%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE167+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:13:08 AM UTC 2025
% Result : Theorem 0.14s 0.42s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : KLE167+1 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Jun 19 19:06:53 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.14/0.42 % SZS status Theorem
% 0.14/0.42 % SZS output start Proof
% 0.14/0.42 tff(tptp_fun_X0_1_type, type, (
% 0.14/0.42 tptp_fun_X0_1: $i)).
% 0.14/0.42 tff(addition_type, type, (
% 0.14/0.42 addition: ( $i * $i ) > $i)).
% 0.14/0.42 tff(multiplication_type, type, (
% 0.14/0.42 multiplication: ( $i * $i ) > $i)).
% 0.14/0.42 tff(tptp_fun_X1_0_type, type, (
% 0.14/0.42 tptp_fun_X1_0: $i)).
% 0.14/0.42 tff(zero_type, type, (
% 0.14/0.42 zero: $i)).
% 0.14/0.42 tff(leq_type, type, (
% 0.14/0.42 leq: ( $i * $i ) > $o)).
% 0.14/0.42 tff(star_type, type, (
% 0.14/0.42 star: $i > $i)).
% 0.14/0.42 tff(one_type, type, (
% 0.14/0.42 one: $i)).
% 0.14/0.42 tff(1,plain,
% 0.14/0.42 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(2,plain,
% 0.14/0.42 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.14/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.42 tff(3,plain,
% 0.14/0.42 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(4,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','additive_identity')).
% 0.14/0.42 tff(5,plain,
% 0.14/0.42 (![A: $i] : (addition(A, zero) = A)),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.14/0.42 tff(6,plain,(
% 0.14/0.42 ![A: $i] : (addition(A, zero) = A)),
% 0.14/0.42 inference(skolemize,[status(sab)],[5])).
% 0.14/0.42 tff(7,plain,
% 0.14/0.42 (![A: $i] : (addition(A, zero) = A)),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.14/0.42 tff(8,plain,
% 0.14/0.42 ((~![A: $i] : (addition(A, zero) = A)) | (addition(X0!1, zero) = X0!1)),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(9,plain,
% 0.14/0.42 (addition(X0!1, zero) = X0!1),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.14/0.42 tff(10,plain,
% 0.14/0.42 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(11,plain,
% 0.14/0.42 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[10])).
% 0.14/0.42 tff(12,plain,
% 0.14/0.42 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(13,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','additive_commutativity')).
% 0.14/0.42 tff(14,plain,
% 0.14/0.42 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.14/0.42 tff(15,plain,(
% 0.14/0.42 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.14/0.42 inference(skolemize,[status(sab)],[14])).
% 0.14/0.42 tff(16,plain,
% 0.14/0.42 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.14/0.42 tff(17,plain,
% 0.14/0.42 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(zero, X0!1) = addition(X0!1, zero))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(18,plain,
% 0.14/0.42 (addition(zero, X0!1) = addition(X0!1, zero)),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.14/0.42 tff(19,plain,
% 0.14/0.42 (^[A: $i] : refl((addition(one, multiplication(A, star(A))) = star(A)) <=> (addition(one, multiplication(A, star(A))) = star(A)))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(20,plain,
% 0.14/0.42 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A)) <=> ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[19])).
% 0.14/0.42 tff(21,plain,
% 0.14/0.42 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A)) <=> ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(22,axiom,(![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','star_unfold1')).
% 0.14/0.42 tff(23,plain,
% 0.14/0.42 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.14/0.42 tff(24,plain,(
% 0.14/0.42 ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.14/0.42 inference(skolemize,[status(sab)],[23])).
% 0.14/0.42 tff(25,plain,
% 0.14/0.42 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.14/0.42 tff(26,plain,
% 0.14/0.42 ((~![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))) | (addition(one, multiplication(X1!0, star(X1!0))) = star(X1!0))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(27,plain,
% 0.22/0.42 (addition(one, multiplication(X1!0, star(X1!0))) = star(X1!0)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.22/0.42 tff(28,plain,
% 0.22/0.42 (multiplication(X0!1, addition(one, multiplication(X1!0, star(X1!0)))) = multiplication(X0!1, star(X1!0))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[27])).
% 0.22/0.42 tff(29,plain,
% 0.22/0.42 (^[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))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(30,plain,
% 0.22/0.42 (![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)))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[29])).
% 0.22/0.42 tff(31,plain,
% 0.22/0.42 (![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)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(32,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/KLE004+0.ax','distributivity1')).
% 0.22/0.42 tff(33,plain,
% 0.22/0.42 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.22/0.42 tff(34,plain,(
% 0.22/0.42 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.22/0.42 inference(skolemize,[status(sab)],[33])).
% 0.22/0.42 tff(35,plain,
% 0.22/0.42 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.22/0.42 tff(36,plain,
% 0.22/0.42 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!1, addition(one, multiplication(X1!0, star(X1!0)))) = addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(X1!0, star(X1!0)))))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(37,plain,
% 0.22/0.42 (multiplication(X0!1, addition(one, multiplication(X1!0, star(X1!0)))) = addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(X1!0, star(X1!0))))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.22/0.42 tff(38,plain,
% 0.22/0.42 (addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(X1!0, star(X1!0)))) = multiplication(X0!1, addition(one, multiplication(X1!0, star(X1!0))))),
% 0.22/0.42 inference(symmetry,[status(thm)],[37])).
% 0.22/0.42 tff(39,plain,
% 0.22/0.42 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(X1!0, star(X1!0)))) = addition(multiplication(X0!1, multiplication(X1!0, star(X1!0))), multiplication(X0!1, one)))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(40,plain,
% 0.22/0.42 (addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(X1!0, star(X1!0)))) = addition(multiplication(X0!1, multiplication(X1!0, star(X1!0))), multiplication(X0!1, one))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[39, 16])).
% 0.22/0.42 tff(41,plain,
% 0.22/0.42 (addition(multiplication(X0!1, multiplication(X1!0, star(X1!0))), multiplication(X0!1, one)) = addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(X1!0, star(X1!0))))),
% 0.22/0.42 inference(symmetry,[status(thm)],[40])).
% 0.22/0.42 tff(42,plain,
% 0.22/0.42 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(43,plain,
% 0.22/0.42 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.22/0.42 inference(quant_intro,[status(thm)],[42])).
% 0.22/0.42 tff(44,plain,
% 0.22/0.42 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(45,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','multiplicative_right_identity')).
% 0.22/0.42 tff(46,plain,
% 0.22/0.42 (![A: $i] : (multiplication(A, one) = A)),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.22/0.42 tff(47,plain,(
% 0.22/0.42 ![A: $i] : (multiplication(A, one) = A)),
% 0.22/0.42 inference(skolemize,[status(sab)],[46])).
% 0.22/0.42 tff(48,plain,
% 0.22/0.42 (![A: $i] : (multiplication(A, one) = A)),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.22/0.42 tff(49,plain,
% 0.22/0.42 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(X0!1, one) = X0!1)),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(50,plain,
% 0.22/0.42 (multiplication(X0!1, one) = X0!1),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.22/0.42 tff(51,plain,
% 0.22/0.42 (X0!1 = multiplication(X0!1, one)),
% 0.22/0.42 inference(symmetry,[status(thm)],[50])).
% 0.22/0.42 tff(52,plain,
% 0.22/0.42 (addition(multiplication(X0!1, multiplication(X1!0, star(X1!0))), X0!1) = addition(multiplication(X0!1, multiplication(X1!0, star(X1!0))), multiplication(X0!1, one))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[51])).
% 0.22/0.42 tff(53,plain,
% 0.22/0.42 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(54,plain,
% 0.22/0.42 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.22/0.42 inference(quant_intro,[status(thm)],[53])).
% 0.22/0.42 tff(55,plain,
% 0.22/0.42 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(56,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','idempotence')).
% 0.22/0.42 tff(57,plain,
% 0.22/0.42 (![A: $i] : (addition(A, A) = A)),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.22/0.42 tff(58,plain,(
% 0.22/0.42 ![A: $i] : (addition(A, A) = A)),
% 0.22/0.42 inference(skolemize,[status(sab)],[57])).
% 0.22/0.42 tff(59,plain,
% 0.22/0.42 (![A: $i] : (addition(A, A) = A)),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.22/0.42 tff(60,plain,
% 0.22/0.42 ((~![A: $i] : (addition(A, A) = A)) | (addition(X0!1, X0!1) = X0!1)),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(61,plain,
% 0.22/0.42 (addition(X0!1, X0!1) = X0!1),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.22/0.42 tff(62,plain,
% 0.22/0.42 (^[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)))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(63,plain,
% 0.22/0.42 (![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))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[62])).
% 0.22/0.42 tff(64,plain,
% 0.22/0.42 (![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))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(65,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','multiplicative_associativity')).
% 0.22/0.42 tff(66,plain,
% 0.22/0.42 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.22/0.42 tff(67,plain,(
% 0.22/0.42 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.22/0.42 inference(skolemize,[status(sab)],[66])).
% 0.22/0.42 tff(68,plain,
% 0.22/0.42 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.22/0.42 tff(69,plain,
% 0.22/0.42 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X0!1, multiplication(X1!0, star(X1!0))) = multiplication(multiplication(X0!1, X1!0), star(X1!0)))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(70,plain,
% 0.22/0.43 (multiplication(X0!1, multiplication(X1!0, star(X1!0))) = multiplication(multiplication(X0!1, X1!0), star(X1!0))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.22/0.43 tff(71,plain,
% 0.22/0.43 (multiplication(multiplication(X0!1, X1!0), star(X1!0)) = multiplication(X0!1, multiplication(X1!0, star(X1!0)))),
% 0.22/0.43 inference(symmetry,[status(thm)],[70])).
% 0.22/0.43 tff(72,plain,
% 0.22/0.43 (addition(multiplication(multiplication(X0!1, X1!0), star(X1!0)), addition(X0!1, X0!1)) = addition(multiplication(X0!1, multiplication(X1!0, star(X1!0))), X0!1)),
% 0.22/0.43 inference(monotonicity,[status(thm)],[71, 61])).
% 0.22/0.43 tff(73,plain,
% 0.22/0.43 (^[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)))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(74,plain,
% 0.22/0.43 (![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))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[73])).
% 0.22/0.43 tff(75,plain,
% 0.22/0.43 (![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))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(76,axiom,(![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','additive_associativity')).
% 0.22/0.43 tff(77,plain,
% 0.22/0.43 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.22/0.43 tff(78,plain,(
% 0.22/0.43 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.22/0.43 inference(skolemize,[status(sab)],[77])).
% 0.22/0.43 tff(79,plain,
% 0.22/0.43 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.22/0.43 tff(80,plain,
% 0.22/0.43 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(multiplication(X0!1, X1!0), star(X1!0)), addition(X0!1, X0!1)) = addition(addition(multiplication(multiplication(X0!1, X1!0), star(X1!0)), X0!1), X0!1))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(81,plain,
% 0.22/0.43 (addition(multiplication(multiplication(X0!1, X1!0), star(X1!0)), addition(X0!1, X0!1)) = addition(addition(multiplication(multiplication(X0!1, X1!0), star(X1!0)), X0!1), X0!1)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.22/0.43 tff(82,plain,
% 0.22/0.43 (addition(addition(multiplication(multiplication(X0!1, X1!0), star(X1!0)), X0!1), X0!1) = addition(multiplication(multiplication(X0!1, X1!0), star(X1!0)), addition(X0!1, X0!1))),
% 0.22/0.43 inference(symmetry,[status(thm)],[81])).
% 0.22/0.43 tff(83,plain,
% 0.22/0.43 (addition(multiplication(multiplication(X0!1, X1!0), star(X1!0)), X0!1) = addition(multiplication(X0!1, multiplication(X1!0, star(X1!0))), X0!1)),
% 0.22/0.43 inference(monotonicity,[status(thm)],[71])).
% 0.22/0.43 tff(84,plain,
% 0.22/0.43 (addition(multiplication(X0!1, multiplication(X1!0, star(X1!0))), X0!1) = addition(multiplication(multiplication(X0!1, X1!0), star(X1!0)), X0!1)),
% 0.22/0.43 inference(symmetry,[status(thm)],[83])).
% 0.22/0.43 tff(85,plain,
% 0.22/0.43 (addition(multiplication(X0!1, multiplication(X1!0, star(X1!0))), multiplication(X0!1, one)) = addition(multiplication(X0!1, multiplication(X1!0, star(X1!0))), X0!1)),
% 0.22/0.43 inference(symmetry,[status(thm)],[52])).
% 0.22/0.43 tff(86,plain,
% 0.22/0.43 (multiplication(X0!1, star(X1!0)) = multiplication(X0!1, addition(one, multiplication(X1!0, star(X1!0))))),
% 0.22/0.43 inference(symmetry,[status(thm)],[28])).
% 0.22/0.43 tff(87,plain,
% 0.22/0.43 (multiplication(X0!1, star(X1!0)) = addition(multiplication(multiplication(X0!1, X1!0), star(X1!0)), X0!1)),
% 0.22/0.43 inference(transitivity,[status(thm)],[86, 37, 40, 85, 84])).
% 0.22/0.43 tff(88,plain,
% 0.22/0.43 (addition(multiplication(X0!1, star(X1!0)), X0!1) = addition(addition(multiplication(multiplication(X0!1, X1!0), star(X1!0)), X0!1), X0!1)),
% 0.22/0.43 inference(monotonicity,[status(thm)],[87])).
% 0.22/0.43 tff(89,plain,
% 0.22/0.43 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X0!1, multiplication(X0!1, star(X1!0))) = addition(multiplication(X0!1, star(X1!0)), X0!1))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(90,plain,
% 0.22/0.43 (addition(X0!1, multiplication(X0!1, star(X1!0))) = addition(multiplication(X0!1, star(X1!0)), X0!1)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[89, 16])).
% 0.22/0.43 tff(91,plain,
% 0.22/0.43 (addition(X0!1, multiplication(X0!1, star(X1!0))) = multiplication(X0!1, star(X1!0))),
% 0.22/0.43 inference(transitivity,[status(thm)],[90, 88, 82, 72, 52, 41, 38, 28])).
% 0.22/0.43 tff(92,plain,
% 0.22/0.43 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(93,plain,
% 0.22/0.43 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[92])).
% 0.22/0.43 tff(94,plain,
% 0.22/0.43 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(95,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','order')).
% 0.22/0.43 tff(96,plain,
% 0.22/0.43 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.22/0.43 tff(97,plain,(
% 0.22/0.43 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.22/0.43 inference(skolemize,[status(sab)],[96])).
% 0.22/0.43 tff(98,plain,
% 0.22/0.43 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.22/0.43 tff(99,plain,
% 0.22/0.43 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(X0!1, multiplication(X0!1, star(X1!0))) <=> (addition(X0!1, multiplication(X0!1, star(X1!0))) = multiplication(X0!1, star(X1!0))))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(100,plain,
% 0.22/0.43 (leq(X0!1, multiplication(X0!1, star(X1!0))) <=> (addition(X0!1, multiplication(X0!1, star(X1!0))) = multiplication(X0!1, star(X1!0)))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.22/0.43 tff(101,assumption,(~leq(X0!1, multiplication(X0!1, star(X1!0)))), introduced(assumption)).
% 0.22/0.43 tff(102,plain,
% 0.22/0.43 ((~(leq(X0!1, multiplication(X0!1, star(X1!0))) <=> (addition(X0!1, multiplication(X0!1, star(X1!0))) = multiplication(X0!1, star(X1!0))))) | leq(X0!1, multiplication(X0!1, star(X1!0))) | (~(addition(X0!1, multiplication(X0!1, star(X1!0))) = multiplication(X0!1, star(X1!0))))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(103,plain,
% 0.22/0.43 ((~(leq(X0!1, multiplication(X0!1, star(X1!0))) <=> (addition(X0!1, multiplication(X0!1, star(X1!0))) = multiplication(X0!1, star(X1!0))))) | (~(addition(X0!1, multiplication(X0!1, star(X1!0))) = multiplication(X0!1, star(X1!0))))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.22/0.43 tff(104,plain,
% 0.22/0.43 (~(addition(X0!1, multiplication(X0!1, star(X1!0))) = multiplication(X0!1, star(X1!0)))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[103, 100])).
% 0.22/0.43 tff(105,plain,
% 0.22/0.43 ($false),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[104, 91])).
% 0.22/0.43 tff(106,plain,(leq(X0!1, multiplication(X0!1, star(X1!0)))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.43 tff(107,plain,
% 0.22/0.43 ((~(~((~((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, star(X1!0)), X0!1))) | (~leq(X0!1, multiplication(X0!1, star(X1!0))))))) <=> ((~((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, star(X1!0)), X0!1))) | (~leq(X0!1, multiplication(X0!1, star(X1!0)))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(108,plain,
% 0.22/0.43 ((((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, star(X1!0)), X0!1)) & leq(X0!1, multiplication(X0!1, star(X1!0)))) <=> (~((~((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, star(X1!0)), X0!1))) | (~leq(X0!1, multiplication(X0!1, star(X1!0))))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(109,plain,
% 0.22/0.43 ((~(((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, star(X1!0)), X0!1)) & leq(X0!1, multiplication(X0!1, star(X1!0))))) <=> (~(~((~((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, star(X1!0)), X0!1))) | (~leq(X0!1, multiplication(X0!1, star(X1!0)))))))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[108])).
% 0.22/0.43 tff(110,plain,
% 0.22/0.43 ((~(((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, star(X1!0)), X0!1)) & leq(X0!1, multiplication(X0!1, star(X1!0))))) <=> ((~((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, star(X1!0)), X0!1))) | (~leq(X0!1, multiplication(X0!1, star(X1!0)))))),
% 0.22/0.43 inference(transitivity,[status(thm)],[109, 107])).
% 0.22/0.43 tff(111,plain,
% 0.22/0.43 ((~![X0: $i, X1: $i] : (((~(multiplication(X0, X1) = zero)) | leq(multiplication(X0, star(X1)), X0)) & leq(X0, multiplication(X0, star(X1))))) <=> (~![X0: $i, X1: $i] : (((~(multiplication(X0, X1) = zero)) | leq(multiplication(X0, star(X1)), X0)) & leq(X0, multiplication(X0, star(X1)))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(112,plain,
% 0.22/0.43 ((~![X0: $i, X1: $i] : (((multiplication(X0, X1) = zero) => leq(multiplication(X0, star(X1)), X0)) & leq(X0, multiplication(X0, star(X1))))) <=> (~![X0: $i, X1: $i] : (((~(multiplication(X0, X1) = zero)) | leq(multiplication(X0, star(X1)), X0)) & leq(X0, multiplication(X0, star(X1)))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(113,axiom,(~![X0: $i, X1: $i] : (((multiplication(X0, X1) = zero) => leq(multiplication(X0, star(X1)), X0)) & leq(X0, multiplication(X0, star(X1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 0.22/0.43 tff(114,plain,
% 0.22/0.43 (~![X0: $i, X1: $i] : (((~(multiplication(X0, X1) = zero)) | leq(multiplication(X0, star(X1)), X0)) & leq(X0, multiplication(X0, star(X1))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.22/0.43 tff(115,plain,
% 0.22/0.43 (~![X0: $i, X1: $i] : (((~(multiplication(X0, X1) = zero)) | leq(multiplication(X0, star(X1)), X0)) & leq(X0, multiplication(X0, star(X1))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[114, 111])).
% 0.22/0.43 tff(116,plain,
% 0.22/0.43 (~![X0: $i, X1: $i] : (((~(multiplication(X0, X1) = zero)) | leq(multiplication(X0, star(X1)), X0)) & leq(X0, multiplication(X0, star(X1))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[115, 111])).
% 0.22/0.43 tff(117,plain,
% 0.22/0.43 (~![X0: $i, X1: $i] : (((~(multiplication(X0, X1) = zero)) | leq(multiplication(X0, star(X1)), X0)) & leq(X0, multiplication(X0, star(X1))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[116, 111])).
% 0.22/0.43 tff(118,plain,(
% 0.22/0.43 ~(((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, star(X1!0)), X0!1)) & leq(X0!1, multiplication(X0!1, star(X1!0))))),
% 0.22/0.43 inference(skolemize,[status(sab)],[117])).
% 0.22/0.43 tff(119,plain,
% 0.22/0.43 ((~((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, star(X1!0)), X0!1))) | (~leq(X0!1, multiplication(X0!1, star(X1!0))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[118, 110])).
% 0.22/0.43 tff(120,plain,
% 0.22/0.43 (~((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, star(X1!0)), X0!1))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[119, 106])).
% 0.22/0.43 tff(121,plain,
% 0.22/0.43 (((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, star(X1!0)), X0!1)) | (multiplication(X0!1, X1!0) = zero)),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(122,plain,
% 0.22/0.43 (multiplication(X0!1, X1!0) = zero),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.22/0.43 tff(123,plain,
% 0.22/0.43 (addition(multiplication(X0!1, X1!0), X0!1) = addition(zero, X0!1)),
% 0.22/0.43 inference(monotonicity,[status(thm)],[122])).
% 0.22/0.43 tff(124,plain,
% 0.22/0.43 (zero = multiplication(X0!1, X1!0)),
% 0.22/0.43 inference(symmetry,[status(thm)],[122])).
% 0.22/0.43 tff(125,plain,
% 0.22/0.43 (addition(zero, addition(X0!1, X0!1)) = addition(multiplication(X0!1, X1!0), X0!1)),
% 0.22/0.43 inference(monotonicity,[status(thm)],[124, 61])).
% 0.22/0.43 tff(126,plain,
% 0.22/0.43 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(zero, addition(X0!1, X0!1)) = addition(addition(zero, X0!1), X0!1))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(127,plain,
% 0.22/0.43 (addition(zero, addition(X0!1, X0!1)) = addition(addition(zero, X0!1), X0!1)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[126, 79])).
% 0.22/0.43 tff(128,plain,
% 0.22/0.43 (addition(addition(zero, X0!1), X0!1) = addition(zero, addition(X0!1, X0!1))),
% 0.22/0.43 inference(symmetry,[status(thm)],[127])).
% 0.22/0.43 tff(129,plain,
% 0.22/0.43 (addition(addition(multiplication(X0!1, X1!0), X0!1), X0!1) = addition(addition(zero, X0!1), X0!1)),
% 0.22/0.43 inference(monotonicity,[status(thm)],[123])).
% 0.22/0.43 tff(130,plain,
% 0.22/0.43 (addition(addition(multiplication(X0!1, X1!0), X0!1), X0!1) = X0!1),
% 0.22/0.43 inference(transitivity,[status(thm)],[129, 128, 125, 123, 18, 9])).
% 0.22/0.43 tff(131,plain,
% 0.22/0.43 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(multiplication(X0!1, X1!0), X0!1), X0!1) <=> (addition(addition(multiplication(X0!1, X1!0), X0!1), X0!1) = X0!1))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(132,plain,
% 0.22/0.43 (leq(addition(multiplication(X0!1, X1!0), X0!1), X0!1) <=> (addition(addition(multiplication(X0!1, X1!0), X0!1), X0!1) = X0!1)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[131, 98])).
% 0.22/0.43 tff(133,plain,
% 0.22/0.43 (((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, star(X1!0)), X0!1)) | (~leq(multiplication(X0!1, star(X1!0)), X0!1))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(134,plain,
% 0.22/0.43 (~leq(multiplication(X0!1, star(X1!0)), X0!1)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[133, 120])).
% 0.22/0.43 tff(135,plain,
% 0.22/0.43 (^[A: $i, B: $i, C: $i] : refl(((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C)) <=> ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C)))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(136,plain,
% 0.22/0.43 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[135])).
% 0.22/0.43 tff(137,plain,
% 0.22/0.43 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(138,plain,
% 0.22/0.43 (^[A: $i, B: $i, C: $i] : rewrite((leq(addition(multiplication(C, A), B), C) => leq(multiplication(B, star(A)), C)) <=> ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C)))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(139,plain,
% 0.22/0.43 (![A: $i, B: $i, C: $i] : (leq(addition(multiplication(C, A), B), C) => leq(multiplication(B, star(A)), C)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[138])).
% 0.22/0.43 tff(140,axiom,(![A: $i, B: $i, C: $i] : (leq(addition(multiplication(C, A), B), C) => leq(multiplication(B, star(A)), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','star_induction2')).
% 0.22/0.43 tff(141,plain,
% 0.22/0.43 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.22/0.43 tff(142,plain,
% 0.22/0.43 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[141, 137])).
% 0.22/0.43 tff(143,plain,(
% 0.22/0.43 ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))),
% 0.22/0.43 inference(skolemize,[status(sab)],[142])).
% 0.22/0.43 tff(144,plain,
% 0.22/0.43 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[143, 136])).
% 0.22/0.43 tff(145,plain,
% 0.22/0.43 (((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))) | ((~leq(addition(multiplication(X0!1, X1!0), X0!1), X0!1)) | leq(multiplication(X0!1, star(X1!0)), X0!1))) <=> ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))) | (~leq(addition(multiplication(X0!1, X1!0), X0!1), X0!1)) | leq(multiplication(X0!1, star(X1!0)), X0!1))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(146,plain,
% 0.22/0.43 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))) | ((~leq(addition(multiplication(X0!1, X1!0), X0!1), X0!1)) | leq(multiplication(X0!1, star(X1!0)), X0!1))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(147,plain,
% 0.22/0.44 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))) | (~leq(addition(multiplication(X0!1, X1!0), X0!1), X0!1)) | leq(multiplication(X0!1, star(X1!0)), X0!1)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.22/0.44 tff(148,plain,
% 0.22/0.44 (~leq(addition(multiplication(X0!1, X1!0), X0!1), X0!1)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[147, 144, 134])).
% 0.22/0.44 tff(149,plain,
% 0.22/0.44 ((~(leq(addition(multiplication(X0!1, X1!0), X0!1), X0!1) <=> (addition(addition(multiplication(X0!1, X1!0), X0!1), X0!1) = X0!1))) | leq(addition(multiplication(X0!1, X1!0), X0!1), X0!1) | (~(addition(addition(multiplication(X0!1, X1!0), X0!1), X0!1) = X0!1))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(150,plain,
% 0.22/0.44 ((~(leq(addition(multiplication(X0!1, X1!0), X0!1), X0!1) <=> (addition(addition(multiplication(X0!1, X1!0), X0!1), X0!1) = X0!1))) | (~(addition(addition(multiplication(X0!1, X1!0), X0!1), X0!1) = X0!1))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.22/0.44 tff(151,plain,
% 0.22/0.44 (~(addition(addition(multiplication(X0!1, X1!0), X0!1), X0!1) = X0!1)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[150, 132])).
% 0.22/0.44 tff(152,plain,
% 0.22/0.44 ($false),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[151, 130])).
% 0.22/0.44 % SZS output end Proof
% 0.22/0.44 % E exiting
%------------------------------------------------------------------------------