%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE035+2 : 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 05:12:54 AM UTC 2025
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE035+2 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 18:56:16 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(zero_type, type, (
% 0.20/0.38 zero: $i)).
% 0.20/0.38 tff(addition_type, type, (
% 0.20/0.38 addition: ( $i * $i ) > $i)).
% 0.20/0.38 tff(multiplication_type, type, (
% 0.20/0.38 multiplication: ( $i * $i ) > $i)).
% 0.20/0.38 tff(c_type, type, (
% 0.20/0.38 c: $i > $i)).
% 0.20/0.38 tff(tptp_fun_X3_1_type, type, (
% 0.20/0.38 tptp_fun_X3_1: $i)).
% 0.20/0.38 tff(tptp_fun_X1_3_type, type, (
% 0.20/0.38 tptp_fun_X1_3: $i)).
% 0.20/0.38 tff(tptp_fun_X0_4_type, type, (
% 0.20/0.38 tptp_fun_X0_4: $i)).
% 0.20/0.38 tff(tptp_fun_X2_2_type, type, (
% 0.20/0.38 tptp_fun_X2_2: $i)).
% 0.20/0.38 tff(leq_type, type, (
% 0.20/0.38 leq: ( $i * $i ) > $o)).
% 0.20/0.38 tff(test_type, type, (
% 0.20/0.38 test: $i > $o)).
% 0.20/0.38 tff(1,plain,
% 0.20/0.38 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.20/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(4,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_identity')).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 (![A: $i] : (addition(A, zero) = A)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.38 tff(6,plain,(
% 0.20/0.38 ![A: $i] : (addition(A, zero) = A)),
% 0.20/0.38 inference(skolemize,[status(sab)],[5])).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (![A: $i] : (addition(A, zero) = A)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 ((~![A: $i] : (addition(A, zero) = A)) | (addition(multiplication(multiplication(X2!2, addition(X0!4, X1!3)), c(X3!1)), zero) = multiplication(multiplication(X2!2, addition(X0!4, X1!3)), c(X3!1)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 (addition(multiplication(multiplication(X2!2, addition(X0!4, X1!3)), c(X3!1)), zero) = multiplication(multiplication(X2!2, addition(X0!4, X1!3)), c(X3!1))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 ((addition(multiplication(multiplication(X2!2, addition(X0!4, X1!3)), c(X3!1)), zero) = zero) <=> (multiplication(multiplication(X2!2, addition(X0!4, X1!3)), c(X3!1)) = zero)),
% 0.20/0.38 inference(monotonicity,[status(thm)],[9])).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 ((multiplication(multiplication(X2!2, addition(X0!4, X1!3)), c(X3!1)) = zero) <=> (addition(multiplication(multiplication(X2!2, addition(X0!4, X1!3)), c(X3!1)), zero) = zero)),
% 0.20/0.38 inference(symmetry,[status(thm)],[10])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(15,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','order')).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.38 tff(17,plain,(
% 0.20/0.38 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.20/0.38 inference(skolemize,[status(sab)],[16])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(multiplication(multiplication(X2!2, X1!3), c(X3!1)), zero) <=> (addition(multiplication(multiplication(X2!2, X1!3), c(X3!1)), zero) = zero))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 (leq(multiplication(multiplication(X2!2, X1!3), c(X3!1)), zero) <=> (addition(multiplication(multiplication(X2!2, X1!3), c(X3!1)), zero) = zero)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 ((~![X0: $i, X1: $i, X2: $i, X3: $i] : ((~(test(X3) & test(X2) & leq(multiplication(multiplication(X2, X0), c(X3)), zero) & leq(multiplication(multiplication(X2, X1), c(X3)), zero))) | leq(multiplication(multiplication(X2, addition(X0, X1)), c(X3)), zero))) <=> (~![X0: $i, X1: $i, X2: $i, X3: $i] : ((~(test(X3) & test(X2) & leq(multiplication(multiplication(X2, X0), c(X3)), zero) & leq(multiplication(multiplication(X2, X1), c(X3)), zero))) | leq(multiplication(multiplication(X2, addition(X0, X1)), c(X3)), zero)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 ((~![X0: $i, X1: $i, X2: $i, X3: $i] : ((((test(X3) & test(X2)) & leq(multiplication(multiplication(X2, X0), c(X3)), zero)) & leq(multiplication(multiplication(X2, X1), c(X3)), zero)) => leq(multiplication(multiplication(X2, addition(X0, X1)), c(X3)), zero))) <=> (~![X0: $i, X1: $i, X2: $i, X3: $i] : ((~(test(X3) & test(X2) & leq(multiplication(multiplication(X2, X0), c(X3)), zero) & leq(multiplication(multiplication(X2, X1), c(X3)), zero))) | leq(multiplication(multiplication(X2, addition(X0, X1)), c(X3)), zero)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(23,axiom,(~![X0: $i, X1: $i, X2: $i, X3: $i] : ((((test(X3) & test(X2)) & leq(multiplication(multiplication(X2, X0), c(X3)), zero)) & leq(multiplication(multiplication(X2, X1), c(X3)), zero)) => leq(multiplication(multiplication(X2, addition(X0, X1)), c(X3)), zero))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 (~![X0: $i, X1: $i, X2: $i, X3: $i] : ((~(test(X3) & test(X2) & leq(multiplication(multiplication(X2, X0), c(X3)), zero) & leq(multiplication(multiplication(X2, X1), c(X3)), zero))) | leq(multiplication(multiplication(X2, addition(X0, X1)), c(X3)), zero))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 (~![X0: $i, X1: $i, X2: $i, X3: $i] : ((~(test(X3) & test(X2) & leq(multiplication(multiplication(X2, X0), c(X3)), zero) & leq(multiplication(multiplication(X2, X1), c(X3)), zero))) | leq(multiplication(multiplication(X2, addition(X0, X1)), c(X3)), zero))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 (~![X0: $i, X1: $i, X2: $i, X3: $i] : ((~(test(X3) & test(X2) & leq(multiplication(multiplication(X2, X0), c(X3)), zero) & leq(multiplication(multiplication(X2, X1), c(X3)), zero))) | leq(multiplication(multiplication(X2, addition(X0, X1)), c(X3)), zero))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 (~![X0: $i, X1: $i, X2: $i, X3: $i] : ((~(test(X3) & test(X2) & leq(multiplication(multiplication(X2, X0), c(X3)), zero) & leq(multiplication(multiplication(X2, X1), c(X3)), zero))) | leq(multiplication(multiplication(X2, addition(X0, X1)), c(X3)), zero))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.20/0.38 tff(28,plain,(
% 0.20/0.38 ~((~(test(X3!1) & test(X2!2) & leq(multiplication(multiplication(X2!2, X0!4), c(X3!1)), zero) & leq(multiplication(multiplication(X2!2, X1!3), c(X3!1)), zero))) | leq(multiplication(multiplication(X2!2, addition(X0!4, X1!3)), c(X3!1)), zero))),
% 0.20/0.38 inference(skolemize,[status(sab)],[27])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 (test(X3!1) & test(X2!2) & leq(multiplication(multiplication(X2!2, X0!4), c(X3!1)), zero) & leq(multiplication(multiplication(X2!2, X1!3), c(X3!1)), zero)),
% 0.20/0.38 inference(or_elim,[status(thm)],[28])).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 (leq(multiplication(multiplication(X2!2, X1!3), c(X3!1)), zero)),
% 0.20/0.38 inference(and_elim,[status(thm)],[29])).
% 0.20/0.38 tff(31,plain,
% 0.20/0.38 ((~(leq(multiplication(multiplication(X2!2, X1!3), c(X3!1)), zero) <=> (addition(multiplication(multiplication(X2!2, X1!3), c(X3!1)), zero) = zero))) | (~leq(multiplication(multiplication(X2!2, X1!3), c(X3!1)), zero)) | (addition(multiplication(multiplication(X2!2, X1!3), c(X3!1)), zero) = zero)),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 ((~(leq(multiplication(multiplication(X2!2, X1!3), c(X3!1)), zero) <=> (addition(multiplication(multiplication(X2!2, X1!3), c(X3!1)), zero) = zero))) | (addition(multiplication(multiplication(X2!2, X1!3), c(X3!1)), zero) = zero)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.20/0.38 tff(33,plain,
% 0.20/0.38 (addition(multiplication(multiplication(X2!2, X1!3), c(X3!1)), zero) = zero),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[32, 20])).
% 0.20/0.39 tff(34,plain,
% 0.20/0.39 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[34])).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(37,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 0.20/0.39 tff(38,plain,
% 0.20/0.39 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.39 tff(39,plain,(
% 0.20/0.39 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.20/0.39 inference(skolemize,[status(sab)],[38])).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(multiplication(X2!2, X1!3), c(X3!1)), zero) = addition(zero, multiplication(multiplication(X2!2, X1!3), c(X3!1))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 (addition(multiplication(multiplication(X2!2, X1!3), c(X3!1)), zero) = addition(zero, multiplication(multiplication(X2!2, X1!3), c(X3!1)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 (addition(zero, multiplication(multiplication(X2!2, X1!3), c(X3!1))) = addition(multiplication(multiplication(X2!2, X1!3), c(X3!1)), zero)),
% 0.20/0.39 inference(symmetry,[status(thm)],[42])).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(multiplication(multiplication(X2!2, X0!4), c(X3!1)), zero) <=> (addition(multiplication(multiplication(X2!2, X0!4), c(X3!1)), zero) = zero))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 (leq(multiplication(multiplication(X2!2, X0!4), c(X3!1)), zero) <=> (addition(multiplication(multiplication(X2!2, X0!4), c(X3!1)), zero) = zero)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[44, 18])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 (leq(multiplication(multiplication(X2!2, X0!4), c(X3!1)), zero)),
% 0.20/0.39 inference(and_elim,[status(thm)],[29])).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 ((~(leq(multiplication(multiplication(X2!2, X0!4), c(X3!1)), zero) <=> (addition(multiplication(multiplication(X2!2, X0!4), c(X3!1)), zero) = zero))) | (~leq(multiplication(multiplication(X2!2, X0!4), c(X3!1)), zero)) | (addition(multiplication(multiplication(X2!2, X0!4), c(X3!1)), zero) = zero)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 ((~(leq(multiplication(multiplication(X2!2, X0!4), c(X3!1)), zero) <=> (addition(multiplication(multiplication(X2!2, X0!4), c(X3!1)), zero) = zero))) | (addition(multiplication(multiplication(X2!2, X0!4), c(X3!1)), zero) = zero)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 (addition(multiplication(multiplication(X2!2, X0!4), c(X3!1)), zero) = zero),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[48, 45])).
% 0.20/0.39 tff(50,plain,
% 0.20/0.39 ((~![A: $i] : (addition(A, zero) = A)) | (addition(multiplication(multiplication(X2!2, X0!4), c(X3!1)), zero) = multiplication(multiplication(X2!2, X0!4), c(X3!1)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 (addition(multiplication(multiplication(X2!2, X0!4), c(X3!1)), zero) = multiplication(multiplication(X2!2, X0!4), c(X3!1))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[50, 7])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 (multiplication(multiplication(X2!2, X0!4), c(X3!1)) = addition(multiplication(multiplication(X2!2, X0!4), c(X3!1)), zero)),
% 0.20/0.39 inference(symmetry,[status(thm)],[51])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 (multiplication(multiplication(X2!2, X0!4), c(X3!1)) = zero),
% 0.20/0.39 inference(transitivity,[status(thm)],[52, 49])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 (addition(multiplication(multiplication(X2!2, X0!4), c(X3!1)), multiplication(multiplication(X2!2, X1!3), c(X3!1))) = addition(zero, multiplication(multiplication(X2!2, X1!3), c(X3!1)))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[53])).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 (^[A: $i, B: $i, C: $i] : refl((multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))) <=> (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[55])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(58,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')).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.39 tff(60,plain,(
% 0.20/0.39 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[59])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(multiplication(X2!2, X0!4), multiplication(X2!2, X1!3)), c(X3!1)) = addition(multiplication(multiplication(X2!2, X0!4), c(X3!1)), multiplication(multiplication(X2!2, X1!3), c(X3!1))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 (multiplication(addition(multiplication(X2!2, X0!4), multiplication(X2!2, X1!3)), c(X3!1)) = addition(multiplication(multiplication(X2!2, X0!4), c(X3!1)), multiplication(multiplication(X2!2, X1!3), c(X3!1)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 (^[A: $i, B: $i, C: $i] : refl((multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[64])).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(67,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','right_distributivity')).
% 0.20/0.39 tff(68,plain,
% 0.20/0.39 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.20/0.39 tff(69,plain,(
% 0.20/0.39 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[68])).
% 0.20/0.39 tff(70,plain,
% 0.20/0.39 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.20/0.39 tff(71,plain,
% 0.20/0.39 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X2!2, addition(X0!4, X1!3)) = addition(multiplication(X2!2, X0!4), multiplication(X2!2, X1!3)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(72,plain,
% 0.20/0.39 (multiplication(X2!2, addition(X0!4, X1!3)) = addition(multiplication(X2!2, X0!4), multiplication(X2!2, X1!3))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.20/0.39 tff(73,plain,
% 0.20/0.39 (multiplication(multiplication(X2!2, addition(X0!4, X1!3)), c(X3!1)) = multiplication(addition(multiplication(X2!2, X0!4), multiplication(X2!2, X1!3)), c(X3!1))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[72])).
% 0.20/0.39 tff(74,plain,
% 0.20/0.39 (multiplication(multiplication(X2!2, addition(X0!4, X1!3)), c(X3!1)) = zero),
% 0.20/0.39 inference(transitivity,[status(thm)],[73, 63, 54, 43, 33])).
% 0.20/0.39 tff(75,plain,
% 0.20/0.39 (addition(multiplication(multiplication(X2!2, addition(X0!4, X1!3)), c(X3!1)), zero) = zero),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[74, 11])).
% 0.20/0.39 tff(76,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(multiplication(multiplication(X2!2, addition(X0!4, X1!3)), c(X3!1)), zero) <=> (addition(multiplication(multiplication(X2!2, addition(X0!4, X1!3)), c(X3!1)), zero) = zero))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(77,plain,
% 0.20/0.39 (leq(multiplication(multiplication(X2!2, addition(X0!4, X1!3)), c(X3!1)), zero) <=> (addition(multiplication(multiplication(X2!2, addition(X0!4, X1!3)), c(X3!1)), zero) = zero)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[76, 18])).
% 0.20/0.39 tff(78,plain,
% 0.20/0.39 (~leq(multiplication(multiplication(X2!2, addition(X0!4, X1!3)), c(X3!1)), zero)),
% 0.20/0.39 inference(or_elim,[status(thm)],[28])).
% 0.20/0.39 tff(79,plain,
% 0.20/0.39 ((~(leq(multiplication(multiplication(X2!2, addition(X0!4, X1!3)), c(X3!1)), zero) <=> (addition(multiplication(multiplication(X2!2, addition(X0!4, X1!3)), c(X3!1)), zero) = zero))) | leq(multiplication(multiplication(X2!2, addition(X0!4, X1!3)), c(X3!1)), zero) | (~(addition(multiplication(multiplication(X2!2, addition(X0!4, X1!3)), c(X3!1)), zero) = zero))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(80,plain,
% 0.20/0.39 ((~(leq(multiplication(multiplication(X2!2, addition(X0!4, X1!3)), c(X3!1)), zero) <=> (addition(multiplication(multiplication(X2!2, addition(X0!4, X1!3)), c(X3!1)), zero) = zero))) | (~(addition(multiplication(multiplication(X2!2, addition(X0!4, X1!3)), c(X3!1)), zero) = zero))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.20/0.39 tff(81,plain,
% 0.20/0.39 (~(addition(multiplication(multiplication(X2!2, addition(X0!4, X1!3)), c(X3!1)), zero) = zero)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[80, 77])).
% 0.20/0.39 tff(82,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[81, 75])).
% 0.20/0.39 % SZS output end Proof
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------