%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE048+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:12:56 AM UTC 2025
% Result : Theorem 6.31s 6.53s
% Output : Proof 6.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE048+1 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n011.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 18:56:26 EDT 2025
% 0.12/0.34 % CPUTime :
% 6.31/6.53 % SZS status Theorem
% 6.31/6.53 % SZS output start Proof
% 6.31/6.53 tff(leq_type, type, (
% 6.31/6.53 leq: ( $i * $i ) > $o)).
% 6.31/6.53 tff(one_type, type, (
% 6.31/6.53 one: $i)).
% 6.31/6.53 tff(multiplication_type, type, (
% 6.31/6.53 multiplication: ( $i * $i ) > $i)).
% 6.31/6.53 tff(star_type, type, (
% 6.31/6.53 star: $i > $i)).
% 6.31/6.53 tff(tptp_fun_X0_1_type, type, (
% 6.31/6.53 tptp_fun_X0_1: $i)).
% 6.31/6.53 tff(addition_type, type, (
% 6.31/6.53 addition: ( $i * $i ) > $i)).
% 6.31/6.53 tff(test_type, type, (
% 6.31/6.53 test: $i > $o)).
% 6.31/6.53 tff(tptp_fun_X1_0_type, type, (
% 6.31/6.53 tptp_fun_X1_0: $i > $i)).
% 6.31/6.53 tff(zero_type, type, (
% 6.31/6.53 zero: $i)).
% 6.31/6.53 tff(complement_type, type, (
% 6.31/6.53 complement: ( $i * $i ) > $o)).
% 6.31/6.53 tff(1,plain,
% 6.31/6.53 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 6.31/6.53 inference(bind,[status(th)],[])).
% 6.31/6.53 tff(2,plain,
% 6.31/6.53 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 6.31/6.53 inference(quant_intro,[status(thm)],[1])).
% 6.31/6.53 tff(3,plain,
% 6.31/6.53 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 6.31/6.53 inference(rewrite,[status(thm)],[])).
% 6.31/6.53 tff(4,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','multiplicative_left_identity')).
% 6.31/6.53 tff(5,plain,
% 6.31/6.53 (![A: $i] : (multiplication(one, A) = A)),
% 6.31/6.53 inference(modus_ponens,[status(thm)],[4, 3])).
% 6.31/6.53 tff(6,plain,(
% 6.31/6.53 ![A: $i] : (multiplication(one, A) = A)),
% 6.31/6.53 inference(skolemize,[status(sab)],[5])).
% 6.31/6.53 tff(7,plain,
% 6.31/6.53 (![A: $i] : (multiplication(one, A) = A)),
% 6.31/6.53 inference(modus_ponens,[status(thm)],[6, 2])).
% 6.31/6.53 tff(8,plain,
% 6.31/6.53 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, star(X0!1)) = star(X0!1))),
% 6.31/6.53 inference(quant_inst,[status(thm)],[])).
% 6.31/6.53 tff(9,plain,
% 6.31/6.53 (multiplication(one, star(X0!1)) = star(X0!1)),
% 6.31/6.53 inference(unit_resolution,[status(thm)],[8, 7])).
% 6.31/6.53 tff(10,plain,
% 6.31/6.53 (leq(multiplication(one, star(X0!1)), one) <=> leq(star(X0!1), one)),
% 6.31/6.53 inference(monotonicity,[status(thm)],[9])).
% 6.31/6.53 tff(11,plain,
% 6.31/6.53 (leq(star(X0!1), one) <=> leq(multiplication(one, star(X0!1)), one)),
% 6.31/6.53 inference(symmetry,[status(thm)],[10])).
% 6.31/6.53 tff(12,plain,
% 6.31/6.53 ((~leq(star(X0!1), one)) <=> (~leq(multiplication(one, star(X0!1)), one))),
% 6.31/6.53 inference(monotonicity,[status(thm)],[11])).
% 6.31/6.53 tff(13,plain,
% 6.31/6.53 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 6.31/6.53 inference(bind,[status(th)],[])).
% 6.31/6.53 tff(14,plain,
% 6.31/6.53 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 6.31/6.53 inference(quant_intro,[status(thm)],[13])).
% 6.31/6.53 tff(15,plain,
% 6.31/6.53 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 6.31/6.53 inference(rewrite,[status(thm)],[])).
% 6.31/6.53 tff(16,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','order')).
% 6.31/6.53 tff(17,plain,
% 6.31/6.53 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 6.31/6.53 inference(modus_ponens,[status(thm)],[16, 15])).
% 6.31/6.53 tff(18,plain,(
% 6.31/6.53 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 6.31/6.53 inference(skolemize,[status(sab)],[17])).
% 6.31/6.53 tff(19,plain,
% 6.31/6.53 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 6.31/6.53 inference(modus_ponens,[status(thm)],[18, 14])).
% 6.31/6.53 tff(20,plain,
% 6.31/6.53 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(star(X0!1), one) <=> (addition(star(X0!1), one) = one))),
% 6.31/6.53 inference(quant_inst,[status(thm)],[])).
% 6.31/6.53 tff(21,plain,
% 6.31/6.53 (leq(star(X0!1), one) <=> (addition(star(X0!1), one) = one)),
% 6.31/6.53 inference(unit_resolution,[status(thm)],[20, 19])).
% 6.31/6.53 tff(22,plain,
% 6.31/6.53 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 6.31/6.53 inference(bind,[status(th)],[])).
% 6.31/6.53 tff(23,plain,
% 6.31/6.53 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 6.31/6.53 inference(quant_intro,[status(thm)],[22])).
% 6.31/6.53 tff(24,plain,
% 6.31/6.53 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 6.31/6.53 inference(rewrite,[status(thm)],[])).
% 6.31/6.53 tff(25,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','additive_commutativity')).
% 6.31/6.53 tff(26,plain,
% 6.31/6.53 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 6.31/6.53 inference(modus_ponens,[status(thm)],[25, 24])).
% 6.31/6.53 tff(27,plain,(
% 6.31/6.53 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 6.31/6.53 inference(skolemize,[status(sab)],[26])).
% 6.31/6.53 tff(28,plain,
% 6.31/6.53 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 6.31/6.53 inference(modus_ponens,[status(thm)],[27, 23])).
% 6.31/6.53 tff(29,plain,
% 6.31/6.53 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, star(X0!1)) = addition(star(X0!1), one))),
% 6.31/6.53 inference(quant_inst,[status(thm)],[])).
% 6.31/6.53 tff(30,plain,
% 6.31/6.53 (addition(one, star(X0!1)) = addition(star(X0!1), one)),
% 6.31/6.53 inference(unit_resolution,[status(thm)],[29, 28])).
% 6.31/6.53 tff(31,plain,
% 6.31/6.53 (addition(star(X0!1), one) = addition(one, star(X0!1))),
% 6.31/6.53 inference(symmetry,[status(thm)],[30])).
% 6.31/6.53 tff(32,plain,
% 6.31/6.53 ((addition(star(X0!1), one) = one) <=> (addition(one, star(X0!1)) = one)),
% 6.31/6.53 inference(monotonicity,[status(thm)],[31])).
% 6.31/6.53 tff(33,plain,
% 6.31/6.53 ((addition(one, star(X0!1)) = one) <=> (addition(star(X0!1), one) = one)),
% 6.31/6.53 inference(symmetry,[status(thm)],[32])).
% 6.31/6.53 tff(34,plain,
% 6.31/6.53 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(one, multiplication(star(X0!1), X0!1)), star(X0!1)) <=> (addition(addition(one, multiplication(star(X0!1), X0!1)), star(X0!1)) = star(X0!1)))),
% 6.31/6.53 inference(quant_inst,[status(thm)],[])).
% 6.31/6.53 tff(35,plain,
% 6.31/6.53 (leq(addition(one, multiplication(star(X0!1), X0!1)), star(X0!1)) <=> (addition(addition(one, multiplication(star(X0!1), X0!1)), star(X0!1)) = star(X0!1))),
% 6.31/6.53 inference(unit_resolution,[status(thm)],[34, 19])).
% 6.31/6.53 tff(36,plain,
% 6.31/6.53 (^[A: $i] : refl(leq(addition(one, multiplication(star(A), A)), star(A)) <=> leq(addition(one, multiplication(star(A), A)), star(A)))),
% 6.31/6.53 inference(bind,[status(th)],[])).
% 6.31/6.53 tff(37,plain,
% 6.31/6.53 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 6.31/6.53 inference(quant_intro,[status(thm)],[36])).
% 6.31/6.53 tff(38,plain,
% 6.31/6.53 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 6.31/6.53 inference(rewrite,[status(thm)],[])).
% 6.31/6.53 tff(39,axiom,(![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','star_unfold_left')).
% 6.31/6.53 tff(40,plain,
% 6.31/6.53 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 6.31/6.53 inference(modus_ponens,[status(thm)],[39, 38])).
% 6.31/6.53 tff(41,plain,(
% 6.31/6.53 ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 6.31/6.53 inference(skolemize,[status(sab)],[40])).
% 6.31/6.53 tff(42,plain,
% 6.31/6.53 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 6.31/6.53 inference(modus_ponens,[status(thm)],[41, 37])).
% 6.31/6.53 tff(43,plain,
% 6.31/6.53 ((~![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))) | leq(addition(one, multiplication(star(X0!1), X0!1)), star(X0!1))),
% 6.31/6.53 inference(quant_inst,[status(thm)],[])).
% 6.31/6.53 tff(44,plain,
% 6.31/6.53 (leq(addition(one, multiplication(star(X0!1), X0!1)), star(X0!1))),
% 6.31/6.53 inference(unit_resolution,[status(thm)],[43, 42])).
% 6.31/6.53 tff(45,plain,
% 6.31/6.53 ((~(leq(addition(one, multiplication(star(X0!1), X0!1)), star(X0!1)) <=> (addition(addition(one, multiplication(star(X0!1), X0!1)), star(X0!1)) = star(X0!1)))) | (~leq(addition(one, multiplication(star(X0!1), X0!1)), star(X0!1))) | (addition(addition(one, multiplication(star(X0!1), X0!1)), star(X0!1)) = star(X0!1))),
% 6.31/6.53 inference(tautology,[status(thm)],[])).
% 6.31/6.53 tff(46,plain,
% 6.31/6.53 ((~(leq(addition(one, multiplication(star(X0!1), X0!1)), star(X0!1)) <=> (addition(addition(one, multiplication(star(X0!1), X0!1)), star(X0!1)) = star(X0!1)))) | (addition(addition(one, multiplication(star(X0!1), X0!1)), star(X0!1)) = star(X0!1))),
% 6.31/6.53 inference(unit_resolution,[status(thm)],[45, 44])).
% 6.31/6.53 tff(47,plain,
% 6.31/6.53 (addition(addition(one, multiplication(star(X0!1), X0!1)), star(X0!1)) = star(X0!1)),
% 6.31/6.53 inference(unit_resolution,[status(thm)],[46, 35])).
% 6.31/6.53 tff(48,plain,
% 6.31/6.53 (^[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)))),
% 6.31/6.53 inference(bind,[status(th)],[])).
% 6.31/6.53 tff(49,plain,
% 6.31/6.53 (![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))),
% 6.31/6.53 inference(quant_intro,[status(thm)],[48])).
% 6.31/6.53 tff(50,plain,
% 6.31/6.53 (![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))),
% 6.31/6.53 inference(rewrite,[status(thm)],[])).
% 6.31/6.53 tff(51,axiom,(![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','additive_associativity')).
% 6.31/6.53 tff(52,plain,
% 6.31/6.53 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 6.31/6.53 inference(modus_ponens,[status(thm)],[51, 50])).
% 6.31/6.53 tff(53,plain,(
% 6.31/6.53 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 6.31/6.53 inference(skolemize,[status(sab)],[52])).
% 6.31/6.53 tff(54,plain,
% 6.31/6.53 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 6.31/6.53 inference(modus_ponens,[status(thm)],[53, 49])).
% 6.31/6.53 tff(55,plain,
% 6.31/6.53 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(multiplication(star(X0!1), X0!1), star(X0!1))) = addition(addition(one, multiplication(star(X0!1), X0!1)), star(X0!1)))),
% 6.31/6.53 inference(quant_inst,[status(thm)],[])).
% 6.31/6.53 tff(56,plain,
% 6.31/6.53 (addition(one, addition(multiplication(star(X0!1), X0!1), star(X0!1))) = addition(addition(one, multiplication(star(X0!1), X0!1)), star(X0!1))),
% 6.31/6.53 inference(unit_resolution,[status(thm)],[55, 54])).
% 6.31/6.53 tff(57,plain,
% 6.31/6.53 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 6.31/6.53 inference(bind,[status(th)],[])).
% 6.31/6.53 tff(58,plain,
% 6.31/6.53 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 6.31/6.53 inference(quant_intro,[status(thm)],[57])).
% 6.31/6.53 tff(59,plain,
% 6.31/6.53 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 6.31/6.53 inference(rewrite,[status(thm)],[])).
% 6.31/6.53 tff(60,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','additive_idempotence')).
% 6.31/6.53 tff(61,plain,
% 6.31/6.53 (![A: $i] : (addition(A, A) = A)),
% 6.31/6.53 inference(modus_ponens,[status(thm)],[60, 59])).
% 6.31/6.53 tff(62,plain,(
% 6.31/6.53 ![A: $i] : (addition(A, A) = A)),
% 6.31/6.53 inference(skolemize,[status(sab)],[61])).
% 6.31/6.53 tff(63,plain,
% 6.31/6.53 (![A: $i] : (addition(A, A) = A)),
% 6.31/6.53 inference(modus_ponens,[status(thm)],[62, 58])).
% 6.31/6.53 tff(64,plain,
% 6.31/6.53 ((~![A: $i] : (addition(A, A) = A)) | (addition(one, one) = one)),
% 6.31/6.53 inference(quant_inst,[status(thm)],[])).
% 6.31/6.53 tff(65,plain,
% 6.31/6.53 (addition(one, one) = one),
% 6.31/6.53 inference(unit_resolution,[status(thm)],[64, 63])).
% 6.31/6.53 tff(66,plain,
% 6.31/6.53 (addition(addition(one, one), addition(multiplication(star(X0!1), X0!1), star(X0!1))) = addition(one, addition(multiplication(star(X0!1), X0!1), star(X0!1)))),
% 6.31/6.53 inference(monotonicity,[status(thm)],[65])).
% 6.31/6.53 tff(67,plain,
% 6.31/6.53 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(one, addition(multiplication(star(X0!1), X0!1), star(X0!1)))) = addition(addition(one, one), addition(multiplication(star(X0!1), X0!1), star(X0!1))))),
% 6.31/6.53 inference(quant_inst,[status(thm)],[])).
% 6.31/6.53 tff(68,plain,
% 6.31/6.53 (addition(one, addition(one, addition(multiplication(star(X0!1), X0!1), star(X0!1)))) = addition(addition(one, one), addition(multiplication(star(X0!1), X0!1), star(X0!1)))),
% 6.31/6.53 inference(unit_resolution,[status(thm)],[67, 54])).
% 6.31/6.53 tff(69,plain,
% 6.31/6.53 (addition(addition(one, multiplication(star(X0!1), X0!1)), star(X0!1)) = addition(one, addition(multiplication(star(X0!1), X0!1), star(X0!1)))),
% 6.31/6.53 inference(symmetry,[status(thm)],[56])).
% 6.31/6.53 tff(70,plain,
% 6.31/6.53 (star(X0!1) = addition(addition(one, multiplication(star(X0!1), X0!1)), star(X0!1))),
% 6.31/6.53 inference(symmetry,[status(thm)],[47])).
% 6.31/6.53 tff(71,plain,
% 6.31/6.53 (star(X0!1) = addition(one, addition(multiplication(star(X0!1), X0!1), star(X0!1)))),
% 6.31/6.53 inference(transitivity,[status(thm)],[70, 69])).
% 6.31/6.53 tff(72,plain,
% 6.31/6.53 (addition(one, star(X0!1)) = addition(one, addition(one, addition(multiplication(star(X0!1), X0!1), star(X0!1))))),
% 6.31/6.53 inference(monotonicity,[status(thm)],[71])).
% 6.31/6.53 tff(73,plain,
% 6.31/6.53 (addition(one, star(X0!1)) = star(X0!1)),
% 6.31/6.53 inference(transitivity,[status(thm)],[72, 68, 66, 56, 47])).
% 6.31/6.53 tff(74,plain,
% 6.31/6.53 ((addition(one, star(X0!1)) = one) <=> (star(X0!1) = one)),
% 6.31/6.53 inference(monotonicity,[status(thm)],[73])).
% 6.31/6.53 tff(75,plain,
% 6.31/6.53 ((star(X0!1) = one) <=> (addition(one, star(X0!1)) = one)),
% 6.31/6.53 inference(symmetry,[status(thm)],[74])).
% 6.31/6.53 tff(76,plain,
% 6.31/6.53 ((star(X0!1) = one) <=> (addition(star(X0!1), one) = one)),
% 6.31/6.53 inference(transitivity,[status(thm)],[75, 33])).
% 6.31/6.53 tff(77,plain,
% 6.31/6.53 ((~(star(X0!1) = one)) <=> (~(addition(star(X0!1), one) = one))),
% 6.31/6.53 inference(monotonicity,[status(thm)],[76])).
% 6.31/6.53 tff(78,plain,
% 6.31/6.53 ((~![X0: $i] : ((~test(X0)) | (star(X0) = one))) <=> (~![X0: $i] : ((~test(X0)) | (star(X0) = one)))),
% 6.31/6.53 inference(rewrite,[status(thm)],[])).
% 6.31/6.53 tff(79,plain,
% 6.31/6.53 ((~![X0: $i] : (test(X0) => (star(X0) = one))) <=> (~![X0: $i] : ((~test(X0)) | (star(X0) = one)))),
% 6.31/6.53 inference(rewrite,[status(thm)],[])).
% 6.31/6.53 tff(80,axiom,(~![X0: $i] : (test(X0) => (star(X0) = one))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 6.31/6.53 tff(81,plain,
% 6.31/6.53 (~![X0: $i] : ((~test(X0)) | (star(X0) = one))),
% 6.31/6.53 inference(modus_ponens,[status(thm)],[80, 79])).
% 6.31/6.53 tff(82,plain,
% 6.31/6.53 (~![X0: $i] : ((~test(X0)) | (star(X0) = one))),
% 6.31/6.53 inference(modus_ponens,[status(thm)],[81, 78])).
% 6.31/6.53 tff(83,plain,
% 6.31/6.53 (~![X0: $i] : ((~test(X0)) | (star(X0) = one))),
% 6.31/6.53 inference(modus_ponens,[status(thm)],[82, 78])).
% 6.31/6.53 tff(84,plain,
% 6.31/6.53 (~![X0: $i] : ((~test(X0)) | (star(X0) = one))),
% 6.31/6.53 inference(modus_ponens,[status(thm)],[83, 78])).
% 6.31/6.53 tff(85,plain,(
% 6.31/6.53 ~((~test(X0!1)) | (star(X0!1) = one))),
% 6.31/6.53 inference(skolemize,[status(sab)],[84])).
% 6.31/6.53 tff(86,plain,
% 6.31/6.53 (~(star(X0!1) = one)),
% 6.31/6.53 inference(or_elim,[status(thm)],[85])).
% 6.31/6.53 tff(87,plain,
% 6.31/6.53 (~(addition(star(X0!1), one) = one)),
% 6.31/6.53 inference(modus_ponens,[status(thm)],[86, 77])).
% 6.31/6.53 tff(88,plain,
% 6.31/6.53 ((~(leq(star(X0!1), one) <=> (addition(star(X0!1), one) = one))) | (~leq(star(X0!1), one)) | (addition(star(X0!1), one) = one)),
% 6.31/6.53 inference(tautology,[status(thm)],[])).
% 6.31/6.53 tff(89,plain,
% 6.31/6.53 (~leq(star(X0!1), one)),
% 6.31/6.53 inference(unit_resolution,[status(thm)],[88, 87, 21])).
% 6.31/6.53 tff(90,plain,
% 6.31/6.53 (~leq(multiplication(one, star(X0!1)), one)),
% 6.31/6.53 inference(modus_ponens,[status(thm)],[89, 12])).
% 6.31/6.53 tff(91,plain,
% 6.31/6.53 (^[X0: $i, X1: $i] : refl((~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0))) <=> (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0))))),
% 6.31/6.53 inference(bind,[status(th)],[])).
% 6.31/6.53 tff(92,plain,
% 6.31/6.53 (![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0))) <=> ![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 6.31/6.53 inference(quant_intro,[status(thm)],[91])).
% 6.31/6.53 tff(93,plain,
% 6.31/6.53 (^[X0: $i, X1: $i] : trans(trans(monotonicity(rewrite(((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))))), ((complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one))) <=> (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))))))), rewrite((complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))))) <=> (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))), ((complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one))) <=> (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0))))), rewrite((~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0))) <=> (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))), ((complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one))) <=> (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))))),
% 6.31/6.53 inference(bind,[status(th)],[])).
% 6.31/6.53 tff(94,plain,
% 6.31/6.53 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one))) <=> ![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 6.31/6.53 inference(quant_intro,[status(thm)],[93])).
% 6.31/6.53 tff(95,plain,
% 6.31/6.53 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one))) <=> ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 6.31/6.53 inference(rewrite,[status(thm)],[])).
% 6.31/6.53 tff(96,plain,
% 6.31/6.53 (^[X0: $i, X1: $i] : rewrite((complement(X1, X0) <=> (((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero)) & (addition(X0, X1) = one))) <=> (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one))))),
% 6.31/6.53 inference(bind,[status(th)],[])).
% 6.31/6.53 tff(97,plain,
% 6.31/6.53 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero)) & (addition(X0, X1) = one))) <=> ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 6.31/6.53 inference(quant_intro,[status(thm)],[96])).
% 6.31/6.53 tff(98,axiom,(![X0: $i, X1: $i] : (complement(X1, X0) <=> (((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero)) & (addition(X0, X1) = one)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax','test_2')).
% 6.31/6.53 tff(99,plain,
% 6.31/6.53 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 6.31/6.53 inference(modus_ponens,[status(thm)],[98, 97])).
% 6.31/6.53 tff(100,plain,
% 6.31/6.53 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 6.31/6.53 inference(modus_ponens,[status(thm)],[99, 95])).
% 6.31/6.53 tff(101,plain,(
% 6.31/6.53 ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 6.31/6.53 inference(skolemize,[status(sab)],[100])).
% 6.31/6.53 tff(102,plain,
% 6.31/6.53 (![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 6.31/6.53 inference(modus_ponens,[status(thm)],[101, 94])).
% 6.31/6.53 tff(103,plain,
% 6.31/6.53 (![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 6.31/6.53 inference(modus_ponens,[status(thm)],[102, 92])).
% 6.31/6.53 tff(104,plain,
% 6.31/6.53 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X0!1, tptp_fun_X1_0(X0!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!1), X0!1) = zero)) | (~(addition(X0!1, tptp_fun_X1_0(X0!1)) = one))) <=> complement(tptp_fun_X1_0(X0!1), X0!1)))),
% 6.31/6.53 inference(quant_inst,[status(thm)],[])).
% 6.31/6.53 tff(105,plain,
% 6.31/6.53 (~(((~(multiplication(X0!1, tptp_fun_X1_0(X0!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!1), X0!1) = zero)) | (~(addition(X0!1, tptp_fun_X1_0(X0!1)) = one))) <=> complement(tptp_fun_X1_0(X0!1), X0!1))),
% 6.31/6.53 inference(unit_resolution,[status(thm)],[104, 103])).
% 6.31/6.53 tff(106,plain,
% 6.31/6.53 (^[X0: $i] : refl((~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0)))))) <=> (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0)))))))),
% 6.31/6.53 inference(bind,[status(th)],[])).
% 6.31/6.53 tff(107,plain,
% 6.31/6.53 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0)))))) <=> ![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 6.31/6.53 inference(quant_intro,[status(thm)],[106])).
% 6.31/6.53 tff(108,plain,
% 6.31/6.53 (^[X0: $i] : rewrite((~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0)))))) <=> (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0)))))))),
% 6.31/6.54 inference(bind,[status(th)],[])).
% 6.31/6.54 tff(109,plain,
% 6.31/6.54 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0)))))) <=> ![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 6.31/6.54 inference(quant_intro,[status(thm)],[108])).
% 6.31/6.54 tff(110,plain,
% 6.31/6.54 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0)))))) <=> ![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 6.31/6.54 inference(transitivity,[status(thm)],[109, 107])).
% 6.31/6.54 tff(111,plain,
% 6.31/6.54 (^[X0: $i] : trans(monotonicity(rewrite((test(X0) | ![X1: $i] : (~complement(X1, X0))) <=> (test(X0) | ![X1: $i] : (~complement(X1, X0)))), ((((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0)))) <=> (((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0)))))), rewrite((((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0)))) <=> (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))), ((((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0)))) <=> (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))))),
% 6.31/6.54 inference(bind,[status(th)],[])).
% 6.31/6.54 tff(112,plain,
% 6.31/6.54 (![X0: $i] : (((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0)))) <=> ![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 6.31/6.54 inference(quant_intro,[status(thm)],[111])).
% 6.31/6.54 tff(113,plain,
% 6.31/6.54 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0)) <=> ![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 6.31/6.54 inference(rewrite,[status(thm)],[])).
% 6.31/6.54 tff(114,axiom,(![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax','test_1')).
% 6.31/6.54 tff(115,plain,
% 6.31/6.54 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 6.31/6.54 inference(modus_ponens,[status(thm)],[114, 113])).
% 6.31/6.54 tff(116,plain,(
% 6.31/6.54 ![X0: $i] : (((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0))))),
% 6.31/6.54 inference(skolemize,[status(sab)],[115])).
% 6.31/6.54 tff(117,plain,
% 6.31/6.54 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 6.31/6.54 inference(modus_ponens,[status(thm)],[116, 112])).
% 6.31/6.54 tff(118,plain,
% 6.31/6.54 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 6.31/6.54 inference(modus_ponens,[status(thm)],[117, 110])).
% 6.31/6.54 tff(119,plain,
% 6.31/6.54 ((~![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))) | (~((~((~test(X0!1)) | complement(tptp_fun_X1_0(X0!1), X0!1))) | (~(test(X0!1) | ![X1: $i] : (~complement(X1, X0!1))))))),
% 6.31/6.54 inference(quant_inst,[status(thm)],[])).
% 6.31/6.54 tff(120,plain,
% 6.31/6.54 (~((~((~test(X0!1)) | complement(tptp_fun_X1_0(X0!1), X0!1))) | (~(test(X0!1) | ![X1: $i] : (~complement(X1, X0!1)))))),
% 6.31/6.54 inference(unit_resolution,[status(thm)],[119, 118])).
% 6.31/6.54 tff(121,plain,
% 6.31/6.54 (((~((~test(X0!1)) | complement(tptp_fun_X1_0(X0!1), X0!1))) | (~(test(X0!1) | ![X1: $i] : (~complement(X1, X0!1))))) | ((~test(X0!1)) | complement(tptp_fun_X1_0(X0!1), X0!1))),
% 6.31/6.54 inference(tautology,[status(thm)],[])).
% 6.31/6.54 tff(122,plain,
% 6.31/6.54 ((~test(X0!1)) | complement(tptp_fun_X1_0(X0!1), X0!1)),
% 6.31/6.54 inference(unit_resolution,[status(thm)],[121, 120])).
% 6.31/6.54 tff(123,plain,
% 6.31/6.54 (test(X0!1)),
% 6.31/6.54 inference(or_elim,[status(thm)],[85])).
% 6.31/6.54 tff(124,plain,
% 6.31/6.54 ((~((~test(X0!1)) | complement(tptp_fun_X1_0(X0!1), X0!1))) | (~test(X0!1)) | complement(tptp_fun_X1_0(X0!1), X0!1)),
% 6.31/6.54 inference(tautology,[status(thm)],[])).
% 6.31/6.54 tff(125,plain,
% 6.31/6.54 ((~((~test(X0!1)) | complement(tptp_fun_X1_0(X0!1), X0!1))) | complement(tptp_fun_X1_0(X0!1), X0!1)),
% 6.31/6.54 inference(unit_resolution,[status(thm)],[124, 123])).
% 6.31/6.54 tff(126,plain,
% 6.31/6.54 (complement(tptp_fun_X1_0(X0!1), X0!1)),
% 6.31/6.54 inference(unit_resolution,[status(thm)],[125, 122])).
% 6.31/6.54 tff(127,plain,
% 6.31/6.54 ((((~(multiplication(X0!1, tptp_fun_X1_0(X0!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!1), X0!1) = zero)) | (~(addition(X0!1, tptp_fun_X1_0(X0!1)) = one))) <=> complement(tptp_fun_X1_0(X0!1), X0!1)) | (~((~(multiplication(X0!1, tptp_fun_X1_0(X0!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!1), X0!1) = zero)) | (~(addition(X0!1, tptp_fun_X1_0(X0!1)) = one)))) | (~complement(tptp_fun_X1_0(X0!1), X0!1))),
% 6.31/6.54 inference(tautology,[status(thm)],[])).
% 6.31/6.54 tff(128,plain,
% 6.31/6.54 ((((~(multiplication(X0!1, tptp_fun_X1_0(X0!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!1), X0!1) = zero)) | (~(addition(X0!1, tptp_fun_X1_0(X0!1)) = one))) <=> complement(tptp_fun_X1_0(X0!1), X0!1)) | (~((~(multiplication(X0!1, tptp_fun_X1_0(X0!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!1), X0!1) = zero)) | (~(addition(X0!1, tptp_fun_X1_0(X0!1)) = one))))),
% 6.31/6.54 inference(unit_resolution,[status(thm)],[127, 126])).
% 6.31/6.54 tff(129,plain,
% 6.31/6.54 (~((~(multiplication(X0!1, tptp_fun_X1_0(X0!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!1), X0!1) = zero)) | (~(addition(X0!1, tptp_fun_X1_0(X0!1)) = one)))),
% 6.31/6.54 inference(unit_resolution,[status(thm)],[128, 105])).
% 6.31/6.54 tff(130,plain,
% 6.31/6.54 (((~(multiplication(X0!1, tptp_fun_X1_0(X0!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!1), X0!1) = zero)) | (~(addition(X0!1, tptp_fun_X1_0(X0!1)) = one))) | (addition(X0!1, tptp_fun_X1_0(X0!1)) = one)),
% 6.31/6.54 inference(tautology,[status(thm)],[])).
% 6.31/6.54 tff(131,plain,
% 6.31/6.54 (addition(X0!1, tptp_fun_X1_0(X0!1)) = one),
% 6.31/6.54 inference(unit_resolution,[status(thm)],[130, 129])).
% 6.31/6.54 tff(132,plain,
% 6.31/6.54 (addition(addition(X0!1, tptp_fun_X1_0(X0!1)), one) = addition(one, one)),
% 6.31/6.54 inference(monotonicity,[status(thm)],[131])).
% 6.31/6.54 tff(133,plain,
% 6.31/6.54 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X0!1, addition(tptp_fun_X1_0(X0!1), one)) = addition(addition(X0!1, tptp_fun_X1_0(X0!1)), one))),
% 6.31/6.54 inference(quant_inst,[status(thm)],[])).
% 6.31/6.54 tff(134,plain,
% 6.31/6.54 (addition(X0!1, addition(tptp_fun_X1_0(X0!1), one)) = addition(addition(X0!1, tptp_fun_X1_0(X0!1)), one)),
% 6.31/6.54 inference(unit_resolution,[status(thm)],[133, 54])).
% 6.31/6.54 tff(135,plain,
% 6.31/6.54 ((~![A: $i] : (addition(A, A) = A)) | (addition(X0!1, X0!1) = X0!1)),
% 6.31/6.54 inference(quant_inst,[status(thm)],[])).
% 6.31/6.54 tff(136,plain,
% 6.31/6.54 (addition(X0!1, X0!1) = X0!1),
% 6.31/6.54 inference(unit_resolution,[status(thm)],[135, 63])).
% 6.31/6.54 tff(137,plain,
% 6.31/6.54 (addition(addition(X0!1, X0!1), addition(tptp_fun_X1_0(X0!1), one)) = addition(X0!1, addition(tptp_fun_X1_0(X0!1), one))),
% 6.31/6.54 inference(monotonicity,[status(thm)],[136])).
% 6.31/6.54 tff(138,plain,
% 6.31/6.54 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X0!1, addition(X0!1, addition(tptp_fun_X1_0(X0!1), one))) = addition(addition(X0!1, X0!1), addition(tptp_fun_X1_0(X0!1), one)))),
% 6.31/6.54 inference(quant_inst,[status(thm)],[])).
% 6.31/6.54 tff(139,plain,
% 6.31/6.54 (addition(X0!1, addition(X0!1, addition(tptp_fun_X1_0(X0!1), one))) = addition(addition(X0!1, X0!1), addition(tptp_fun_X1_0(X0!1), one))),
% 6.31/6.54 inference(unit_resolution,[status(thm)],[138, 54])).
% 6.31/6.54 tff(140,plain,
% 6.31/6.54 (addition(addition(X0!1, tptp_fun_X1_0(X0!1)), one) = addition(X0!1, addition(tptp_fun_X1_0(X0!1), one))),
% 6.31/6.54 inference(symmetry,[status(thm)],[134])).
% 6.31/6.54 tff(141,plain,
% 6.31/6.54 (addition(one, one) = addition(addition(X0!1, tptp_fun_X1_0(X0!1)), one)),
% 6.31/6.54 inference(symmetry,[status(thm)],[132])).
% 6.31/6.54 tff(142,plain,
% 6.31/6.54 (one = addition(one, one)),
% 6.31/6.54 inference(symmetry,[status(thm)],[65])).
% 6.31/6.54 tff(143,plain,
% 6.31/6.54 (one = addition(X0!1, addition(tptp_fun_X1_0(X0!1), one))),
% 6.31/6.54 inference(transitivity,[status(thm)],[142, 141, 140])).
% 6.31/6.54 tff(144,plain,
% 6.31/6.54 (addition(X0!1, one) = addition(X0!1, addition(X0!1, addition(tptp_fun_X1_0(X0!1), one)))),
% 6.31/6.54 inference(monotonicity,[status(thm)],[143])).
% 6.31/6.54 tff(145,plain,
% 6.31/6.54 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X0!1) = X0!1)),
% 6.31/6.54 inference(quant_inst,[status(thm)],[])).
% 6.31/6.54 tff(146,plain,
% 6.31/6.54 (multiplication(one, X0!1) = X0!1),
% 6.31/6.54 inference(unit_resolution,[status(thm)],[145, 7])).
% 6.31/6.54 tff(147,plain,
% 6.31/6.54 (addition(multiplication(one, X0!1), one) = addition(X0!1, one)),
% 6.31/6.54 inference(monotonicity,[status(thm)],[146])).
% 6.31/6.54 tff(148,plain,
% 6.31/6.54 (addition(multiplication(one, X0!1), one) = one),
% 6.31/6.54 inference(transitivity,[status(thm)],[147, 144, 139, 137, 134, 132, 65])).
% 6.31/6.54 tff(149,plain,
% 6.31/6.54 (leq(addition(multiplication(one, X0!1), one), one) <=> leq(one, one)),
% 6.31/6.54 inference(monotonicity,[status(thm)],[148])).
% 6.31/6.54 tff(150,plain,
% 6.31/6.54 (leq(one, one) <=> leq(addition(multiplication(one, X0!1), one), one)),
% 6.31/6.54 inference(symmetry,[status(thm)],[149])).
% 6.31/6.54 tff(151,plain,
% 6.31/6.54 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(one, one) <=> (addition(one, one) = one))),
% 6.31/6.54 inference(quant_inst,[status(thm)],[])).
% 6.31/6.54 tff(152,plain,
% 6.31/6.54 (leq(one, one) <=> (addition(one, one) = one)),
% 6.31/6.54 inference(unit_resolution,[status(thm)],[151, 19])).
% 6.31/6.54 tff(153,plain,
% 6.31/6.54 ((~(leq(one, one) <=> (addition(one, one) = one))) | leq(one, one) | (~(addition(one, one) = one))),
% 6.31/6.54 inference(tautology,[status(thm)],[])).
% 6.31/6.54 tff(154,plain,
% 6.31/6.54 (leq(one, one)),
% 6.31/6.54 inference(unit_resolution,[status(thm)],[153, 65, 152])).
% 6.31/6.54 tff(155,plain,
% 6.31/6.54 (leq(addition(multiplication(one, X0!1), one), one)),
% 6.31/6.54 inference(modus_ponens,[status(thm)],[154, 150])).
% 6.31/6.54 tff(156,plain,
% 6.31/6.54 (^[A: $i, B: $i, C: $i] : refl(((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A)) <=> ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A)))),
% 6.31/6.54 inference(bind,[status(th)],[])).
% 6.31/6.54 tff(157,plain,
% 6.31/6.54 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 6.31/6.54 inference(quant_intro,[status(thm)],[156])).
% 6.31/6.54 tff(158,plain,
% 6.31/6.54 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 6.31/6.54 inference(rewrite,[status(thm)],[])).
% 6.31/6.54 tff(159,plain,
% 6.31/6.54 (^[A: $i, B: $i, C: $i] : rewrite((leq(addition(multiplication(A, B), C), A) => leq(multiplication(C, star(B)), A)) <=> ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A)))),
% 6.31/6.54 inference(bind,[status(th)],[])).
% 6.31/6.54 tff(160,plain,
% 6.31/6.54 (![A: $i, B: $i, C: $i] : (leq(addition(multiplication(A, B), C), A) => leq(multiplication(C, star(B)), A)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 6.31/6.54 inference(quant_intro,[status(thm)],[159])).
% 6.31/6.54 tff(161,axiom,(![A: $i, B: $i, C: $i] : (leq(addition(multiplication(A, B), C), A) => leq(multiplication(C, star(B)), A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','star_induction_right')).
% 6.31/6.54 tff(162,plain,
% 6.31/6.54 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 6.31/6.54 inference(modus_ponens,[status(thm)],[161, 160])).
% 6.31/6.54 tff(163,plain,
% 6.31/6.54 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 6.31/6.54 inference(modus_ponens,[status(thm)],[162, 158])).
% 6.31/6.54 tff(164,plain,(
% 6.31/6.54 ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 6.31/6.54 inference(skolemize,[status(sab)],[163])).
% 6.31/6.54 tff(165,plain,
% 6.31/6.54 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 6.31/6.54 inference(modus_ponens,[status(thm)],[164, 157])).
% 6.31/6.54 tff(166,plain,
% 6.31/6.54 (((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))) | ((~leq(addition(multiplication(one, X0!1), one), one)) | leq(multiplication(one, star(X0!1)), one))) <=> ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))) | (~leq(addition(multiplication(one, X0!1), one), one)) | leq(multiplication(one, star(X0!1)), one))),
% 6.31/6.54 inference(rewrite,[status(thm)],[])).
% 6.31/6.54 tff(167,plain,
% 6.31/6.54 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))) | ((~leq(addition(multiplication(one, X0!1), one), one)) | leq(multiplication(one, star(X0!1)), one))),
% 6.31/6.54 inference(quant_inst,[status(thm)],[])).
% 6.31/6.54 tff(168,plain,
% 6.31/6.54 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))) | (~leq(addition(multiplication(one, X0!1), one), one)) | leq(multiplication(one, star(X0!1)), one)),
% 6.31/6.54 inference(modus_ponens,[status(thm)],[167, 166])).
% 6.31/6.54 tff(169,plain,
% 6.31/6.54 ((~leq(addition(multiplication(one, X0!1), one), one)) | leq(multiplication(one, star(X0!1)), one)),
% 6.31/6.54 inference(unit_resolution,[status(thm)],[168, 165])).
% 6.31/6.54 tff(170,plain,
% 6.31/6.54 ($false),
% 6.31/6.54 inference(unit_resolution,[status(thm)],[169, 155, 90])).
% 6.31/6.54 % SZS output end Proof
% 6.31/6.55 % E exiting
%------------------------------------------------------------------------------