.83/6.05 inference(symmetry,[status(thm)],[248])).
% 5.83/6.05 tff(250,plain,
% 5.83/6.05 ((~![X0: $i] : (multiplication(antidomain(X0), X0) = zero)) | (multiplication(antidomain(antidomain(antidomain(X1!1))), antidomain(antidomain(X1!1))) = zero)),
% 5.83/6.05 inference(quant_inst,[status(thm)],[])).
% 5.83/6.05 tff(251,plain,
% 5.83/6.05 (multiplication(antidomain(antidomain(antidomain(X1!1))), antidomain(antidomain(X1!1))) = zero),
% 5.83/6.05 inference(unit_resolution,[status(thm)],[250, 246])).
% 5.83/6.05 tff(252,plain,
% 5.83/6.05 (multiplication(antidomain(domain(X1!1)), antidomain(antidomain(X1!1))) = multiplication(antidomain(antidomain(antidomain(X1!1))), antidomain(antidomain(X1!1)))),
% 5.83/6.05 inference(monotonicity,[status(thm)],[217])).
% 5.83/6.05 tff(253,plain,
% 5.83/6.05 (multiplication(antidomain(domain(X1!1)), antidomain(antidomain(X1!1))) = multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(domain(X1!1)))),
% 5.83/6.05 inference(transitivity,[status(thm)],[252, 251, 249, 239])).
% 5.83/6.05 tff(254,plain,
% 5.83/6.05 (addition(multiplication(antidomain(domain(X1!1)), antidomain(antidomain(X1!1))), multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(antidomain(X1!1)))) = addition(multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(domain(X1!1))), multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(antidomain(X1!1))))),
% 5.83/6.05 inference(monotonicity,[status(thm)],[253])).
% 5.83/6.05 tff(255,plain,
% 5.83/6.05 (addition(multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(domain(X1!1))), multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(antidomain(X1!1)))) = addition(multiplication(antidomain(domain(X1!1)), antidomain(antidomain(X1!1))), multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(antidomain(X1!1))))),
% 5.83/6.05 inference(symmetry,[status(thm)],[254])).
% 5.83/6.05 tff(256,plain,
% 5.83/6.05 (^[A: $i, B: $i, C: $i] : refl((multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))))),
% 5.83/6.05 inference(bind,[status(th)],[])).
% 5.83/6.05 tff(257,plain,
% 5.83/6.05 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 5.83/6.05 inference(quant_intro,[status(thm)],[256])).
% 5.83/6.05 tff(258,plain,
% 5.83/6.05 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 5.83/6.05 inference(rewrite,[status(thm)],[])).
% 5.83/6.05 tff(259,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','right_distributivity')).
% 5.83/6.05 tff(260,plain,
% 5.83/6.05 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 5.83/6.05 inference(modus_ponens,[status(thm)],[259, 258])).
% 5.83/6.05 tff(261,plain,(
% 5.83/6.05 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 5.83/6.05 inference(skolemize,[status(sab)],[260])).
% 5.83/6.05 tff(262,plain,
% 5.83/6.05 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 5.83/6.05 inference(modus_ponens,[status(thm)],[261, 257])).
% 5.83/6.05 tff(263,plain,
% 5.83/6.05 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), addition(antidomain(domain(X1!1)), antidomain(antidomain(X1!1)))) = addition(multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(domain(X1!1))), multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(antidomain(X1!1)))))),
% 5.83/6.05 inference(quant_inst,[status(thm)],[])).
% 5.83/6.05 tff(264,plain,
% 5.83/6.05 (multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), addition(antidomain(domain(X1!1)), antidomain(antidomain(X1!1)))) = addition(multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(domain(X1!1))), multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(antidomain(X1!1))))),
% 5.83/6.05 inference(unit_resolution,[status(thm)],[263, 262])).
% 5.83/6.05 tff(265,plain,
% 5.83/6.05 ((~![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)) | (addition(antidomain(antidomain(antidomain(X1!1))), antidomain(antidomain(X1!1))) = one)),
% 5.83/6.05 inference(quant_inst,[status(thm)],[])).
% 5.83/6.05 tff(266,plain,
% 5.83/6.05 (addition(antidomain(antidomain(antidomain(X1!1))), antidomain(antidomain(X1!1))) = one),
% 5.83/6.05 inference(unit_resolution,[status(thm)],[265, 62])).
% 5.83/6.05 tff(267,plain,
% 5.83/6.05 (addition(antidomain(domain(X1!1)), antidomain(antidomain(X1!1))) = addition(antidomain(antidomain(antidomain(X1!1))), antidomain(antidomain(X1!1)))),
% 5.83/6.05 inference(monotonicity,[status(thm)],[217])).
% 5.83/6.05 tff(268,plain,
% 5.83/6.05 (addition(antidomain(domain(X1!1)), antidomain(antidomain(X1!1))) = antidomain(multiplication(X0!0, antidomain(antidomain(zero))))),
% 5.83/6.05 inference(transitivity,[status(thm)],[267, 266, 133, 130, 127, 125, 55])).
% 5.83/6.05 tff(269,plain,
% 5.83/6.05 (multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), addition(antidomain(domain(X1!1)), antidomain(antidomain(X1!1)))) = multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(multiplication(X0!0, antidomain(antidomain(zero)))))),
% 5.83/6.05 inference(monotonicity,[status(thm)],[268])).
% 5.83/6.05 tff(270,plain,
% 5.83/6.05 (multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(multiplication(X0!0, antidomain(antidomain(zero))))) = multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), addition(antidomain(domain(X1!1)), antidomain(antidomain(X1!1))))),
% 5.83/6.05 inference(symmetry,[status(thm)],[269])).
% 5.83/6.05 tff(271,plain,
% 5.83/6.05 (addition(addition(zero, antidomain(multiplication(X0!0, zero))), antidomain(multiplication(X0!0, antidomain(antidomain(zero))))) = addition(zero, addition(antidomain(multiplication(X0!0, zero)), antidomain(multiplication(X0!0, antidomain(antidomain(zero))))))),
% 5.83/6.05 inference(symmetry,[status(thm)],[127])).
% 5.83/6.05 tff(272,plain,
% 5.83/6.05 (antidomain(multiplication(X0!0, antidomain(antidomain(zero)))) = addition(antidomain(multiplication(X0!0, zero)), antidomain(multiplication(X0!0, antidomain(antidomain(zero)))))),
% 5.83/6.05 inference(symmetry,[status(thm)],[55])).
% 5.83/6.05 tff(273,plain,
% 5.83/6.05 (antidomain(multiplication(X0!0, antidomain(antidomain(zero)))) = one),
% 5.83/6.05 inference(transitivity,[status(thm)],[272, 124, 271, 129, 132])).
% 5.83/6.05 tff(274,plain,
% 5.83/6.05 (multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(multiplication(X0!0, antidomain(antidomain(zero))))) = multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), one)),
% 5.83/6.05 inference(monotonicity,[status(thm)],[273])).
% 5.83/6.05 tff(275,plain,
% 5.83/6.05 (multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), one) = multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(multiplication(X0!0, antidomain(antidomain(zero)))))),
% 5.83/6.05 inference(symmetry,[status(thm)],[274])).
% 5.83/6.05 tff(276,plain,
% 5.83/6.05 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 5.83/6.05 inference(bind,[status(th)],[])).
% 5.83/6.05 tff(277,plain,
% 5.83/6.05 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 5.83/6.05 inference(quant_intro,[status(thm)],[276])).
% 5.83/6.05 tff(278,plain,
% 5.83/6.05 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 5.83/6.05 inference(rewrite,[status(thm)],[])).
% 5.83/6.05 tff(279,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_right_identity')).
% 5.83/6.05 tff(280,plain,
% 5.83/6.05 (![A: $i] : (multiplication(A, one) = A)),
% 5.83/6.05 inference(modus_ponens,[status(thm)],[279, 278])).
% 5.83/6.05 tff(281,plain,(
% 5.83/6.05 ![A: $i] : (multiplication(A, one) = A)),
% 5.83/6.05 inference(skolemize,[status(sab)],[280])).
% 5.83/6.05 tff(282,plain,
% 5.83/6.05 (![A: $i] : (multiplication(A, one) = A)),
% 5.83/6.05 inference(modus_ponens,[status(thm)],[281, 277])).
% 5.83/6.05 tff(283,plain,
% 5.83/6.05 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), one) = antidomain(antidomain(antidomain(antidomain(X1!1)))))),
% 5.83/6.05 inference(quant_inst,[status(thm)],[])).
% 5.83/6.05 tff(284,plain,
% 5.83/6.05 (multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), one) = antidomain(antidomain(antidomain(antidomain(X1!1))))),
% 5.83/6.05 inference(unit_resolution,[status(thm)],[283, 282])).
% 5.83/6.05 tff(285,plain,
% 5.83/6.05 (antidomain(antidomain(antidomain(antidomain(X1!1)))) = multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), one)),
% 5.83/6.05 inference(symmetry,[status(thm)],[284])).
% 5.83/6.05 tff(286,plain,
% 5.83/6.05 (antidomain(antidomain(antidomain(antidomain(X1!1)))) = domain(X1!1)),
% 5.83/6.05 inference(transitivity,[status(thm)],[285, 275, 270, 264, 255, 235, 225, 213, 208, 157])).
% 5.83/6.05 tff(287,plain,
% 5.83/6.05 (addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), zero) = addition(domain(X1!1), addition(divergence(X0!0), forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero))))))),
% 5.83/6.05 inference(monotonicity,[status(thm)],[286, 199])).
% 5.83/6.05 tff(288,plain,
% 5.83/6.05 (addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), zero) = zero),
% 5.83/6.05 inference(transitivity,[status(thm)],[287, 192, 154, 153, 151, 145, 143, 41, 137, 39, 29, 19, 17, 8])).
% 5.83/6.05 tff(289,plain,
% 5.83/6.05 ((~![A: $i] : (addition(A, zero) = A)) | (addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), zero) = antidomain(antidomain(antidomain(antidomain(X1!1)))))),
% 5.83/6.05 inference(quant_inst,[status(thm)],[])).
% 5.83/6.05 tff(290,plain,
% 5.83/6.05 (addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), zero) = antidomain(antidomain(antidomain(antidomain(X1!1))))),
% 5.83/6.05 inference(unit_resolution,[status(thm)],[289, 80])).
% 5.83/6.05 tff(291,plain,
% 5.83/6.05 (addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), zero) = domain(X1!1)),
% 5.83/6.05 inference(transitivity,[status(thm)],[290, 285, 275, 270, 264, 255, 235, 225, 213, 208, 157])).
% 5.83/6.05 tff(292,plain,
% 5.83/6.05 ((addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), zero) = zero) <=> (domain(X1!1) = zero)),
% 5.83/6.05 inference(monotonicity,[status(thm)],[291])).
% 5.83/6.05 tff(293,plain,
% 5.83/6.05 ((domain(X1!1) = zero) <=> (addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), zero) = zero)),
% 5.83/6.05 inference(symmetry,[status(thm)],[292])).
% 5.83/6.05 tff(294,plain,
% 5.83/6.05 ((~(domain(X1!1) = zero)) <=> (~(addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), zero) = zero))),
% 5.83/6.05 inference(monotonicity,[status(thm)],[293])).
% 5.83/6.05 tff(295,plain,
% 5.83/6.05 (~(domain(X1!1) = zero)),
% 5.83/6.05 inference(or_elim,[status(thm)],[162])).
% 5.83/6.05 tff(296,plain,
% 5.83/6.05 (~(addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), zero) = zero)),
% 5.83/6.05 inference(modus_ponens,[status(thm)],[295, 294])).
% 5.83/6.05 tff(297,plain,
% 5.83/6.05 ($false),
% 5.83/6.05 inference(unit_resolution,[status(thm)],[296, 288])).
% 5.83/6.05 % SZS output end Proof
% 5.83/6.06 % E exiting
%------------------------------------------------------------------------------