TSTP Solution File: KLE160+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE160+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 Sep 17 17:24:24 EDT 2022
% Result : Theorem 0.20s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE160+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 08:24:07 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 % SZS output start Proof
% 0.20/0.45 tff(multiplication_type, type, (
% 0.20/0.45 multiplication: ( $i * $i ) > $i)).
% 0.20/0.45 tff(star_type, type, (
% 0.20/0.45 star: $i > $i)).
% 0.20/0.45 tff(tptp_fun_X2_0_type, type, (
% 0.20/0.45 tptp_fun_X2_0: $i)).
% 0.20/0.45 tff(tptp_fun_X1_1_type, type, (
% 0.20/0.45 tptp_fun_X1_1: $i)).
% 0.20/0.45 tff(addition_type, type, (
% 0.20/0.45 addition: ( $i * $i ) > $i)).
% 0.20/0.45 tff(tptp_fun_X0_2_type, type, (
% 0.20/0.45 tptp_fun_X0_2: $i)).
% 0.20/0.45 tff(one_type, type, (
% 0.20/0.45 one: $i)).
% 0.20/0.45 tff(leq_type, type, (
% 0.20/0.45 leq: ( $i * $i ) > $o)).
% 0.20/0.45 tff(1,plain,
% 0.20/0.45 (^[A: $i] : refl((addition(one, multiplication(A, star(A))) = star(A)) <=> (addition(one, multiplication(A, star(A))) = star(A)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(2,plain,
% 0.20/0.45 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A)) <=> ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.45 tff(3,plain,
% 0.20/0.45 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A)) <=> ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(4,axiom,(![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','star_unfold1')).
% 0.20/0.45 tff(5,plain,
% 0.20/0.45 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.45 tff(6,plain,(
% 0.20/0.45 ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.20/0.45 inference(skolemize,[status(sab)],[5])).
% 0.20/0.45 tff(7,plain,
% 0.20/0.45 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.45 tff(8,plain,
% 0.20/0.45 ((~![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))) | (addition(one, multiplication(X2!0, star(X2!0))) = star(X2!0))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(9,plain,
% 0.20/0.45 (addition(one, multiplication(X2!0, star(X2!0))) = star(X2!0)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.45 tff(10,plain,
% 0.20/0.45 (multiplication(X1!1, addition(one, multiplication(X2!0, star(X2!0)))) = multiplication(X1!1, star(X2!0))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[9])).
% 0.20/0.45 tff(11,plain,
% 0.20/0.45 (^[A: $i, B: $i, C: $i] : refl((multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(12,plain,
% 0.20/0.45 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.45 tff(13,plain,
% 0.20/0.45 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(14,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/KLE004+0.ax','distributivity1')).
% 0.20/0.45 tff(15,plain,
% 0.20/0.45 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.45 tff(16,plain,(
% 0.20/0.45 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[15])).
% 0.20/0.45 tff(17,plain,
% 0.20/0.45 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.20/0.45 tff(18,plain,
% 0.20/0.45 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X1!1, addition(one, multiplication(X2!0, star(X2!0)))) = addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(X2!0, star(X2!0)))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(19,plain,
% 0.20/0.45 (multiplication(X1!1, addition(one, multiplication(X2!0, star(X2!0)))) = addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(X2!0, star(X2!0))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.20/0.45 tff(20,plain,
% 0.20/0.45 (addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(X2!0, star(X2!0)))) = multiplication(X1!1, addition(one, multiplication(X2!0, star(X2!0))))),
% 0.20/0.45 inference(symmetry,[status(thm)],[19])).
% 0.20/0.45 tff(21,plain,
% 0.20/0.45 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(22,plain,
% 0.20/0.45 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.45 tff(23,plain,
% 0.20/0.45 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(24,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','additive_commutativity')).
% 0.20/0.45 tff(25,plain,
% 0.20/0.45 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.45 tff(26,plain,(
% 0.20/0.45 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.20/0.45 inference(skolemize,[status(sab)],[25])).
% 0.20/0.45 tff(27,plain,
% 0.20/0.45 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.20/0.45 tff(28,plain,
% 0.20/0.45 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(X2!0, star(X2!0)))) = addition(multiplication(X1!1, multiplication(X2!0, star(X2!0))), multiplication(X1!1, one)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(29,plain,
% 0.20/0.45 (addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(X2!0, star(X2!0)))) = addition(multiplication(X1!1, multiplication(X2!0, star(X2!0))), multiplication(X1!1, one))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.20/0.45 tff(30,plain,
% 0.20/0.45 (addition(multiplication(X1!1, multiplication(X2!0, star(X2!0))), multiplication(X1!1, one)) = addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(X2!0, star(X2!0))))),
% 0.20/0.45 inference(symmetry,[status(thm)],[29])).
% 0.20/0.45 tff(31,plain,
% 0.20/0.45 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(32,plain,
% 0.20/0.45 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.20/0.45 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.45 tff(33,plain,
% 0.20/0.45 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(34,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','multiplicative_right_identity')).
% 0.20/0.45 tff(35,plain,
% 0.20/0.45 (![A: $i] : (multiplication(A, one) = A)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.45 tff(36,plain,(
% 0.20/0.45 ![A: $i] : (multiplication(A, one) = A)),
% 0.20/0.45 inference(skolemize,[status(sab)],[35])).
% 0.20/0.45 tff(37,plain,
% 0.20/0.45 (![A: $i] : (multiplication(A, one) = A)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.20/0.45 tff(38,plain,
% 0.20/0.45 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(X1!1, one) = X1!1)),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(39,plain,
% 0.20/0.45 (multiplication(X1!1, one) = X1!1),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.20/0.45 tff(40,plain,
% 0.20/0.45 (X1!1 = multiplication(X1!1, one)),
% 0.20/0.45 inference(symmetry,[status(thm)],[39])).
% 0.20/0.45 tff(41,plain,
% 0.20/0.45 (^[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)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(42,plain,
% 0.20/0.45 (![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))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.45 tff(43,plain,
% 0.20/0.45 (![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))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(44,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','multiplicative_associativity')).
% 0.20/0.45 tff(45,plain,
% 0.20/0.45 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.45 tff(46,plain,(
% 0.20/0.45 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.20/0.45 inference(skolemize,[status(sab)],[45])).
% 0.20/0.45 tff(47,plain,
% 0.20/0.45 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.20/0.45 tff(48,plain,
% 0.20/0.45 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X1!1, multiplication(X2!0, star(X2!0))) = multiplication(multiplication(X1!1, X2!0), star(X2!0)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(49,plain,
% 0.20/0.45 (multiplication(X1!1, multiplication(X2!0, star(X2!0))) = multiplication(multiplication(X1!1, X2!0), star(X2!0))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.20/0.45 tff(50,plain,
% 0.20/0.45 (multiplication(multiplication(X1!1, X2!0), star(X2!0)) = multiplication(X1!1, multiplication(X2!0, star(X2!0)))),
% 0.20/0.45 inference(symmetry,[status(thm)],[49])).
% 0.20/0.45 tff(51,plain,
% 0.20/0.45 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(52,plain,
% 0.20/0.45 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[51])).
% 0.20/0.45 tff(53,plain,
% 0.20/0.45 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(54,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','order')).
% 0.20/0.45 tff(55,plain,
% 0.20/0.45 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.45 tff(56,plain,(
% 0.20/0.45 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.20/0.45 inference(skolemize,[status(sab)],[55])).
% 0.20/0.45 tff(57,plain,
% 0.20/0.45 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.20/0.45 tff(58,plain,
% 0.20/0.45 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0)) <=> (addition(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0)) = multiplication(X1!1, X2!0)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(59,plain,
% 0.20/0.45 (leq(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0)) <=> (addition(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0)) = multiplication(X1!1, X2!0))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.20/0.45 tff(60,plain,
% 0.20/0.45 ((~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X1, X2))) | leq(multiplication(star(X0), X1), multiplication(X1, star(X2))))) <=> (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X1, X2))) | leq(multiplication(star(X0), X1), multiplication(X1, star(X2)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(61,plain,
% 0.20/0.45 ((~![X0: $i, X1: $i, X2: $i] : (leq(multiplication(X0, X1), multiplication(X1, X2)) => leq(multiplication(star(X0), X1), multiplication(X1, star(X2))))) <=> (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X1, X2))) | leq(multiplication(star(X0), X1), multiplication(X1, star(X2)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(62,axiom,(~![X0: $i, X1: $i, X2: $i] : (leq(multiplication(X0, X1), multiplication(X1, X2)) => leq(multiplication(star(X0), X1), multiplication(X1, star(X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.20/0.45 tff(63,plain,
% 0.20/0.45 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X1, X2))) | leq(multiplication(star(X0), X1), multiplication(X1, star(X2))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.45 tff(64,plain,
% 0.20/0.45 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X1, X2))) | leq(multiplication(star(X0), X1), multiplication(X1, star(X2))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[63, 60])).
% 0.20/0.45 tff(65,plain,
% 0.20/0.45 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X1, X2))) | leq(multiplication(star(X0), X1), multiplication(X1, star(X2))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.20/0.45 tff(66,plain,
% 0.20/0.45 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X1, X2))) | leq(multiplication(star(X0), X1), multiplication(X1, star(X2))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[65, 60])).
% 0.20/0.45 tff(67,plain,
% 0.20/0.45 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X1, X2))) | leq(multiplication(star(X0), X1), multiplication(X1, star(X2))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[66, 60])).
% 0.20/0.45 tff(68,plain,
% 0.20/0.45 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X1, X2))) | leq(multiplication(star(X0), X1), multiplication(X1, star(X2))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.20/0.45 tff(69,plain,
% 0.20/0.45 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X1, X2))) | leq(multiplication(star(X0), X1), multiplication(X1, star(X2))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[68, 60])).
% 0.20/0.45 tff(70,plain,(
% 0.20/0.45 ~((~leq(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0))) | leq(multiplication(star(X0!2), X1!1), multiplication(X1!1, star(X2!0))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[69])).
% 0.20/0.45 tff(71,plain,
% 0.20/0.45 (leq(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0))),
% 0.20/0.45 inference(or_elim,[status(thm)],[70])).
% 0.20/0.45 tff(72,plain,
% 0.20/0.45 ((~(leq(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0)) <=> (addition(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0)) = multiplication(X1!1, X2!0)))) | (~leq(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0))) | (addition(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0)) = multiplication(X1!1, X2!0))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(73,plain,
% 0.20/0.45 ((~(leq(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0)) <=> (addition(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0)) = multiplication(X1!1, X2!0)))) | (addition(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0)) = multiplication(X1!1, X2!0))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.20/0.45 tff(74,plain,
% 0.20/0.45 (addition(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0)) = multiplication(X1!1, X2!0)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[73, 59])).
% 0.20/0.45 tff(75,plain,
% 0.20/0.45 (multiplication(addition(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0)), star(X2!0)) = multiplication(multiplication(X1!1, X2!0), star(X2!0))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[74])).
% 0.20/0.45 tff(76,plain,
% 0.20/0.45 (^[A: $i, B: $i, C: $i] : refl((multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))) <=> (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(77,plain,
% 0.20/0.45 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[76])).
% 0.20/0.45 tff(78,plain,
% 0.20/0.45 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(79,axiom,(![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','distributivity2')).
% 0.20/0.46 tff(80,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.46 tff(81,plain,(
% 0.20/0.46 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[80])).
% 0.20/0.46 tff(82,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.20/0.46 tff(83,plain,
% 0.20/0.46 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0)), star(X2!0)) = addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), multiplication(multiplication(X1!1, X2!0), star(X2!0))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(84,plain,
% 0.20/0.46 (multiplication(addition(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0)), star(X2!0)) = addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), multiplication(multiplication(X1!1, X2!0), star(X2!0)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.20/0.46 tff(85,plain,
% 0.20/0.46 (addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), multiplication(multiplication(X1!1, X2!0), star(X2!0))) = multiplication(addition(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0)), star(X2!0))),
% 0.20/0.46 inference(symmetry,[status(thm)],[84])).
% 0.20/0.46 tff(86,plain,
% 0.20/0.46 (addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), multiplication(multiplication(X1!1, X2!0), star(X2!0))) = multiplication(X1!1, multiplication(X2!0, star(X2!0)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[85, 75, 50])).
% 0.20/0.46 tff(87,plain,
% 0.20/0.46 (addition(addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), multiplication(multiplication(X1!1, X2!0), star(X2!0))), X1!1) = addition(multiplication(X1!1, multiplication(X2!0, star(X2!0))), multiplication(X1!1, one))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[86, 40])).
% 0.20/0.46 tff(88,plain,
% 0.20/0.46 (^[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)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(89,plain,
% 0.20/0.46 (![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))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[88])).
% 0.20/0.46 tff(90,plain,
% 0.20/0.46 (![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))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(91,axiom,(![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','additive_associativity')).
% 0.20/0.46 tff(92,plain,
% 0.20/0.46 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.20/0.46 tff(93,plain,(
% 0.20/0.46 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.20/0.46 inference(skolemize,[status(sab)],[92])).
% 0.20/0.46 tff(94,plain,
% 0.20/0.46 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.20/0.46 tff(95,plain,
% 0.20/0.46 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), addition(multiplication(multiplication(X1!1, X2!0), star(X2!0)), X1!1)) = addition(addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), multiplication(multiplication(X1!1, X2!0), star(X2!0))), X1!1))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(96,plain,
% 0.20/0.46 (addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), addition(multiplication(multiplication(X1!1, X2!0), star(X2!0)), X1!1)) = addition(addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), multiplication(multiplication(X1!1, X2!0), star(X2!0))), X1!1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.20/0.46 tff(97,plain,
% 0.20/0.46 (addition(multiplication(multiplication(X1!1, X2!0), star(X2!0)), X1!1) = addition(multiplication(X1!1, multiplication(X2!0, star(X2!0))), multiplication(X1!1, one))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[50, 40])).
% 0.20/0.46 tff(98,plain,
% 0.20/0.46 (addition(multiplication(X1!1, multiplication(X2!0, star(X2!0))), multiplication(X1!1, one)) = addition(multiplication(multiplication(X1!1, X2!0), star(X2!0)), X1!1)),
% 0.20/0.46 inference(symmetry,[status(thm)],[97])).
% 0.20/0.46 tff(99,plain,
% 0.20/0.46 (multiplication(X1!1, star(X2!0)) = multiplication(X1!1, addition(one, multiplication(X2!0, star(X2!0))))),
% 0.20/0.46 inference(symmetry,[status(thm)],[10])).
% 0.20/0.46 tff(100,plain,
% 0.20/0.46 (^[A: $i] : refl((addition(one, multiplication(star(A), A)) = star(A)) <=> (addition(one, multiplication(star(A), A)) = star(A)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(101,plain,
% 0.20/0.46 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A)) <=> ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[100])).
% 0.20/0.46 tff(102,plain,
% 0.20/0.46 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A)) <=> ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(103,axiom,(![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','star_unfold2')).
% 0.20/0.46 tff(104,plain,
% 0.20/0.46 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.46 tff(105,plain,(
% 0.20/0.46 ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.20/0.46 inference(skolemize,[status(sab)],[104])).
% 0.20/0.46 tff(106,plain,
% 0.20/0.46 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.20/0.46 tff(107,plain,
% 0.20/0.46 ((~![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))) | (addition(one, multiplication(star(X2!0), X2!0)) = star(X2!0))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(108,plain,
% 0.20/0.46 (addition(one, multiplication(star(X2!0), X2!0)) = star(X2!0)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.20/0.46 tff(109,plain,
% 0.20/0.46 (star(X2!0) = addition(one, multiplication(star(X2!0), X2!0))),
% 0.20/0.46 inference(symmetry,[status(thm)],[108])).
% 0.20/0.46 tff(110,plain,
% 0.20/0.46 (multiplication(X1!1, star(X2!0)) = multiplication(X1!1, addition(one, multiplication(star(X2!0), X2!0)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[109])).
% 0.20/0.46 tff(111,plain,
% 0.20/0.46 (multiplication(X1!1, addition(one, multiplication(star(X2!0), X2!0))) = multiplication(X1!1, star(X2!0))),
% 0.20/0.46 inference(symmetry,[status(thm)],[110])).
% 0.20/0.46 tff(112,plain,
% 0.20/0.46 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X1!1, addition(one, multiplication(star(X2!0), X2!0))) = addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(113,plain,
% 0.20/0.46 (multiplication(X1!1, addition(one, multiplication(star(X2!0), X2!0))) = addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[112, 17])).
% 0.20/0.46 tff(114,plain,
% 0.20/0.46 (addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0))) = multiplication(X1!1, addition(one, multiplication(star(X2!0), X2!0)))),
% 0.20/0.46 inference(symmetry,[status(thm)],[113])).
% 0.20/0.46 tff(115,plain,
% 0.20/0.46 (addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0))) = addition(multiplication(multiplication(X1!1, X2!0), star(X2!0)), X1!1)),
% 0.20/0.46 inference(transitivity,[status(thm)],[114, 111, 99, 19, 29, 98])).
% 0.20/0.46 tff(116,plain,
% 0.20/0.46 (addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0)))) = addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), addition(multiplication(multiplication(X1!1, X2!0), star(X2!0)), X1!1))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[115])).
% 0.20/0.46 tff(117,plain,
% 0.20/0.46 (addition(X1!1, multiplication(multiplication(X1!1, X2!0), star(X2!0))) = addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(X2!0, star(X2!0))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[40, 50])).
% 0.20/0.46 tff(118,plain,
% 0.20/0.46 (addition(X1!1, multiplication(multiplication(X1!1, X2!0), star(X2!0))) = addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[117, 20, 10, 110, 113])).
% 0.20/0.46 tff(119,plain,
% 0.20/0.46 (addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), addition(X1!1, multiplication(multiplication(X1!1, X2!0), star(X2!0)))) = addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[118])).
% 0.20/0.46 tff(120,plain,
% 0.20/0.46 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), addition(X1!1, multiplication(multiplication(X1!1, X2!0), star(X2!0)))) = addition(addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), X1!1), multiplication(multiplication(X1!1, X2!0), star(X2!0))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(121,plain,
% 0.20/0.46 (addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), addition(X1!1, multiplication(multiplication(X1!1, X2!0), star(X2!0)))) = addition(addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), X1!1), multiplication(multiplication(X1!1, X2!0), star(X2!0)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[120, 94])).
% 0.20/0.46 tff(122,plain,
% 0.20/0.46 (addition(addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), X1!1), multiplication(multiplication(X1!1, X2!0), star(X2!0))) = addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), addition(X1!1, multiplication(multiplication(X1!1, X2!0), star(X2!0))))),
% 0.20/0.46 inference(symmetry,[status(thm)],[121])).
% 0.20/0.46 tff(123,plain,
% 0.20/0.46 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X0!2, multiplication(X1!1, star(X2!0))) = multiplication(multiplication(X0!2, X1!1), star(X2!0)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(124,plain,
% 0.20/0.46 (multiplication(X0!2, multiplication(X1!1, star(X2!0))) = multiplication(multiplication(X0!2, X1!1), star(X2!0))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[123, 47])).
% 0.20/0.46 tff(125,plain,
% 0.20/0.46 (multiplication(multiplication(X0!2, X1!1), star(X2!0)) = multiplication(X0!2, multiplication(X1!1, star(X2!0)))),
% 0.20/0.46 inference(symmetry,[status(thm)],[124])).
% 0.20/0.46 tff(126,plain,
% 0.20/0.46 (addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), X1!1) = addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1)),
% 0.20/0.46 inference(monotonicity,[status(thm)],[125])).
% 0.20/0.46 tff(127,plain,
% 0.20/0.46 (addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1) = addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), X1!1)),
% 0.20/0.46 inference(symmetry,[status(thm)],[126])).
% 0.20/0.46 tff(128,plain,
% 0.20/0.46 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(129,plain,
% 0.20/0.46 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.20/0.46 inference(quant_intro,[status(thm)],[128])).
% 0.20/0.46 tff(130,plain,
% 0.20/0.46 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(131,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','idempotence')).
% 0.20/0.46 tff(132,plain,
% 0.20/0.46 (![A: $i] : (addition(A, A) = A)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.20/0.47 tff(133,plain,(
% 0.20/0.47 ![A: $i] : (addition(A, A) = A)),
% 0.20/0.47 inference(skolemize,[status(sab)],[132])).
% 0.20/0.47 tff(134,plain,
% 0.20/0.47 (![A: $i] : (addition(A, A) = A)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.20/0.47 tff(135,plain,
% 0.20/0.47 ((~![A: $i] : (addition(A, A) = A)) | (addition(X1!1, X1!1) = X1!1)),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(136,plain,
% 0.20/0.47 (addition(X1!1, X1!1) = X1!1),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.20/0.47 tff(137,plain,
% 0.20/0.47 (addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), addition(X1!1, X1!1)) = addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[125, 136])).
% 0.20/0.47 tff(138,plain,
% 0.20/0.47 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), addition(X1!1, X1!1)) = addition(addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), X1!1), X1!1))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(139,plain,
% 0.20/0.47 (addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), addition(X1!1, X1!1)) = addition(addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), X1!1), X1!1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[138, 94])).
% 0.20/0.47 tff(140,plain,
% 0.20/0.47 (addition(addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), X1!1), X1!1) = addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), addition(X1!1, X1!1))),
% 0.20/0.47 inference(symmetry,[status(thm)],[139])).
% 0.20/0.47 tff(141,plain,
% 0.20/0.47 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1) = addition(X1!1, multiplication(X0!2, multiplication(X1!1, star(X2!0)))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(142,plain,
% 0.20/0.47 (addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1) = addition(X1!1, multiplication(X0!2, multiplication(X1!1, star(X2!0))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[141, 27])).
% 0.20/0.47 tff(143,plain,
% 0.20/0.47 (addition(X1!1, multiplication(X0!2, multiplication(X1!1, star(X2!0)))) = addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1)),
% 0.20/0.47 inference(symmetry,[status(thm)],[142])).
% 0.20/0.47 tff(144,plain,
% 0.20/0.47 (addition(X1!1, multiplication(X0!2, multiplication(X1!1, star(X2!0)))) = addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), X1!1)),
% 0.20/0.47 inference(transitivity,[status(thm)],[143, 127])).
% 0.20/0.47 tff(145,plain,
% 0.20/0.47 (addition(addition(X1!1, multiplication(X0!2, multiplication(X1!1, star(X2!0)))), multiplication(X1!1, one)) = addition(addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), X1!1), X1!1)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[144, 39])).
% 0.20/0.47 tff(146,plain,
% 0.20/0.47 (addition(addition(X1!1, multiplication(X0!2, multiplication(X1!1, star(X2!0)))), multiplication(X1!1, one)) = addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), X1!1)),
% 0.20/0.47 inference(transitivity,[status(thm)],[145, 140, 137, 127])).
% 0.20/0.47 tff(147,plain,
% 0.20/0.47 (addition(addition(addition(X1!1, multiplication(X0!2, multiplication(X1!1, star(X2!0)))), multiplication(X1!1, one)), multiplication(X1!1, multiplication(X2!0, star(X2!0)))) = addition(addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), X1!1), multiplication(multiplication(X1!1, X2!0), star(X2!0)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[146, 49])).
% 0.20/0.47 tff(148,plain,
% 0.20/0.47 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(X1!1, multiplication(X0!2, multiplication(X1!1, star(X2!0)))), addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(X2!0, star(X2!0))))) = addition(addition(addition(X1!1, multiplication(X0!2, multiplication(X1!1, star(X2!0)))), multiplication(X1!1, one)), multiplication(X1!1, multiplication(X2!0, star(X2!0)))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(149,plain,
% 0.20/0.47 (addition(addition(X1!1, multiplication(X0!2, multiplication(X1!1, star(X2!0)))), addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(X2!0, star(X2!0))))) = addition(addition(addition(X1!1, multiplication(X0!2, multiplication(X1!1, star(X2!0)))), multiplication(X1!1, one)), multiplication(X1!1, multiplication(X2!0, star(X2!0))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[148, 94])).
% 0.20/0.47 tff(150,plain,
% 0.20/0.47 (multiplication(X1!1, star(X2!0)) = addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(X2!0, star(X2!0))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[99, 19])).
% 0.20/0.47 tff(151,plain,
% 0.20/0.47 (addition(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0))) = addition(addition(X1!1, multiplication(X0!2, multiplication(X1!1, star(X2!0)))), addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(X2!0, star(X2!0)))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[142, 150])).
% 0.20/0.47 tff(152,plain,
% 0.20/0.47 (addition(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0))) = multiplication(X1!1, star(X2!0))),
% 0.20/0.47 inference(transitivity,[status(thm)],[151, 149, 147, 122, 119, 116, 96, 87, 30, 20, 10])).
% 0.20/0.47 tff(153,plain,
% 0.20/0.47 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0))) <=> (addition(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0))) = multiplication(X1!1, star(X2!0))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(154,plain,
% 0.20/0.47 (leq(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0))) <=> (addition(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0))) = multiplication(X1!1, star(X2!0)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[153, 57])).
% 0.20/0.47 tff(155,plain,
% 0.20/0.47 (~leq(multiplication(star(X0!2), X1!1), multiplication(X1!1, star(X2!0)))),
% 0.20/0.47 inference(or_elim,[status(thm)],[70])).
% 0.20/0.47 tff(156,plain,
% 0.20/0.47 (^[A: $i, B: $i, C: $i] : refl(((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C)) <=> ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(157,plain,
% 0.20/0.47 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[156])).
% 0.20/0.47 tff(158,plain,
% 0.20/0.47 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(159,plain,
% 0.20/0.47 (^[A: $i, B: $i, C: $i] : rewrite((leq(addition(multiplication(A, C), B), C) => leq(multiplication(star(A), B), C)) <=> ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(160,plain,
% 0.20/0.47 (![A: $i, B: $i, C: $i] : (leq(addition(multiplication(A, C), B), C) => leq(multiplication(star(A), B), C)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[159])).
% 0.20/0.47 tff(161,axiom,(![A: $i, B: $i, C: $i] : (leq(addition(multiplication(A, C), B), C) => leq(multiplication(star(A), B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','star_induction1')).
% 0.20/0.47 tff(162,plain,
% 0.20/0.47 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.20/0.47 tff(163,plain,
% 0.20/0.47 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[162, 158])).
% 0.20/0.47 tff(164,plain,(
% 0.20/0.47 ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 0.20/0.47 inference(skolemize,[status(sab)],[163])).
% 0.20/0.47 tff(165,plain,
% 0.20/0.47 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[164, 157])).
% 0.20/0.47 tff(166,plain,
% 0.20/0.47 (((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))) | ((~leq(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0)))) | leq(multiplication(star(X0!2), X1!1), multiplication(X1!1, star(X2!0))))) <=> ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))) | (~leq(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0)))) | leq(multiplication(star(X0!2), X1!1), multiplication(X1!1, star(X2!0))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(167,plain,
% 0.20/0.47 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))) | ((~leq(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0)))) | leq(multiplication(star(X0!2), X1!1), multiplication(X1!1, star(X2!0))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(168,plain,
% 0.20/0.47 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))) | (~leq(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0)))) | leq(multiplication(star(X0!2), X1!1), multiplication(X1!1, star(X2!0)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.20/0.47 tff(169,plain,
% 0.20/0.47 (~leq(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[168, 165, 155])).
% 0.20/0.47 tff(170,plain,
% 0.20/0.47 ((~(leq(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0))) <=> (addition(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0))) = multiplication(X1!1, star(X2!0))))) | leq(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0))) | (~(addition(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0))) = multiplication(X1!1, star(X2!0))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(171,plain,
% 0.20/0.47 ((~(leq(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0))) <=> (addition(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0))) = multiplication(X1!1, star(X2!0))))) | (~(addition(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0))) = multiplication(X1!1, star(X2!0))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[170, 169])).
% 0.20/0.47 tff(172,plain,
% 0.20/0.47 (~(addition(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0))) = multiplication(X1!1, star(X2!0)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[171, 154])).
% 0.20/0.47 tff(173,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[172, 152])).
% 0.20/0.47 % SZS output end Proof
%------------------------------------------------------------------------------