%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE081+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:13:00 AM UTC 2025
% Result : Theorem 16.45s 16.61s
% Output : Proof 16.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE081+1 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n014.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 18:58:24 EDT 2025
% 0.13/0.34 % CPUTime :
% 16.45/16.61 % SZS status Theorem
% 16.45/16.61 % SZS output start Proof
% 16.45/16.61 tff(zero_type, type, (
% 16.45/16.61 zero: $i)).
% 16.45/16.61 tff(multiplication_type, type, (
% 16.45/16.61 multiplication: ( $i * $i ) > $i)).
% 16.45/16.61 tff(tptp_fun_X0_0_type, type, (
% 16.45/16.61 tptp_fun_X0_0: $i)).
% 16.45/16.61 tff(antidomain_type, type, (
% 16.45/16.61 antidomain: $i > $i)).
% 16.45/16.61 tff(domain_type, type, (
% 16.45/16.61 domain: $i > $i)).
% 16.45/16.61 tff(one_type, type, (
% 16.45/16.61 one: $i)).
% 16.45/16.61 tff(addition_type, type, (
% 16.45/16.61 addition: ( $i * $i ) > $i)).
% 16.45/16.61 tff(1,plain,
% 16.45/16.61 (^[A: $i] : refl((multiplication(zero, A) = zero) <=> (multiplication(zero, A) = zero))),
% 16.45/16.61 inference(bind,[status(th)],[])).
% 16.45/16.61 tff(2,plain,
% 16.45/16.61 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 16.45/16.61 inference(quant_intro,[status(thm)],[1])).
% 16.45/16.61 tff(3,plain,
% 16.45/16.61 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 16.45/16.61 inference(rewrite,[status(thm)],[])).
% 16.45/16.61 tff(4,axiom,(![A: $i] : (multiplication(zero, A) = zero)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','left_annihilation')).
% 16.45/16.61 tff(5,plain,
% 16.45/16.61 (![A: $i] : (multiplication(zero, A) = zero)),
% 16.45/16.61 inference(modus_ponens,[status(thm)],[4, 3])).
% 16.45/16.61 tff(6,plain,(
% 16.45/16.61 ![A: $i] : (multiplication(zero, A) = zero)),
% 16.45/16.61 inference(skolemize,[status(sab)],[5])).
% 16.45/16.61 tff(7,plain,
% 16.45/16.61 (![A: $i] : (multiplication(zero, A) = zero)),
% 16.45/16.61 inference(modus_ponens,[status(thm)],[6, 2])).
% 16.45/16.61 tff(8,plain,
% 16.45/16.61 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, X0!0) = zero)),
% 16.45/16.61 inference(quant_inst,[status(thm)],[])).
% 16.45/16.61 tff(9,plain,
% 16.45/16.61 (multiplication(zero, X0!0) = zero),
% 16.45/16.61 inference(unit_resolution,[status(thm)],[8, 7])).
% 16.45/16.61 tff(10,plain,
% 16.45/16.61 (^[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)))))),
% 16.45/16.61 inference(bind,[status(th)],[])).
% 16.45/16.61 tff(11,plain,
% 16.45/16.61 (![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))))),
% 16.45/16.61 inference(quant_intro,[status(thm)],[10])).
% 16.45/16.61 tff(12,plain,
% 16.45/16.61 (^[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)))))),
% 16.45/16.61 inference(bind,[status(th)],[])).
% 16.45/16.61 tff(13,plain,
% 16.45/16.61 (![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))))),
% 16.45/16.61 inference(quant_intro,[status(thm)],[12])).
% 16.45/16.61 tff(14,plain,
% 16.45/16.61 ((![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero)) & (~(multiplication(antidomain(X0!0), X0!0) = zero))) <=> (![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero)) & (~(multiplication(antidomain(X0!0), X0!0) = zero)))),
% 16.45/16.61 inference(rewrite,[status(thm)],[])).
% 16.45/16.61 tff(15,plain,
% 16.45/16.61 ((~![X0: $i] : ((~![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero))) | (multiplication(antidomain(X0), X0) = zero))) <=> (~![X0: $i] : ((~![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero))) | (multiplication(antidomain(X0), X0) = zero)))),
% 16.45/16.61 inference(rewrite,[status(thm)],[])).
% 16.45/16.61 tff(16,plain,
% 16.45/16.61 ((~![X0: $i] : (![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero)) => (multiplication(antidomain(X0), X0) = zero))) <=> (~![X0: $i] : ((~![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero))) | (multiplication(antidomain(X0), X0) = zero)))),
% 16.45/16.61 inference(rewrite,[status(thm)],[])).
% 16.45/16.61 tff(17,axiom,(~![X0: $i] : (![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero)) => (multiplication(antidomain(X0), X0) = zero))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 16.45/16.61 tff(18,plain,
% 16.45/16.61 (~![X0: $i] : ((~![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero))) | (multiplication(antidomain(X0), X0) = zero))),
% 16.45/16.61 inference(modus_ponens,[status(thm)],[17, 16])).
% 16.45/16.61 tff(19,plain,
% 16.45/16.61 (~![X0: $i] : ((~![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero))) | (multiplication(antidomain(X0), X0) = zero))),
% 16.45/16.61 inference(modus_ponens,[status(thm)],[18, 15])).
% 16.45/16.61 tff(20,plain,
% 16.45/16.61 (~![X0: $i] : ((~![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero))) | (multiplication(antidomain(X0), X0) = zero))),
% 16.45/16.61 inference(modus_ponens,[status(thm)],[19, 15])).
% 16.45/16.61 tff(21,plain,
% 16.45/16.61 (~![X0: $i] : ((~![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero))) | (multiplication(antidomain(X0), X0) = zero))),
% 16.45/16.61 inference(modus_ponens,[status(thm)],[20, 15])).
% 16.45/16.61 tff(22,plain,
% 16.45/16.61 (![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero)) & (~(multiplication(antidomain(X0!0), X0!0) = zero))),
% 16.45/16.61 inference(modus_ponens,[status(thm)],[21, 14])).
% 16.45/16.61 tff(23,plain,
% 16.45/16.61 (![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero))),
% 16.45/16.61 inference(and_elim,[status(thm)],[22])).
% 16.45/16.61 tff(24,plain,
% 16.45/16.61 (![X1: $i] : (~((~(addition(domain(X1), antidomain(X1)) = one)) | (~(multiplication(domain(X1), antidomain(X1)) = zero))))),
% 16.45/16.61 inference(modus_ponens,[status(thm)],[23, 13])).
% 16.45/16.61 tff(25,plain,
% 16.45/16.61 (![X1: $i] : (~((~(addition(domain(X1), antidomain(X1)) = one)) | (~(multiplication(domain(X1), antidomain(X1)) = zero))))),
% 16.45/16.61 inference(modus_ponens,[status(thm)],[24, 11])).
% 16.45/16.61 tff(26,plain,
% 16.45/16.61 ((~![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))))),
% 16.45/16.61 inference(quant_inst,[status(thm)],[])).
% 16.45/16.61 tff(27,plain,
% 16.45/16.61 (~((~(addition(domain(X0!0), antidomain(X0!0)) = one)) | (~(multiplication(domain(X0!0), antidomain(X0!0)) = zero)))),
% 16.45/16.61 inference(unit_resolution,[status(thm)],[26, 25])).
% 16.45/16.61 tff(28,plain,
% 16.45/16.61 (((~(addition(domain(X0!0), antidomain(X0!0)) = one)) | (~(multiplication(domain(X0!0), antidomain(X0!0)) = zero))) | (multiplication(domain(X0!0), antidomain(X0!0)) = zero)),
% 16.45/16.61 inference(tautology,[status(thm)],[])).
% 16.45/16.61 tff(29,plain,
% 16.45/16.61 (multiplication(domain(X0!0), antidomain(X0!0)) = zero),
% 16.45/16.61 inference(unit_resolution,[status(thm)],[28, 27])).
% 16.45/16.61 tff(30,plain,
% 16.45/16.61 (multiplication(multiplication(domain(X0!0), antidomain(X0!0)), X0!0) = multiplication(zero, X0!0)),
% 16.45/16.61 inference(monotonicity,[status(thm)],[29])).
% 16.45/16.61 tff(31,plain,
% 16.45/16.61 (^[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)))),
% 16.45/16.61 inference(bind,[status(th)],[])).
% 16.45/16.61 tff(32,plain,
% 16.45/16.61 (![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))),
% 16.45/16.61 inference(quant_intro,[status(thm)],[31])).
% 16.45/16.61 tff(33,plain,
% 16.45/16.61 (![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))),
% 16.45/16.61 inference(rewrite,[status(thm)],[])).
% 16.45/16.61 tff(34,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','multiplicative_associativity')).
% 16.45/16.61 tff(35,plain,
% 16.45/16.61 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 16.45/16.61 inference(modus_ponens,[status(thm)],[34, 33])).
% 16.45/16.61 tff(36,plain,(
% 16.45/16.61 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 16.45/16.61 inference(skolemize,[status(sab)],[35])).
% 16.45/16.61 tff(37,plain,
% 16.45/16.61 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 16.45/16.61 inference(modus_ponens,[status(thm)],[36, 32])).
% 16.45/16.61 tff(38,plain,
% 16.45/16.61 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(domain(X0!0), multiplication(antidomain(X0!0), X0!0)) = multiplication(multiplication(domain(X0!0), antidomain(X0!0)), X0!0))),
% 16.45/16.61 inference(quant_inst,[status(thm)],[])).
% 16.45/16.61 tff(39,plain,
% 16.45/16.61 (multiplication(domain(X0!0), multiplication(antidomain(X0!0), X0!0)) = multiplication(multiplication(domain(X0!0), antidomain(X0!0)), X0!0)),
% 16.45/16.61 inference(unit_resolution,[status(thm)],[38, 37])).
% 16.45/16.61 tff(40,plain,
% 16.45/16.61 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 16.45/16.61 inference(bind,[status(th)],[])).
% 16.45/16.61 tff(41,plain,
% 16.45/16.61 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 16.45/16.61 inference(quant_intro,[status(thm)],[40])).
% 16.45/16.61 tff(42,plain,
% 16.45/16.61 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 16.45/16.61 inference(rewrite,[status(thm)],[])).
% 16.45/16.61 tff(43,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','multiplicative_left_identity')).
% 16.45/16.61 tff(44,plain,
% 16.45/16.61 (![A: $i] : (multiplication(one, A) = A)),
% 16.45/16.61 inference(modus_ponens,[status(thm)],[43, 42])).
% 16.45/16.61 tff(45,plain,(
% 16.45/16.61 ![A: $i] : (multiplication(one, A) = A)),
% 16.45/16.61 inference(skolemize,[status(sab)],[44])).
% 16.45/16.61 tff(46,plain,
% 16.45/16.61 (![A: $i] : (multiplication(one, A) = A)),
% 16.45/16.61 inference(modus_ponens,[status(thm)],[45, 41])).
% 16.45/16.61 tff(47,plain,
% 16.45/16.61 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X0!0) = X0!0)),
% 16.45/16.61 inference(quant_inst,[status(thm)],[])).
% 16.45/16.61 tff(48,plain,
% 16.45/16.61 (multiplication(one, X0!0) = X0!0),
% 16.45/16.61 inference(unit_resolution,[status(thm)],[47, 46])).
% 16.45/16.61 tff(49,plain,
% 16.45/16.61 (domain(multiplication(one, X0!0)) = domain(X0!0)),
% 16.45/16.61 inference(monotonicity,[status(thm)],[48])).
% 16.45/16.61 tff(50,plain,
% 16.45/16.61 (^[X0: $i, X1: $i] : refl((domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1)))) <=> (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1)))))),
% 16.45/16.61 inference(bind,[status(th)],[])).
% 16.45/16.61 tff(51,plain,
% 16.45/16.61 (![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))))),
% 16.45/16.61 inference(quant_intro,[status(thm)],[50])).
% 16.45/16.61 tff(52,plain,
% 16.45/16.61 (![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))))),
% 16.45/16.61 inference(rewrite,[status(thm)],[])).
% 16.45/16.61 tff(53,axiom,(![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax','domain2')).
% 16.45/16.61 tff(54,plain,
% 16.45/16.61 (![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))),
% 16.45/16.61 inference(modus_ponens,[status(thm)],[53, 52])).
% 16.45/16.61 tff(55,plain,(
% 16.45/16.61 ![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))),
% 16.45/16.61 inference(skolemize,[status(sab)],[54])).
% 16.45/16.61 tff(56,plain,
% 16.45/16.61 (![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))),
% 16.45/16.61 inference(modus_ponens,[status(thm)],[55, 51])).
% 16.45/16.61 tff(57,plain,
% 16.45/16.61 ((~![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))) | (domain(multiplication(one, X0!0)) = domain(multiplication(one, domain(X0!0))))),
% 16.45/16.61 inference(quant_inst,[status(thm)],[])).
% 16.45/16.61 tff(58,plain,
% 16.45/16.61 (domain(multiplication(one, X0!0)) = domain(multiplication(one, domain(X0!0)))),
% 16.45/16.61 inference(unit_resolution,[status(thm)],[57, 56])).
% 16.45/16.61 tff(59,plain,
% 16.45/16.61 (domain(multiplication(one, domain(X0!0))) = domain(multiplication(one, X0!0))),
% 16.45/16.61 inference(symmetry,[status(thm)],[58])).
% 16.45/16.61 tff(60,plain,
% 16.45/16.61 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, domain(X0!0)) = domain(X0!0))),
% 16.45/16.61 inference(quant_inst,[status(thm)],[])).
% 16.45/16.61 tff(61,plain,
% 16.45/16.61 (multiplication(one, domain(X0!0)) = domain(X0!0)),
% 16.45/16.61 inference(unit_resolution,[status(thm)],[60, 46])).
% 16.45/16.61 tff(62,plain,
% 16.45/16.61 (domain(X0!0) = multiplication(one, domain(X0!0))),
% 16.45/16.61 inference(symmetry,[status(thm)],[61])).
% 16.45/16.61 tff(63,plain,
% 16.45/16.61 (domain(domain(X0!0)) = domain(multiplication(one, domain(X0!0)))),
% 16.45/16.61 inference(monotonicity,[status(thm)],[62])).
% 16.45/16.61 tff(64,plain,
% 16.45/16.61 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 16.45/16.61 inference(bind,[status(th)],[])).
% 16.45/16.61 tff(65,plain,
% 16.45/16.61 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 16.45/16.61 inference(quant_intro,[status(thm)],[64])).
% 16.45/16.61 tff(66,plain,
% 16.45/16.61 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 16.45/16.61 inference(rewrite,[status(thm)],[])).
% 16.45/16.61 tff(67,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_identity')).
% 16.45/16.61 tff(68,plain,
% 16.45/16.61 (![A: $i] : (addition(A, zero) = A)),
% 16.45/16.61 inference(modus_ponens,[status(thm)],[67, 66])).
% 16.45/16.61 tff(69,plain,(
% 16.45/16.61 ![A: $i] : (addition(A, zero) = A)),
% 16.45/16.61 inference(skolemize,[status(sab)],[68])).
% 16.45/16.61 tff(70,plain,
% 16.45/16.61 (![A: $i] : (addition(A, zero) = A)),
% 16.45/16.61 inference(modus_ponens,[status(thm)],[69, 65])).
% 16.45/16.61 tff(71,plain,
% 16.45/16.61 ((~![A: $i] : (addition(A, zero) = A)) | (addition(domain(X0!0), zero) = domain(X0!0))),
% 16.45/16.61 inference(quant_inst,[status(thm)],[])).
% 16.45/16.61 tff(72,plain,
% 16.45/16.61 (addition(domain(X0!0), zero) = domain(X0!0)),
% 16.45/16.61 inference(unit_resolution,[status(thm)],[71, 70])).
% 16.45/16.61 tff(73,plain,
% 16.45/16.61 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 16.45/16.61 inference(bind,[status(th)],[])).
% 16.45/16.61 tff(74,plain,
% 16.45/16.61 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 16.45/16.61 inference(quant_intro,[status(thm)],[73])).
% 16.45/16.61 tff(75,plain,
% 16.45/16.61 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 16.45/16.61 inference(rewrite,[status(thm)],[])).
% 16.45/16.61 tff(76,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 16.45/16.61 tff(77,plain,
% 16.45/16.61 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 16.45/16.61 inference(modus_ponens,[status(thm)],[76, 75])).
% 16.45/16.61 tff(78,plain,(
% 16.45/16.61 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 16.45/16.61 inference(skolemize,[status(sab)],[77])).
% 16.45/16.61 tff(79,plain,
% 16.45/16.61 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 16.45/16.61 inference(modus_ponens,[status(thm)],[78, 74])).
% 16.45/16.61 tff(80,plain,
% 16.45/16.61 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(zero, domain(X0!0)) = addition(domain(X0!0), zero))),
% 16.45/16.61 inference(quant_inst,[status(thm)],[])).
% 16.45/16.61 tff(81,plain,
% 16.45/16.61 (addition(zero, domain(X0!0)) = addition(domain(X0!0), zero)),
% 16.45/16.61 inference(unit_resolution,[status(thm)],[80, 79])).
% 16.45/16.61 tff(82,plain,
% 16.45/16.61 (addition(zero, domain(X0!0)) = domain(X0!0)),
% 16.45/16.61 inference(transitivity,[status(thm)],[81, 72])).
% 16.45/16.61 tff(83,plain,
% 16.45/16.61 (domain(addition(zero, domain(X0!0))) = domain(domain(X0!0))),
% 16.45/16.61 inference(monotonicity,[status(thm)],[82])).
% 16.45/16.61 tff(84,plain,
% 16.45/16.61 (addition(domain(X0!0), zero) = addition(zero, domain(X0!0))),
% 16.45/16.61 inference(symmetry,[status(thm)],[81])).
% 16.45/16.61 tff(85,plain,
% 16.45/16.61 (domain(X0!0) = addition(domain(X0!0), zero)),
% 16.45/16.61 inference(symmetry,[status(thm)],[72])).
% 16.45/16.61 tff(86,plain,
% 16.45/16.61 ((~![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))))),
% 16.45/16.61 inference(quant_inst,[status(thm)],[])).
% 16.45/16.61 tff(87,plain,
% 16.45/16.61 (~((~(addition(domain(zero), antidomain(zero)) = one)) | (~(multiplication(domain(zero), antidomain(zero)) = zero)))),
% 16.45/16.61 inference(unit_resolution,[status(thm)],[86, 25])).
% 16.45/16.61 tff(88,plain,
% 16.45/16.61 (((~(addition(domain(zero), antidomain(zero)) = one)) | (~(multiplication(domain(zero), antidomain(zero)) = zero))) | (addition(domain(zero), antidomain(zero)) = one)),
% 16.45/16.61 inference(tautology,[status(thm)],[])).
% 16.45/16.61 tff(89,plain,
% 16.45/16.61 (addition(domain(zero), antidomain(zero)) = one),
% 16.45/16.61 inference(unit_resolution,[status(thm)],[88, 87])).
% 16.45/16.61 tff(90,plain,
% 16.45/16.61 ((domain(zero) = zero) <=> (domain(zero) = zero)),
% 16.45/16.61 inference(rewrite,[status(thm)],[])).
% 16.45/16.61 tff(91,axiom,(domain(zero) = zero), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax','domain4')).
% 16.45/16.61 tff(92,plain,
% 16.45/16.61 (domain(zero) = zero),
% 16.45/16.61 inference(modus_ponens,[status(thm)],[91, 90])).
% 16.45/16.61 tff(93,plain,
% 16.45/16.61 (zero = domain(zero)),
% 16.45/16.61 inference(symmetry,[status(thm)],[92])).
% 16.45/16.61 tff(94,plain,
% 16.45/16.61 (addition(zero, antidomain(zero)) = addition(domain(zero), antidomain(zero))),
% 16.45/16.61 inference(monotonicity,[status(thm)],[93])).
% 16.45/16.61 tff(95,plain,
% 16.45/16.61 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(zero, antidomain(zero)) = addition(antidomain(zero), zero))),
% 16.45/16.61 inference(quant_inst,[status(thm)],[])).
% 16.45/16.61 tff(96,plain,
% 16.45/16.61 (addition(zero, antidomain(zero)) = addition(antidomain(zero), zero)),
% 16.45/16.61 inference(unit_resolution,[status(thm)],[95, 79])).
% 16.45/16.61 tff(97,plain,
% 16.45/16.61 (addition(antidomain(zero), zero) = addition(zero, antidomain(zero))),
% 16.45/16.61 inference(symmetry,[status(thm)],[96])).
% 16.45/16.61 tff(98,plain,
% 16.45/16.61 ((~![A: $i] : (addition(A, zero) = A)) | (addition(antidomain(zero), zero) = antidomain(zero))),
% 16.45/16.61 inference(quant_inst,[status(thm)],[])).
% 16.45/16.61 tff(99,plain,
% 16.45/16.61 (addition(antidomain(zero), zero) = antidomain(zero)),
% 16.45/16.61 inference(unit_resolution,[status(thm)],[98, 70])).
% 16.45/16.61 tff(100,plain,
% 16.45/16.61 (antidomain(zero) = addition(antidomain(zero), zero)),
% 16.45/16.61 inference(symmetry,[status(thm)],[99])).
% 16.45/16.61 tff(101,plain,
% 16.45/16.61 (antidomain(zero) = one),
% 16.45/16.61 inference(transitivity,[status(thm)],[100, 97, 94, 89])).
% 16.45/16.61 tff(102,plain,
% 16.45/16.61 (multiplication(antidomain(zero), domain(X0!0)) = multiplication(one, domain(X0!0))),
% 16.45/16.61 inference(monotonicity,[status(thm)],[101])).
% 16.45/16.61 tff(103,plain,
% 16.45/16.61 (addition(domain(zero), antidomain(zero)) = addition(zero, antidomain(zero))),
% 16.45/16.61 inference(symmetry,[status(thm)],[94])).
% 16.45/16.61 tff(104,plain,
% 16.45/16.61 (one = addition(domain(zero), antidomain(zero))),
% 16.45/16.61 inference(symmetry,[status(thm)],[89])).
% 16.45/16.61 tff(105,plain,
% 16.45/16.61 (one = antidomain(zero)),
% 16.45/16.61 inference(transitivity,[status(thm)],[104, 103, 96, 99])).
% 16.45/16.61 tff(106,plain,
% 16.45/16.61 (multiplication(one, addition(domain(X0!0), zero)) = multiplication(antidomain(zero), domain(X0!0))),
% 16.45/16.61 inference(monotonicity,[status(thm)],[105, 72])).
% 16.45/16.61 tff(107,plain,
% 16.45/16.61 (^[X0: $i] : refl((addition(domain(X0), one) = one) <=> (addition(domain(X0), one) = one))),
% 16.45/16.61 inference(bind,[status(th)],[])).
% 16.45/16.61 tff(108,plain,
% 16.45/16.61 (![X0: $i] : (addition(domain(X0), one) = one) <=> ![X0: $i] : (addition(domain(X0), one) = one)),
% 16.45/16.61 inference(quant_intro,[status(thm)],[107])).
% 16.45/16.61 tff(109,plain,
% 16.45/16.61 (![X0: $i] : (addition(domain(X0), one) = one) <=> ![X0: $i] : (addition(domain(X0), one) = one)),
% 16.45/16.61 inference(rewrite,[status(thm)],[])).
% 16.45/16.61 tff(110,axiom,(![X0: $i] : (addition(domain(X0), one) = one)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax','domain3')).
% 16.45/16.61 tff(111,plain,
% 16.45/16.61 (![X0: $i] : (addition(domain(X0), one) = one)),
% 16.45/16.61 inference(modus_ponens,[status(thm)],[110, 109])).
% 16.45/16.61 tff(112,plain,(
% 16.45/16.61 ![X0: $i] : (addition(domain(X0), one) = one)),
% 16.45/16.61 inference(skolemize,[status(sab)],[111])).
% 16.45/16.61 tff(113,plain,
% 16.45/16.61 (![X0: $i] : (addition(domain(X0), one) = one)),
% 16.45/16.61 inference(modus_ponens,[status(thm)],[112, 108])).
% 16.45/16.61 tff(114,plain,
% 16.45/16.61 ((~![X0: $i] : (addition(domain(X0), one) = one)) | (addition(domain(zero), one) = one)),
% 16.45/16.61 inference(quant_inst,[status(thm)],[])).
% 16.45/16.61 tff(115,plain,
% 16.45/16.61 (addition(domain(zero), one) = one),
% 16.45/16.61 inference(unit_resolution,[status(thm)],[114, 113])).
% 16.45/16.61 tff(116,plain,
% 16.45/16.61 (((~(addition(domain(X0!0), antidomain(X0!0)) = one)) | (~(multiplication(domain(X0!0), antidomain(X0!0)) = zero))) | (addition(domain(X0!0), antidomain(X0!0)) = one)),
% 16.45/16.61 inference(tautology,[status(thm)],[])).
% 16.45/16.61 tff(117,plain,
% 16.45/16.61 (addition(domain(X0!0), antidomain(X0!0)) = one),
% 16.45/16.61 inference(unit_resolution,[status(thm)],[116, 27])).
% 16.45/16.61 tff(118,plain,
% 16.45/16.61 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(domain(X0!0), antidomain(X0!0)) = addition(antidomain(X0!0), domain(X0!0)))),
% 16.45/16.61 inference(quant_inst,[status(thm)],[])).
% 16.45/16.61 tff(119,plain,
% 16.45/16.61 (addition(domain(X0!0), antidomain(X0!0)) = addition(antidomain(X0!0), domain(X0!0))),
% 16.45/16.61 inference(unit_resolution,[status(thm)],[118, 79])).
% 16.45/16.61 tff(120,plain,
% 16.45/16.61 (addition(antidomain(X0!0), domain(X0!0)) = addition(domain(X0!0), antidomain(X0!0))),
% 16.45/16.61 inference(symmetry,[status(thm)],[119])).
% 16.45/16.61 tff(121,plain,
% 16.45/16.61 (addition(antidomain(X0!0), domain(X0!0)) = one),
% 16.45/16.61 inference(transitivity,[status(thm)],[120, 117])).
% 16.45/16.61 tff(122,plain,
% 16.45/16.61 (addition(zero, addition(antidomain(X0!0), domain(X0!0))) = addition(domain(zero), one)),
% 16.45/16.61 inference(monotonicity,[status(thm)],[93, 121])).
% 16.45/16.61 tff(123,plain,
% 16.45/16.61 (^[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)))),
% 16.45/16.61 inference(bind,[status(th)],[])).
% 16.45/16.61 tff(124,plain,
% 16.45/16.61 (![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))),
% 16.45/16.61 inference(quant_intro,[status(thm)],[123])).
% 16.45/16.61 tff(125,plain,
% 16.45/16.61 (![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))),
% 16.45/16.61 inference(rewrite,[status(thm)],[])).
% 16.45/16.61 tff(126,axiom,(![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_associativity')).
% 16.45/16.61 tff(127,plain,
% 16.45/16.61 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 16.45/16.61 inference(modus_ponens,[status(thm)],[126, 125])).
% 16.45/16.61 tff(128,plain,(
% 16.45/16.61 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 16.45/16.61 inference(skolemize,[status(sab)],[127])).
% 16.45/16.61 tff(129,plain,
% 16.45/16.61 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 16.45/16.61 inference(modus_ponens,[status(thm)],[128, 124])).
% 16.45/16.61 tff(130,plain,
% 16.45/16.61 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(zero, addition(antidomain(X0!0), domain(X0!0))) = addition(addition(zero, antidomain(X0!0)), domain(X0!0)))),
% 16.45/16.61 inference(quant_inst,[status(thm)],[])).
% 16.45/16.61 tff(131,plain,
% 16.45/16.61 (addition(zero, addition(antidomain(X0!0), domain(X0!0))) = addition(addition(zero, antidomain(X0!0)), domain(X0!0))),
% 16.45/16.61 inference(unit_resolution,[status(thm)],[130, 129])).
% 16.45/16.61 tff(132,plain,
% 16.45/16.61 (addition(addition(zero, antidomain(X0!0)), domain(X0!0)) = addition(zero, addition(antidomain(X0!0), domain(X0!0)))),
% 16.45/16.61 inference(symmetry,[status(thm)],[131])).
% 16.45/16.61 tff(133,plain,
% 16.45/16.61 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(zero, antidomain(X0!0)), domain(X0!0)) = addition(domain(X0!0), addition(zero, antidomain(X0!0))))),
% 16.45/16.61 inference(quant_inst,[status(thm)],[])).
% 16.45/16.61 tff(134,plain,
% 16.45/16.61 (addition(addition(zero, antidomain(X0!0)), domain(X0!0)) = addition(domain(X0!0), addition(zero, antidomain(X0!0)))),
% 16.45/16.61 inference(unit_resolution,[status(thm)],[133, 79])).
% 16.45/16.61 tff(135,plain,
% 16.45/16.61 (addition(domain(X0!0), addition(zero, antidomain(X0!0))) = addition(addition(zero, antidomain(X0!0)), domain(X0!0))),
% 16.45/16.61 inference(symmetry,[status(thm)],[134])).
% 16.45/16.61 tff(136,plain,
% 16.45/16.61 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(domain(X0!0), addition(zero, antidomain(X0!0))) = addition(addition(domain(X0!0), zero), antidomain(X0!0)))),
% 16.45/16.61 inference(quant_inst,[status(thm)],[])).
% 16.45/16.61 tff(137,plain,
% 16.45/16.61 (addition(domain(X0!0), addition(zero, antidomain(X0!0))) = addition(addition(domain(X0!0), zero), antidomain(X0!0))),
% 16.45/16.61 inference(unit_resolution,[status(thm)],[136, 129])).
% 16.45/16.61 tff(138,plain,
% 16.45/16.61 (addition(addition(domain(X0!0), zero), antidomain(X0!0)) = addition(domain(X0!0), addition(zero, antidomain(X0!0)))),
% 16.45/16.61 inference(symmetry,[status(thm)],[137])).
% 16.45/16.61 tff(139,plain,
% 16.45/16.61 (addition(addition(domain(X0!0), zero), antidomain(X0!0)) = one),
% 16.45/16.61 inference(transitivity,[status(thm)],[138, 135, 132, 122, 115])).
% 16.45/16.61 tff(140,plain,
% 16.45/16.61 (multiplication(addition(addition(domain(X0!0), zero), antidomain(X0!0)), domain(X0!0)) = multiplication(one, addition(domain(X0!0), zero))),
% 16.45/16.61 inference(monotonicity,[status(thm)],[139, 85])).
% 16.45/16.61 tff(141,plain,
% 16.45/16.61 (^[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))))),
% 16.45/16.61 inference(bind,[status(th)],[])).
% 16.45/16.61 tff(142,plain,
% 16.45/16.61 (![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)))),
% 16.45/16.61 inference(quant_intro,[status(thm)],[141])).
% 16.45/16.61 tff(143,plain,
% 16.45/16.61 (![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)))),
% 16.45/16.61 inference(rewrite,[status(thm)],[])).
% 16.45/16.61 tff(144,axiom,(![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','left_distributivity')).
% 16.45/16.61 tff(145,plain,
% 16.45/16.61 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 16.45/16.61 inference(modus_ponens,[status(thm)],[144, 143])).
% 16.45/16.61 tff(146,plain,(
% 16.45/16.61 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 16.45/16.61 inference(skolemize,[status(sab)],[145])).
% 16.45/16.61 tff(147,plain,
% 16.45/16.61 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 16.45/16.61 inference(modus_ponens,[status(thm)],[146, 142])).
% 16.45/16.61 tff(148,plain,
% 16.45/16.61 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(addition(domain(X0!0), zero), antidomain(X0!0)), domain(X0!0)) = addition(multiplication(addition(domain(X0!0), zero), domain(X0!0)), multiplication(antidomain(X0!0), domain(X0!0))))),
% 16.45/16.61 inference(quant_inst,[status(thm)],[])).
% 16.45/16.61 tff(149,plain,
% 16.45/16.61 (multiplication(addition(addition(domain(X0!0), zero), antidomain(X0!0)), domain(X0!0)) = addition(multiplication(addition(domain(X0!0), zero), domain(X0!0)), multiplication(antidomain(X0!0), domain(X0!0)))),
% 16.45/16.61 inference(unit_resolution,[status(thm)],[148, 147])).
% 16.45/16.61 tff(150,plain,
% 16.45/16.61 (addition(multiplication(addition(domain(X0!0), zero), domain(X0!0)), multiplication(antidomain(X0!0), domain(X0!0))) = multiplication(addition(addition(domain(X0!0), zero), antidomain(X0!0)), domain(X0!0))),
% 16.45/16.61 inference(symmetry,[status(thm)],[149])).
% 16.45/16.61 tff(151,plain,
% 16.45/16.61 (multiplication(antidomain(X0!0), domain(X0!0)) = multiplication(antidomain(X0!0), multiplication(one, domain(X0!0)))),
% 16.45/16.61 inference(monotonicity,[status(thm)],[62])).
% 16.45/16.61 tff(152,plain,
% 16.45/16.61 (multiplication(antidomain(X0!0), multiplication(one, domain(X0!0))) = multiplication(antidomain(X0!0), domain(X0!0))),
% 16.45/16.61 inference(symmetry,[status(thm)],[151])).
% 16.45/16.61 tff(153,plain,
% 16.45/16.61 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(antidomain(X0!0), multiplication(one, domain(X0!0))) = multiplication(multiplication(antidomain(X0!0), one), domain(X0!0)))),
% 16.45/16.61 inference(quant_inst,[status(thm)],[])).
% 16.45/16.61 tff(154,plain,
% 16.45/16.61 (multiplication(antidomain(X0!0), multiplication(one, domain(X0!0))) = multiplication(multiplication(antidomain(X0!0), one), domain(X0!0))),
% 16.45/16.62 inference(unit_resolution,[status(thm)],[153, 37])).
% 16.45/16.62 tff(155,plain,
% 16.45/16.62 (multiplication(multiplication(antidomain(X0!0), one), domain(X0!0)) = multiplication(antidomain(X0!0), multiplication(one, domain(X0!0)))),
% 16.45/16.62 inference(symmetry,[status(thm)],[154])).
% 16.45/16.62 tff(156,plain,
% 16.45/16.62 (multiplication(multiplication(antidomain(X0!0), one), domain(X0!0)) = multiplication(antidomain(X0!0), domain(X0!0))),
% 16.45/16.62 inference(transitivity,[status(thm)],[155, 152])).
% 16.45/16.62 tff(157,plain,
% 16.45/16.62 (addition(multiplication(addition(domain(X0!0), zero), domain(X0!0)), multiplication(multiplication(antidomain(X0!0), one), domain(X0!0))) = addition(multiplication(addition(domain(X0!0), zero), domain(X0!0)), multiplication(antidomain(X0!0), domain(X0!0)))),
% 16.45/16.62 inference(monotonicity,[status(thm)],[156])).
% 16.45/16.62 tff(158,plain,
% 16.45/16.62 (addition(multiplication(addition(domain(X0!0), zero), domain(X0!0)), multiplication(multiplication(antidomain(X0!0), one), domain(X0!0))) = addition(zero, domain(X0!0))),
% 16.45/16.62 inference(transitivity,[status(thm)],[157, 150, 140, 106, 102, 61, 85, 84])).
% 16.45/16.62 tff(159,plain,
% 16.45/16.62 (domain(addition(multiplication(addition(domain(X0!0), zero), domain(X0!0)), multiplication(multiplication(antidomain(X0!0), one), domain(X0!0)))) = domain(addition(zero, domain(X0!0)))),
% 16.45/16.62 inference(monotonicity,[status(thm)],[158])).
% 16.45/16.62 tff(160,plain,
% 16.45/16.62 (^[X0: $i, X1: $i] : refl((domain(addition(X0, X1)) = addition(domain(X0), domain(X1))) <=> (domain(addition(X0, X1)) = addition(domain(X0), domain(X1))))),
% 16.45/16.62 inference(bind,[status(th)],[])).
% 16.45/16.62 tff(161,plain,
% 16.45/16.62 (![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)))),
% 16.45/16.62 inference(quant_intro,[status(thm)],[160])).
% 16.45/16.62 tff(162,plain,
% 16.45/16.62 (![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)))),
% 16.45/16.62 inference(rewrite,[status(thm)],[])).
% 16.45/16.62 tff(163,axiom,(![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax','domain5')).
% 16.45/16.62 tff(164,plain,
% 16.45/16.62 (![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 16.45/16.62 inference(modus_ponens,[status(thm)],[163, 162])).
% 16.45/16.62 tff(165,plain,(
% 16.45/16.62 ![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 16.45/16.62 inference(skolemize,[status(sab)],[164])).
% 16.45/16.62 tff(166,plain,
% 16.45/16.62 (![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 16.45/16.62 inference(modus_ponens,[status(thm)],[165, 161])).
% 16.45/16.62 tff(167,plain,
% 16.45/16.62 ((~![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))) | (domain(addition(multiplication(addition(domain(X0!0), zero), domain(X0!0)), multiplication(multiplication(antidomain(X0!0), one), domain(X0!0)))) = addition(domain(multiplication(addition(domain(X0!0), zero), domain(X0!0))), domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0)))))),
% 16.45/16.62 inference(quant_inst,[status(thm)],[])).
% 16.45/16.62 tff(168,plain,
% 16.45/16.62 (domain(addition(multiplication(addition(domain(X0!0), zero), domain(X0!0)), multiplication(multiplication(antidomain(X0!0), one), domain(X0!0)))) = addition(domain(multiplication(addition(domain(X0!0), zero), domain(X0!0))), domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0))))),
% 16.45/16.62 inference(unit_resolution,[status(thm)],[167, 166])).
% 16.45/16.62 tff(169,plain,
% 16.45/16.62 (addition(domain(multiplication(addition(domain(X0!0), zero), domain(X0!0))), domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0)))) = domain(addition(multiplication(addition(domain(X0!0), zero), domain(X0!0)), multiplication(multiplication(antidomain(X0!0), one), domain(X0!0))))),
% 16.45/16.62 inference(symmetry,[status(thm)],[168])).
% 16.45/16.62 tff(170,plain,
% 16.45/16.62 (domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0))) = domain(multiplication(antidomain(X0!0), domain(X0!0)))),
% 16.45/16.62 inference(monotonicity,[status(thm)],[156])).
% 16.45/16.62 tff(171,plain,
% 16.45/16.62 (domain(multiplication(antidomain(X0!0), domain(X0!0))) = domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0)))),
% 16.45/16.62 inference(symmetry,[status(thm)],[170])).
% 16.45/16.62 tff(172,plain,
% 16.45/16.62 ((~![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))) | (domain(multiplication(addition(domain(X0!0), zero), X0!0)) = domain(multiplication(addition(domain(X0!0), zero), domain(X0!0))))),
% 16.45/16.62 inference(quant_inst,[status(thm)],[])).
% 16.45/16.62 tff(173,plain,
% 16.45/16.62 (domain(multiplication(addition(domain(X0!0), zero), X0!0)) = domain(multiplication(addition(domain(X0!0), zero), domain(X0!0)))),
% 16.45/16.62 inference(unit_resolution,[status(thm)],[172, 56])).
% 16.45/16.62 tff(174,plain,
% 16.45/16.62 (^[X0: $i] : refl((addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)))),
% 16.45/16.62 inference(bind,[status(th)],[])).
% 16.45/16.62 tff(175,plain,
% 16.45/16.62 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 16.45/16.62 inference(quant_intro,[status(thm)],[174])).
% 16.45/16.62 tff(176,plain,
% 16.45/16.62 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 16.45/16.62 inference(rewrite,[status(thm)],[])).
% 16.45/16.62 tff(177,axiom,(![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax','domain1')).
% 16.45/16.62 tff(178,plain,
% 16.45/16.62 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 16.45/16.62 inference(modus_ponens,[status(thm)],[177, 176])).
% 16.45/16.62 tff(179,plain,(
% 16.45/16.62 ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 16.45/16.62 inference(skolemize,[status(sab)],[178])).
% 16.45/16.62 tff(180,plain,
% 16.45/16.62 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 16.45/16.62 inference(modus_ponens,[status(thm)],[179, 175])).
% 16.45/16.62 tff(181,plain,
% 16.45/16.62 ((~![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))),
% 16.45/16.62 inference(quant_inst,[status(thm)],[])).
% 16.45/16.62 tff(182,plain,
% 16.45/16.62 (addition(X0!0, multiplication(domain(X0!0), X0!0)) = multiplication(domain(X0!0), X0!0)),
% 16.45/16.62 inference(unit_resolution,[status(thm)],[181, 180])).
% 16.45/16.62 tff(183,plain,
% 16.45/16.62 (multiplication(domain(X0!0), X0!0) = addition(X0!0, multiplication(domain(X0!0), X0!0))),
% 16.45/16.62 inference(symmetry,[status(thm)],[182])).
% 16.45/16.62 tff(184,plain,
% 16.45/16.62 (multiplication(addition(domain(X0!0), zero), X0!0) = multiplication(domain(X0!0), X0!0)),
% 16.45/16.62 inference(monotonicity,[status(thm)],[72])).
% 16.45/16.62 tff(185,plain,
% 16.45/16.62 (multiplication(addition(domain(X0!0), zero), X0!0) = addition(X0!0, multiplication(domain(X0!0), X0!0))),
% 16.45/16.62 inference(transitivity,[status(thm)],[184, 183])).
% 16.45/16.62 tff(186,plain,
% 16.45/16.62 (domain(multiplication(addition(domain(X0!0), zero), X0!0)) = domain(addition(X0!0, multiplication(domain(X0!0), X0!0)))),
% 16.45/16.62 inference(monotonicity,[status(thm)],[185])).
% 16.45/16.62 tff(187,plain,
% 16.45/16.62 (domain(addition(X0!0, multiplication(domain(X0!0), X0!0))) = domain(multiplication(addition(domain(X0!0), zero), X0!0))),
% 16.45/16.62 inference(symmetry,[status(thm)],[186])).
% 16.45/16.62 tff(188,plain,
% 16.45/16.62 ((~![X0: $i] : (addition(domain(X0), one) = one)) | (addition(domain(X0!0), one) = one)),
% 16.45/16.62 inference(quant_inst,[status(thm)],[])).
% 16.45/16.62 tff(189,plain,
% 16.45/16.62 (addition(domain(X0!0), one) = one),
% 16.45/16.62 inference(unit_resolution,[status(thm)],[188, 113])).
% 16.45/16.62 tff(190,plain,
% 16.45/16.62 (addition(zero, one) = addition(domain(zero), one)),
% 16.45/16.62 inference(monotonicity,[status(thm)],[93])).
% 16.45/16.62 tff(191,plain,
% 16.45/16.62 (addition(zero, one) = one),
% 16.45/16.62 inference(transitivity,[status(thm)],[190, 115])).
% 16.45/16.62 tff(192,plain,
% 16.45/16.62 (addition(domain(X0!0), addition(zero, one)) = addition(domain(X0!0), one)),
% 16.45/16.62 inference(monotonicity,[status(thm)],[191])).
% 16.45/16.62 tff(193,plain,
% 16.45/16.62 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(domain(X0!0), addition(zero, one)) = addition(addition(domain(X0!0), zero), one))),
% 16.45/16.62 inference(quant_inst,[status(thm)],[])).
% 16.45/16.62 tff(194,plain,
% 16.45/16.62 (addition(domain(X0!0), addition(zero, one)) = addition(addition(domain(X0!0), zero), one)),
% 16.45/16.62 inference(unit_resolution,[status(thm)],[193, 129])).
% 16.45/16.62 tff(195,plain,
% 16.45/16.62 (addition(addition(domain(X0!0), zero), one) = addition(domain(X0!0), addition(zero, one))),
% 16.45/16.62 inference(symmetry,[status(thm)],[194])).
% 16.45/16.62 tff(196,plain,
% 16.45/16.62 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(domain(X0!0), zero), one) = addition(one, addition(domain(X0!0), zero)))),
% 16.45/16.62 inference(quant_inst,[status(thm)],[])).
% 16.45/16.62 tff(197,plain,
% 16.45/16.62 (addition(addition(domain(X0!0), zero), one) = addition(one, addition(domain(X0!0), zero))),
% 16.45/16.62 inference(unit_resolution,[status(thm)],[196, 79])).
% 16.45/16.62 tff(198,plain,
% 16.45/16.62 (addition(one, addition(domain(X0!0), zero)) = addition(addition(domain(X0!0), zero), one)),
% 16.45/16.62 inference(symmetry,[status(thm)],[197])).
% 16.45/16.62 tff(199,plain,
% 16.45/16.62 (addition(one, addition(domain(X0!0), zero)) = one),
% 16.45/16.62 inference(transitivity,[status(thm)],[198, 195, 192, 189])).
% 16.45/16.62 tff(200,plain,
% 16.45/16.62 (multiplication(addition(one, addition(domain(X0!0), zero)), X0!0) = multiplication(one, X0!0)),
% 16.45/16.62 inference(monotonicity,[status(thm)],[199])).
% 16.45/16.62 tff(201,plain,
% 16.45/16.62 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(one, addition(domain(X0!0), zero)), X0!0) = addition(multiplication(one, X0!0), multiplication(addition(domain(X0!0), zero), X0!0)))),
% 16.45/16.62 inference(quant_inst,[status(thm)],[])).
% 16.45/16.62 tff(202,plain,
% 16.45/16.62 (multiplication(addition(one, addition(domain(X0!0), zero)), X0!0) = addition(multiplication(one, X0!0), multiplication(addition(domain(X0!0), zero), X0!0))),
% 16.45/16.62 inference(unit_resolution,[status(thm)],[201, 147])).
% 16.45/16.62 tff(203,plain,
% 16.45/16.62 (addition(multiplication(one, X0!0), multiplication(addition(domain(X0!0), zero), X0!0)) = multiplication(addition(one, addition(domain(X0!0), zero)), X0!0)),
% 16.45/16.62 inference(symmetry,[status(thm)],[202])).
% 16.45/16.62 tff(204,plain,
% 16.45/16.62 (multiplication(domain(X0!0), X0!0) = multiplication(addition(domain(X0!0), zero), X0!0)),
% 16.45/16.62 inference(symmetry,[status(thm)],[184])).
% 16.45/16.62 tff(205,plain,
% 16.45/16.62 (X0!0 = multiplication(one, X0!0)),
% 16.45/16.62 inference(symmetry,[status(thm)],[48])).
% 16.45/16.62 tff(206,plain,
% 16.45/16.62 (addition(X0!0, multiplication(domain(X0!0), X0!0)) = addition(multiplication(one, X0!0), multiplication(addition(domain(X0!0), zero), X0!0))),
% 16.45/16.62 inference(monotonicity,[status(thm)],[205, 204])).
% 16.45/16.62 tff(207,plain,
% 16.45/16.62 (addition(X0!0, multiplication(domain(X0!0), X0!0)) = X0!0),
% 16.45/16.62 inference(transitivity,[status(thm)],[206, 203, 200, 48])).
% 16.45/16.62 tff(208,plain,
% 16.45/16.62 (domain(addition(X0!0, multiplication(domain(X0!0), X0!0))) = domain(X0!0)),
% 16.45/16.62 inference(monotonicity,[status(thm)],[207])).
% 16.45/16.62 tff(209,plain,
% 16.45/16.62 (domain(X0!0) = domain(addition(X0!0, multiplication(domain(X0!0), X0!0)))),
% 16.45/16.62 inference(symmetry,[status(thm)],[208])).
% 16.45/16.62 tff(210,plain,
% 16.45/16.62 (addition(domain(X0!0), zero) = domain(multiplication(addition(domain(X0!0), zero), domain(X0!0)))),
% 16.45/16.62 inference(transitivity,[status(thm)],[72, 209, 187, 173])).
% 16.45/16.62 tff(211,plain,
% 16.45/16.62 (addition(addition(domain(X0!0), zero), domain(multiplication(antidomain(X0!0), domain(X0!0)))) = addition(domain(multiplication(addition(domain(X0!0), zero), domain(X0!0))), domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0))))),
% 16.45/16.62 inference(monotonicity,[status(thm)],[210, 171])).
% 16.45/16.62 tff(212,plain,
% 16.45/16.62 (addition(addition(domain(X0!0), zero), domain(multiplication(antidomain(X0!0), domain(X0!0)))) = domain(X0!0)),
% 16.45/16.62 inference(transitivity,[status(thm)],[211, 169, 159, 83, 63, 59, 49])).
% 16.45/16.62 tff(213,plain,
% 16.45/16.62 (multiplication(addition(addition(domain(X0!0), zero), domain(multiplication(antidomain(X0!0), domain(X0!0)))), multiplication(antidomain(X0!0), X0!0)) = multiplication(domain(X0!0), multiplication(antidomain(X0!0), X0!0))),
% 16.45/16.62 inference(monotonicity,[status(thm)],[212])).
% 16.45/16.62 tff(214,plain,
% 16.45/16.62 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(addition(domain(X0!0), zero), domain(multiplication(antidomain(X0!0), domain(X0!0)))), multiplication(antidomain(X0!0), X0!0)) = addition(multiplication(addition(domain(X0!0), zero), multiplication(antidomain(X0!0), X0!0)), multiplication(domain(multiplication(antidomain(X0!0), domain(X0!0))), multiplication(antidomain(X0!0), X0!0))))),
% 16.45/16.62 inference(quant_inst,[status(thm)],[])).
% 16.45/16.62 tff(215,plain,
% 16.45/16.62 (multiplication(addition(addition(domain(X0!0), zero), domain(multiplication(antidomain(X0!0), domain(X0!0)))), multiplication(antidomain(X0!0), X0!0)) = addition(multiplication(addition(domain(X0!0), zero), multiplication(antidomain(X0!0), X0!0)), multiplication(domain(multiplication(antidomain(X0!0), domain(X0!0))), multiplication(antidomain(X0!0), X0!0)))),
% 16.45/16.62 inference(unit_resolution,[status(thm)],[214, 147])).
% 16.45/16.62 tff(216,plain,
% 16.45/16.62 (addition(multiplication(addition(domain(X0!0), zero), multiplication(antidomain(X0!0), X0!0)), multiplication(domain(multiplication(antidomain(X0!0), domain(X0!0))), multiplication(antidomain(X0!0), X0!0))) = multiplication(addition(addition(domain(X0!0), zero), domain(multiplication(antidomain(X0!0), domain(X0!0)))), multiplication(antidomain(X0!0), X0!0))),
% 16.45/16.62 inference(symmetry,[status(thm)],[215])).
% 16.45/16.62 tff(217,plain,
% 16.45/16.62 ((~![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))))),
% 16.45/16.62 inference(quant_inst,[status(thm)],[])).
% 16.45/16.62 tff(218,plain,
% 16.45/16.62 (domain(multiplication(antidomain(X0!0), X0!0)) = domain(multiplication(antidomain(X0!0), domain(X0!0)))),
% 16.45/16.62 inference(unit_resolution,[status(thm)],[217, 56])).
% 16.45/16.62 tff(219,plain,
% 16.45/16.62 (domain(multiplication(antidomain(X0!0), domain(X0!0))) = domain(multiplication(antidomain(X0!0), X0!0))),
% 16.45/16.62 inference(symmetry,[status(thm)],[218])).
% 16.45/16.62 tff(220,plain,
% 16.45/16.62 (multiplication(domain(multiplication(antidomain(X0!0), domain(X0!0))), multiplication(antidomain(X0!0), X0!0)) = multiplication(domain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), X0!0))),
% 16.45/16.62 inference(monotonicity,[status(thm)],[219])).
% 16.45/16.62 tff(221,plain,
% 16.45/16.62 (multiplication(domain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), X0!0)) = multiplication(domain(multiplication(antidomain(X0!0), domain(X0!0))), multiplication(antidomain(X0!0), X0!0))),
% 16.45/16.62 inference(symmetry,[status(thm)],[220])).
% 16.45/16.62 tff(222,plain,
% 16.45/16.62 (multiplication(addition(domain(X0!0), zero), multiplication(antidomain(X0!0), X0!0)) = multiplication(domain(X0!0), multiplication(antidomain(X0!0), X0!0))),
% 16.45/16.62 inference(monotonicity,[status(thm)],[72])).
% 16.45/16.62 tff(223,plain,
% 16.45/16.62 (multiplication(domain(X0!0), multiplication(antidomain(X0!0), X0!0)) = multiplication(addition(domain(X0!0), zero), multiplication(antidomain(X0!0), X0!0))),
% 16.45/16.62 inference(symmetry,[status(thm)],[222])).
% 16.45/16.62 tff(224,plain,
% 16.45/16.62 (multiplication(multiplication(domain(X0!0), antidomain(X0!0)), X0!0) = multiplication(domain(X0!0), multiplication(antidomain(X0!0), X0!0))),
% 16.45/16.62 inference(symmetry,[status(thm)],[39])).
% 16.45/16.62 tff(225,plain,
% 16.45/16.62 (multiplication(zero, X0!0) = multiplication(multiplication(domain(X0!0), antidomain(X0!0)), X0!0)),
% 16.45/16.62 inference(symmetry,[status(thm)],[30])).
% 16.45/16.62 tff(226,plain,
% 16.45/16.62 (zero = multiplication(zero, X0!0)),
% 16.45/16.62 inference(symmetry,[status(thm)],[9])).
% 16.45/16.62 tff(227,plain,
% 16.45/16.62 (zero = multiplication(addition(domain(X0!0), zero), multiplication(antidomain(X0!0), X0!0))),
% 16.45/16.62 inference(transitivity,[status(thm)],[226, 225, 224, 223])).
% 16.45/16.62 tff(228,plain,
% 16.45/16.62 (addition(zero, multiplication(domain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), X0!0))) = addition(multiplication(addition(domain(X0!0), zero), multiplication(antidomain(X0!0), X0!0)), multiplication(domain(multiplication(antidomain(X0!0), domain(X0!0))), multiplication(antidomain(X0!0), X0!0)))),
% 16.45/16.62 inference(monotonicity,[status(thm)],[227, 221])).
% 16.45/16.62 tff(229,plain,
% 16.45/16.62 ((~![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))) | (addition(multiplication(antidomain(X0!0), X0!0), multiplication(domain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), X0!0))) = multiplication(domain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), X0!0)))),
% 16.45/16.62 inference(quant_inst,[status(thm)],[])).
% 16.45/16.62 tff(230,plain,
% 16.45/16.62 (addition(multiplication(antidomain(X0!0), X0!0), multiplication(domain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), X0!0))) = multiplication(domain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), X0!0))),
% 16.45/16.62 inference(unit_resolution,[status(thm)],[229, 180])).
% 16.45/16.62 tff(231,plain,
% 16.45/16.62 (addition(zero, addition(multiplication(antidomain(X0!0), X0!0), multiplication(domain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), X0!0)))) = addition(zero, multiplication(domain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), X0!0)))),
% 16.45/16.62 inference(monotonicity,[status(thm)],[230])).
% 16.45/16.62 tff(232,plain,
% 16.45/16.62 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(zero, addition(multiplication(antidomain(X0!0), X0!0), multiplication(domain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), X0!0)))) = addition(addition(zero, multiplication(antidomain(X0!0), X0!0)), multiplication(domain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), X0!0))))),
% 16.45/16.62 inference(quant_inst,[status(thm)],[])).
% 16.45/16.62 tff(233,plain,
% 16.45/16.62 (addition(zero, addition(multiplication(antidomain(X0!0), X0!0), multiplication(domain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), X0!0)))) = addition(addition(zero, multiplication(antidomain(X0!0), X0!0)), multiplication(domain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), X0!0)))),
% 16.45/16.62 inference(unit_resolution,[status(thm)],[232, 129])).
% 16.45/16.62 tff(234,plain,
% 16.45/16.62 (addition(addition(zero, multiplication(antidomain(X0!0), X0!0)), multiplication(domain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), X0!0))) = addition(zero, addition(multiplication(antidomain(X0!0), X0!0), multiplication(domain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), X0!0))))),
% 16.45/16.62 inference(symmetry,[status(thm)],[233])).
% 16.45/16.62 tff(235,plain,
% 16.45/16.62 (addition(zero, multiplication(antidomain(X0!0), X0!0)) = addition(multiplication(zero, X0!0), multiplication(antidomain(X0!0), X0!0))),
% 16.45/16.62 inference(monotonicity,[status(thm)],[226])).
% 16.45/16.62 tff(236,plain,
% 16.45/16.62 (addition(multiplication(zero, X0!0), multiplication(antidomain(X0!0), X0!0)) = addition(zero, multiplication(antidomain(X0!0), X0!0))),
% 16.45/16.62 inference(symmetry,[status(thm)],[235])).
% 16.45/16.62 tff(237,plain,
% 16.45/16.62 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(zero, antidomain(X0!0)), X0!0) = addition(multiplication(zero, X0!0), multiplication(antidomain(X0!0), X0!0)))),
% 16.45/16.62 inference(quant_inst,[status(thm)],[])).
% 16.45/16.62 tff(238,plain,
% 16.45/16.62 (multiplication(addition(zero, antidomain(X0!0)), X0!0) = addition(multiplication(zero, X0!0), multiplication(antidomain(X0!0), X0!0))),
% 16.45/16.62 inference(unit_resolution,[status(thm)],[237, 147])).
% 16.45/16.62 tff(239,plain,
% 16.45/16.62 ((~![A: $i] : (addition(A, zero) = A)) | (addition(antidomain(X0!0), zero) = antidomain(X0!0))),
% 16.45/16.62 inference(quant_inst,[status(thm)],[])).
% 16.45/16.62 tff(240,plain,
% 16.45/16.62 (addition(antidomain(X0!0), zero) = antidomain(X0!0)),
% 16.45/16.62 inference(unit_resolution,[status(thm)],[239, 70])).
% 16.45/16.62 tff(241,plain,
% 16.45/16.62 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(antidomain(X0!0), zero) = addition(zero, antidomain(X0!0)))),
% 16.45/16.62 inference(quant_inst,[status(thm)],[])).
% 16.45/16.62 tff(242,plain,
% 16.45/16.62 (addition(antidomain(X0!0), zero) = addition(zero, antidomain(X0!0))),
% 16.45/16.62 inference(unit_resolution,[status(thm)],[241, 79])).
% 16.45/16.62 tff(243,plain,
% 16.45/16.62 (addition(zero, antidomain(X0!0)) = addition(antidomain(X0!0), zero)),
% 16.45/16.62 inference(symmetry,[status(thm)],[242])).
% 16.45/16.62 tff(244,plain,
% 16.45/16.62 (addition(zero, antidomain(X0!0)) = antidomain(X0!0)),
% 16.45/16.62 inference(transitivity,[status(thm)],[243, 240])).
% 16.45/16.62 tff(245,plain,
% 16.45/16.62 (multiplication(addition(zero, antidomain(X0!0)), X0!0) = multiplication(antidomain(X0!0), X0!0)),
% 16.45/16.62 inference(monotonicity,[status(thm)],[244])).
% 16.45/16.62 tff(246,plain,
% 16.45/16.62 (multiplication(antidomain(X0!0), X0!0) = multiplication(addition(zero, antidomain(X0!0)), X0!0)),
% 16.45/16.62 inference(symmetry,[status(thm)],[245])).
% 16.45/16.62 tff(247,plain,
% 16.45/16.62 (multiplication(antidomain(X0!0), X0!0) = addition(zero, multiplication(antidomain(X0!0), X0!0))),
% 16.45/16.62 inference(transitivity,[status(thm)],[246, 238, 236])).
% 16.45/16.62 tff(248,plain,
% 16.45/16.62 (addition(multiplication(antidomain(X0!0), X0!0), multiplication(domain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), X0!0))) = addition(addition(zero, multiplication(antidomain(X0!0), X0!0)), multiplication(domain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), X0!0)))),
% 16.45/16.62 inference(monotonicity,[status(thm)],[247])).
% 16.45/16.62 tff(249,plain,
% 16.45/16.62 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(antidomain(X0!0), X0!0), multiplication(domain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), X0!0))) = addition(multiplication(domain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), X0!0)))),
% 16.45/16.62 inference(quant_inst,[status(thm)],[])).
% 16.45/16.62 tff(250,plain,
% 16.45/16.62 (addition(multiplication(antidomain(X0!0), X0!0), multiplication(domain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), X0!0))) = addition(multiplication(domain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), X0!0))),
% 16.45/16.62 inference(unit_resolution,[status(thm)],[249, 79])).
% 16.45/16.62 tff(251,plain,
% 16.45/16.62 (addition(multiplication(domain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), X0!0)) = addition(multiplication(antidomain(X0!0), X0!0), multiplication(domain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), X0!0)))),
% 16.45/16.62 inference(symmetry,[status(thm)],[250])).
% 16.45/16.62 tff(252,plain,
% 16.45/16.62 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, multiplication(antidomain(X0!0), X0!0)) = multiplication(antidomain(X0!0), X0!0))),
% 16.45/16.62 inference(quant_inst,[status(thm)],[])).
% 16.45/16.62 tff(253,plain,
% 16.45/16.62 (multiplication(one, multiplication(antidomain(X0!0), X0!0)) = multiplication(antidomain(X0!0), X0!0)),
% 16.45/16.62 inference(unit_resolution,[status(thm)],[252, 46])).
% 16.45/16.62 tff(254,plain,
% 16.45/16.62 (addition(multiplication(domain(multiplication(antidomain(X0!0), domain(X0!0))), multiplication(antidomain(X0!0), X0!0)), multiplication(one, multiplication(antidomain(X0!0), X0!0))) = addition(multiplication(domain(multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), X0!0)), multiplication(antidomain(X0!0), X0!0))),
% 16.45/16.62 inference(monotonicity,[status(thm)],[220, 253])).
% 16.45/16.62 tff(255,plain,
% 16.45/16.62 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(domain(multiplication(antidomain(X0!0), domain(X0!0))), one), multiplication(antidomain(X0!0), X0!0)) = addition(multiplication(domain(multiplication(antidomain(X0!0), domain(X0!0))), multiplication(antidomain(X0!0), X0!0)), multiplication(one, multiplication(antidomain(X0!0), X0!0))))),
% 16.45/16.62 inference(quant_inst,[status(thm)],[])).
% 16.45/16.62 tff(256,plain,
% 16.45/16.62 (multiplication(addition(domain(multiplication(antidomain(X0!0), domain(X0!0))), one), multiplication(antidomain(X0!0), X0!0)) = addition(multiplication(domain(multiplication(antidomain(X0!0), domain(X0!0))), multiplication(antidomain(X0!0), X0!0)), multiplication(one, multiplication(antidomain(X0!0), X0!0)))),
% 16.45/16.62 inference(unit_resolution,[status(thm)],[255, 147])).
% 16.45/16.63 tff(257,plain,
% 16.45/16.63 (addition(domain(multiplication(antidomain(X0!0), domain(X0!0))), one) = addition(domain(multiplication(antidomain(X0!0), X0!0)), one)),
% 16.45/16.63 inference(monotonicity,[status(thm)],[219])).
% 16.45/16.63 tff(258,plain,
% 16.45/16.63 (addition(domain(multiplication(antidomain(X0!0), X0!0)), one) = addition(domain(multiplication(antidomain(X0!0), domain(X0!0))), one)),
% 16.45/16.63 inference(symmetry,[status(thm)],[257])).
% 16.45/16.63 tff(259,plain,
% 16.45/16.63 ((~![X0: $i] : (addition(domain(X0), one) = one)) | (addition(domain(multiplication(antidomain(X0!0), X0!0)), one) = one)),
% 16.45/16.63 inference(quant_inst,[status(thm)],[])).
% 16.45/16.63 tff(260,plain,
% 16.45/16.63 (addition(domain(multiplication(antidomain(X0!0), X0!0)), one) = one),
% 16.45/16.63 inference(unit_resolution,[status(thm)],[259, 113])).
% 16.45/16.63 tff(261,plain,
% 16.45/16.63 (one = addition(domain(multiplication(antidomain(X0!0), X0!0)), one)),
% 16.45/16.63 inference(symmetry,[status(thm)],[260])).
% 16.45/16.63 tff(262,plain,
% 16.45/16.63 (one = addition(domain(multiplication(antidomain(X0!0), domain(X0!0))), one)),
% 16.45/16.63 inference(transitivity,[status(thm)],[261, 258])).
% 16.45/16.63 tff(263,plain,
% 16.45/16.63 (multiplication(one, multiplication(antidomain(X0!0), X0!0)) = multiplication(addition(domain(multiplication(antidomain(X0!0), domain(X0!0))), one), multiplication(antidomain(X0!0), X0!0))),
% 16.45/16.63 inference(monotonicity,[status(thm)],[262])).
% 16.45/16.63 tff(264,plain,
% 16.45/16.63 (multiplication(antidomain(X0!0), X0!0) = multiplication(one, multiplication(antidomain(X0!0), X0!0))),
% 16.45/16.63 inference(symmetry,[status(thm)],[253])).
% 16.45/16.63 tff(265,plain,
% 16.45/16.63 (multiplication(antidomain(X0!0), X0!0) = zero),
% 16.45/16.63 inference(transitivity,[status(thm)],[264, 263, 256, 254, 251, 248, 234, 231, 228, 216, 213, 39, 30, 9])).
% 16.45/16.63 tff(266,plain,
% 16.45/16.63 (~(multiplication(antidomain(X0!0), X0!0) = zero)),
% 16.45/16.63 inference(and_elim,[status(thm)],[22])).
% 16.45/16.63 tff(267,plain,
% 16.45/16.63 ($false),
% 16.45/16.63 inference(unit_resolution,[status(thm)],[266, 265])).
% 16.45/16.63 % SZS output end Proof
% 16.45/16.63 % E exiting
%------------------------------------------------------------------------------