%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE041+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:12:55 AM UTC 2025
% Result : Theorem 11.29s 11.49s
% Output : Proof 11.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : KLE041+1 : TPTP v9.0.0. Released v4.0.0.
% 0.05/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Jun 19 18:55:33 EDT 2025
% 0.14/0.35 % CPUTime :
% 11.29/11.49 % SZS status Theorem
% 11.29/11.49 % SZS output start Proof
% 11.29/11.49 tff(star_type, type, (
% 11.29/11.49 star: $i > $i)).
% 11.29/11.49 tff(tptp_fun_X1_0_type, type, (
% 11.29/11.49 tptp_fun_X1_0: $i)).
% 11.29/11.49 tff(addition_type, type, (
% 11.29/11.49 addition: ( $i * $i ) > $i)).
% 11.29/11.49 tff(one_type, type, (
% 11.29/11.49 one: $i)).
% 11.29/11.49 tff(multiplication_type, type, (
% 11.29/11.49 multiplication: ( $i * $i ) > $i)).
% 11.29/11.49 tff(tptp_fun_X0_1_type, type, (
% 11.29/11.49 tptp_fun_X0_1: $i)).
% 11.29/11.49 tff(leq_type, type, (
% 11.29/11.49 leq: ( $i * $i ) > $o)).
% 11.29/11.49 tff(1,plain,
% 11.29/11.49 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 11.29/11.49 inference(bind,[status(th)],[])).
% 11.29/11.49 tff(2,plain,
% 11.29/11.49 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 11.29/11.49 inference(quant_intro,[status(thm)],[1])).
% 11.29/11.49 tff(3,plain,
% 11.29/11.49 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 11.29/11.49 inference(rewrite,[status(thm)],[])).
% 11.29/11.49 tff(4,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','order')).
% 11.29/11.49 tff(5,plain,
% 11.29/11.49 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 11.29/11.49 inference(modus_ponens,[status(thm)],[4, 3])).
% 11.29/11.49 tff(6,plain,(
% 11.29/11.49 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 11.29/11.49 inference(skolemize,[status(sab)],[5])).
% 11.29/11.49 tff(7,plain,
% 11.29/11.49 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 11.29/11.49 inference(modus_ponens,[status(thm)],[6, 2])).
% 11.29/11.49 tff(8,plain,
% 11.29/11.49 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(multiplication(star(X1!0), X0!1), one), star(X1!0)) <=> (addition(addition(multiplication(star(X1!0), X0!1), one), star(X1!0)) = star(X1!0)))),
% 11.29/11.49 inference(quant_inst,[status(thm)],[])).
% 11.29/11.49 tff(9,plain,
% 11.29/11.49 (leq(addition(multiplication(star(X1!0), X0!1), one), star(X1!0)) <=> (addition(addition(multiplication(star(X1!0), X0!1), one), star(X1!0)) = star(X1!0))),
% 11.29/11.49 inference(unit_resolution,[status(thm)],[8, 7])).
% 11.29/11.49 tff(10,plain,
% 11.29/11.49 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 11.29/11.49 inference(bind,[status(th)],[])).
% 11.29/11.49 tff(11,plain,
% 11.29/11.49 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 11.29/11.49 inference(quant_intro,[status(thm)],[10])).
% 11.29/11.49 tff(12,plain,
% 11.29/11.49 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 11.29/11.49 inference(rewrite,[status(thm)],[])).
% 11.29/11.49 tff(13,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','multiplicative_left_identity')).
% 11.29/11.49 tff(14,plain,
% 11.29/11.49 (![A: $i] : (multiplication(one, A) = A)),
% 11.29/11.49 inference(modus_ponens,[status(thm)],[13, 12])).
% 11.29/11.49 tff(15,plain,(
% 11.29/11.49 ![A: $i] : (multiplication(one, A) = A)),
% 11.29/11.49 inference(skolemize,[status(sab)],[14])).
% 11.29/11.49 tff(16,plain,
% 11.29/11.49 (![A: $i] : (multiplication(one, A) = A)),
% 11.29/11.49 inference(modus_ponens,[status(thm)],[15, 11])).
% 11.29/11.49 tff(17,plain,
% 11.29/11.49 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, star(X0!1)) = star(X0!1))),
% 11.29/11.49 inference(quant_inst,[status(thm)],[])).
% 11.29/11.49 tff(18,plain,
% 11.29/11.49 (multiplication(one, star(X0!1)) = star(X0!1)),
% 11.29/11.49 inference(unit_resolution,[status(thm)],[17, 16])).
% 11.29/11.49 tff(19,plain,
% 11.29/11.49 (leq(multiplication(one, star(X0!1)), star(X1!0)) <=> leq(star(X0!1), star(X1!0))),
% 11.29/11.49 inference(monotonicity,[status(thm)],[18])).
% 11.29/11.49 tff(20,plain,
% 11.29/11.49 (leq(star(X0!1), star(X1!0)) <=> leq(multiplication(one, star(X0!1)), star(X1!0))),
% 11.29/11.49 inference(symmetry,[status(thm)],[19])).
% 11.29/11.49 tff(21,plain,
% 11.29/11.49 ((~leq(star(X0!1), star(X1!0))) <=> (~leq(multiplication(one, star(X0!1)), star(X1!0)))),
% 11.29/11.49 inference(monotonicity,[status(thm)],[20])).
% 11.29/11.49 tff(22,plain,
% 11.29/11.49 ((~![X0: $i, X1: $i] : ((~leq(X0, X1)) | leq(star(X0), star(X1)))) <=> (~![X0: $i, X1: $i] : ((~leq(X0, X1)) | leq(star(X0), star(X1))))),
% 11.29/11.49 inference(rewrite,[status(thm)],[])).
% 11.29/11.49 tff(23,plain,
% 11.29/11.49 ((~![X0: $i, X1: $i] : (leq(X0, X1) => leq(star(X0), star(X1)))) <=> (~![X0: $i, X1: $i] : ((~leq(X0, X1)) | leq(star(X0), star(X1))))),
% 11.29/11.49 inference(rewrite,[status(thm)],[])).
% 11.29/11.49 tff(24,axiom,(~![X0: $i, X1: $i] : (leq(X0, X1) => leq(star(X0), star(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 11.29/11.49 tff(25,plain,
% 11.29/11.49 (~![X0: $i, X1: $i] : ((~leq(X0, X1)) | leq(star(X0), star(X1)))),
% 11.29/11.49 inference(modus_ponens,[status(thm)],[24, 23])).
% 11.29/11.49 tff(26,plain,
% 11.29/11.49 (~![X0: $i, X1: $i] : ((~leq(X0, X1)) | leq(star(X0), star(X1)))),
% 11.29/11.49 inference(modus_ponens,[status(thm)],[25, 22])).
% 11.29/11.49 tff(27,plain,
% 11.29/11.49 (~![X0: $i, X1: $i] : ((~leq(X0, X1)) | leq(star(X0), star(X1)))),
% 11.29/11.49 inference(modus_ponens,[status(thm)],[26, 22])).
% 11.29/11.49 tff(28,plain,
% 11.29/11.49 (~![X0: $i, X1: $i] : ((~leq(X0, X1)) | leq(star(X0), star(X1)))),
% 11.29/11.49 inference(modus_ponens,[status(thm)],[27, 22])).
% 11.29/11.49 tff(29,plain,(
% 11.29/11.49 ~((~leq(X0!1, X1!0)) | leq(star(X0!1), star(X1!0)))),
% 11.29/11.49 inference(skolemize,[status(sab)],[28])).
% 11.29/11.49 tff(30,plain,
% 11.29/11.49 (~leq(star(X0!1), star(X1!0))),
% 11.29/11.49 inference(or_elim,[status(thm)],[29])).
% 11.29/11.49 tff(31,plain,
% 11.29/11.49 (~leq(multiplication(one, star(X0!1)), star(X1!0))),
% 11.29/11.49 inference(modus_ponens,[status(thm)],[30, 21])).
% 11.29/11.49 tff(32,plain,
% 11.29/11.49 (^[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)))),
% 11.29/11.49 inference(bind,[status(th)],[])).
% 11.29/11.49 tff(33,plain,
% 11.29/11.49 (![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))),
% 11.29/11.49 inference(quant_intro,[status(thm)],[32])).
% 11.29/11.49 tff(34,plain,
% 11.29/11.49 (![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))),
% 11.29/11.49 inference(rewrite,[status(thm)],[])).
% 11.29/11.49 tff(35,plain,
% 11.29/11.49 (^[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)))),
% 11.29/11.49 inference(bind,[status(th)],[])).
% 11.29/11.49 tff(36,plain,
% 11.29/11.49 (![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))),
% 11.29/11.49 inference(quant_intro,[status(thm)],[35])).
% 11.29/11.49 tff(37,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')).
% 11.29/11.49 tff(38,plain,
% 11.29/11.49 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 11.29/11.49 inference(modus_ponens,[status(thm)],[37, 36])).
% 11.29/11.49 tff(39,plain,
% 11.29/11.49 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 11.29/11.49 inference(modus_ponens,[status(thm)],[38, 34])).
% 11.29/11.49 tff(40,plain,(
% 11.29/11.49 ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 11.29/11.49 inference(skolemize,[status(sab)],[39])).
% 11.29/11.49 tff(41,plain,
% 11.29/11.49 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 11.29/11.49 inference(modus_ponens,[status(thm)],[40, 33])).
% 11.29/11.49 tff(42,plain,
% 11.29/11.49 (((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))) | ((~leq(addition(multiplication(star(X1!0), X0!1), one), star(X1!0))) | leq(multiplication(one, star(X0!1)), star(X1!0)))) <=> ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))) | (~leq(addition(multiplication(star(X1!0), X0!1), one), star(X1!0))) | leq(multiplication(one, star(X0!1)), star(X1!0)))),
% 11.29/11.49 inference(rewrite,[status(thm)],[])).
% 11.29/11.49 tff(43,plain,
% 11.29/11.49 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))) | ((~leq(addition(multiplication(star(X1!0), X0!1), one), star(X1!0))) | leq(multiplication(one, star(X0!1)), star(X1!0)))),
% 11.29/11.49 inference(quant_inst,[status(thm)],[])).
% 11.29/11.49 tff(44,plain,
% 11.29/11.49 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))) | (~leq(addition(multiplication(star(X1!0), X0!1), one), star(X1!0))) | leq(multiplication(one, star(X0!1)), star(X1!0))),
% 11.29/11.49 inference(modus_ponens,[status(thm)],[43, 42])).
% 11.29/11.49 tff(45,plain,
% 11.29/11.49 ((~leq(addition(multiplication(star(X1!0), X0!1), one), star(X1!0))) | leq(multiplication(one, star(X0!1)), star(X1!0))),
% 11.29/11.49 inference(unit_resolution,[status(thm)],[44, 41])).
% 11.29/11.49 tff(46,plain,
% 11.29/11.49 (~leq(addition(multiplication(star(X1!0), X0!1), one), star(X1!0))),
% 11.29/11.49 inference(unit_resolution,[status(thm)],[45, 31])).
% 11.29/11.49 tff(47,plain,
% 11.29/11.49 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0)) <=> (addition(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0)) = star(X1!0)))),
% 11.29/11.49 inference(quant_inst,[status(thm)],[])).
% 11.29/11.49 tff(48,plain,
% 11.29/11.49 (leq(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0)) <=> (addition(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0)) = star(X1!0))),
% 11.29/11.49 inference(unit_resolution,[status(thm)],[47, 7])).
% 11.29/11.49 tff(49,plain,
% 11.29/11.49 (^[A: $i] : refl(leq(addition(one, multiplication(star(A), A)), star(A)) <=> leq(addition(one, multiplication(star(A), A)), star(A)))),
% 11.29/11.49 inference(bind,[status(th)],[])).
% 11.29/11.49 tff(50,plain,
% 11.29/11.49 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 11.29/11.49 inference(quant_intro,[status(thm)],[49])).
% 11.29/11.49 tff(51,plain,
% 11.29/11.49 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 11.29/11.49 inference(rewrite,[status(thm)],[])).
% 11.29/11.49 tff(52,axiom,(![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','star_unfold_left')).
% 11.29/11.49 tff(53,plain,
% 11.29/11.49 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 11.29/11.49 inference(modus_ponens,[status(thm)],[52, 51])).
% 11.29/11.49 tff(54,plain,(
% 11.29/11.49 ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 11.29/11.49 inference(skolemize,[status(sab)],[53])).
% 11.29/11.49 tff(55,plain,
% 11.29/11.49 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 11.29/11.49 inference(modus_ponens,[status(thm)],[54, 50])).
% 11.29/11.49 tff(56,plain,
% 11.29/11.49 ((~![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))) | leq(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0))),
% 11.29/11.49 inference(quant_inst,[status(thm)],[])).
% 11.29/11.49 tff(57,plain,
% 11.29/11.49 (leq(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0))),
% 11.29/11.49 inference(unit_resolution,[status(thm)],[56, 55])).
% 11.29/11.49 tff(58,plain,
% 11.29/11.49 ((~(leq(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0)) <=> (addition(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0)) = star(X1!0)))) | (~leq(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0))) | (addition(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0)) = star(X1!0))),
% 11.29/11.49 inference(tautology,[status(thm)],[])).
% 11.29/11.49 tff(59,plain,
% 11.29/11.49 ((~(leq(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0)) <=> (addition(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0)) = star(X1!0)))) | (addition(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0)) = star(X1!0))),
% 11.29/11.49 inference(unit_resolution,[status(thm)],[58, 57])).
% 11.29/11.49 tff(60,plain,
% 11.29/11.49 (addition(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0)) = star(X1!0)),
% 11.29/11.49 inference(unit_resolution,[status(thm)],[59, 48])).
% 11.29/11.49 tff(61,plain,
% 11.29/11.49 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(X0!1, X1!0) <=> (addition(X0!1, X1!0) = X1!0))),
% 11.29/11.49 inference(quant_inst,[status(thm)],[])).
% 11.29/11.49 tff(62,plain,
% 11.29/11.49 (leq(X0!1, X1!0) <=> (addition(X0!1, X1!0) = X1!0)),
% 11.29/11.49 inference(unit_resolution,[status(thm)],[61, 7])).
% 11.29/11.49 tff(63,plain,
% 11.29/11.49 (leq(X0!1, X1!0)),
% 11.29/11.49 inference(or_elim,[status(thm)],[29])).
% 11.29/11.49 tff(64,plain,
% 11.29/11.49 ((~(leq(X0!1, X1!0) <=> (addition(X0!1, X1!0) = X1!0))) | (~leq(X0!1, X1!0)) | (addition(X0!1, X1!0) = X1!0)),
% 11.29/11.49 inference(tautology,[status(thm)],[])).
% 11.29/11.49 tff(65,plain,
% 11.29/11.49 ((~(leq(X0!1, X1!0) <=> (addition(X0!1, X1!0) = X1!0))) | (addition(X0!1, X1!0) = X1!0)),
% 11.29/11.49 inference(unit_resolution,[status(thm)],[64, 63])).
% 11.29/11.49 tff(66,plain,
% 11.29/11.49 (addition(X0!1, X1!0) = X1!0),
% 11.29/11.49 inference(unit_resolution,[status(thm)],[65, 62])).
% 11.29/11.49 tff(67,plain,
% 11.29/11.49 (X1!0 = addition(X0!1, X1!0)),
% 11.29/11.49 inference(symmetry,[status(thm)],[66])).
% 11.29/11.49 tff(68,plain,
% 11.29/11.49 (multiplication(star(X1!0), X1!0) = multiplication(star(X1!0), addition(X0!1, X1!0))),
% 11.29/11.49 inference(monotonicity,[status(thm)],[67])).
% 11.29/11.49 tff(69,plain,
% 11.29/11.49 (multiplication(star(X1!0), addition(X0!1, X1!0)) = multiplication(star(X1!0), X1!0)),
% 11.29/11.49 inference(symmetry,[status(thm)],[68])).
% 11.29/11.49 tff(70,plain,
% 11.29/11.49 (^[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))))),
% 11.29/11.49 inference(bind,[status(th)],[])).
% 11.29/11.49 tff(71,plain,
% 11.29/11.49 (![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)))),
% 11.29/11.49 inference(quant_intro,[status(thm)],[70])).
% 11.29/11.49 tff(72,plain,
% 11.29/11.49 (![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)))),
% 11.29/11.49 inference(rewrite,[status(thm)],[])).
% 11.29/11.49 tff(73,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','right_distributivity')).
% 11.29/11.49 tff(74,plain,
% 11.29/11.49 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 11.29/11.49 inference(modus_ponens,[status(thm)],[73, 72])).
% 11.29/11.49 tff(75,plain,(
% 11.29/11.49 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 11.29/11.49 inference(skolemize,[status(sab)],[74])).
% 11.29/11.49 tff(76,plain,
% 11.29/11.49 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 11.29/11.49 inference(modus_ponens,[status(thm)],[75, 71])).
% 11.29/11.49 tff(77,plain,
% 11.29/11.49 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(star(X1!0), addition(X0!1, X1!0)) = addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)))),
% 11.29/11.49 inference(quant_inst,[status(thm)],[])).
% 11.29/11.49 tff(78,plain,
% 11.29/11.49 (multiplication(star(X1!0), addition(X0!1, X1!0)) = addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0))),
% 11.29/11.49 inference(unit_resolution,[status(thm)],[77, 76])).
% 11.29/11.49 tff(79,plain,
% 11.29/11.49 (addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)) = multiplication(star(X1!0), addition(X0!1, X1!0))),
% 11.29/11.49 inference(symmetry,[status(thm)],[78])).
% 11.29/11.49 tff(80,plain,
% 11.29/11.49 (addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)) = multiplication(star(X1!0), X1!0)),
% 11.29/11.49 inference(transitivity,[status(thm)],[79, 69])).
% 11.29/11.49 tff(81,plain,
% 11.29/11.49 (addition(one, addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0))) = addition(one, multiplication(star(X1!0), X1!0))),
% 11.29/11.49 inference(monotonicity,[status(thm)],[80])).
% 11.29/11.49 tff(82,plain,
% 11.29/11.49 (addition(addition(one, addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0))), star(X1!0)) = addition(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0))),
% 11.29/11.49 inference(monotonicity,[status(thm)],[81])).
% 11.29/11.49 tff(83,plain,
% 11.29/11.49 (^[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)))),
% 11.29/11.49 inference(bind,[status(th)],[])).
% 11.29/11.49 tff(84,plain,
% 11.29/11.49 (![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))),
% 11.29/11.50 inference(quant_intro,[status(thm)],[83])).
% 11.29/11.50 tff(85,plain,
% 11.29/11.50 (![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))),
% 11.29/11.50 inference(rewrite,[status(thm)],[])).
% 11.29/11.50 tff(86,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')).
% 11.29/11.50 tff(87,plain,
% 11.29/11.50 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 11.29/11.50 inference(modus_ponens,[status(thm)],[86, 85])).
% 11.29/11.50 tff(88,plain,(
% 11.29/11.50 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 11.29/11.50 inference(skolemize,[status(sab)],[87])).
% 11.29/11.50 tff(89,plain,
% 11.29/11.50 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 11.29/11.50 inference(modus_ponens,[status(thm)],[88, 84])).
% 11.29/11.50 tff(90,plain,
% 11.29/11.50 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), star(X1!0))) = addition(addition(one, addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0))), star(X1!0)))),
% 11.29/11.50 inference(quant_inst,[status(thm)],[])).
% 11.29/11.50 tff(91,plain,
% 11.29/11.50 (addition(one, addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), star(X1!0))) = addition(addition(one, addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0))), star(X1!0))),
% 11.29/11.50 inference(unit_resolution,[status(thm)],[90, 89])).
% 11.29/11.50 tff(92,plain,
% 11.29/11.50 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 11.29/11.50 inference(bind,[status(th)],[])).
% 11.29/11.50 tff(93,plain,
% 11.29/11.50 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 11.29/11.50 inference(quant_intro,[status(thm)],[92])).
% 11.29/11.50 tff(94,plain,
% 11.29/11.50 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 11.29/11.50 inference(rewrite,[status(thm)],[])).
% 11.29/11.50 tff(95,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','additive_idempotence')).
% 11.29/11.50 tff(96,plain,
% 11.29/11.50 (![A: $i] : (addition(A, A) = A)),
% 11.29/11.50 inference(modus_ponens,[status(thm)],[95, 94])).
% 11.29/11.50 tff(97,plain,(
% 11.29/11.50 ![A: $i] : (addition(A, A) = A)),
% 11.29/11.50 inference(skolemize,[status(sab)],[96])).
% 11.29/11.50 tff(98,plain,
% 11.29/11.50 (![A: $i] : (addition(A, A) = A)),
% 11.29/11.50 inference(modus_ponens,[status(thm)],[97, 93])).
% 11.29/11.50 tff(99,plain,
% 11.29/11.50 ((~![A: $i] : (addition(A, A) = A)) | (addition(one, one) = one)),
% 11.29/11.50 inference(quant_inst,[status(thm)],[])).
% 11.29/11.50 tff(100,plain,
% 11.29/11.50 (addition(one, one) = one),
% 11.29/11.50 inference(unit_resolution,[status(thm)],[99, 98])).
% 11.29/11.50 tff(101,plain,
% 11.29/11.50 (addition(addition(one, one), addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), star(X1!0))) = addition(one, addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), star(X1!0)))),
% 11.29/11.50 inference(monotonicity,[status(thm)],[100])).
% 11.29/11.50 tff(102,plain,
% 11.29/11.50 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(one, addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), star(X1!0)))) = addition(addition(one, one), addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), star(X1!0))))),
% 11.29/11.50 inference(quant_inst,[status(thm)],[])).
% 11.29/11.50 tff(103,plain,
% 11.29/11.50 (addition(one, addition(one, addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), star(X1!0)))) = addition(addition(one, one), addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), star(X1!0)))),
% 11.29/11.50 inference(unit_resolution,[status(thm)],[102, 89])).
% 11.29/11.50 tff(104,plain,
% 11.29/11.50 (addition(addition(one, addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0))), star(X1!0)) = addition(one, addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), star(X1!0)))),
% 11.29/11.50 inference(symmetry,[status(thm)],[91])).
% 11.29/11.50 tff(105,plain,
% 11.29/11.50 (addition(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0)) = addition(addition(one, addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0))), star(X1!0))),
% 11.29/11.50 inference(symmetry,[status(thm)],[82])).
% 11.29/11.50 tff(106,plain,
% 11.29/11.50 (star(X1!0) = addition(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0))),
% 11.29/11.50 inference(symmetry,[status(thm)],[60])).
% 11.29/11.50 tff(107,plain,
% 11.29/11.50 (star(X1!0) = addition(one, addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), star(X1!0)))),
% 11.29/11.50 inference(transitivity,[status(thm)],[106, 105, 104])).
% 11.29/11.50 tff(108,plain,
% 11.29/11.50 (addition(one, star(X1!0)) = addition(one, addition(one, addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), star(X1!0))))),
% 11.29/11.50 inference(monotonicity,[status(thm)],[107])).
% 11.29/11.50 tff(109,plain,
% 11.29/11.50 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 11.29/11.50 inference(bind,[status(th)],[])).
% 11.29/11.50 tff(110,plain,
% 11.29/11.50 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 11.29/11.50 inference(quant_intro,[status(thm)],[109])).
% 11.29/11.50 tff(111,plain,
% 11.29/11.50 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 11.29/11.50 inference(rewrite,[status(thm)],[])).
% 11.29/11.50 tff(112,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','additive_commutativity')).
% 11.29/11.50 tff(113,plain,
% 11.29/11.50 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 11.29/11.50 inference(modus_ponens,[status(thm)],[112, 111])).
% 11.29/11.50 tff(114,plain,(
% 11.29/11.50 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 11.29/11.50 inference(skolemize,[status(sab)],[113])).
% 11.29/11.50 tff(115,plain,
% 11.29/11.50 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 11.29/11.50 inference(modus_ponens,[status(thm)],[114, 110])).
% 11.29/11.50 tff(116,plain,
% 11.29/11.50 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, star(X1!0)) = addition(star(X1!0), one))),
% 11.29/11.50 inference(quant_inst,[status(thm)],[])).
% 11.29/11.50 tff(117,plain,
% 11.29/11.50 (addition(one, star(X1!0)) = addition(star(X1!0), one)),
% 11.29/11.50 inference(unit_resolution,[status(thm)],[116, 115])).
% 11.29/11.50 tff(118,plain,
% 11.29/11.50 (addition(star(X1!0), one) = addition(one, star(X1!0))),
% 11.29/11.50 inference(symmetry,[status(thm)],[117])).
% 11.29/11.50 tff(119,plain,
% 11.29/11.50 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, multiplication(star(X1!0), X1!0)) = addition(multiplication(star(X1!0), X1!0), one))),
% 11.29/11.50 inference(quant_inst,[status(thm)],[])).
% 11.29/11.50 tff(120,plain,
% 11.29/11.50 (addition(one, multiplication(star(X1!0), X1!0)) = addition(multiplication(star(X1!0), X1!0), one)),
% 11.29/11.50 inference(unit_resolution,[status(thm)],[119, 115])).
% 11.29/11.50 tff(121,plain,
% 11.29/11.50 (addition(multiplication(star(X1!0), X1!0), one) = addition(one, multiplication(star(X1!0), X1!0))),
% 11.29/11.50 inference(symmetry,[status(thm)],[120])).
% 11.29/11.50 tff(122,plain,
% 11.29/11.50 (addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), one) = addition(multiplication(star(X1!0), X1!0), one)),
% 11.29/11.50 inference(monotonicity,[status(thm)],[80])).
% 11.29/11.50 tff(123,plain,
% 11.29/11.50 (addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), one) = addition(one, multiplication(star(X1!0), X1!0))),
% 11.29/11.50 inference(transitivity,[status(thm)],[122, 121])).
% 11.29/11.50 tff(124,plain,
% 11.29/11.50 (addition(addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), one), star(X1!0)) = addition(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0))),
% 11.29/11.50 inference(monotonicity,[status(thm)],[123])).
% 11.29/11.50 tff(125,plain,
% 11.29/11.50 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), addition(one, star(X1!0))) = addition(addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), one), star(X1!0)))),
% 11.29/11.50 inference(quant_inst,[status(thm)],[])).
% 11.29/11.50 tff(126,plain,
% 11.29/11.50 (addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), addition(one, star(X1!0))) = addition(addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), one), star(X1!0))),
% 11.29/11.50 inference(unit_resolution,[status(thm)],[125, 89])).
% 11.29/11.50 tff(127,plain,
% 11.29/11.50 (addition(multiplication(star(X1!0), X0!1), addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0))) = addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0))),
% 11.29/11.50 inference(monotonicity,[status(thm)],[80])).
% 11.29/11.50 tff(128,plain,
% 11.29/11.50 (addition(addition(multiplication(star(X1!0), X0!1), addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0))), addition(one, star(X1!0))) = addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), addition(one, star(X1!0)))),
% 11.29/11.50 inference(monotonicity,[status(thm)],[127])).
% 11.29/11.50 tff(129,plain,
% 11.29/11.50 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(star(X1!0), X0!1), addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), addition(one, star(X1!0)))) = addition(addition(multiplication(star(X1!0), X0!1), addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0))), addition(one, star(X1!0))))),
% 11.29/11.50 inference(quant_inst,[status(thm)],[])).
% 11.29/11.50 tff(130,plain,
% 11.29/11.50 (addition(multiplication(star(X1!0), X0!1), addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), addition(one, star(X1!0)))) = addition(addition(multiplication(star(X1!0), X0!1), addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0))), addition(one, star(X1!0)))),
% 11.29/11.50 inference(unit_resolution,[status(thm)],[129, 89])).
% 11.29/11.50 tff(131,plain,
% 11.29/11.50 (addition(addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), one), star(X1!0)) = addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), addition(one, star(X1!0)))),
% 11.29/11.50 inference(symmetry,[status(thm)],[126])).
% 11.29/11.50 tff(132,plain,
% 11.29/11.50 (addition(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0)) = addition(addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), one), star(X1!0))),
% 11.29/11.50 inference(symmetry,[status(thm)],[124])).
% 11.29/11.50 tff(133,plain,
% 11.29/11.50 (star(X1!0) = addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), addition(one, star(X1!0)))),
% 11.29/11.50 inference(transitivity,[status(thm)],[106, 132, 131])).
% 11.29/11.50 tff(134,plain,
% 11.29/11.50 (addition(multiplication(star(X1!0), X0!1), star(X1!0)) = addition(multiplication(star(X1!0), X0!1), addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), addition(one, star(X1!0))))),
% 11.29/11.50 inference(monotonicity,[status(thm)],[133])).
% 11.29/11.50 tff(135,plain,
% 11.29/11.50 (addition(multiplication(star(X1!0), X0!1), star(X1!0)) = star(X1!0)),
% 11.29/11.50 inference(transitivity,[status(thm)],[134, 130, 128, 126, 124, 60])).
% 11.29/11.50 tff(136,plain,
% 11.29/11.50 (addition(addition(multiplication(star(X1!0), X0!1), star(X1!0)), one) = addition(star(X1!0), one)),
% 11.29/11.50 inference(monotonicity,[status(thm)],[135])).
% 11.29/11.50 tff(137,plain,
% 11.29/11.50 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(star(X1!0), X0!1), addition(star(X1!0), one)) = addition(addition(multiplication(star(X1!0), X0!1), star(X1!0)), one))),
% 11.29/11.50 inference(quant_inst,[status(thm)],[])).
% 11.29/11.50 tff(138,plain,
% 11.29/11.50 (addition(multiplication(star(X1!0), X0!1), addition(star(X1!0), one)) = addition(addition(multiplication(star(X1!0), X0!1), star(X1!0)), one)),
% 11.29/11.50 inference(unit_resolution,[status(thm)],[137, 89])).
% 11.29/11.50 tff(139,plain,
% 11.29/11.50 (addition(multiplication(star(X1!0), X0!1), addition(one, star(X1!0))) = addition(multiplication(star(X1!0), X0!1), addition(star(X1!0), one))),
% 11.29/11.50 inference(monotonicity,[status(thm)],[117])).
% 11.29/11.50 tff(140,plain,
% 11.29/11.50 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(star(X1!0), X0!1), addition(one, star(X1!0))) = addition(addition(multiplication(star(X1!0), X0!1), one), star(X1!0)))),
% 11.29/11.50 inference(quant_inst,[status(thm)],[])).
% 11.29/11.52 tff(141,plain,
% 11.29/11.52 (addition(multiplication(star(X1!0), X0!1), addition(one, star(X1!0))) = addition(addition(multiplication(star(X1!0), X0!1), one), star(X1!0))),
% 11.29/11.52 inference(unit_resolution,[status(thm)],[140, 89])).
% 11.29/11.52 tff(142,plain,
% 11.29/11.52 (addition(addition(multiplication(star(X1!0), X0!1), one), star(X1!0)) = addition(multiplication(star(X1!0), X0!1), addition(one, star(X1!0)))),
% 11.29/11.52 inference(symmetry,[status(thm)],[141])).
% 11.29/11.52 tff(143,plain,
% 11.29/11.52 (addition(addition(multiplication(star(X1!0), X0!1), one), star(X1!0)) = star(X1!0)),
% 11.29/11.52 inference(transitivity,[status(thm)],[142, 139, 138, 136, 118, 108, 103, 101, 91, 82, 60])).
% 11.29/11.52 tff(144,plain,
% 11.29/11.52 ((~(leq(addition(multiplication(star(X1!0), X0!1), one), star(X1!0)) <=> (addition(addition(multiplication(star(X1!0), X0!1), one), star(X1!0)) = star(X1!0)))) | leq(addition(multiplication(star(X1!0), X0!1), one), star(X1!0)) | (~(addition(addition(multiplication(star(X1!0), X0!1), one), star(X1!0)) = star(X1!0)))),
% 11.29/11.52 inference(tautology,[status(thm)],[])).
% 11.29/11.52 tff(145,plain,
% 11.29/11.52 ((~(leq(addition(multiplication(star(X1!0), X0!1), one), star(X1!0)) <=> (addition(addition(multiplication(star(X1!0), X0!1), one), star(X1!0)) = star(X1!0)))) | leq(addition(multiplication(star(X1!0), X0!1), one), star(X1!0))),
% 11.29/11.52 inference(unit_resolution,[status(thm)],[144, 143])).
% 11.29/11.52 tff(146,plain,
% 11.29/11.52 ($false),
% 11.29/11.52 inference(unit_resolution,[status(thm)],[145, 46, 9])).
% 11.29/11.52 % SZS output end Proof
% 11.37/11.55 % E exiting
%------------------------------------------------------------------------------