%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE079+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:12:59 AM UTC 2025
% Result : Theorem 89.51s 89.69s
% Output : Proof 89.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE079+1 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 18:59:01 EDT 2025
% 0.13/0.34 % CPUTime :
% 89.51/89.69 % SZS status Theorem
% 89.51/89.69 % SZS output start Proof
% 89.51/89.69 tff(zero_type, type, (
% 89.51/89.69 zero: $i)).
% 89.51/89.69 tff(multiplication_type, type, (
% 89.51/89.69 multiplication: ( $i * $i ) > $i)).
% 89.51/89.69 tff(domain_type, type, (
% 89.51/89.69 domain: $i > $i)).
% 89.51/89.69 tff(tptp_fun_X0_0_type, type, (
% 89.51/89.69 tptp_fun_X0_0: $i)).
% 89.51/89.69 tff(antidomain_type, type, (
% 89.51/89.69 antidomain: $i > $i)).
% 89.51/89.69 tff(one_type, type, (
% 89.51/89.69 one: $i)).
% 89.51/89.69 tff(addition_type, type, (
% 89.51/89.69 addition: ( $i * $i ) > $i)).
% 89.51/89.69 tff(1,plain,
% 89.51/89.69 (^[A: $i] : refl((multiplication(zero, A) = zero) <=> (multiplication(zero, A) = zero))),
% 89.51/89.69 inference(bind,[status(th)],[])).
% 89.51/89.69 tff(2,plain,
% 89.51/89.69 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 89.51/89.69 inference(quant_intro,[status(thm)],[1])).
% 89.51/89.69 tff(3,plain,
% 89.51/89.69 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 89.51/89.69 inference(rewrite,[status(thm)],[])).
% 89.51/89.69 tff(4,axiom,(![A: $i] : (multiplication(zero, A) = zero)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','left_annihilation')).
% 89.51/89.69 tff(5,plain,
% 89.51/89.69 (![A: $i] : (multiplication(zero, A) = zero)),
% 89.51/89.69 inference(modus_ponens,[status(thm)],[4, 3])).
% 89.51/89.69 tff(6,plain,(
% 89.51/89.69 ![A: $i] : (multiplication(zero, A) = zero)),
% 89.51/89.69 inference(skolemize,[status(sab)],[5])).
% 89.51/89.69 tff(7,plain,
% 89.51/89.69 (![A: $i] : (multiplication(zero, A) = zero)),
% 89.51/89.69 inference(modus_ponens,[status(thm)],[6, 2])).
% 89.51/89.69 tff(8,plain,
% 89.51/89.69 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, domain(X0!0)) = zero)),
% 89.51/89.69 inference(quant_inst,[status(thm)],[])).
% 89.51/89.69 tff(9,plain,
% 89.51/89.69 (multiplication(zero, domain(X0!0)) = zero),
% 89.51/89.69 inference(unit_resolution,[status(thm)],[8, 7])).
% 89.51/89.69 tff(10,plain,
% 89.51/89.69 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, zero) = zero)),
% 89.51/89.69 inference(quant_inst,[status(thm)],[])).
% 89.51/89.69 tff(11,plain,
% 89.51/89.69 (multiplication(zero, zero) = zero),
% 89.51/89.69 inference(unit_resolution,[status(thm)],[10, 7])).
% 89.51/89.69 tff(12,plain,
% 89.51/89.69 ((domain(zero) = zero) <=> (domain(zero) = zero)),
% 89.51/89.69 inference(rewrite,[status(thm)],[])).
% 89.51/89.69 tff(13,axiom,(domain(zero) = zero), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax','domain4')).
% 89.51/89.69 tff(14,plain,
% 89.51/89.69 (domain(zero) = zero),
% 89.51/89.69 inference(modus_ponens,[status(thm)],[13, 12])).
% 89.51/89.69 tff(15,plain,
% 89.51/89.69 (multiplication(domain(zero), zero) = multiplication(zero, zero)),
% 89.51/89.69 inference(monotonicity,[status(thm)],[14])).
% 89.51/89.69 tff(16,plain,
% 89.51/89.69 (^[X1: $i] : refl((~((~(addition(domain(X1), antidomain(X1)) = one)) | (~(multiplication(domain(X1), antidomain(X1)) = zero)))) <=> (~((~(addition(domain(X1), antidomain(X1)) = one)) | (~(multiplication(domain(X1), antidomain(X1)) = zero)))))),
% 89.51/89.69 inference(bind,[status(th)],[])).
% 89.51/89.69 tff(17,plain,
% 89.51/89.69 (![X1: $i] : (~((~(addition(domain(X1), antidomain(X1)) = one)) | (~(multiplication(domain(X1), antidomain(X1)) = zero)))) <=> ![X1: $i] : (~((~(addition(domain(X1), antidomain(X1)) = one)) | (~(multiplication(domain(X1), antidomain(X1)) = zero))))),
% 89.51/89.69 inference(quant_intro,[status(thm)],[16])).
% 89.51/89.69 tff(18,plain,
% 89.51/89.69 (^[X1: $i] : rewrite(((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero)) <=> (~((~(addition(domain(X1), antidomain(X1)) = one)) | (~(multiplication(domain(X1), antidomain(X1)) = zero)))))),
% 89.51/89.69 inference(bind,[status(th)],[])).
% 89.51/89.69 tff(19,plain,
% 89.51/89.69 (![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero)) <=> ![X1: $i] : (~((~(addition(domain(X1), antidomain(X1)) = one)) | (~(multiplication(domain(X1), antidomain(X1)) = zero))))),
% 89.51/89.69 inference(quant_intro,[status(thm)],[18])).
% 89.51/89.69 tff(20,plain,
% 89.51/89.69 ((![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero)) & (~(multiplication(antidomain(X0!0), domain(X0!0)) = zero))) <=> (![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero)) & (~(multiplication(antidomain(X0!0), domain(X0!0)) = zero)))),
% 89.51/89.69 inference(rewrite,[status(thm)],[])).
% 89.51/89.69 tff(21,plain,
% 89.51/89.69 ((~![X0: $i] : ((~![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero))) | (multiplication(antidomain(X0), domain(X0)) = zero))) <=> (~![X0: $i] : ((~![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero))) | (multiplication(antidomain(X0), domain(X0)) = zero)))),
% 89.51/89.69 inference(rewrite,[status(thm)],[])).
% 89.51/89.69 tff(22,plain,
% 89.51/89.69 ((~![X0: $i] : (![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero)) => (multiplication(antidomain(X0), domain(X0)) = zero))) <=> (~![X0: $i] : ((~![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero))) | (multiplication(antidomain(X0), domain(X0)) = zero)))),
% 89.51/89.69 inference(rewrite,[status(thm)],[])).
% 89.51/89.69 tff(23,axiom,(~![X0: $i] : (![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero)) => (multiplication(antidomain(X0), domain(X0)) = zero))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 89.51/89.69 tff(24,plain,
% 89.51/89.69 (~![X0: $i] : ((~![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero))) | (multiplication(antidomain(X0), domain(X0)) = zero))),
% 89.51/89.69 inference(modus_ponens,[status(thm)],[23, 22])).
% 89.51/89.69 tff(25,plain,
% 89.51/89.69 (~![X0: $i] : ((~![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero))) | (multiplication(antidomain(X0), domain(X0)) = zero))),
% 89.51/89.69 inference(modus_ponens,[status(thm)],[24, 21])).
% 89.51/89.69 tff(26,plain,
% 89.51/89.69 (~![X0: $i] : ((~![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero))) | (multiplication(antidomain(X0), domain(X0)) = zero))),
% 89.51/89.69 inference(modus_ponens,[status(thm)],[25, 21])).
% 89.51/89.69 tff(27,plain,
% 89.51/89.69 (~![X0: $i] : ((~![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero))) | (multiplication(antidomain(X0), domain(X0)) = zero))),
% 89.51/89.69 inference(modus_ponens,[status(thm)],[26, 21])).
% 89.51/89.69 tff(28,plain,
% 89.51/89.69 (![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero)) & (~(multiplication(antidomain(X0!0), domain(X0!0)) = zero))),
% 89.51/89.69 inference(modus_ponens,[status(thm)],[27, 20])).
% 89.51/89.69 tff(29,plain,
% 89.51/89.69 (![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero))),
% 89.51/89.69 inference(and_elim,[status(thm)],[28])).
% 89.51/89.69 tff(30,plain,
% 89.51/89.69 (![X1: $i] : (~((~(addition(domain(X1), antidomain(X1)) = one)) | (~(multiplication(domain(X1), antidomain(X1)) = zero))))),
% 89.51/89.69 inference(modus_ponens,[status(thm)],[29, 19])).
% 89.51/89.69 tff(31,plain,
% 89.51/89.69 (![X1: $i] : (~((~(addition(domain(X1), antidomain(X1)) = one)) | (~(multiplication(domain(X1), antidomain(X1)) = zero))))),
% 89.51/89.69 inference(modus_ponens,[status(thm)],[30, 17])).
% 89.51/89.69 tff(32,plain,
% 89.51/89.69 ((~![X1: $i] : (~((~(addition(domain(X1), antidomain(X1)) = one)) | (~(multiplication(domain(X1), antidomain(X1)) = zero))))) | (~((~(addition(domain(X0!0), antidomain(X0!0)) = one)) | (~(multiplication(domain(X0!0), antidomain(X0!0)) = zero))))),
% 89.51/89.69 inference(quant_inst,[status(thm)],[])).
% 89.51/89.69 tff(33,plain,
% 89.51/89.69 (~((~(addition(domain(X0!0), antidomain(X0!0)) = one)) | (~(multiplication(domain(X0!0), antidomain(X0!0)) = zero)))),
% 89.51/89.69 inference(unit_resolution,[status(thm)],[32, 31])).
% 89.51/89.69 tff(34,plain,
% 89.51/89.69 (((~(addition(domain(X0!0), antidomain(X0!0)) = one)) | (~(multiplication(domain(X0!0), antidomain(X0!0)) = zero))) | (multiplication(domain(X0!0), antidomain(X0!0)) = zero)),
% 89.51/89.69 inference(tautology,[status(thm)],[])).
% 89.51/89.69 tff(35,plain,
% 89.51/89.69 (multiplication(domain(X0!0), antidomain(X0!0)) = zero),
% 89.51/89.69 inference(unit_resolution,[status(thm)],[34, 33])).
% 89.51/89.69 tff(36,plain,
% 89.51/89.69 (zero = domain(zero)),
% 89.51/89.69 inference(symmetry,[status(thm)],[14])).
% 89.51/89.69 tff(37,plain,
% 89.51/89.69 (multiplication(zero, multiplication(domain(X0!0), antidomain(X0!0))) = multiplication(domain(zero), zero)),
% 89.51/89.69 inference(monotonicity,[status(thm)],[36, 35])).
% 89.51/89.69 tff(38,plain,
% 89.51/89.69 (^[A: $i, B: $i, C: $i] : refl((multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)))),
% 89.51/89.69 inference(bind,[status(th)],[])).
% 89.51/89.69 tff(39,plain,
% 89.51/89.69 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 89.51/89.69 inference(quant_intro,[status(thm)],[38])).
% 89.51/89.69 tff(40,plain,
% 89.51/89.69 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 89.51/89.69 inference(rewrite,[status(thm)],[])).
% 89.51/89.69 tff(41,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_associativity')).
% 89.51/89.69 tff(42,plain,
% 89.51/89.69 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 89.51/89.69 inference(modus_ponens,[status(thm)],[41, 40])).
% 89.51/89.69 tff(43,plain,(
% 89.51/89.69 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 89.51/89.69 inference(skolemize,[status(sab)],[42])).
% 89.51/89.69 tff(44,plain,
% 89.51/89.69 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 89.51/89.69 inference(modus_ponens,[status(thm)],[43, 39])).
% 89.51/89.69 tff(45,plain,
% 89.51/89.69 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(zero, multiplication(domain(X0!0), antidomain(X0!0))) = multiplication(multiplication(zero, domain(X0!0)), antidomain(X0!0)))),
% 89.51/89.69 inference(quant_inst,[status(thm)],[])).
% 89.51/89.69 tff(46,plain,
% 89.51/89.69 (multiplication(zero, multiplication(domain(X0!0), antidomain(X0!0))) = multiplication(multiplication(zero, domain(X0!0)), antidomain(X0!0))),
% 89.51/89.69 inference(unit_resolution,[status(thm)],[45, 44])).
% 89.51/89.69 tff(47,plain,
% 89.51/89.69 (multiplication(multiplication(zero, domain(X0!0)), antidomain(X0!0)) = multiplication(zero, multiplication(domain(X0!0), antidomain(X0!0)))),
% 89.51/89.69 inference(symmetry,[status(thm)],[46])).
% 89.51/89.69 tff(48,plain,
% 89.51/89.69 (multiplication(multiplication(zero, domain(X0!0)), antidomain(X0!0)) = zero),
% 89.51/89.69 inference(transitivity,[status(thm)],[47, 37, 15, 11])).
% 89.51/89.69 tff(49,plain,
% 89.51/89.69 (multiplication(multiplication(multiplication(zero, domain(X0!0)), antidomain(X0!0)), domain(X0!0)) = multiplication(zero, domain(X0!0))),
% 89.51/89.69 inference(monotonicity,[status(thm)],[48])).
% 89.51/89.69 tff(50,plain,
% 89.51/89.69 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(multiplication(zero, domain(X0!0)), multiplication(antidomain(X0!0), domain(X0!0))) = multiplication(multiplication(multiplication(zero, domain(X0!0)), antidomain(X0!0)), domain(X0!0)))),
% 89.51/89.69 inference(quant_inst,[status(thm)],[])).
% 89.51/89.69 tff(51,plain,
% 89.51/89.69 (multiplication(multiplication(zero, domain(X0!0)), multiplication(antidomain(X0!0), domain(X0!0))) = multiplication(multiplication(multiplication(zero, domain(X0!0)), antidomain(X0!0)), domain(X0!0))),
% 89.51/89.69 inference(unit_resolution,[status(thm)],[50, 44])).
% 89.51/89.69 tff(52,plain,
% 89.51/89.69 (zero = multiplication(zero, domain(X0!0))),
% 89.51/89.69 inference(symmetry,[status(thm)],[9])).
% 89.51/89.69 tff(53,plain,
% 89.51/89.69 ((~![X1: $i] : (~((~(addition(domain(X1), antidomain(X1)) = one)) | (~(multiplication(domain(X1), antidomain(X1)) = zero))))) | (~((~(addition(domain(multiplication(antidomain(X0!0), X0!0)), antidomain(multiplication(antidomain(X0!0), X0!0))) = one)) | (~(multiplication(domain(multiplication(antidomain(X0!0), X0!0)), antidomain(multiplication(antidomain(X0!0), X0!0))) = zero))))),
% 89.51/89.69 inference(quant_inst,[status(thm)],[])).
% 89.51/89.69 tff(54,plain,
% 89.51/89.69 (~((~(addition(domain(multiplication(antidomain(X0!0), X0!0)), antidomain(multiplication(antidomain(X0!0), X0!0))) = one)) | (~(multiplication(domain(multiplication(antidomain(X0!0), X0!0)), antidomain(multiplication(antidomain(X0!0), X0!0))) = zero)))),
% 89.51/89.70 inference(unit_resolution,[status(thm)],[53, 31])).
% 89.51/89.70 tff(55,plain,
% 89.51/89.70 (((~(addition(domain(multiplication(antidomain(X0!0), X0!0)), antidomain(multiplication(antidomain(X0!0), X0!0))) = one)) | (~(multiplication(domain(multiplication(antidomain(X0!0), X0!0)), antidomain(multiplication(antidomain(X0!0), X0!0))) = zero))) | (multiplication(domain(multiplication(antidomain(X0!0), X0!0)), antidomain(multiplication(antidomain(X0!0), X0!0))) = zero)),
% 89.51/89.70 inference(tautology,[status(thm)],[])).
% 89.51/89.70 tff(56,plain,
% 89.51/89.70 (multiplication(domain(multiplication(antidomain(X0!0), X0!0)), antidomain(multiplication(antidomain(X0!0), X0!0))) = zero),
% 89.51/89.70 inference(unit_resolution,[status(thm)],[55, 54])).
% 89.51/89.70 tff(57,plain,
% 89.51/89.70 (^[X0: $i, X1: $i] : refl((domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1)))) <=> (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1)))))),
% 89.51/89.70 inference(bind,[status(th)],[])).
% 89.51/89.70 tff(58,plain,
% 89.51/89.70 (![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))))),
% 89.51/89.70 inference(quant_intro,[status(thm)],[57])).
% 89.51/89.70 tff(59,plain,
% 89.51/89.70 (![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))))),
% 89.51/89.70 inference(rewrite,[status(thm)],[])).
% 89.51/89.70 tff(60,axiom,(![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax','domain2')).
% 89.51/89.70 tff(61,plain,
% 89.51/89.70 (![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))),
% 89.51/89.70 inference(modus_ponens,[status(thm)],[60, 59])).
% 89.51/89.70 tff(62,plain,(
% 89.51/89.70 ![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))),
% 89.51/89.70 inference(skolemize,[status(sab)],[61])).
% 89.51/89.70 tff(63,plain,
% 89.51/89.70 (![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))),
% 89.51/89.70 inference(modus_ponens,[status(thm)],[62, 58])).
% 89.51/89.70 tff(64,plain,
% 89.51/89.70 ((~![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))) | (domain(multiplication(antidomain(X0!0), X0!0)) = domain(multiplication(antidomain(X0!0), domain(X0!0))))),
% 89.51/89.70 inference(quant_inst,[status(thm)],[])).
% 89.51/89.70 tff(65,plain,
% 89.51/89.70 (domain(multiplication(antidomain(X0!0), X0!0)) = domain(multiplication(antidomain(X0!0), domain(X0!0)))),
% 89.51/89.70 inference(unit_resolution,[status(thm)],[64, 63])).
% 89.51/89.70 tff(66,plain,
% 89.51/89.70 (domain(multiplication(antidomain(X0!0), domain(X0!0))) = domain(multiplication(antidomain(X0!0), X0!0))),
% 89.51/89.70 inference(symmetry,[status(thm)],[65])).
% 89.51/89.70 tff(67,plain,
% 89.51/89.70 (multiplication(domain(multiplication(antidomain(X0!0), domain(X0!0))), antidomain(multiplication(antidomain(X0!0), X0!0))) = multiplication(domain(multiplication(antidomain(X0!0), X0!0)), antidomain(multiplication(antidomain(X0!0), X0!0)))),
% 89.51/89.70 inference(monotonicity,[status(thm)],[66])).
% 89.51/89.70 tff(68,plain,
% 89.51/89.70 (multiplication(domain(multiplication(antidomain(X0!0), domain(X0!0))), antidomain(multiplication(antidomain(X0!0), X0!0))) = multiplication(zero, domain(X0!0))),
% 89.51/89.70 inference(transitivity,[status(thm)],[67, 56, 52])).
% 89.51/89.70 tff(69,plain,
% 89.51/89.70 (multiplication(multiplication(domain(multiplication(antidomain(X0!0), domain(X0!0))), antidomain(multiplication(antidomain(X0!0), X0!0))), multiplication(antidomain(X0!0), domain(X0!0))) = multiplication(multiplication(zero, domain(X0!0)), multiplication(antidomain(X0!0), domain(X0!0)))),
% 89.51/89.70 inference(monotonicity,[status(thm)],[68])).
% 89.51/89.70 tff(70,plain,
% 89.51/89.70 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(domain(multiplication(antidomain(X0!0), domain(X0!0))), multiplication(antidomain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), domain(X0!0)))) = multiplication(multiplication(domain(multiplication(antidomain(X0!0), domain(X0!0))), antidomain(multiplication(antidomain(X0!0), X0!0))), multiplication(antidomain(X0!0), domain(X0!0))))),
% 89.51/89.70 inference(quant_inst,[status(thm)],[])).
% 89.51/89.70 tff(71,plain,
% 89.51/89.70 (multiplication(domain(multiplication(antidomain(X0!0), domain(X0!0))), multiplication(antidomain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), domain(X0!0)))) = multiplication(multiplication(domain(multiplication(antidomain(X0!0), domain(X0!0))), antidomain(multiplication(antidomain(X0!0), X0!0))), multiplication(antidomain(X0!0), domain(X0!0)))),
% 89.51/89.70 inference(unit_resolution,[status(thm)],[70, 44])).
% 89.51/89.70 tff(72,plain,
% 89.51/89.70 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 89.51/89.70 inference(bind,[status(th)],[])).
% 89.51/89.70 tff(73,plain,
% 89.51/89.70 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 89.51/89.70 inference(quant_intro,[status(thm)],[72])).
% 89.51/89.70 tff(74,plain,
% 89.51/89.70 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 89.51/89.70 inference(rewrite,[status(thm)],[])).
% 89.51/89.70 tff(75,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 89.51/89.70 tff(76,plain,
% 89.51/89.70 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 89.51/89.70 inference(modus_ponens,[status(thm)],[75, 74])).
% 89.51/89.70 tff(77,plain,(
% 89.51/89.70 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 89.51/89.70 inference(skolemize,[status(sab)],[76])).
% 89.51/89.70 tff(78,plain,
% 89.51/89.70 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 89.51/89.70 inference(modus_ponens,[status(thm)],[77, 73])).
% 89.51/89.70 tff(79,plain,
% 89.51/89.70 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(antidomain(multiplication(antidomain(X0!0), X0!0)), zero) = addition(zero, antidomain(multiplication(antidomain(X0!0), X0!0))))),
% 89.51/89.70 inference(quant_inst,[status(thm)],[])).
% 89.51/89.70 tff(80,plain,
% 89.51/89.70 (addition(antidomain(multiplication(antidomain(X0!0), X0!0)), zero) = addition(zero, antidomain(multiplication(antidomain(X0!0), X0!0)))),
% 89.51/89.70 inference(unit_resolution,[status(thm)],[79, 78])).
% 89.51/89.70 tff(81,plain,
% 89.51/89.70 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 89.51/89.70 inference(bind,[status(th)],[])).
% 89.51/89.70 tff(82,plain,
% 89.51/89.70 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 89.51/89.70 inference(quant_intro,[status(thm)],[81])).
% 89.51/89.70 tff(83,plain,
% 89.51/89.70 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 89.51/89.70 inference(rewrite,[status(thm)],[])).
% 89.51/89.70 tff(84,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_identity')).
% 89.51/89.70 tff(85,plain,
% 89.51/89.70 (![A: $i] : (addition(A, zero) = A)),
% 89.51/89.70 inference(modus_ponens,[status(thm)],[84, 83])).
% 89.51/89.70 tff(86,plain,(
% 89.51/89.70 ![A: $i] : (addition(A, zero) = A)),
% 89.51/89.70 inference(skolemize,[status(sab)],[85])).
% 89.51/89.70 tff(87,plain,
% 89.51/89.70 (![A: $i] : (addition(A, zero) = A)),
% 89.51/89.70 inference(modus_ponens,[status(thm)],[86, 82])).
% 89.51/89.70 tff(88,plain,
% 89.51/89.70 ((~![A: $i] : (addition(A, zero) = A)) | (addition(antidomain(multiplication(antidomain(X0!0), X0!0)), zero) = antidomain(multiplication(antidomain(X0!0), X0!0)))),
% 89.51/89.70 inference(quant_inst,[status(thm)],[])).
% 89.51/89.70 tff(89,plain,
% 89.51/89.70 (addition(antidomain(multiplication(antidomain(X0!0), X0!0)), zero) = antidomain(multiplication(antidomain(X0!0), X0!0))),
% 89.51/89.70 inference(unit_resolution,[status(thm)],[88, 87])).
% 89.51/89.70 tff(90,plain,
% 89.51/89.70 (antidomain(multiplication(antidomain(X0!0), X0!0)) = addition(antidomain(multiplication(antidomain(X0!0), X0!0)), zero)),
% 89.51/89.70 inference(symmetry,[status(thm)],[89])).
% 89.51/89.70 tff(91,plain,
% 89.51/89.70 (antidomain(multiplication(antidomain(X0!0), X0!0)) = addition(zero, antidomain(multiplication(antidomain(X0!0), X0!0)))),
% 89.51/89.70 inference(transitivity,[status(thm)],[90, 80])).
% 89.51/89.70 tff(92,plain,
% 89.51/89.70 (multiplication(antidomain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), domain(X0!0))) = multiplication(addition(zero, antidomain(multiplication(antidomain(X0!0), X0!0))), multiplication(antidomain(X0!0), domain(X0!0)))),
% 89.51/89.70 inference(monotonicity,[status(thm)],[91])).
% 89.51/89.70 tff(93,plain,
% 89.51/89.70 (multiplication(addition(zero, antidomain(multiplication(antidomain(X0!0), X0!0))), multiplication(antidomain(X0!0), domain(X0!0))) = multiplication(antidomain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), domain(X0!0)))),
% 89.51/89.70 inference(symmetry,[status(thm)],[92])).
% 89.51/89.70 tff(94,plain,
% 89.51/89.70 (^[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))))),
% 89.51/89.70 inference(bind,[status(th)],[])).
% 89.51/89.70 tff(95,plain,
% 89.51/89.70 (![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)))),
% 89.51/89.70 inference(quant_intro,[status(thm)],[94])).
% 89.51/89.70 tff(96,plain,
% 89.51/89.70 (![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)))),
% 89.51/89.70 inference(rewrite,[status(thm)],[])).
% 89.51/89.70 tff(97,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')).
% 89.51/89.70 tff(98,plain,
% 89.51/89.70 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 89.51/89.70 inference(modus_ponens,[status(thm)],[97, 96])).
% 89.51/89.70 tff(99,plain,(
% 89.51/89.70 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 89.51/89.70 inference(skolemize,[status(sab)],[98])).
% 89.51/89.70 tff(100,plain,
% 89.51/89.70 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 89.51/89.70 inference(modus_ponens,[status(thm)],[99, 95])).
% 89.51/89.70 tff(101,plain,
% 89.51/89.70 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(zero, antidomain(multiplication(antidomain(X0!0), X0!0))), multiplication(antidomain(X0!0), domain(X0!0))) = addition(multiplication(zero, multiplication(antidomain(X0!0), domain(X0!0))), multiplication(antidomain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), domain(X0!0)))))),
% 89.51/89.70 inference(quant_inst,[status(thm)],[])).
% 89.51/89.70 tff(102,plain,
% 89.51/89.70 (multiplication(addition(zero, antidomain(multiplication(antidomain(X0!0), X0!0))), multiplication(antidomain(X0!0), domain(X0!0))) = addition(multiplication(zero, multiplication(antidomain(X0!0), domain(X0!0))), multiplication(antidomain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), domain(X0!0))))),
% 89.51/89.70 inference(unit_resolution,[status(thm)],[101, 100])).
% 89.51/89.70 tff(103,plain,
% 89.51/89.70 (addition(multiplication(zero, multiplication(antidomain(X0!0), domain(X0!0))), multiplication(antidomain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), domain(X0!0)))) = multiplication(addition(zero, antidomain(multiplication(antidomain(X0!0), X0!0))), multiplication(antidomain(X0!0), domain(X0!0)))),
% 89.51/89.70 inference(symmetry,[status(thm)],[102])).
% 89.51/89.70 tff(104,plain,
% 89.51/89.70 (^[A: $i] : refl((multiplication(A, zero) = zero) <=> (multiplication(A, zero) = zero))),
% 89.51/89.70 inference(bind,[status(th)],[])).
% 89.51/89.70 tff(105,plain,
% 89.51/89.70 (![A: $i] : (multiplication(A, zero) = zero) <=> ![A: $i] : (multiplication(A, zero) = zero)),
% 89.51/89.70 inference(quant_intro,[status(thm)],[104])).
% 89.51/89.70 tff(106,plain,
% 89.51/89.70 (![A: $i] : (multiplication(A, zero) = zero) <=> ![A: $i] : (multiplication(A, zero) = zero)),
% 89.51/89.70 inference(rewrite,[status(thm)],[])).
% 89.51/89.70 tff(107,axiom,(![A: $i] : (multiplication(A, zero) = zero)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','right_annihilation')).
% 89.51/89.70 tff(108,plain,
% 89.51/89.70 (![A: $i] : (multiplication(A, zero) = zero)),
% 89.51/89.70 inference(modus_ponens,[status(thm)],[107, 106])).
% 89.51/89.70 tff(109,plain,(
% 89.51/89.70 ![A: $i] : (multiplication(A, zero) = zero)),
% 89.51/89.70 inference(skolemize,[status(sab)],[108])).
% 89.51/89.70 tff(110,plain,
% 89.51/89.70 (![A: $i] : (multiplication(A, zero) = zero)),
% 89.51/89.70 inference(modus_ponens,[status(thm)],[109, 105])).
% 89.51/89.70 tff(111,plain,
% 89.51/89.70 ((~![A: $i] : (multiplication(A, zero) = zero)) | (multiplication(antidomain(multiplication(antidomain(X0!0), X0!0)), zero) = zero)),
% 89.51/89.70 inference(quant_inst,[status(thm)],[])).
% 89.51/89.70 tff(112,plain,
% 89.51/89.70 (multiplication(antidomain(multiplication(antidomain(X0!0), X0!0)), zero) = zero),
% 89.51/89.70 inference(unit_resolution,[status(thm)],[111, 110])).
% 89.51/89.70 tff(113,plain,
% 89.51/89.70 (zero = multiplication(antidomain(multiplication(antidomain(X0!0), X0!0)), zero)),
% 89.51/89.70 inference(symmetry,[status(thm)],[112])).
% 89.51/89.70 tff(114,plain,
% 89.51/89.70 (multiplication(zero, multiplication(antidomain(X0!0), domain(X0!0))) = multiplication(multiplication(zero, domain(X0!0)), multiplication(antidomain(X0!0), domain(X0!0)))),
% 89.51/89.70 inference(monotonicity,[status(thm)],[52])).
% 89.51/89.70 tff(115,plain,
% 89.51/89.70 (multiplication(zero, multiplication(antidomain(X0!0), domain(X0!0))) = multiplication(antidomain(multiplication(antidomain(X0!0), X0!0)), zero)),
% 89.51/89.70 inference(transitivity,[status(thm)],[114, 51, 49, 9, 113])).
% 89.51/89.70 tff(116,plain,
% 89.51/89.70 (addition(multiplication(zero, multiplication(antidomain(X0!0), domain(X0!0))), multiplication(antidomain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), domain(X0!0)))) = addition(multiplication(antidomain(multiplication(antidomain(X0!0), X0!0)), zero), multiplication(antidomain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), domain(X0!0))))),
% 89.51/89.70 inference(monotonicity,[status(thm)],[115])).
% 89.51/89.70 tff(117,plain,
% 89.51/89.70 (addition(multiplication(antidomain(multiplication(antidomain(X0!0), X0!0)), zero), multiplication(antidomain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), domain(X0!0)))) = addition(multiplication(zero, multiplication(antidomain(X0!0), domain(X0!0))), multiplication(antidomain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), domain(X0!0))))),
% 89.51/89.70 inference(symmetry,[status(thm)],[116])).
% 89.51/89.70 tff(118,plain,
% 89.51/89.70 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 89.51/89.70 inference(bind,[status(th)],[])).
% 89.51/89.70 tff(119,plain,
% 89.51/89.70 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 89.51/89.70 inference(quant_intro,[status(thm)],[118])).
% 89.51/89.70 tff(120,plain,
% 89.51/89.70 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 89.51/89.70 inference(rewrite,[status(thm)],[])).
% 89.51/89.70 tff(121,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_left_identity')).
% 89.51/89.70 tff(122,plain,
% 89.51/89.70 (![A: $i] : (multiplication(one, A) = A)),
% 89.51/89.70 inference(modus_ponens,[status(thm)],[121, 120])).
% 89.51/89.70 tff(123,plain,(
% 89.51/89.70 ![A: $i] : (multiplication(one, A) = A)),
% 89.51/89.70 inference(skolemize,[status(sab)],[122])).
% 89.51/89.70 tff(124,plain,
% 89.51/89.70 (![A: $i] : (multiplication(one, A) = A)),
% 89.51/89.70 inference(modus_ponens,[status(thm)],[123, 119])).
% 89.51/89.70 tff(125,plain,
% 89.51/89.70 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X0!0) = X0!0)),
% 89.51/89.70 inference(quant_inst,[status(thm)],[])).
% 89.51/89.70 tff(126,plain,
% 89.51/89.70 (multiplication(one, X0!0) = X0!0),
% 89.51/89.70 inference(unit_resolution,[status(thm)],[125, 124])).
% 89.51/89.70 tff(127,plain,
% 89.51/89.70 (domain(multiplication(one, X0!0)) = domain(X0!0)),
% 89.51/89.70 inference(monotonicity,[status(thm)],[126])).
% 89.51/89.70 tff(128,plain,
% 89.51/89.70 ((~![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))) | (domain(multiplication(one, X0!0)) = domain(multiplication(one, domain(X0!0))))),
% 89.51/89.70 inference(quant_inst,[status(thm)],[])).
% 89.51/89.70 tff(129,plain,
% 89.51/89.70 (domain(multiplication(one, X0!0)) = domain(multiplication(one, domain(X0!0)))),
% 89.51/89.70 inference(unit_resolution,[status(thm)],[128, 63])).
% 89.51/89.70 tff(130,plain,
% 89.51/89.70 (domain(multiplication(one, domain(X0!0))) = domain(multiplication(one, X0!0))),
% 89.51/89.70 inference(symmetry,[status(thm)],[129])).
% 89.51/89.70 tff(131,plain,
% 89.51/89.70 ((~![A: $i] : (addition(A, zero) = A)) | (addition(antidomain(zero), zero) = antidomain(zero))),
% 89.51/89.70 inference(quant_inst,[status(thm)],[])).
% 89.51/89.70 tff(132,plain,
% 89.51/89.70 (addition(antidomain(zero), zero) = antidomain(zero)),
% 89.51/89.70 inference(unit_resolution,[status(thm)],[131, 87])).
% 89.51/89.70 tff(133,plain,
% 89.51/89.70 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(zero, antidomain(zero)) = addition(antidomain(zero), zero))),
% 89.51/89.70 inference(quant_inst,[status(thm)],[])).
% 89.51/89.70 tff(134,plain,
% 89.51/89.70 (addition(zero, antidomain(zero)) = addition(antidomain(zero), zero)),
% 89.51/89.70 inference(unit_resolution,[status(thm)],[133, 78])).
% 89.51/89.70 tff(135,plain,
% 89.51/89.70 (addition(zero, antidomain(zero)) = addition(domain(zero), antidomain(zero))),
% 89.51/89.70 inference(monotonicity,[status(thm)],[36])).
% 89.51/89.70 tff(136,plain,
% 89.51/89.70 (addition(domain(zero), antidomain(zero)) = addition(zero, antidomain(zero))),
% 89.51/89.70 inference(symmetry,[status(thm)],[135])).
% 89.51/89.70 tff(137,plain,
% 89.51/89.70 ((~![X1: $i] : (~((~(addition(domain(X1), antidomain(X1)) = one)) | (~(multiplication(domain(X1), antidomain(X1)) = zero))))) | (~((~(addition(domain(zero), antidomain(zero)) = one)) | (~(multiplication(domain(zero), antidomain(zero)) = zero))))),
% 89.51/89.70 inference(quant_inst,[status(thm)],[])).
% 89.51/89.70 tff(138,plain,
% 89.51/89.70 (~((~(addition(domain(zero), antidomain(zero)) = one)) | (~(multiplication(domain(zero), antidomain(zero)) = zero)))),
% 89.51/89.70 inference(unit_resolution,[status(thm)],[137, 31])).
% 89.51/89.70 tff(139,plain,
% 89.51/89.70 (((~(addition(domain(zero), antidomain(zero)) = one)) | (~(multiplication(domain(zero), antidomain(zero)) = zero))) | (addition(domain(zero), antidomain(zero)) = one)),
% 89.51/89.70 inference(tautology,[status(thm)],[])).
% 89.51/89.70 tff(140,plain,
% 89.51/89.70 (addition(domain(zero), antidomain(zero)) = one),
% 89.51/89.70 inference(unit_resolution,[status(thm)],[139, 138])).
% 89.51/89.70 tff(141,plain,
% 89.51/89.70 (one = addition(domain(zero), antidomain(zero))),
% 89.51/89.70 inference(symmetry,[status(thm)],[140])).
% 89.51/89.70 tff(142,plain,
% 89.51/89.70 (one = antidomain(zero)),
% 89.51/89.70 inference(transitivity,[status(thm)],[141, 136, 134, 132])).
% 89.51/89.70 tff(143,plain,
% 89.51/89.70 (multiplication(one, domain(X0!0)) = multiplication(antidomain(zero), domain(X0!0))),
% 89.51/89.70 inference(monotonicity,[status(thm)],[142])).
% 89.51/89.70 tff(144,plain,
% 89.51/89.70 (multiplication(antidomain(zero), domain(X0!0)) = multiplication(one, domain(X0!0))),
% 89.51/89.70 inference(symmetry,[status(thm)],[143])).
% 89.51/89.70 tff(145,plain,
% 89.51/89.70 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 89.51/89.70 inference(bind,[status(th)],[])).
% 89.51/89.70 tff(146,plain,
% 89.51/89.70 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 89.51/89.70 inference(quant_intro,[status(thm)],[145])).
% 89.51/89.70 tff(147,plain,
% 89.51/89.70 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 89.51/89.70 inference(rewrite,[status(thm)],[])).
% 89.51/89.70 tff(148,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_idempotence')).
% 89.51/89.70 tff(149,plain,
% 89.51/89.70 (![A: $i] : (addition(A, A) = A)),
% 89.51/89.70 inference(modus_ponens,[status(thm)],[148, 147])).
% 89.51/89.70 tff(150,plain,(
% 89.51/89.70 ![A: $i] : (addition(A, A) = A)),
% 89.51/89.70 inference(skolemize,[status(sab)],[149])).
% 89.51/89.70 tff(151,plain,
% 89.51/89.70 (![A: $i] : (addition(A, A) = A)),
% 89.51/89.70 inference(modus_ponens,[status(thm)],[150, 146])).
% 89.51/89.70 tff(152,plain,
% 89.51/89.70 ((~![A: $i] : (addition(A, A) = A)) | (addition(domain(X0!0), domain(X0!0)) = domain(X0!0))),
% 89.51/89.70 inference(quant_inst,[status(thm)],[])).
% 89.51/89.70 tff(153,plain,
% 89.51/89.70 (addition(domain(X0!0), domain(X0!0)) = domain(X0!0)),
% 89.51/89.70 inference(unit_resolution,[status(thm)],[152, 151])).
% 89.51/89.70 tff(154,plain,
% 89.51/89.70 (domain(X0!0) = addition(domain(X0!0), domain(X0!0))),
% 89.51/89.70 inference(symmetry,[status(thm)],[153])).
% 89.51/89.70 tff(155,plain,
% 89.51/89.70 (addition(antidomain(zero), zero) = addition(zero, antidomain(zero))),
% 89.51/89.70 inference(symmetry,[status(thm)],[134])).
% 89.51/89.70 tff(156,plain,
% 89.51/89.70 (antidomain(zero) = addition(antidomain(zero), zero)),
% 89.51/89.70 inference(symmetry,[status(thm)],[132])).
% 89.51/89.70 tff(157,plain,
% 89.51/89.70 (antidomain(zero) = one),
% 89.51/89.70 inference(transitivity,[status(thm)],[156, 155, 135, 140])).
% 89.51/89.70 tff(158,plain,
% 89.51/89.70 (multiplication(antidomain(zero), domain(X0!0)) = multiplication(one, addition(domain(X0!0), domain(X0!0)))),
% 89.51/89.70 inference(monotonicity,[status(thm)],[157, 154])).
% 89.51/89.70 tff(159,plain,
% 89.51/89.70 (multiplication(one, addition(domain(X0!0), domain(X0!0))) = multiplication(antidomain(zero), domain(X0!0))),
% 89.51/89.70 inference(symmetry,[status(thm)],[158])).
% 89.51/89.70 tff(160,plain,
% 89.51/89.70 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, addition(domain(X0!0), domain(X0!0))) = addition(domain(X0!0), domain(X0!0)))),
% 89.51/89.70 inference(quant_inst,[status(thm)],[])).
% 89.51/89.70 tff(161,plain,
% 89.51/89.70 (multiplication(one, addition(domain(X0!0), domain(X0!0))) = addition(domain(X0!0), domain(X0!0))),
% 89.51/89.70 inference(unit_resolution,[status(thm)],[160, 124])).
% 89.51/89.70 tff(162,plain,
% 89.51/89.70 (addition(domain(X0!0), domain(X0!0)) = multiplication(one, addition(domain(X0!0), domain(X0!0)))),
% 89.51/89.70 inference(symmetry,[status(thm)],[161])).
% 89.51/89.70 tff(163,plain,
% 89.51/89.70 (addition(domain(X0!0), domain(X0!0)) = multiplication(one, domain(X0!0))),
% 89.51/89.70 inference(transitivity,[status(thm)],[162, 159, 144])).
% 89.51/89.70 tff(164,plain,
% 89.51/89.70 (domain(addition(domain(X0!0), domain(X0!0))) = domain(multiplication(one, domain(X0!0)))),
% 89.51/89.70 inference(monotonicity,[status(thm)],[163])).
% 89.51/89.70 tff(165,plain,
% 89.51/89.70 (^[X0: $i] : refl((addition(domain(X0), one) = one) <=> (addition(domain(X0), one) = one))),
% 89.51/89.70 inference(bind,[status(th)],[])).
% 89.51/89.70 tff(166,plain,
% 89.51/89.70 (![X0: $i] : (addition(domain(X0), one) = one) <=> ![X0: $i] : (addition(domain(X0), one) = one)),
% 89.51/89.70 inference(quant_intro,[status(thm)],[165])).
% 89.51/89.70 tff(167,plain,
% 89.51/89.70 (![X0: $i] : (addition(domain(X0), one) = one) <=> ![X0: $i] : (addition(domain(X0), one) = one)),
% 89.51/89.70 inference(rewrite,[status(thm)],[])).
% 89.51/89.70 tff(168,axiom,(![X0: $i] : (addition(domain(X0), one) = one)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax','domain3')).
% 89.51/89.70 tff(169,plain,
% 89.51/89.70 (![X0: $i] : (addition(domain(X0), one) = one)),
% 89.51/89.70 inference(modus_ponens,[status(thm)],[168, 167])).
% 89.51/89.70 tff(170,plain,(
% 89.51/89.70 ![X0: $i] : (addition(domain(X0), one) = one)),
% 89.51/89.70 inference(skolemize,[status(sab)],[169])).
% 89.51/89.70 tff(171,plain,
% 89.51/89.70 (![X0: $i] : (addition(domain(X0), one) = one)),
% 89.51/89.70 inference(modus_ponens,[status(thm)],[170, 166])).
% 89.51/89.70 tff(172,plain,
% 89.51/89.70 ((~![X0: $i] : (addition(domain(X0), one) = one)) | (addition(domain(X0!0), one) = one)),
% 89.51/89.70 inference(quant_inst,[status(thm)],[])).
% 89.51/89.70 tff(173,plain,
% 89.51/89.70 (addition(domain(X0!0), one) = one),
% 89.51/89.70 inference(unit_resolution,[status(thm)],[172, 171])).
% 89.51/89.70 tff(174,plain,
% 89.51/89.70 (((~(addition(domain(X0!0), antidomain(X0!0)) = one)) | (~(multiplication(domain(X0!0), antidomain(X0!0)) = zero))) | (addition(domain(X0!0), antidomain(X0!0)) = one)),
% 89.51/89.70 inference(tautology,[status(thm)],[])).
% 89.51/89.70 tff(175,plain,
% 89.51/89.70 (addition(domain(X0!0), antidomain(X0!0)) = one),
% 89.51/89.70 inference(unit_resolution,[status(thm)],[174, 33])).
% 89.51/89.70 tff(176,plain,
% 89.51/89.70 (addition(domain(X0!0), addition(domain(X0!0), antidomain(X0!0))) = addition(domain(X0!0), one)),
% 89.51/89.70 inference(monotonicity,[status(thm)],[175])).
% 89.51/89.70 tff(177,plain,
% 89.51/89.70 (^[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)))),
% 89.51/89.70 inference(bind,[status(th)],[])).
% 89.51/89.70 tff(178,plain,
% 89.51/89.70 (![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))),
% 89.51/89.70 inference(quant_intro,[status(thm)],[177])).
% 89.51/89.70 tff(179,plain,
% 89.51/89.70 (![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))),
% 89.51/89.70 inference(rewrite,[status(thm)],[])).
% 89.51/89.70 tff(180,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')).
% 89.51/89.70 tff(181,plain,
% 89.51/89.70 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 89.51/89.70 inference(modus_ponens,[status(thm)],[180, 179])).
% 89.51/89.70 tff(182,plain,(
% 89.51/89.70 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 89.51/89.70 inference(skolemize,[status(sab)],[181])).
% 89.51/89.70 tff(183,plain,
% 89.51/89.70 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 89.51/89.70 inference(modus_ponens,[status(thm)],[182, 178])).
% 89.51/89.70 tff(184,plain,
% 89.51/89.70 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(domain(X0!0), addition(domain(X0!0), antidomain(X0!0))) = addition(addition(domain(X0!0), domain(X0!0)), antidomain(X0!0)))),
% 89.51/89.70 inference(quant_inst,[status(thm)],[])).
% 89.51/89.70 tff(185,plain,
% 89.51/89.70 (addition(domain(X0!0), addition(domain(X0!0), antidomain(X0!0))) = addition(addition(domain(X0!0), domain(X0!0)), antidomain(X0!0))),
% 89.51/89.70 inference(unit_resolution,[status(thm)],[184, 183])).
% 89.51/89.70 tff(186,plain,
% 89.51/89.70 (addition(addition(domain(X0!0), domain(X0!0)), antidomain(X0!0)) = addition(domain(X0!0), addition(domain(X0!0), antidomain(X0!0)))),
% 89.51/89.70 inference(symmetry,[status(thm)],[185])).
% 89.51/89.70 tff(187,plain,
% 89.51/89.70 (addition(addition(domain(X0!0), domain(X0!0)), antidomain(X0!0)) = antidomain(zero)),
% 89.51/89.70 inference(transitivity,[status(thm)],[186, 176, 173, 141, 136, 134, 132])).
% 89.51/89.70 tff(188,plain,
% 89.51/89.70 (multiplication(addition(addition(domain(X0!0), domain(X0!0)), antidomain(X0!0)), addition(domain(X0!0), domain(X0!0))) = multiplication(antidomain(zero), domain(X0!0))),
% 89.51/89.70 inference(monotonicity,[status(thm)],[187, 153])).
% 89.51/89.70 tff(189,plain,
% 89.51/89.70 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(addition(domain(X0!0), domain(X0!0)), antidomain(X0!0)), addition(domain(X0!0), domain(X0!0))) = addition(multiplication(addition(domain(X0!0), domain(X0!0)), addition(domain(X0!0), domain(X0!0))), multiplication(antidomain(X0!0), addition(domain(X0!0), domain(X0!0)))))),
% 89.51/89.70 inference(quant_inst,[status(thm)],[])).
% 89.51/89.70 tff(190,plain,
% 89.51/89.70 (multiplication(addition(addition(domain(X0!0), domain(X0!0)), antidomain(X0!0)), addition(domain(X0!0), domain(X0!0))) = addition(multiplication(addition(domain(X0!0), domain(X0!0)), addition(domain(X0!0), domain(X0!0))), multiplication(antidomain(X0!0), addition(domain(X0!0), domain(X0!0))))),
% 89.51/89.70 inference(unit_resolution,[status(thm)],[189, 100])).
% 89.51/89.70 tff(191,plain,
% 89.51/89.70 (addition(multiplication(addition(domain(X0!0), domain(X0!0)), addition(domain(X0!0), domain(X0!0))), multiplication(antidomain(X0!0), addition(domain(X0!0), domain(X0!0)))) = multiplication(addition(addition(domain(X0!0), domain(X0!0)), antidomain(X0!0)), addition(domain(X0!0), domain(X0!0)))),
% 89.51/89.70 inference(symmetry,[status(thm)],[190])).
% 89.51/89.70 tff(192,plain,
% 89.51/89.70 (multiplication(antidomain(X0!0), addition(domain(X0!0), domain(X0!0))) = multiplication(antidomain(X0!0), domain(X0!0))),
% 89.51/89.70 inference(monotonicity,[status(thm)],[153])).
% 89.51/89.70 tff(193,plain,
% 89.51/89.70 (multiplication(antidomain(X0!0), domain(X0!0)) = multiplication(antidomain(X0!0), addition(domain(X0!0), domain(X0!0)))),
% 89.51/89.70 inference(symmetry,[status(thm)],[192])).
% 89.51/89.70 tff(194,plain,
% 89.51/89.70 (addition(multiplication(addition(domain(X0!0), domain(X0!0)), addition(domain(X0!0), domain(X0!0))), multiplication(antidomain(X0!0), domain(X0!0))) = addition(multiplication(addition(domain(X0!0), domain(X0!0)), addition(domain(X0!0), domain(X0!0))), multiplication(antidomain(X0!0), addition(domain(X0!0), domain(X0!0))))),
% 89.51/89.70 inference(monotonicity,[status(thm)],[193])).
% 89.51/89.70 tff(195,plain,
% 89.51/89.70 (addition(multiplication(addition(domain(X0!0), domain(X0!0)), addition(domain(X0!0), domain(X0!0))), multiplication(antidomain(X0!0), domain(X0!0))) = addition(domain(X0!0), domain(X0!0))),
% 89.51/89.70 inference(transitivity,[status(thm)],[194, 191, 188, 158, 161])).
% 89.51/89.70 tff(196,plain,
% 89.51/89.70 (domain(addition(multiplication(addition(domain(X0!0), domain(X0!0)), addition(domain(X0!0), domain(X0!0))), multiplication(antidomain(X0!0), domain(X0!0)))) = domain(addition(domain(X0!0), domain(X0!0)))),
% 89.51/89.70 inference(monotonicity,[status(thm)],[195])).
% 89.51/89.70 tff(197,plain,
% 89.51/89.70 (^[X0: $i, X1: $i] : refl((domain(addition(X0, X1)) = addition(domain(X0), domain(X1))) <=> (domain(addition(X0, X1)) = addition(domain(X0), domain(X1))))),
% 89.51/89.70 inference(bind,[status(th)],[])).
% 89.51/89.70 tff(198,plain,
% 89.51/89.70 (![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1))) <=> ![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 89.51/89.70 inference(quant_intro,[status(thm)],[197])).
% 89.51/89.70 tff(199,plain,
% 89.51/89.70 (![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1))) <=> ![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 89.51/89.70 inference(rewrite,[status(thm)],[])).
% 89.51/89.70 tff(200,axiom,(![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax','domain5')).
% 89.51/89.70 tff(201,plain,
% 89.51/89.70 (![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 89.51/89.70 inference(modus_ponens,[status(thm)],[200, 199])).
% 89.51/89.70 tff(202,plain,(
% 89.51/89.70 ![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 89.51/89.70 inference(skolemize,[status(sab)],[201])).
% 89.51/89.70 tff(203,plain,
% 89.51/89.70 (![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 89.51/89.70 inference(modus_ponens,[status(thm)],[202, 198])).
% 89.51/89.70 tff(204,plain,
% 89.51/89.70 ((~![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))) | (domain(addition(multiplication(addition(domain(X0!0), domain(X0!0)), addition(domain(X0!0), domain(X0!0))), multiplication(antidomain(X0!0), domain(X0!0)))) = addition(domain(multiplication(addition(domain(X0!0), domain(X0!0)), addition(domain(X0!0), domain(X0!0)))), domain(multiplication(antidomain(X0!0), domain(X0!0)))))),
% 89.51/89.70 inference(quant_inst,[status(thm)],[])).
% 89.51/89.70 tff(205,plain,
% 89.51/89.70 (domain(addition(multiplication(addition(domain(X0!0), domain(X0!0)), addition(domain(X0!0), domain(X0!0))), multiplication(antidomain(X0!0), domain(X0!0)))) = addition(domain(multiplication(addition(domain(X0!0), domain(X0!0)), addition(domain(X0!0), domain(X0!0)))), domain(multiplication(antidomain(X0!0), domain(X0!0))))),
% 89.51/89.70 inference(unit_resolution,[status(thm)],[204, 203])).
% 89.51/89.70 tff(206,plain,
% 89.51/89.70 (addition(domain(multiplication(addition(domain(X0!0), domain(X0!0)), addition(domain(X0!0), domain(X0!0)))), domain(multiplication(antidomain(X0!0), domain(X0!0)))) = domain(addition(multiplication(addition(domain(X0!0), domain(X0!0)), addition(domain(X0!0), domain(X0!0))), multiplication(antidomain(X0!0), domain(X0!0))))),
% 89.51/89.70 inference(symmetry,[status(thm)],[205])).
% 89.51/89.70 tff(207,plain,
% 89.51/89.70 (multiplication(addition(domain(X0!0), domain(X0!0)), domain(X0!0)) = multiplication(addition(domain(X0!0), domain(X0!0)), addition(domain(X0!0), domain(X0!0)))),
% 89.51/89.70 inference(monotonicity,[status(thm)],[154])).
% 89.51/89.70 tff(208,plain,
% 89.51/89.70 (domain(multiplication(addition(domain(X0!0), domain(X0!0)), domain(X0!0))) = domain(multiplication(addition(domain(X0!0), domain(X0!0)), addition(domain(X0!0), domain(X0!0))))),
% 89.51/89.70 inference(monotonicity,[status(thm)],[207])).
% 89.51/89.70 tff(209,plain,
% 89.51/89.70 ((~![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))) | (domain(multiplication(addition(domain(X0!0), domain(X0!0)), X0!0)) = domain(multiplication(addition(domain(X0!0), domain(X0!0)), domain(X0!0))))),
% 89.51/89.70 inference(quant_inst,[status(thm)],[])).
% 89.51/89.70 tff(210,plain,
% 89.51/89.70 (domain(multiplication(addition(domain(X0!0), domain(X0!0)), X0!0)) = domain(multiplication(addition(domain(X0!0), domain(X0!0)), domain(X0!0)))),
% 89.51/89.70 inference(unit_resolution,[status(thm)],[209, 63])).
% 89.51/89.70 tff(211,plain,
% 89.51/89.70 (multiplication(addition(domain(X0!0), domain(X0!0)), X0!0) = multiplication(domain(X0!0), X0!0)),
% 89.51/89.70 inference(monotonicity,[status(thm)],[153])).
% 89.51/89.70 tff(212,plain,
% 89.51/89.70 (multiplication(domain(X0!0), X0!0) = multiplication(addition(domain(X0!0), domain(X0!0)), X0!0)),
% 89.51/89.70 inference(symmetry,[status(thm)],[211])).
% 89.51/89.70 tff(213,plain,
% 89.51/89.70 (^[X0: $i] : refl((addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)))),
% 89.51/89.70 inference(bind,[status(th)],[])).
% 89.51/89.70 tff(214,plain,
% 89.51/89.70 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 89.51/89.70 inference(quant_intro,[status(thm)],[213])).
% 89.51/89.70 tff(215,plain,
% 89.51/89.70 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 89.51/89.70 inference(rewrite,[status(thm)],[])).
% 89.51/89.70 tff(216,axiom,(![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax','domain1')).
% 89.51/89.70 tff(217,plain,
% 89.51/89.70 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 89.51/89.70 inference(modus_ponens,[status(thm)],[216, 215])).
% 89.51/89.70 tff(218,plain,(
% 89.51/89.70 ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 89.51/89.70 inference(skolemize,[status(sab)],[217])).
% 89.51/89.70 tff(219,plain,
% 89.51/89.70 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 89.51/89.70 inference(modus_ponens,[status(thm)],[218, 214])).
% 89.51/89.70 tff(220,plain,
% 89.51/89.70 ((~![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))) | (addition(X0!0, multiplication(domain(X0!0), X0!0)) = multiplication(domain(X0!0), X0!0))),
% 89.51/89.70 inference(quant_inst,[status(thm)],[])).
% 89.51/89.70 tff(221,plain,
% 89.51/89.70 (addition(X0!0, multiplication(domain(X0!0), X0!0)) = multiplication(domain(X0!0), X0!0)),
% 89.51/89.70 inference(unit_resolution,[status(thm)],[220, 219])).
% 89.51/89.70 tff(222,plain,
% 89.51/89.70 (addition(X0!0, multiplication(domain(X0!0), X0!0)) = multiplication(addition(domain(X0!0), domain(X0!0)), X0!0)),
% 89.51/89.70 inference(transitivity,[status(thm)],[221, 212])).
% 89.51/89.70 tff(223,plain,
% 89.51/89.70 (domain(addition(X0!0, multiplication(domain(X0!0), X0!0))) = domain(multiplication(addition(domain(X0!0), domain(X0!0)), X0!0))),
% 89.51/89.70 inference(monotonicity,[status(thm)],[222])).
% 89.51/89.70 tff(224,plain,
% 89.51/89.70 ((~![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))) | (domain(addition(X0!0, multiplication(domain(X0!0), X0!0))) = addition(domain(X0!0), domain(multiplication(domain(X0!0), X0!0))))),
% 89.51/89.70 inference(quant_inst,[status(thm)],[])).
% 89.51/89.70 tff(225,plain,
% 89.51/89.70 (domain(addition(X0!0, multiplication(domain(X0!0), X0!0))) = addition(domain(X0!0), domain(multiplication(domain(X0!0), X0!0)))),
% 89.51/89.70 inference(unit_resolution,[status(thm)],[224, 203])).
% 89.51/89.70 tff(226,plain,
% 89.51/89.70 (addition(domain(X0!0), domain(multiplication(domain(X0!0), X0!0))) = domain(addition(X0!0, multiplication(domain(X0!0), X0!0)))),
% 89.51/89.70 inference(symmetry,[status(thm)],[225])).
% 89.51/89.70 tff(227,plain,
% 89.51/89.70 (addition(domain(X0!0), domain(multiplication(domain(X0!0), X0!0))) = domain(multiplication(addition(domain(X0!0), domain(X0!0)), addition(domain(X0!0), domain(X0!0))))),
% 89.51/89.70 inference(transitivity,[status(thm)],[226, 223, 210, 208])).
% 89.51/89.70 tff(228,plain,
% 89.51/89.70 (addition(addition(domain(X0!0), domain(multiplication(domain(X0!0), X0!0))), domain(multiplication(antidomain(X0!0), domain(X0!0)))) = addition(domain(multiplication(addition(domain(X0!0), domain(X0!0)), addition(domain(X0!0), domain(X0!0)))), domain(multiplication(antidomain(X0!0), domain(X0!0))))),
% 89.51/89.70 inference(monotonicity,[status(thm)],[227])).
% 89.51/89.70 tff(229,plain,
% 89.51/89.70 (addition(addition(domain(X0!0), domain(multiplication(domain(X0!0), X0!0))), domain(multiplication(antidomain(X0!0), domain(X0!0)))) = domain(X0!0)),
% 89.51/89.70 inference(transitivity,[status(thm)],[228, 206, 196, 164, 130, 127])).
% 89.51/89.70 tff(230,plain,
% 89.51/89.70 (multiplication(addition(addition(domain(X0!0), domain(multiplication(domain(X0!0), X0!0))), domain(multiplication(antidomain(X0!0), domain(X0!0)))), multiplication(antidomain(X0!0), domain(X0!0))) = multiplication(domain(X0!0), multiplication(antidomain(X0!0), domain(X0!0)))),
% 89.51/89.70 inference(monotonicity,[status(thm)],[229])).
% 89.51/89.70 tff(231,plain,
% 89.51/89.70 (multiplication(domain(X0!0), multiplication(antidomain(X0!0), domain(X0!0))) = multiplication(addition(addition(domain(X0!0), domain(multiplication(domain(X0!0), X0!0))), domain(multiplication(antidomain(X0!0), domain(X0!0)))), multiplication(antidomain(X0!0), domain(X0!0)))),
% 89.51/89.70 inference(symmetry,[status(thm)],[230])).
% 89.51/89.70 tff(232,plain,
% 89.51/89.70 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(domain(X0!0), multiplication(antidomain(X0!0), domain(X0!0))) = multiplication(multiplication(domain(X0!0), antidomain(X0!0)), domain(X0!0)))),
% 89.51/89.70 inference(quant_inst,[status(thm)],[])).
% 89.51/89.70 tff(233,plain,
% 89.51/89.70 (multiplication(domain(X0!0), multiplication(antidomain(X0!0), domain(X0!0))) = multiplication(multiplication(domain(X0!0), antidomain(X0!0)), domain(X0!0))),
% 89.51/89.70 inference(unit_resolution,[status(thm)],[232, 44])).
% 89.51/89.70 tff(234,plain,
% 89.51/89.70 (multiplication(multiplication(domain(X0!0), antidomain(X0!0)), domain(X0!0)) = multiplication(domain(X0!0), multiplication(antidomain(X0!0), domain(X0!0)))),
% 89.51/89.70 inference(symmetry,[status(thm)],[233])).
% 89.51/89.70 tff(235,plain,
% 89.51/89.70 (multiplication(multiplication(domain(X0!0), antidomain(X0!0)), domain(X0!0)) = multiplication(zero, domain(X0!0))),
% 89.51/89.70 inference(monotonicity,[status(thm)],[35])).
% 89.51/89.70 tff(236,plain,
% 89.51/89.70 (multiplication(zero, domain(X0!0)) = multiplication(multiplication(domain(X0!0), antidomain(X0!0)), domain(X0!0))),
% 89.51/89.70 inference(symmetry,[status(thm)],[235])).
% 89.51/89.70 tff(237,plain,
% 89.51/89.70 (multiplication(antidomain(multiplication(antidomain(X0!0), X0!0)), zero) = multiplication(addition(addition(domain(X0!0), domain(multiplication(domain(X0!0), X0!0))), domain(multiplication(antidomain(X0!0), domain(X0!0)))), multiplication(antidomain(X0!0), domain(X0!0)))),
% 89.51/89.70 inference(transitivity,[status(thm)],[112, 52, 236, 234, 231])).
% 89.51/89.70 tff(238,plain,
% 89.51/89.70 (addition(multiplication(antidomain(multiplication(antidomain(X0!0), X0!0)), zero), multiplication(antidomain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), domain(X0!0)))) = addition(multiplication(addition(addition(domain(X0!0), domain(multiplication(domain(X0!0), X0!0))), domain(multiplication(antidomain(X0!0), domain(X0!0)))), multiplication(antidomain(X0!0), domain(X0!0))), multiplication(antidomain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), domain(X0!0))))),
% 89.51/89.70 inference(monotonicity,[status(thm)],[237])).
% 89.51/89.70 tff(239,plain,
% 89.51/89.70 (addition(multiplication(addition(addition(domain(X0!0), domain(multiplication(domain(X0!0), X0!0))), domain(multiplication(antidomain(X0!0), domain(X0!0)))), multiplication(antidomain(X0!0), domain(X0!0))), multiplication(antidomain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), domain(X0!0)))) = addition(multiplication(antidomain(multiplication(antidomain(X0!0), X0!0)), zero), multiplication(antidomain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), domain(X0!0))))),
% 89.51/89.70 inference(symmetry,[status(thm)],[238])).
% 89.51/89.70 tff(240,plain,
% 89.51/89.70 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(addition(addition(domain(X0!0), domain(multiplication(domain(X0!0), X0!0))), domain(multiplication(antidomain(X0!0), domain(X0!0)))), antidomain(multiplication(antidomain(X0!0), X0!0))), multiplication(antidomain(X0!0), domain(X0!0))) = addition(multiplication(addition(addition(domain(X0!0), domain(multiplication(domain(X0!0), X0!0))), domain(multiplication(antidomain(X0!0), domain(X0!0)))), multiplication(antidomain(X0!0), domain(X0!0))), multiplication(antidomain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), domain(X0!0)))))),
% 89.51/89.70 inference(quant_inst,[status(thm)],[])).
% 89.51/89.70 tff(241,plain,
% 89.51/89.70 (multiplication(addition(addition(addition(domain(X0!0), domain(multiplication(domain(X0!0), X0!0))), domain(multiplication(antidomain(X0!0), domain(X0!0)))), antidomain(multiplication(antidomain(X0!0), X0!0))), multiplication(antidomain(X0!0), domain(X0!0))) = addition(multiplication(addition(addition(domain(X0!0), domain(multiplication(domain(X0!0), X0!0))), domain(multiplication(antidomain(X0!0), domain(X0!0)))), multiplication(antidomain(X0!0), domain(X0!0))), multiplication(antidomain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), domain(X0!0))))),
% 89.51/89.70 inference(unit_resolution,[status(thm)],[240, 100])).
% 89.51/89.70 tff(242,plain,
% 89.51/89.70 ((~![X0: $i] : (addition(domain(X0), one) = one)) | (addition(domain(multiplication(domain(X0!0), X0!0)), one) = one)),
% 89.51/89.71 inference(quant_inst,[status(thm)],[])).
% 89.51/89.71 tff(243,plain,
% 89.51/89.71 (addition(domain(multiplication(domain(X0!0), X0!0)), one) = one),
% 89.51/89.71 inference(unit_resolution,[status(thm)],[242, 171])).
% 89.51/89.71 tff(244,plain,
% 89.51/89.71 (((~(addition(domain(multiplication(antidomain(X0!0), X0!0)), antidomain(multiplication(antidomain(X0!0), X0!0))) = one)) | (~(multiplication(domain(multiplication(antidomain(X0!0), X0!0)), antidomain(multiplication(antidomain(X0!0), X0!0))) = zero))) | (addition(domain(multiplication(antidomain(X0!0), X0!0)), antidomain(multiplication(antidomain(X0!0), X0!0))) = one)),
% 89.51/89.71 inference(tautology,[status(thm)],[])).
% 89.51/89.71 tff(245,plain,
% 89.51/89.71 (addition(domain(multiplication(antidomain(X0!0), X0!0)), antidomain(multiplication(antidomain(X0!0), X0!0))) = one),
% 89.51/89.71 inference(unit_resolution,[status(thm)],[244, 54])).
% 89.51/89.71 tff(246,plain,
% 89.51/89.71 (addition(domain(multiplication(antidomain(X0!0), domain(X0!0))), antidomain(multiplication(antidomain(X0!0), X0!0))) = addition(domain(multiplication(antidomain(X0!0), X0!0)), antidomain(multiplication(antidomain(X0!0), X0!0)))),
% 89.51/89.71 inference(monotonicity,[status(thm)],[66])).
% 89.51/89.71 tff(247,plain,
% 89.51/89.71 (addition(domain(multiplication(antidomain(X0!0), domain(X0!0))), antidomain(multiplication(antidomain(X0!0), X0!0))) = one),
% 89.51/89.71 inference(transitivity,[status(thm)],[246, 245])).
% 89.51/89.71 tff(248,plain,
% 89.51/89.71 (multiplication(domain(X0!0), X0!0) = addition(X0!0, multiplication(domain(X0!0), X0!0))),
% 89.51/89.71 inference(symmetry,[status(thm)],[221])).
% 89.51/89.71 tff(249,plain,
% 89.51/89.71 (domain(multiplication(domain(X0!0), X0!0)) = domain(addition(X0!0, multiplication(domain(X0!0), X0!0)))),
% 89.51/89.71 inference(monotonicity,[status(thm)],[248])).
% 89.51/89.71 tff(250,plain,
% 89.51/89.71 (domain(addition(X0!0, multiplication(domain(X0!0), X0!0))) = domain(multiplication(domain(X0!0), X0!0))),
% 89.51/89.71 inference(symmetry,[status(thm)],[249])).
% 89.51/89.71 tff(251,plain,
% 89.51/89.71 (addition(domain(X0!0), domain(multiplication(domain(X0!0), X0!0))) = domain(multiplication(domain(X0!0), X0!0))),
% 89.51/89.71 inference(transitivity,[status(thm)],[226, 250])).
% 89.51/89.71 tff(252,plain,
% 89.51/89.71 (addition(addition(domain(X0!0), domain(multiplication(domain(X0!0), X0!0))), addition(domain(multiplication(antidomain(X0!0), domain(X0!0))), antidomain(multiplication(antidomain(X0!0), X0!0)))) = addition(domain(multiplication(domain(X0!0), X0!0)), one)),
% 89.51/89.71 inference(monotonicity,[status(thm)],[251, 247])).
% 89.51/89.71 tff(253,plain,
% 89.51/89.71 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(domain(X0!0), domain(multiplication(domain(X0!0), X0!0))), addition(domain(multiplication(antidomain(X0!0), domain(X0!0))), antidomain(multiplication(antidomain(X0!0), X0!0)))) = addition(addition(addition(domain(X0!0), domain(multiplication(domain(X0!0), X0!0))), domain(multiplication(antidomain(X0!0), domain(X0!0)))), antidomain(multiplication(antidomain(X0!0), X0!0))))),
% 89.51/89.71 inference(quant_inst,[status(thm)],[])).
% 89.51/89.71 tff(254,plain,
% 89.51/89.71 (addition(addition(domain(X0!0), domain(multiplication(domain(X0!0), X0!0))), addition(domain(multiplication(antidomain(X0!0), domain(X0!0))), antidomain(multiplication(antidomain(X0!0), X0!0)))) = addition(addition(addition(domain(X0!0), domain(multiplication(domain(X0!0), X0!0))), domain(multiplication(antidomain(X0!0), domain(X0!0)))), antidomain(multiplication(antidomain(X0!0), X0!0)))),
% 89.51/89.71 inference(unit_resolution,[status(thm)],[253, 183])).
% 89.51/89.71 tff(255,plain,
% 89.51/89.71 (addition(addition(addition(domain(X0!0), domain(multiplication(domain(X0!0), X0!0))), domain(multiplication(antidomain(X0!0), domain(X0!0)))), antidomain(multiplication(antidomain(X0!0), X0!0))) = addition(addition(domain(X0!0), domain(multiplication(domain(X0!0), X0!0))), addition(domain(multiplication(antidomain(X0!0), domain(X0!0))), antidomain(multiplication(antidomain(X0!0), X0!0))))),
% 89.51/89.71 inference(symmetry,[status(thm)],[254])).
% 89.51/89.71 tff(256,plain,
% 89.51/89.71 (addition(addition(addition(domain(X0!0), domain(multiplication(domain(X0!0), X0!0))), domain(multiplication(antidomain(X0!0), domain(X0!0)))), antidomain(multiplication(antidomain(X0!0), X0!0))) = one),
% 89.51/89.71 inference(transitivity,[status(thm)],[255, 252, 243])).
% 89.51/89.71 tff(257,plain,
% 89.51/89.71 (multiplication(addition(addition(addition(domain(X0!0), domain(multiplication(domain(X0!0), X0!0))), domain(multiplication(antidomain(X0!0), domain(X0!0)))), antidomain(multiplication(antidomain(X0!0), X0!0))), multiplication(antidomain(X0!0), domain(X0!0))) = multiplication(one, multiplication(antidomain(X0!0), domain(X0!0)))),
% 89.51/89.71 inference(monotonicity,[status(thm)],[256])).
% 89.51/89.71 tff(258,plain,
% 89.51/89.71 (multiplication(one, multiplication(antidomain(X0!0), domain(X0!0))) = multiplication(addition(addition(addition(domain(X0!0), domain(multiplication(domain(X0!0), X0!0))), domain(multiplication(antidomain(X0!0), domain(X0!0)))), antidomain(multiplication(antidomain(X0!0), X0!0))), multiplication(antidomain(X0!0), domain(X0!0)))),
% 89.51/89.71 inference(symmetry,[status(thm)],[257])).
% 89.51/89.71 tff(259,plain,
% 89.51/89.71 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, multiplication(antidomain(X0!0), domain(X0!0))) = multiplication(antidomain(X0!0), domain(X0!0)))),
% 89.51/89.71 inference(quant_inst,[status(thm)],[])).
% 89.51/89.71 tff(260,plain,
% 89.51/89.71 (multiplication(one, multiplication(antidomain(X0!0), domain(X0!0))) = multiplication(antidomain(X0!0), domain(X0!0))),
% 89.51/89.71 inference(unit_resolution,[status(thm)],[259, 124])).
% 89.51/89.71 tff(261,plain,
% 89.51/89.71 (multiplication(antidomain(X0!0), domain(X0!0)) = multiplication(one, multiplication(antidomain(X0!0), domain(X0!0)))),
% 89.51/89.71 inference(symmetry,[status(thm)],[260])).
% 89.51/89.71 tff(262,plain,
% 89.51/89.71 (multiplication(antidomain(X0!0), domain(X0!0)) = multiplication(antidomain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), domain(X0!0)))),
% 89.51/89.71 inference(transitivity,[status(thm)],[261, 258, 241, 239, 117, 103, 93])).
% 89.51/89.71 tff(263,plain,
% 89.51/89.71 (multiplication(domain(multiplication(antidomain(X0!0), domain(X0!0))), multiplication(antidomain(X0!0), domain(X0!0))) = multiplication(domain(multiplication(antidomain(X0!0), domain(X0!0))), multiplication(antidomain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), domain(X0!0))))),
% 89.51/89.71 inference(monotonicity,[status(thm)],[262])).
% 89.51/89.71 tff(264,plain,
% 89.51/89.71 ((~![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))) | (addition(multiplication(antidomain(X0!0), domain(X0!0)), multiplication(domain(multiplication(antidomain(X0!0), domain(X0!0))), multiplication(antidomain(X0!0), domain(X0!0)))) = multiplication(domain(multiplication(antidomain(X0!0), domain(X0!0))), multiplication(antidomain(X0!0), domain(X0!0))))),
% 89.51/89.71 inference(quant_inst,[status(thm)],[])).
% 89.51/89.71 tff(265,plain,
% 89.51/89.71 (addition(multiplication(antidomain(X0!0), domain(X0!0)), multiplication(domain(multiplication(antidomain(X0!0), domain(X0!0))), multiplication(antidomain(X0!0), domain(X0!0)))) = multiplication(domain(multiplication(antidomain(X0!0), domain(X0!0))), multiplication(antidomain(X0!0), domain(X0!0)))),
% 89.51/89.71 inference(unit_resolution,[status(thm)],[264, 219])).
% 89.51/89.71 tff(266,plain,
% 89.51/89.71 (addition(multiplication(one, multiplication(antidomain(X0!0), domain(X0!0))), multiplication(domain(multiplication(antidomain(X0!0), domain(X0!0))), multiplication(antidomain(X0!0), domain(X0!0)))) = addition(multiplication(antidomain(X0!0), domain(X0!0)), multiplication(domain(multiplication(antidomain(X0!0), domain(X0!0))), multiplication(antidomain(X0!0), domain(X0!0))))),
% 89.51/89.71 inference(monotonicity,[status(thm)],[260])).
% 89.51/89.71 tff(267,plain,
% 89.51/89.71 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(one, domain(multiplication(antidomain(X0!0), domain(X0!0)))), multiplication(antidomain(X0!0), domain(X0!0))) = addition(multiplication(one, multiplication(antidomain(X0!0), domain(X0!0))), multiplication(domain(multiplication(antidomain(X0!0), domain(X0!0))), multiplication(antidomain(X0!0), domain(X0!0)))))),
% 89.51/89.71 inference(quant_inst,[status(thm)],[])).
% 89.51/89.71 tff(268,plain,
% 89.51/89.71 (multiplication(addition(one, domain(multiplication(antidomain(X0!0), domain(X0!0)))), multiplication(antidomain(X0!0), domain(X0!0))) = addition(multiplication(one, multiplication(antidomain(X0!0), domain(X0!0))), multiplication(domain(multiplication(antidomain(X0!0), domain(X0!0))), multiplication(antidomain(X0!0), domain(X0!0))))),
% 89.51/89.71 inference(unit_resolution,[status(thm)],[267, 100])).
% 89.51/89.71 tff(269,plain,
% 89.51/89.71 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(domain(multiplication(antidomain(X0!0), domain(X0!0))), one) = addition(one, domain(multiplication(antidomain(X0!0), domain(X0!0)))))),
% 89.51/89.71 inference(quant_inst,[status(thm)],[])).
% 89.51/89.71 tff(270,plain,
% 89.51/89.71 (addition(domain(multiplication(antidomain(X0!0), domain(X0!0))), one) = addition(one, domain(multiplication(antidomain(X0!0), domain(X0!0))))),
% 89.51/89.71 inference(unit_resolution,[status(thm)],[269, 78])).
% 89.51/89.71 tff(271,plain,
% 89.51/89.71 ((~![X0: $i] : (addition(domain(X0), one) = one)) | (addition(domain(multiplication(antidomain(X0!0), domain(X0!0))), one) = one)),
% 89.51/89.71 inference(quant_inst,[status(thm)],[])).
% 89.51/89.71 tff(272,plain,
% 89.51/89.71 (addition(domain(multiplication(antidomain(X0!0), domain(X0!0))), one) = one),
% 89.51/89.71 inference(unit_resolution,[status(thm)],[271, 171])).
% 89.51/89.71 tff(273,plain,
% 89.51/89.71 (one = addition(domain(multiplication(antidomain(X0!0), domain(X0!0))), one)),
% 89.51/89.71 inference(symmetry,[status(thm)],[272])).
% 89.51/89.71 tff(274,plain,
% 89.51/89.71 (one = addition(one, domain(multiplication(antidomain(X0!0), domain(X0!0))))),
% 89.51/89.71 inference(transitivity,[status(thm)],[273, 270])).
% 89.51/89.71 tff(275,plain,
% 89.51/89.71 (multiplication(one, multiplication(antidomain(X0!0), domain(X0!0))) = multiplication(addition(one, domain(multiplication(antidomain(X0!0), domain(X0!0)))), multiplication(antidomain(X0!0), domain(X0!0)))),
% 89.51/89.71 inference(monotonicity,[status(thm)],[274])).
% 89.51/89.71 tff(276,plain,
% 89.51/89.71 (multiplication(antidomain(X0!0), domain(X0!0)) = zero),
% 89.51/89.71 inference(transitivity,[status(thm)],[261, 275, 268, 266, 265, 263, 71, 69, 51, 49, 9])).
% 89.51/89.71 tff(277,plain,
% 89.51/89.71 (~(multiplication(antidomain(X0!0), domain(X0!0)) = zero)),
% 89.51/89.71 inference(and_elim,[status(thm)],[28])).
% 89.51/89.71 tff(278,plain,
% 89.51/89.71 ($false),
% 89.51/89.71 inference(unit_resolution,[status(thm)],[277, 276])).
% 89.51/89.71 % SZS output end Proof
% 89.51/89.72 % E exiting
%------------------------------------------------------------------------------