TSTP Solution File: KLE043+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE043+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 Sep 17 17:23:59 EDT 2022
% Result : Theorem 0.51s 0.60s
% Output : Proof 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE043+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 08:05:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.51/0.60 % SZS status Theorem
% 0.51/0.60 % SZS output start Proof
% 0.51/0.60 tff(addition_type, type, (
% 0.51/0.60 addition: ( $i * $i ) > $i)).
% 0.51/0.60 tff(tptp_fun_X1_0_type, type, (
% 0.51/0.60 tptp_fun_X1_0: $i)).
% 0.51/0.60 tff(multiplication_type, type, (
% 0.51/0.60 multiplication: ( $i * $i ) > $i)).
% 0.51/0.60 tff(star_type, type, (
% 0.51/0.60 star: $i > $i)).
% 0.51/0.60 tff(tptp_fun_X0_1_type, type, (
% 0.51/0.60 tptp_fun_X0_1: $i)).
% 0.51/0.60 tff(leq_type, type, (
% 0.51/0.60 leq: ( $i * $i ) > $o)).
% 0.51/0.60 tff(one_type, type, (
% 0.51/0.60 one: $i)).
% 0.51/0.60 tff(1,plain,
% 0.51/0.60 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 0.51/0.60 inference(bind,[status(th)],[])).
% 0.51/0.60 tff(2,plain,
% 0.51/0.60 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.51/0.60 inference(quant_intro,[status(thm)],[1])).
% 0.51/0.60 tff(3,plain,
% 0.51/0.60 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.51/0.60 inference(rewrite,[status(thm)],[])).
% 0.51/0.60 tff(4,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','additive_idempotence')).
% 0.51/0.60 tff(5,plain,
% 0.51/0.60 (![A: $i] : (addition(A, A) = A)),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.51/0.60 tff(6,plain,(
% 0.51/0.60 ![A: $i] : (addition(A, A) = A)),
% 0.51/0.60 inference(skolemize,[status(sab)],[5])).
% 0.51/0.60 tff(7,plain,
% 0.51/0.60 (![A: $i] : (addition(A, A) = A)),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.51/0.60 tff(8,plain,
% 0.51/0.60 ((~![A: $i] : (addition(A, A) = A)) | (addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) = addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0))),
% 0.51/0.60 inference(quant_inst,[status(thm)],[])).
% 0.51/0.60 tff(9,plain,
% 0.51/0.60 (addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) = addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.51/0.60 tff(10,plain,
% 0.51/0.60 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.51/0.60 inference(bind,[status(th)],[])).
% 0.51/0.60 tff(11,plain,
% 0.51/0.60 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.51/0.60 inference(quant_intro,[status(thm)],[10])).
% 0.51/0.60 tff(12,plain,
% 0.51/0.60 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.51/0.60 inference(rewrite,[status(thm)],[])).
% 0.51/0.60 tff(13,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','additive_commutativity')).
% 0.51/0.60 tff(14,plain,
% 0.51/0.60 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.51/0.60 tff(15,plain,(
% 0.51/0.60 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.51/0.60 inference(skolemize,[status(sab)],[14])).
% 0.51/0.60 tff(16,plain,
% 0.51/0.60 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.51/0.60 tff(17,plain,
% 0.51/0.60 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)) = addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0))),
% 0.51/0.60 inference(quant_inst,[status(thm)],[])).
% 0.51/0.60 tff(18,plain,
% 0.51/0.60 (addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)) = addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.51/0.60 tff(19,plain,
% 0.51/0.60 (^[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)))),
% 0.51/0.60 inference(bind,[status(th)],[])).
% 0.51/0.60 tff(20,plain,
% 0.51/0.60 (![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))),
% 0.51/0.60 inference(quant_intro,[status(thm)],[19])).
% 0.51/0.60 tff(21,plain,
% 0.51/0.60 (![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))),
% 0.51/0.60 inference(rewrite,[status(thm)],[])).
% 0.51/0.60 tff(22,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','multiplicative_associativity')).
% 0.51/0.60 tff(23,plain,
% 0.51/0.60 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.51/0.60 tff(24,plain,(
% 0.51/0.60 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.51/0.60 inference(skolemize,[status(sab)],[23])).
% 0.51/0.60 tff(25,plain,
% 0.51/0.60 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.51/0.60 tff(26,plain,
% 0.51/0.60 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X0!1, multiplication(star(X0!1), X1!0)) = multiplication(multiplication(X0!1, star(X0!1)), X1!0))),
% 0.51/0.60 inference(quant_inst,[status(thm)],[])).
% 0.51/0.60 tff(27,plain,
% 0.51/0.60 (multiplication(X0!1, multiplication(star(X0!1), X1!0)) = multiplication(multiplication(X0!1, star(X0!1)), X1!0)),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.51/0.60 tff(28,plain,
% 0.51/0.60 (addition(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) = addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), multiplication(star(X0!1), X1!0))),
% 0.51/0.60 inference(monotonicity,[status(thm)],[18])).
% 0.51/0.60 tff(29,plain,
% 0.51/0.60 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 0.51/0.60 inference(bind,[status(th)],[])).
% 0.51/0.60 tff(30,plain,
% 0.51/0.60 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.51/0.60 inference(quant_intro,[status(thm)],[29])).
% 0.51/0.60 tff(31,plain,
% 0.51/0.60 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.51/0.60 inference(rewrite,[status(thm)],[])).
% 0.51/0.60 tff(32,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','order')).
% 0.51/0.60 tff(33,plain,
% 0.51/0.60 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.51/0.60 tff(34,plain,(
% 0.51/0.60 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.51/0.60 inference(skolemize,[status(sab)],[33])).
% 0.51/0.60 tff(35,plain,
% 0.51/0.60 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.51/0.60 tff(36,plain,
% 0.51/0.60 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) <=> (addition(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) = multiplication(star(X0!1), X1!0)))),
% 0.51/0.60 inference(quant_inst,[status(thm)],[])).
% 0.51/0.60 tff(37,plain,
% 0.51/0.60 (leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) <=> (addition(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) = multiplication(star(X0!1), X1!0))),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.51/0.60 tff(38,plain,
% 0.51/0.60 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(one, multiplication(X0!1, star(X0!1))), star(X0!1)) <=> (addition(addition(one, multiplication(X0!1, star(X0!1))), star(X0!1)) = star(X0!1)))),
% 0.51/0.60 inference(quant_inst,[status(thm)],[])).
% 0.51/0.60 tff(39,plain,
% 0.51/0.60 (leq(addition(one, multiplication(X0!1, star(X0!1))), star(X0!1)) <=> (addition(addition(one, multiplication(X0!1, star(X0!1))), star(X0!1)) = star(X0!1))),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[38, 35])).
% 0.51/0.60 tff(40,plain,
% 0.51/0.60 (^[A: $i] : refl(leq(addition(one, multiplication(A, star(A))), star(A)) <=> leq(addition(one, multiplication(A, star(A))), star(A)))),
% 0.51/0.60 inference(bind,[status(th)],[])).
% 0.51/0.60 tff(41,plain,
% 0.51/0.60 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 0.51/0.60 inference(quant_intro,[status(thm)],[40])).
% 0.51/0.60 tff(42,plain,
% 0.51/0.60 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 0.51/0.60 inference(rewrite,[status(thm)],[])).
% 0.51/0.60 tff(43,axiom,(![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','star_unfold_right')).
% 0.51/0.60 tff(44,plain,
% 0.51/0.60 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.51/0.60 tff(45,plain,(
% 0.51/0.60 ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 0.51/0.60 inference(skolemize,[status(sab)],[44])).
% 0.51/0.60 tff(46,plain,
% 0.51/0.60 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.51/0.60 tff(47,plain,
% 0.51/0.60 ((~![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))) | leq(addition(one, multiplication(X0!1, star(X0!1))), star(X0!1))),
% 0.51/0.60 inference(quant_inst,[status(thm)],[])).
% 0.51/0.60 tff(48,plain,
% 0.51/0.60 (leq(addition(one, multiplication(X0!1, star(X0!1))), star(X0!1))),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.51/0.60 tff(49,plain,
% 0.51/0.60 ((~(leq(addition(one, multiplication(X0!1, star(X0!1))), star(X0!1)) <=> (addition(addition(one, multiplication(X0!1, star(X0!1))), star(X0!1)) = star(X0!1)))) | (~leq(addition(one, multiplication(X0!1, star(X0!1))), star(X0!1))) | (addition(addition(one, multiplication(X0!1, star(X0!1))), star(X0!1)) = star(X0!1))),
% 0.51/0.60 inference(tautology,[status(thm)],[])).
% 0.51/0.60 tff(50,plain,
% 0.51/0.60 ((~(leq(addition(one, multiplication(X0!1, star(X0!1))), star(X0!1)) <=> (addition(addition(one, multiplication(X0!1, star(X0!1))), star(X0!1)) = star(X0!1)))) | (addition(addition(one, multiplication(X0!1, star(X0!1))), star(X0!1)) = star(X0!1))),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.51/0.60 tff(51,plain,
% 0.51/0.60 (addition(addition(one, multiplication(X0!1, star(X0!1))), star(X0!1)) = star(X0!1)),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[50, 39])).
% 0.51/0.60 tff(52,plain,
% 0.51/0.60 (^[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)))),
% 0.51/0.60 inference(bind,[status(th)],[])).
% 0.51/0.60 tff(53,plain,
% 0.51/0.60 (![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))),
% 0.51/0.60 inference(quant_intro,[status(thm)],[52])).
% 0.51/0.60 tff(54,plain,
% 0.51/0.60 (![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))),
% 0.51/0.60 inference(rewrite,[status(thm)],[])).
% 0.51/0.60 tff(55,axiom,(![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','additive_associativity')).
% 0.51/0.60 tff(56,plain,
% 0.51/0.60 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.51/0.60 tff(57,plain,(
% 0.51/0.60 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.51/0.60 inference(skolemize,[status(sab)],[56])).
% 0.51/0.60 tff(58,plain,
% 0.51/0.60 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.51/0.60 tff(59,plain,
% 0.51/0.60 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(multiplication(X0!1, star(X0!1)), star(X0!1))) = addition(addition(one, multiplication(X0!1, star(X0!1))), star(X0!1)))),
% 0.51/0.60 inference(quant_inst,[status(thm)],[])).
% 0.51/0.60 tff(60,plain,
% 0.51/0.60 (addition(one, addition(multiplication(X0!1, star(X0!1)), star(X0!1))) = addition(addition(one, multiplication(X0!1, star(X0!1))), star(X0!1))),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.51/0.60 tff(61,plain,
% 0.51/0.60 (addition(one, addition(multiplication(X0!1, star(X0!1)), star(X0!1))) = star(X0!1)),
% 0.51/0.60 inference(transitivity,[status(thm)],[60, 51])).
% 0.51/0.60 tff(62,plain,
% 0.51/0.60 (multiplication(addition(one, addition(multiplication(X0!1, star(X0!1)), star(X0!1))), X1!0) = multiplication(star(X0!1), X1!0)),
% 0.51/0.60 inference(monotonicity,[status(thm)],[61])).
% 0.51/0.60 tff(63,plain,
% 0.51/0.60 (^[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))))),
% 0.51/0.60 inference(bind,[status(th)],[])).
% 0.51/0.60 tff(64,plain,
% 0.51/0.60 (![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)))),
% 0.51/0.60 inference(quant_intro,[status(thm)],[63])).
% 0.51/0.60 tff(65,plain,
% 0.51/0.60 (![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)))),
% 0.51/0.60 inference(rewrite,[status(thm)],[])).
% 0.51/0.60 tff(66,axiom,(![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','left_distributivity')).
% 0.51/0.60 tff(67,plain,
% 0.51/0.60 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.51/0.60 tff(68,plain,(
% 0.51/0.60 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.51/0.60 inference(skolemize,[status(sab)],[67])).
% 0.51/0.60 tff(69,plain,
% 0.51/0.60 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.51/0.60 tff(70,plain,
% 0.51/0.60 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(one, addition(multiplication(X0!1, star(X0!1)), star(X0!1))), X1!0) = addition(multiplication(one, X1!0), multiplication(addition(multiplication(X0!1, star(X0!1)), star(X0!1)), X1!0)))),
% 0.51/0.60 inference(quant_inst,[status(thm)],[])).
% 0.51/0.60 tff(71,plain,
% 0.51/0.60 (multiplication(addition(one, addition(multiplication(X0!1, star(X0!1)), star(X0!1))), X1!0) = addition(multiplication(one, X1!0), multiplication(addition(multiplication(X0!1, star(X0!1)), star(X0!1)), X1!0))),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.51/0.60 tff(72,plain,
% 0.51/0.60 (addition(multiplication(one, X1!0), multiplication(addition(multiplication(X0!1, star(X0!1)), star(X0!1)), X1!0)) = multiplication(addition(one, addition(multiplication(X0!1, star(X0!1)), star(X0!1))), X1!0)),
% 0.51/0.60 inference(symmetry,[status(thm)],[71])).
% 0.51/0.60 tff(73,plain,
% 0.51/0.60 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(multiplication(X0!1, star(X0!1)), star(X0!1)), X1!0) = addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), multiplication(star(X0!1), X1!0)))),
% 0.51/0.60 inference(quant_inst,[status(thm)],[])).
% 0.51/0.60 tff(74,plain,
% 0.51/0.60 (multiplication(addition(multiplication(X0!1, star(X0!1)), star(X0!1)), X1!0) = addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), multiplication(star(X0!1), X1!0))),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[73, 69])).
% 0.51/0.60 tff(75,plain,
% 0.51/0.60 (addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), multiplication(star(X0!1), X1!0)) = multiplication(addition(multiplication(X0!1, star(X0!1)), star(X0!1)), X1!0)),
% 0.51/0.60 inference(symmetry,[status(thm)],[74])).
% 0.51/0.60 tff(76,plain,
% 0.51/0.60 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 0.51/0.60 inference(bind,[status(th)],[])).
% 0.51/0.60 tff(77,plain,
% 0.51/0.60 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.51/0.60 inference(quant_intro,[status(thm)],[76])).
% 0.51/0.60 tff(78,plain,
% 0.51/0.60 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.51/0.60 inference(rewrite,[status(thm)],[])).
% 0.51/0.60 tff(79,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','multiplicative_left_identity')).
% 0.51/0.60 tff(80,plain,
% 0.51/0.60 (![A: $i] : (multiplication(one, A) = A)),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.51/0.60 tff(81,plain,(
% 0.51/0.60 ![A: $i] : (multiplication(one, A) = A)),
% 0.51/0.60 inference(skolemize,[status(sab)],[80])).
% 0.51/0.60 tff(82,plain,
% 0.51/0.60 (![A: $i] : (multiplication(one, A) = A)),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.51/0.60 tff(83,plain,
% 0.51/0.60 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X1!0) = X1!0)),
% 0.51/0.60 inference(quant_inst,[status(thm)],[])).
% 0.51/0.60 tff(84,plain,
% 0.51/0.60 (multiplication(one, X1!0) = X1!0),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.51/0.60 tff(85,plain,
% 0.51/0.60 (X1!0 = multiplication(one, X1!0)),
% 0.51/0.60 inference(symmetry,[status(thm)],[84])).
% 0.51/0.60 tff(86,plain,
% 0.51/0.60 (addition(X1!0, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), multiplication(star(X0!1), X1!0))) = addition(multiplication(one, X1!0), multiplication(addition(multiplication(X0!1, star(X0!1)), star(X0!1)), X1!0))),
% 0.51/0.60 inference(monotonicity,[status(thm)],[85, 75])).
% 0.51/0.60 tff(87,plain,
% 0.51/0.60 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X1!0, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), multiplication(star(X0!1), X1!0))) = addition(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)))),
% 0.51/0.60 inference(quant_inst,[status(thm)],[])).
% 0.51/0.60 tff(88,plain,
% 0.51/0.60 (addition(X1!0, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), multiplication(star(X0!1), X1!0))) = addition(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0))),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[87, 58])).
% 0.51/0.60 tff(89,plain,
% 0.51/0.60 (addition(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) = addition(X1!0, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), multiplication(star(X0!1), X1!0)))),
% 0.51/0.60 inference(symmetry,[status(thm)],[88])).
% 0.51/0.60 tff(90,plain,
% 0.51/0.60 (addition(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) = multiplication(star(X0!1), X1!0)),
% 0.51/0.60 inference(transitivity,[status(thm)],[89, 86, 72, 62])).
% 0.51/0.60 tff(91,assumption,(~leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0))), introduced(assumption)).
% 0.51/0.60 tff(92,plain,
% 0.51/0.60 ((~(leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) <=> (addition(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) = multiplication(star(X0!1), X1!0)))) | leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) | (~(addition(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) = multiplication(star(X0!1), X1!0)))),
% 0.51/0.60 inference(tautology,[status(thm)],[])).
% 0.51/0.60 tff(93,plain,
% 0.51/0.60 ((~(leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) <=> (addition(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) = multiplication(star(X0!1), X1!0)))) | (~(addition(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) = multiplication(star(X0!1), X1!0)))),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.51/0.60 tff(94,plain,
% 0.51/0.60 (~(addition(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) = multiplication(star(X0!1), X1!0))),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[93, 37])).
% 0.51/0.60 tff(95,plain,
% 0.51/0.60 ($false),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[94, 90])).
% 0.51/0.60 tff(96,plain,(leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.60 tff(97,plain,
% 0.51/0.60 ((~(leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) <=> (addition(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) = multiplication(star(X0!1), X1!0)))) | (~leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0))) | (addition(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) = multiplication(star(X0!1), X1!0))),
% 0.51/0.60 inference(tautology,[status(thm)],[])).
% 0.51/0.60 tff(98,plain,
% 0.51/0.60 ((~(leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) <=> (addition(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) = multiplication(star(X0!1), X1!0)))) | (addition(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) = multiplication(star(X0!1), X1!0))),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.51/0.60 tff(99,plain,
% 0.51/0.60 (addition(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) = multiplication(star(X0!1), X1!0)),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[98, 37])).
% 0.51/0.60 tff(100,plain,
% 0.51/0.60 (multiplication(star(X0!1), X1!0) = addition(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0))),
% 0.51/0.60 inference(symmetry,[status(thm)],[99])).
% 0.51/0.60 tff(101,plain,
% 0.51/0.60 (multiplication(star(X0!1), X1!0) = addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), multiplication(star(X0!1), X1!0))),
% 0.51/0.60 inference(transitivity,[status(thm)],[100, 28])).
% 0.51/0.60 tff(102,plain,
% 0.51/0.60 (multiplication(X0!1, multiplication(star(X0!1), X1!0)) = multiplication(X0!1, addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), multiplication(star(X0!1), X1!0)))),
% 0.51/0.60 inference(monotonicity,[status(thm)],[101])).
% 0.51/0.60 tff(103,plain,
% 0.51/0.60 (multiplication(X0!1, addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), multiplication(star(X0!1), X1!0))) = multiplication(X0!1, multiplication(star(X0!1), X1!0))),
% 0.51/0.60 inference(symmetry,[status(thm)],[102])).
% 0.51/0.60 tff(104,plain,
% 0.51/0.60 (^[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))))),
% 0.51/0.60 inference(bind,[status(th)],[])).
% 0.51/0.60 tff(105,plain,
% 0.51/0.60 (![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)))),
% 0.51/0.60 inference(quant_intro,[status(thm)],[104])).
% 0.51/0.60 tff(106,plain,
% 0.51/0.60 (![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)))),
% 0.51/0.60 inference(rewrite,[status(thm)],[])).
% 0.51/0.60 tff(107,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','right_distributivity')).
% 0.51/0.60 tff(108,plain,
% 0.51/0.60 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.51/0.60 tff(109,plain,(
% 0.51/0.60 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.51/0.60 inference(skolemize,[status(sab)],[108])).
% 0.51/0.60 tff(110,plain,
% 0.51/0.60 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.51/0.61 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.51/0.61 tff(111,plain,
% 0.51/0.61 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!1, addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), multiplication(star(X0!1), X1!0))) = addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))),
% 0.51/0.61 inference(quant_inst,[status(thm)],[])).
% 0.51/0.61 tff(112,plain,
% 0.51/0.61 (multiplication(X0!1, addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), multiplication(star(X0!1), X1!0))) = addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))),
% 0.51/0.61 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.51/0.61 tff(113,plain,
% 0.51/0.61 (addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))) = multiplication(X0!1, addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), multiplication(star(X0!1), X1!0)))),
% 0.51/0.61 inference(symmetry,[status(thm)],[112])).
% 0.51/0.61 tff(114,plain,
% 0.51/0.61 (addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))) = multiplication(multiplication(X0!1, star(X0!1)), X1!0)),
% 0.51/0.61 inference(transitivity,[status(thm)],[113, 103, 27])).
% 0.51/0.61 tff(115,plain,
% 0.51/0.61 (addition(X1!0, addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))) = addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))),
% 0.51/0.61 inference(monotonicity,[status(thm)],[114])).
% 0.51/0.61 tff(116,plain,
% 0.51/0.61 (addition(X1!0, addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))) = addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)),
% 0.51/0.61 inference(transitivity,[status(thm)],[115, 18])).
% 0.51/0.61 tff(117,plain,
% 0.51/0.61 (addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), addition(X1!0, addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))) = addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0))),
% 0.51/0.61 inference(monotonicity,[status(thm)],[116])).
% 0.51/0.61 tff(118,plain,
% 0.51/0.61 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), addition(X1!0, addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))) = addition(addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), X1!0), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))))),
% 0.51/0.61 inference(quant_inst,[status(thm)],[])).
% 0.51/0.61 tff(119,plain,
% 0.51/0.61 (addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), addition(X1!0, addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))) = addition(addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), X1!0), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))),
% 0.51/0.61 inference(unit_resolution,[status(thm)],[118, 58])).
% 0.51/0.61 tff(120,plain,
% 0.51/0.61 (addition(addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), X1!0), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))) = addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), addition(X1!0, addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))))),
% 0.51/0.61 inference(symmetry,[status(thm)],[119])).
% 0.51/0.61 tff(121,plain,
% 0.51/0.61 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))) = addition(multiplication(X0!1, X1!0), multiplication(X0!1, multiplication(multiplication(X0!1, star(X0!1)), X1!0))))),
% 0.51/0.61 inference(quant_inst,[status(thm)],[])).
% 0.51/0.61 tff(122,plain,
% 0.51/0.61 (multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))) = addition(multiplication(X0!1, X1!0), multiplication(X0!1, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))),
% 0.51/0.61 inference(unit_resolution,[status(thm)],[121, 110])).
% 0.51/0.61 tff(123,plain,
% 0.51/0.61 (addition(multiplication(X0!1, X1!0), multiplication(X0!1, multiplication(multiplication(X0!1, star(X0!1)), X1!0))) = multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))),
% 0.51/0.61 inference(symmetry,[status(thm)],[122])).
% 0.51/0.61 tff(124,plain,
% 0.51/0.61 (addition(X1!0, addition(multiplication(X0!1, X1!0), multiplication(X0!1, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))) = addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))))),
% 0.51/0.61 inference(monotonicity,[status(thm)],[123])).
% 0.51/0.61 tff(125,plain,
% 0.51/0.61 (addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))) = addition(X1!0, addition(multiplication(X0!1, X1!0), multiplication(X0!1, multiplication(multiplication(X0!1, star(X0!1)), X1!0))))),
% 0.51/0.61 inference(symmetry,[status(thm)],[124])).
% 0.51/0.61 tff(126,plain,
% 0.51/0.61 (addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))) = addition(addition(X1!0, addition(multiplication(X0!1, X1!0), multiplication(X0!1, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))),
% 0.51/0.61 inference(monotonicity,[status(thm)],[125])).
% 0.51/0.61 tff(127,plain,
% 0.51/0.61 (addition(addition(X1!0, addition(multiplication(X0!1, X1!0), multiplication(X0!1, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))) = addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))),
% 0.51/0.61 inference(symmetry,[status(thm)],[126])).
% 0.51/0.61 tff(128,plain,
% 0.51/0.61 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X1!0, addition(addition(multiplication(X0!1, X1!0), multiplication(X0!1, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))) = addition(addition(X1!0, addition(multiplication(X0!1, X1!0), multiplication(X0!1, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))))),
% 0.51/0.61 inference(quant_inst,[status(thm)],[])).
% 0.51/0.61 tff(129,plain,
% 0.51/0.61 (addition(X1!0, addition(addition(multiplication(X0!1, X1!0), multiplication(X0!1, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))) = addition(addition(X1!0, addition(multiplication(X0!1, X1!0), multiplication(X0!1, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))),
% 0.51/0.61 inference(unit_resolution,[status(thm)],[128, 58])).
% 0.51/0.61 tff(130,plain,
% 0.51/0.61 (addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))) = multiplication(X0!1, multiplication(star(X0!1), X1!0))),
% 0.51/0.61 inference(transitivity,[status(thm)],[113, 103])).
% 0.51/0.61 tff(131,plain,
% 0.51/0.61 (addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0) = addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))),
% 0.51/0.61 inference(symmetry,[status(thm)],[18])).
% 0.51/0.61 tff(132,plain,
% 0.51/0.61 (multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) = multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))),
% 0.51/0.61 inference(monotonicity,[status(thm)],[131])).
% 0.51/0.61 tff(133,plain,
% 0.51/0.61 (multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))) = multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0))),
% 0.51/0.61 inference(symmetry,[status(thm)],[132])).
% 0.51/0.61 tff(134,plain,
% 0.51/0.61 (addition(multiplication(X0!1, X1!0), multiplication(X0!1, multiplication(multiplication(X0!1, star(X0!1)), X1!0))) = multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0))),
% 0.51/0.61 inference(transitivity,[status(thm)],[123, 133])).
% 0.51/0.61 tff(135,plain,
% 0.51/0.61 (addition(addition(multiplication(X0!1, X1!0), multiplication(X0!1, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))) = addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))),
% 0.51/0.61 inference(monotonicity,[status(thm)],[134, 130])).
% 0.51/0.61 tff(136,plain,
% 0.51/0.61 (addition(addition(multiplication(X0!1, X1!0), multiplication(X0!1, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))) = multiplication(multiplication(X0!1, star(X0!1)), X1!0)),
% 0.51/0.61 inference(transitivity,[status(thm)],[135, 113, 103, 27])).
% 0.51/0.61 tff(137,plain,
% 0.51/0.61 (addition(X1!0, addition(addition(multiplication(X0!1, X1!0), multiplication(X0!1, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))) = addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))),
% 0.51/0.61 inference(monotonicity,[status(thm)],[136])).
% 0.51/0.61 tff(138,plain,
% 0.51/0.61 (addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)) = addition(X1!0, addition(addition(multiplication(X0!1, X1!0), multiplication(X0!1, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))))),
% 0.51/0.61 inference(symmetry,[status(thm)],[137])).
% 0.51/0.61 tff(139,plain,
% 0.51/0.61 (addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0) = addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))),
% 0.51/0.61 inference(transitivity,[status(thm)],[131, 138, 129, 127])).
% 0.51/0.61 tff(140,plain,
% 0.51/0.61 (addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), X1!0) = addition(addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))), X1!0)),
% 0.51/0.61 inference(monotonicity,[status(thm)],[139])).
% 0.51/0.61 tff(141,plain,
% 0.51/0.61 (addition(addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))), X1!0) = addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), X1!0)),
% 0.51/0.61 inference(symmetry,[status(thm)],[140])).
% 0.51/0.61 tff(142,plain,
% 0.51/0.61 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))), X1!0)) = addition(addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))), X1!0))),
% 0.51/0.61 inference(quant_inst,[status(thm)],[])).
% 0.51/0.61 tff(143,plain,
% 0.51/0.61 (addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))), X1!0)) = addition(addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))), X1!0)),
% 0.51/0.61 inference(unit_resolution,[status(thm)],[142, 58])).
% 0.51/0.61 tff(144,plain,
% 0.51/0.61 (addition(addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))), X1!0) = addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)),
% 0.51/0.61 inference(monotonicity,[status(thm)],[114])).
% 0.51/0.61 tff(145,plain,
% 0.51/0.61 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0) = addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))))),
% 0.51/0.61 inference(quant_inst,[status(thm)],[])).
% 0.51/0.61 tff(146,plain,
% 0.51/0.61 (addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0) = addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))))),
% 0.51/0.61 inference(unit_resolution,[status(thm)],[145, 16])).
% 0.51/0.61 tff(147,plain,
% 0.51/0.61 (addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))) = addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0)),
% 0.51/0.61 inference(symmetry,[status(thm)],[146])).
% 0.51/0.61 tff(148,plain,
% 0.51/0.61 (addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))), X1!0)) = addition(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0))),
% 0.51/0.61 inference(monotonicity,[status(thm)],[147, 144])).
% 0.51/0.61 tff(149,plain,
% 0.51/0.61 (addition(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) = addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))), X1!0))),
% 0.51/0.61 inference(symmetry,[status(thm)],[148])).
% 0.51/0.61 tff(150,plain,
% 0.51/0.61 (addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)) = addition(X1!0, addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))),
% 0.51/0.61 inference(symmetry,[status(thm)],[115])).
% 0.51/0.61 tff(151,plain,
% 0.51/0.61 (addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0) = addition(X1!0, addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))),
% 0.51/0.61 inference(transitivity,[status(thm)],[131, 150])).
% 0.51/0.61 tff(152,plain,
% 0.51/0.61 (addition(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) = addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(X1!0, addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))))),
% 0.51/0.61 inference(monotonicity,[status(thm)],[146, 151])).
% 0.51/0.61 tff(153,plain,
% 0.51/0.61 (addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(X1!0, addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))) = addition(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0))),
% 0.51/0.61 inference(symmetry,[status(thm)],[152])).
% 0.51/0.61 tff(154,plain,
% 0.51/0.61 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(X1!0, addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))) = addition(addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), X1!0), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))))),
% 0.51/0.61 inference(quant_inst,[status(thm)],[])).
% 0.51/0.61 tff(155,plain,
% 0.51/0.61 (addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(X1!0, addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))) = addition(addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), X1!0), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))),
% 0.51/0.61 inference(unit_resolution,[status(thm)],[154, 58])).
% 0.51/0.61 tff(156,plain,
% 0.51/0.62 (addition(addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), X1!0), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))) = addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(X1!0, addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))))),
% 0.51/0.62 inference(symmetry,[status(thm)],[155])).
% 0.51/0.62 tff(157,plain,
% 0.51/0.62 (addition(addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), X1!0), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))) = addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), X1!0)),
% 0.51/0.62 inference(transitivity,[status(thm)],[156, 153, 149, 143, 141])).
% 0.51/0.62 tff(158,plain,
% 0.51/0.62 (addition(addition(addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), X1!0), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))) = addition(addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), X1!0), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))),
% 0.51/0.62 inference(monotonicity,[status(thm)],[157])).
% 0.51/0.62 tff(159,plain,
% 0.51/0.62 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), X1!0), addition(addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))) = addition(addition(addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), X1!0), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))))),
% 0.51/0.62 inference(quant_inst,[status(thm)],[])).
% 0.51/0.62 tff(160,plain,
% 0.51/0.62 (addition(addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), X1!0), addition(addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))) = addition(addition(addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), X1!0), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))),
% 0.51/0.62 inference(unit_resolution,[status(thm)],[159, 58])).
% 0.51/0.62 tff(161,plain,
% 0.51/0.62 ((~![A: $i] : (addition(A, A) = A)) | (addition(addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))) = addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))),
% 0.51/0.62 inference(quant_inst,[status(thm)],[])).
% 0.51/0.62 tff(162,plain,
% 0.51/0.62 (addition(addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))) = addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))),
% 0.51/0.62 inference(unit_resolution,[status(thm)],[161, 7])).
% 0.51/0.62 tff(163,plain,
% 0.51/0.62 (addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))) = addition(addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))),
% 0.51/0.62 inference(symmetry,[status(thm)],[162])).
% 0.51/0.62 tff(164,plain,
% 0.51/0.62 (addition(addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), X1!0), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))) = addition(addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), X1!0), addition(addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))))),
% 0.51/0.62 inference(monotonicity,[status(thm)],[163])).
% 0.51/0.62 tff(165,plain,
% 0.51/0.62 (addition(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) = addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)),
% 0.51/0.62 inference(transitivity,[status(thm)],[152, 155, 164, 160, 158, 120, 117, 9])).
% 0.51/0.62 tff(166,plain,
% 0.51/0.62 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) <=> (addition(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) = addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)))),
% 0.51/0.62 inference(quant_inst,[status(thm)],[])).
% 0.51/0.62 tff(167,plain,
% 0.51/0.62 (leq(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) <=> (addition(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) = addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0))),
% 0.51/0.62 inference(unit_resolution,[status(thm)],[166, 35])).
% 0.51/0.62 tff(168,plain,
% 0.51/0.62 (leq(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) <=> leq(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))),
% 0.51/0.62 inference(monotonicity,[status(thm)],[131])).
% 0.51/0.62 tff(169,plain,
% 0.51/0.62 (leq(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))) <=> leq(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0))),
% 0.51/0.62 inference(symmetry,[status(thm)],[168])).
% 0.51/0.62 tff(170,plain,
% 0.51/0.62 ((~leq(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))) <=> (~leq(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)))),
% 0.51/0.62 inference(monotonicity,[status(thm)],[169])).
% 0.51/0.62 tff(171,plain,
% 0.51/0.62 ((~(~((~leq(multiplication(star(X0!1), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))) | (~leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)))))) <=> ((~leq(multiplication(star(X0!1), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))) | (~leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0))))),
% 0.51/0.62 inference(rewrite,[status(thm)],[])).
% 0.51/0.62 tff(172,plain,
% 0.51/0.62 ((leq(multiplication(star(X0!1), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))) & leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0))) <=> (~((~leq(multiplication(star(X0!1), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))) | (~leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)))))),
% 0.51/0.62 inference(rewrite,[status(thm)],[])).
% 0.51/0.62 tff(173,plain,
% 0.51/0.62 ((~(leq(multiplication(star(X0!1), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))) & leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)))) <=> (~(~((~leq(multiplication(star(X0!1), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))) | (~leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0))))))),
% 0.51/0.62 inference(monotonicity,[status(thm)],[172])).
% 0.51/0.62 tff(174,plain,
% 0.51/0.62 ((~(leq(multiplication(star(X0!1), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))) & leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)))) <=> ((~leq(multiplication(star(X0!1), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))) | (~leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0))))),
% 0.51/0.62 inference(transitivity,[status(thm)],[173, 171])).
% 0.51/0.62 tff(175,plain,
% 0.51/0.62 ((~![X0: $i, X1: $i] : (leq(multiplication(star(X0), X1), addition(X1, multiplication(multiplication(X0, star(X0)), X1))) & leq(addition(X1, multiplication(multiplication(X0, star(X0)), X1)), multiplication(star(X0), X1)))) <=> (~![X0: $i, X1: $i] : (leq(multiplication(star(X0), X1), addition(X1, multiplication(multiplication(X0, star(X0)), X1))) & leq(addition(X1, multiplication(multiplication(X0, star(X0)), X1)), multiplication(star(X0), X1))))),
% 0.51/0.62 inference(rewrite,[status(thm)],[])).
% 0.51/0.62 tff(176,axiom,(~![X0: $i, X1: $i] : (leq(multiplication(star(X0), X1), addition(X1, multiplication(multiplication(X0, star(X0)), X1))) & leq(addition(X1, multiplication(multiplication(X0, star(X0)), X1)), multiplication(star(X0), X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 0.51/0.62 tff(177,plain,
% 0.51/0.62 (~![X0: $i, X1: $i] : (leq(multiplication(star(X0), X1), addition(X1, multiplication(multiplication(X0, star(X0)), X1))) & leq(addition(X1, multiplication(multiplication(X0, star(X0)), X1)), multiplication(star(X0), X1)))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.51/0.62 tff(178,plain,
% 0.51/0.62 (~![X0: $i, X1: $i] : (leq(multiplication(star(X0), X1), addition(X1, multiplication(multiplication(X0, star(X0)), X1))) & leq(addition(X1, multiplication(multiplication(X0, star(X0)), X1)), multiplication(star(X0), X1)))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[177, 175])).
% 0.51/0.62 tff(179,plain,
% 0.51/0.62 (~![X0: $i, X1: $i] : (leq(multiplication(star(X0), X1), addition(X1, multiplication(multiplication(X0, star(X0)), X1))) & leq(addition(X1, multiplication(multiplication(X0, star(X0)), X1)), multiplication(star(X0), X1)))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[178, 175])).
% 0.51/0.62 tff(180,plain,
% 0.51/0.62 (~![X0: $i, X1: $i] : (leq(multiplication(star(X0), X1), addition(X1, multiplication(multiplication(X0, star(X0)), X1))) & leq(addition(X1, multiplication(multiplication(X0, star(X0)), X1)), multiplication(star(X0), X1)))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[179, 175])).
% 0.51/0.62 tff(181,plain,
% 0.51/0.62 (~![X0: $i, X1: $i] : (leq(multiplication(star(X0), X1), addition(X1, multiplication(multiplication(X0, star(X0)), X1))) & leq(addition(X1, multiplication(multiplication(X0, star(X0)), X1)), multiplication(star(X0), X1)))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[180, 175])).
% 0.51/0.62 tff(182,plain,
% 0.51/0.62 (~![X0: $i, X1: $i] : (leq(multiplication(star(X0), X1), addition(X1, multiplication(multiplication(X0, star(X0)), X1))) & leq(addition(X1, multiplication(multiplication(X0, star(X0)), X1)), multiplication(star(X0), X1)))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[181, 175])).
% 0.51/0.62 tff(183,plain,
% 0.51/0.62 (~![X0: $i, X1: $i] : (leq(multiplication(star(X0), X1), addition(X1, multiplication(multiplication(X0, star(X0)), X1))) & leq(addition(X1, multiplication(multiplication(X0, star(X0)), X1)), multiplication(star(X0), X1)))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[182, 175])).
% 0.51/0.62 tff(184,plain,(
% 0.51/0.62 ~(leq(multiplication(star(X0!1), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))) & leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)))),
% 0.51/0.62 inference(skolemize,[status(sab)],[183])).
% 0.51/0.62 tff(185,plain,
% 0.51/0.62 ((~leq(multiplication(star(X0!1), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))) | (~leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[184, 174])).
% 0.51/0.62 tff(186,plain,
% 0.51/0.62 (~leq(multiplication(star(X0!1), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))),
% 0.51/0.62 inference(unit_resolution,[status(thm)],[185, 96])).
% 0.51/0.62 tff(187,plain,
% 0.51/0.62 (^[A: $i, B: $i, C: $i] : refl(((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B)) <=> ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B)))),
% 0.51/0.62 inference(bind,[status(th)],[])).
% 0.51/0.62 tff(188,plain,
% 0.51/0.62 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 0.51/0.62 inference(quant_intro,[status(thm)],[187])).
% 0.51/0.62 tff(189,plain,
% 0.51/0.62 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 0.51/0.62 inference(rewrite,[status(thm)],[])).
% 0.51/0.62 tff(190,plain,
% 0.51/0.62 (^[A: $i, B: $i, C: $i] : rewrite((leq(addition(multiplication(A, B), C), B) => leq(multiplication(star(A), C), B)) <=> ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B)))),
% 0.51/0.62 inference(bind,[status(th)],[])).
% 0.51/0.62 tff(191,plain,
% 0.51/0.62 (![A: $i, B: $i, C: $i] : (leq(addition(multiplication(A, B), C), B) => leq(multiplication(star(A), C), B)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 0.51/0.62 inference(quant_intro,[status(thm)],[190])).
% 0.51/0.62 tff(192,axiom,(![A: $i, B: $i, C: $i] : (leq(addition(multiplication(A, B), C), B) => leq(multiplication(star(A), C), B))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','star_induction_left')).
% 0.51/0.62 tff(193,plain,
% 0.51/0.62 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.51/0.62 tff(194,plain,
% 0.51/0.62 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[193, 189])).
% 0.51/0.62 tff(195,plain,(
% 0.51/0.62 ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 0.51/0.62 inference(skolemize,[status(sab)],[194])).
% 0.51/0.62 tff(196,plain,
% 0.51/0.62 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[195, 188])).
% 0.51/0.62 tff(197,plain,
% 0.51/0.62 (((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | ((~leq(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))) | leq(multiplication(star(X0!1), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))))) <=> ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | (~leq(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))) | leq(multiplication(star(X0!1), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))))),
% 0.51/0.62 inference(rewrite,[status(thm)],[])).
% 0.51/0.62 tff(198,plain,
% 0.51/0.62 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | ((~leq(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))) | leq(multiplication(star(X0!1), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))))),
% 0.51/0.62 inference(quant_inst,[status(thm)],[])).
% 0.51/0.62 tff(199,plain,
% 0.51/0.62 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | (~leq(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))) | leq(multiplication(star(X0!1), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.51/0.62 tff(200,plain,
% 0.51/0.62 (~leq(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))),
% 0.51/0.62 inference(unit_resolution,[status(thm)],[199, 196, 186])).
% 0.51/0.62 tff(201,plain,
% 0.51/0.62 (~leq(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[200, 170])).
% 0.51/0.62 tff(202,plain,
% 0.51/0.62 ((~(leq(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) <=> (addition(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) = addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)))) | leq(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) | (~(addition(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) = addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)))),
% 0.60/0.63 inference(tautology,[status(thm)],[])).
% 0.60/0.63 tff(203,plain,
% 0.60/0.63 (~(addition(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) = addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0))),
% 0.60/0.63 inference(unit_resolution,[status(thm)],[202, 201, 167])).
% 0.60/0.63 tff(204,plain,
% 0.60/0.63 ($false),
% 0.60/0.63 inference(unit_resolution,[status(thm)],[203, 165])).
% 0.60/0.63 % SZS output end Proof
%------------------------------------------------------------------------------