TSTP Solution File: KLE045+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE045+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 17:24:00 EDT 2022
% Result : Theorem 12.30s 8.12s
% Output : Proof 12.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE045+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n015.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 08:14:37 EDT 2022
% 0.13/0.34 % 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.
% 12.30/8.12 % SZS status Theorem
% 12.30/8.12 % SZS output start Proof
% 12.30/8.12 tff(multiplication_type, type, (
% 12.30/8.12 multiplication: ( $i * $i ) > $i)).
% 12.30/8.12 tff(star_type, type, (
% 12.30/8.12 star: $i > $i)).
% 12.30/8.12 tff(tptp_fun_X1_1_type, type, (
% 12.30/8.12 tptp_fun_X1_1: $i)).
% 12.30/8.12 tff(tptp_fun_X2_0_type, type, (
% 12.30/8.12 tptp_fun_X2_0: $i)).
% 12.30/8.12 tff(addition_type, type, (
% 12.30/8.12 addition: ( $i * $i ) > $i)).
% 12.30/8.12 tff(tptp_fun_X0_2_type, type, (
% 12.30/8.12 tptp_fun_X0_2: $i)).
% 12.30/8.12 tff(one_type, type, (
% 12.30/8.12 one: $i)).
% 12.30/8.12 tff(leq_type, type, (
% 12.30/8.12 leq: ( $i * $i ) > $o)).
% 12.30/8.12 tff(1,plain,
% 12.30/8.12 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 12.30/8.12 inference(bind,[status(th)],[])).
% 12.30/8.12 tff(2,plain,
% 12.30/8.12 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 12.30/8.12 inference(quant_intro,[status(thm)],[1])).
% 12.30/8.12 tff(3,plain,
% 12.30/8.12 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 12.30/8.12 inference(rewrite,[status(thm)],[])).
% 12.30/8.12 tff(4,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','additive_commutativity')).
% 12.30/8.12 tff(5,plain,
% 12.30/8.12 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 12.30/8.12 inference(modus_ponens,[status(thm)],[4, 3])).
% 12.30/8.12 tff(6,plain,(
% 12.30/8.12 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 12.30/8.12 inference(skolemize,[status(sab)],[5])).
% 12.30/8.12 tff(7,plain,
% 12.30/8.12 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 12.30/8.12 inference(modus_ponens,[status(thm)],[6, 2])).
% 12.30/8.12 tff(8,plain,
% 12.30/8.12 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, multiplication(X1!1, star(X1!1))) = addition(multiplication(X1!1, star(X1!1)), one))),
% 12.30/8.12 inference(quant_inst,[status(thm)],[])).
% 12.30/8.12 tff(9,plain,
% 12.30/8.12 (addition(one, multiplication(X1!1, star(X1!1))) = addition(multiplication(X1!1, star(X1!1)), one)),
% 12.30/8.12 inference(unit_resolution,[status(thm)],[8, 7])).
% 12.30/8.12 tff(10,plain,
% 12.30/8.12 (addition(multiplication(X1!1, star(X1!1)), one) = addition(one, multiplication(X1!1, star(X1!1)))),
% 12.30/8.12 inference(symmetry,[status(thm)],[9])).
% 12.30/8.12 tff(11,plain,
% 12.30/8.12 (addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1)) = addition(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1))),
% 12.30/8.12 inference(monotonicity,[status(thm)],[10])).
% 12.30/8.12 tff(12,plain,
% 12.30/8.12 (addition(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1)) = addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1))),
% 12.30/8.12 inference(symmetry,[status(thm)],[11])).
% 12.30/8.12 tff(13,plain,
% 12.30/8.12 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 12.30/8.12 inference(bind,[status(th)],[])).
% 12.30/8.12 tff(14,plain,
% 12.30/8.12 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 12.30/8.12 inference(quant_intro,[status(thm)],[13])).
% 12.30/8.12 tff(15,plain,
% 12.30/8.12 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 12.30/8.12 inference(rewrite,[status(thm)],[])).
% 12.30/8.12 tff(16,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','order')).
% 12.30/8.12 tff(17,plain,
% 12.30/8.12 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 12.30/8.12 inference(modus_ponens,[status(thm)],[16, 15])).
% 12.30/8.12 tff(18,plain,(
% 12.30/8.12 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 12.30/8.12 inference(skolemize,[status(sab)],[17])).
% 12.30/8.12 tff(19,plain,
% 12.30/8.12 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 12.30/8.12 inference(modus_ponens,[status(thm)],[18, 14])).
% 12.30/8.12 tff(20,plain,
% 12.30/8.12 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1)) <=> (addition(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1)) = star(X1!1)))),
% 12.30/8.12 inference(quant_inst,[status(thm)],[])).
% 12.30/8.12 tff(21,plain,
% 12.30/8.12 (leq(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1)) <=> (addition(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1)) = star(X1!1))),
% 12.30/8.12 inference(unit_resolution,[status(thm)],[20, 19])).
% 12.30/8.12 tff(22,plain,
% 12.30/8.12 (^[A: $i] : refl(leq(addition(one, multiplication(A, star(A))), star(A)) <=> leq(addition(one, multiplication(A, star(A))), star(A)))),
% 12.30/8.12 inference(bind,[status(th)],[])).
% 12.30/8.12 tff(23,plain,
% 12.30/8.12 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 12.30/8.12 inference(quant_intro,[status(thm)],[22])).
% 12.30/8.12 tff(24,plain,
% 12.30/8.12 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 12.30/8.12 inference(rewrite,[status(thm)],[])).
% 12.30/8.12 tff(25,axiom,(![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','star_unfold_right')).
% 12.30/8.12 tff(26,plain,
% 12.30/8.12 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 12.30/8.12 inference(modus_ponens,[status(thm)],[25, 24])).
% 12.30/8.12 tff(27,plain,(
% 12.30/8.12 ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 12.30/8.12 inference(skolemize,[status(sab)],[26])).
% 12.30/8.12 tff(28,plain,
% 12.30/8.12 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 12.30/8.12 inference(modus_ponens,[status(thm)],[27, 23])).
% 12.30/8.12 tff(29,plain,
% 12.30/8.12 ((~![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))) | leq(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1))),
% 12.30/8.12 inference(quant_inst,[status(thm)],[])).
% 12.30/8.12 tff(30,plain,
% 12.30/8.12 (leq(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1))),
% 12.30/8.12 inference(unit_resolution,[status(thm)],[29, 28])).
% 12.30/8.12 tff(31,plain,
% 12.30/8.12 ((~(leq(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1)) <=> (addition(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1)) = star(X1!1)))) | (~leq(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1))) | (addition(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1)) = star(X1!1))),
% 12.30/8.12 inference(tautology,[status(thm)],[])).
% 12.30/8.12 tff(32,plain,
% 12.30/8.12 ((~(leq(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1)) <=> (addition(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1)) = star(X1!1)))) | (addition(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1)) = star(X1!1))),
% 12.30/8.12 inference(unit_resolution,[status(thm)],[31, 30])).
% 12.30/8.12 tff(33,plain,
% 12.30/8.12 (addition(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1)) = star(X1!1)),
% 12.30/8.12 inference(unit_resolution,[status(thm)],[32, 21])).
% 12.30/8.12 tff(34,plain,
% 12.30/8.12 (star(X1!1) = addition(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1))),
% 12.30/8.12 inference(symmetry,[status(thm)],[33])).
% 12.30/8.12 tff(35,plain,
% 12.30/8.12 (star(X1!1) = addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1))),
% 12.30/8.12 inference(transitivity,[status(thm)],[34, 12])).
% 12.30/8.12 tff(36,plain,
% 12.30/8.12 (multiplication(X1!1, star(X1!1)) = multiplication(X1!1, addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1)))),
% 12.30/8.12 inference(monotonicity,[status(thm)],[35])).
% 12.30/8.12 tff(37,plain,
% 12.30/8.12 (multiplication(X1!1, addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1))) = multiplication(X1!1, star(X1!1))),
% 12.30/8.12 inference(symmetry,[status(thm)],[36])).
% 12.30/8.12 tff(38,plain,
% 12.30/8.12 (^[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))))),
% 12.30/8.12 inference(bind,[status(th)],[])).
% 12.30/8.12 tff(39,plain,
% 12.30/8.12 (![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)))),
% 12.30/8.12 inference(quant_intro,[status(thm)],[38])).
% 12.30/8.12 tff(40,plain,
% 12.30/8.12 (![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)))),
% 12.30/8.12 inference(rewrite,[status(thm)],[])).
% 12.30/8.12 tff(41,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','right_distributivity')).
% 12.30/8.12 tff(42,plain,
% 12.30/8.12 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 12.30/8.12 inference(modus_ponens,[status(thm)],[41, 40])).
% 12.30/8.12 tff(43,plain,(
% 12.30/8.12 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 12.30/8.12 inference(skolemize,[status(sab)],[42])).
% 12.30/8.12 tff(44,plain,
% 12.30/8.12 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 12.30/8.12 inference(modus_ponens,[status(thm)],[43, 39])).
% 12.30/8.12 tff(45,plain,
% 12.30/8.12 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X1!1, addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1))) = addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))))),
% 12.30/8.12 inference(quant_inst,[status(thm)],[])).
% 12.30/8.12 tff(46,plain,
% 12.30/8.12 (multiplication(X1!1, addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1))) = addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))),
% 12.30/8.12 inference(unit_resolution,[status(thm)],[45, 44])).
% 12.30/8.12 tff(47,plain,
% 12.30/8.12 (addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))) = multiplication(X1!1, addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1)))),
% 12.30/8.12 inference(symmetry,[status(thm)],[46])).
% 12.30/8.12 tff(48,plain,
% 12.30/8.12 (addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))) = multiplication(X1!1, star(X1!1))),
% 12.30/8.12 inference(transitivity,[status(thm)],[47, 37])).
% 12.30/8.12 tff(49,plain,
% 12.30/8.12 (addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(one, star(X1!1))) = addition(multiplication(X1!1, star(X1!1)), addition(one, star(X1!1)))),
% 12.30/8.12 inference(monotonicity,[status(thm)],[48])).
% 12.30/8.12 tff(50,plain,
% 12.30/8.12 (addition(multiplication(X1!1, star(X1!1)), addition(one, star(X1!1))) = addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(one, star(X1!1)))),
% 12.30/8.12 inference(symmetry,[status(thm)],[49])).
% 12.30/8.12 tff(51,plain,
% 12.30/8.12 (^[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)))),
% 12.30/8.12 inference(bind,[status(th)],[])).
% 12.30/8.12 tff(52,plain,
% 12.30/8.12 (![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))),
% 12.30/8.12 inference(quant_intro,[status(thm)],[51])).
% 12.30/8.12 tff(53,plain,
% 12.30/8.12 (![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))),
% 12.30/8.12 inference(rewrite,[status(thm)],[])).
% 12.30/8.12 tff(54,axiom,(![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','additive_associativity')).
% 12.30/8.12 tff(55,plain,
% 12.30/8.12 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 12.30/8.12 inference(modus_ponens,[status(thm)],[54, 53])).
% 12.30/8.12 tff(56,plain,(
% 12.30/8.12 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 12.30/8.12 inference(skolemize,[status(sab)],[55])).
% 12.30/8.12 tff(57,plain,
% 12.30/8.12 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 12.30/8.12 inference(modus_ponens,[status(thm)],[56, 52])).
% 12.30/8.12 tff(58,plain,
% 12.30/8.12 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(X1!1, star(X1!1)), addition(one, star(X1!1))) = addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1)))),
% 12.30/8.12 inference(quant_inst,[status(thm)],[])).
% 12.30/8.12 tff(59,plain,
% 12.30/8.12 (addition(multiplication(X1!1, star(X1!1)), addition(one, star(X1!1))) = addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1))),
% 12.30/8.12 inference(unit_resolution,[status(thm)],[58, 57])).
% 12.30/8.12 tff(60,plain,
% 12.30/8.12 (addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1)) = addition(multiplication(X1!1, star(X1!1)), addition(one, star(X1!1)))),
% 12.30/8.12 inference(symmetry,[status(thm)],[59])).
% 12.30/8.12 tff(61,plain,
% 12.30/8.12 (star(X1!1) = addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(one, star(X1!1)))),
% 12.30/8.12 inference(transitivity,[status(thm)],[34, 12, 60, 50])).
% 12.30/8.12 tff(62,plain,
% 12.30/8.12 (multiplication(X1!1, star(X1!1)) = addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))),
% 12.30/8.12 inference(transitivity,[status(thm)],[36, 46])).
% 12.30/8.12 tff(63,plain,
% 12.30/8.12 (addition(multiplication(X1!1, star(X1!1)), star(X1!1)) = addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(one, star(X1!1))))),
% 12.30/8.12 inference(monotonicity,[status(thm)],[62, 61])).
% 12.30/8.12 tff(64,plain,
% 12.30/8.12 (addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(one, star(X1!1)))) = addition(multiplication(X1!1, star(X1!1)), star(X1!1))),
% 12.30/8.12 inference(symmetry,[status(thm)],[63])).
% 12.30/8.12 tff(65,plain,
% 12.30/8.12 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(one, star(X1!1)))) = addition(addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), addition(one, star(X1!1))))),
% 12.30/8.12 inference(quant_inst,[status(thm)],[])).
% 12.30/8.12 tff(66,plain,
% 12.30/8.12 (addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(one, star(X1!1)))) = addition(addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), addition(one, star(X1!1)))),
% 12.30/8.12 inference(unit_resolution,[status(thm)],[65, 57])).
% 12.30/8.12 tff(67,plain,
% 12.30/8.12 (addition(addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), addition(one, star(X1!1))) = addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(one, star(X1!1))))),
% 12.30/8.12 inference(symmetry,[status(thm)],[66])).
% 12.30/8.12 tff(68,plain,
% 12.30/8.12 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 12.30/8.12 inference(bind,[status(th)],[])).
% 12.30/8.12 tff(69,plain,
% 12.30/8.12 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 12.30/8.12 inference(quant_intro,[status(thm)],[68])).
% 12.30/8.12 tff(70,plain,
% 12.30/8.12 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 12.30/8.12 inference(rewrite,[status(thm)],[])).
% 12.30/8.12 tff(71,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','additive_idempotence')).
% 12.30/8.12 tff(72,plain,
% 12.30/8.12 (![A: $i] : (addition(A, A) = A)),
% 12.30/8.12 inference(modus_ponens,[status(thm)],[71, 70])).
% 12.30/8.12 tff(73,plain,(
% 12.30/8.12 ![A: $i] : (addition(A, A) = A)),
% 12.30/8.12 inference(skolemize,[status(sab)],[72])).
% 12.30/8.12 tff(74,plain,
% 12.30/8.12 (![A: $i] : (addition(A, A) = A)),
% 12.30/8.12 inference(modus_ponens,[status(thm)],[73, 69])).
% 12.30/8.12 tff(75,plain,
% 12.30/8.12 ((~![A: $i] : (addition(A, A) = A)) | (addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))) = addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))))),
% 12.30/8.12 inference(quant_inst,[status(thm)],[])).
% 12.30/8.12 tff(76,plain,
% 12.30/8.12 (addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))) = addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))),
% 12.30/8.12 inference(unit_resolution,[status(thm)],[75, 74])).
% 12.30/8.12 tff(77,plain,
% 12.30/8.12 (addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))) = multiplication(X1!1, star(X1!1))),
% 12.30/8.12 inference(transitivity,[status(thm)],[76, 47, 37])).
% 12.30/8.12 tff(78,plain,
% 12.30/8.12 (addition(addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), addition(one, star(X1!1))) = addition(multiplication(X1!1, star(X1!1)), addition(one, star(X1!1)))),
% 12.30/8.12 inference(monotonicity,[status(thm)],[77])).
% 12.30/8.12 tff(79,plain,
% 12.30/8.12 (addition(multiplication(X1!1, star(X1!1)), addition(one, star(X1!1))) = addition(addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), addition(one, star(X1!1)))),
% 12.30/8.12 inference(symmetry,[status(thm)],[78])).
% 12.30/8.12 tff(80,plain,
% 12.30/8.12 (star(X1!1) = addition(multiplication(X1!1, star(X1!1)), star(X1!1))),
% 12.30/8.12 inference(transitivity,[status(thm)],[34, 12, 60, 79, 67, 64])).
% 12.30/8.12 tff(81,plain,
% 12.30/8.12 (multiplication(X2!0, star(X1!1)) = multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), star(X1!1)))),
% 12.30/8.12 inference(monotonicity,[status(thm)],[80])).
% 12.30/8.12 tff(82,plain,
% 12.30/8.12 (multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), star(X1!1))) = multiplication(X2!0, star(X1!1))),
% 12.30/8.12 inference(symmetry,[status(thm)],[81])).
% 12.30/8.12 tff(83,plain,
% 12.30/8.12 (addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), star(X1!1)) = addition(multiplication(X1!1, star(X1!1)), star(X1!1))),
% 12.30/8.12 inference(monotonicity,[status(thm)],[48])).
% 12.30/8.12 tff(84,plain,
% 12.30/8.12 (addition(multiplication(X1!1, star(X1!1)), star(X1!1)) = addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), star(X1!1))),
% 12.30/8.12 inference(symmetry,[status(thm)],[83])).
% 12.30/8.12 tff(85,plain,
% 12.30/8.12 (multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), star(X1!1))) = multiplication(X2!0, addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), star(X1!1)))),
% 12.30/8.12 inference(monotonicity,[status(thm)],[84])).
% 12.30/8.12 tff(86,plain,
% 12.30/8.12 (multiplication(X2!0, addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), star(X1!1))) = multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), star(X1!1)))),
% 12.30/8.12 inference(symmetry,[status(thm)],[85])).
% 12.30/8.12 tff(87,plain,
% 12.30/8.12 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X2!0, addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), star(X1!1))) = addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), multiplication(X2!0, star(X1!1))))),
% 12.30/8.12 inference(quant_inst,[status(thm)],[])).
% 12.30/8.12 tff(88,plain,
% 12.30/8.12 (multiplication(X2!0, addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), star(X1!1))) = addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), multiplication(X2!0, star(X1!1)))),
% 12.30/8.12 inference(unit_resolution,[status(thm)],[87, 44])).
% 12.30/8.12 tff(89,plain,
% 12.30/8.12 (addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), multiplication(X2!0, star(X1!1))) = multiplication(X2!0, addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), star(X1!1)))),
% 12.30/8.12 inference(symmetry,[status(thm)],[88])).
% 12.30/8.12 tff(90,plain,
% 12.30/8.12 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X2!0, addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1))) = addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))))),
% 12.30/8.12 inference(quant_inst,[status(thm)],[])).
% 12.30/8.12 tff(91,plain,
% 12.30/8.12 (multiplication(X2!0, addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1))) = addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1)))),
% 12.30/8.12 inference(unit_resolution,[status(thm)],[90, 44])).
% 12.30/8.12 tff(92,plain,
% 12.30/8.12 (addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1)) = star(X1!1)),
% 12.30/8.12 inference(transitivity,[status(thm)],[11, 33])).
% 12.30/8.12 tff(93,plain,
% 12.30/8.12 (multiplication(X2!0, addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1))) = multiplication(X2!0, star(X1!1))),
% 12.30/8.12 inference(monotonicity,[status(thm)],[92])).
% 12.30/8.12 tff(94,plain,
% 12.30/8.12 (multiplication(X2!0, star(X1!1)) = multiplication(X2!0, addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1)))),
% 12.30/8.12 inference(symmetry,[status(thm)],[93])).
% 12.30/8.12 tff(95,plain,
% 12.30/8.12 (multiplication(X2!0, star(X1!1)) = addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1)))),
% 12.30/8.12 inference(transitivity,[status(thm)],[94, 91])).
% 12.30/8.12 tff(96,plain,
% 12.30/8.12 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), multiplication(multiplication(X2!0, X1!1), star(X1!1))) = addition(multiplication(multiplication(X2!0, X1!1), star(X1!1)), multiplication(multiplication(X0!2, X2!0), star(X1!1))))),
% 12.30/8.12 inference(quant_inst,[status(thm)],[])).
% 12.30/8.12 tff(97,plain,
% 12.30/8.12 (addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), multiplication(multiplication(X2!0, X1!1), star(X1!1))) = addition(multiplication(multiplication(X2!0, X1!1), star(X1!1)), multiplication(multiplication(X0!2, X2!0), star(X1!1)))),
% 12.30/8.12 inference(unit_resolution,[status(thm)],[96, 7])).
% 12.30/8.12 tff(98,plain,
% 12.30/8.12 (^[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))))),
% 12.30/8.12 inference(bind,[status(th)],[])).
% 12.30/8.12 tff(99,plain,
% 12.30/8.12 (![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)))),
% 12.30/8.12 inference(quant_intro,[status(thm)],[98])).
% 12.30/8.12 tff(100,plain,
% 12.30/8.12 (![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)))),
% 12.30/8.12 inference(rewrite,[status(thm)],[])).
% 12.30/8.12 tff(101,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/KLE002+0.ax','left_distributivity')).
% 12.30/8.12 tff(102,plain,
% 12.30/8.12 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 12.30/8.12 inference(modus_ponens,[status(thm)],[101, 100])).
% 12.30/8.12 tff(103,plain,(
% 12.30/8.12 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 12.30/8.12 inference(skolemize,[status(sab)],[102])).
% 12.30/8.12 tff(104,plain,
% 12.30/8.12 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 12.30/8.12 inference(modus_ponens,[status(thm)],[103, 99])).
% 12.30/8.12 tff(105,plain,
% 12.30/8.12 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1)), star(X1!1)) = addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), multiplication(multiplication(X2!0, X1!1), star(X1!1))))),
% 12.30/8.12 inference(quant_inst,[status(thm)],[])).
% 12.30/8.12 tff(106,plain,
% 12.30/8.12 (multiplication(addition(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1)), star(X1!1)) = addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), multiplication(multiplication(X2!0, X1!1), star(X1!1)))),
% 12.30/8.12 inference(unit_resolution,[status(thm)],[105, 104])).
% 12.30/8.12 tff(107,plain,
% 12.30/8.12 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1)) <=> (addition(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1)) = multiplication(X2!0, X1!1)))),
% 12.30/8.12 inference(quant_inst,[status(thm)],[])).
% 12.30/8.12 tff(108,plain,
% 12.30/8.12 (leq(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1)) <=> (addition(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1)) = multiplication(X2!0, X1!1))),
% 12.30/8.12 inference(unit_resolution,[status(thm)],[107, 19])).
% 12.30/8.12 tff(109,plain,
% 12.30/8.12 ((~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X2), multiplication(X2, X1))) | leq(multiplication(star(X0), X2), multiplication(X2, star(X1))))) <=> (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X2), multiplication(X2, X1))) | leq(multiplication(star(X0), X2), multiplication(X2, star(X1)))))),
% 12.30/8.12 inference(rewrite,[status(thm)],[])).
% 12.30/8.12 tff(110,plain,
% 12.30/8.12 ((~![X0: $i, X1: $i, X2: $i] : (leq(multiplication(X0, X2), multiplication(X2, X1)) => leq(multiplication(star(X0), X2), multiplication(X2, star(X1))))) <=> (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X2), multiplication(X2, X1))) | leq(multiplication(star(X0), X2), multiplication(X2, star(X1)))))),
% 12.30/8.12 inference(rewrite,[status(thm)],[])).
% 12.30/8.12 tff(111,axiom,(~![X0: $i, X1: $i, X2: $i] : (leq(multiplication(X0, X2), multiplication(X2, X1)) => leq(multiplication(star(X0), X2), multiplication(X2, star(X1))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 12.30/8.12 tff(112,plain,
% 12.30/8.12 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X2), multiplication(X2, X1))) | leq(multiplication(star(X0), X2), multiplication(X2, star(X1))))),
% 12.30/8.12 inference(modus_ponens,[status(thm)],[111, 110])).
% 12.30/8.12 tff(113,plain,
% 12.30/8.12 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X2), multiplication(X2, X1))) | leq(multiplication(star(X0), X2), multiplication(X2, star(X1))))),
% 12.30/8.12 inference(modus_ponens,[status(thm)],[112, 109])).
% 12.30/8.12 tff(114,plain,
% 12.30/8.12 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X2), multiplication(X2, X1))) | leq(multiplication(star(X0), X2), multiplication(X2, star(X1))))),
% 12.30/8.12 inference(modus_ponens,[status(thm)],[113, 109])).
% 12.30/8.12 tff(115,plain,
% 12.30/8.12 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X2), multiplication(X2, X1))) | leq(multiplication(star(X0), X2), multiplication(X2, star(X1))))),
% 12.30/8.12 inference(modus_ponens,[status(thm)],[114, 109])).
% 12.30/8.13 tff(116,plain,
% 12.30/8.13 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X2), multiplication(X2, X1))) | leq(multiplication(star(X0), X2), multiplication(X2, star(X1))))),
% 12.30/8.13 inference(modus_ponens,[status(thm)],[115, 109])).
% 12.30/8.13 tff(117,plain,
% 12.30/8.13 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X2), multiplication(X2, X1))) | leq(multiplication(star(X0), X2), multiplication(X2, star(X1))))),
% 12.30/8.13 inference(modus_ponens,[status(thm)],[116, 109])).
% 12.30/8.13 tff(118,plain,
% 12.30/8.13 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X2), multiplication(X2, X1))) | leq(multiplication(star(X0), X2), multiplication(X2, star(X1))))),
% 12.30/8.13 inference(modus_ponens,[status(thm)],[117, 109])).
% 12.30/8.13 tff(119,plain,(
% 12.30/8.13 ~((~leq(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1))) | leq(multiplication(star(X0!2), X2!0), multiplication(X2!0, star(X1!1))))),
% 12.30/8.13 inference(skolemize,[status(sab)],[118])).
% 12.30/8.13 tff(120,plain,
% 12.30/8.13 (leq(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1))),
% 12.30/8.13 inference(or_elim,[status(thm)],[119])).
% 12.30/8.13 tff(121,plain,
% 12.30/8.13 ((~(leq(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1)) <=> (addition(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1)) = multiplication(X2!0, X1!1)))) | (~leq(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1))) | (addition(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1)) = multiplication(X2!0, X1!1))),
% 12.30/8.13 inference(tautology,[status(thm)],[])).
% 12.30/8.13 tff(122,plain,
% 12.30/8.13 ((~(leq(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1)) <=> (addition(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1)) = multiplication(X2!0, X1!1)))) | (addition(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1)) = multiplication(X2!0, X1!1))),
% 12.30/8.13 inference(unit_resolution,[status(thm)],[121, 120])).
% 12.30/8.13 tff(123,plain,
% 12.30/8.13 (addition(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1)) = multiplication(X2!0, X1!1)),
% 12.30/8.13 inference(unit_resolution,[status(thm)],[122, 108])).
% 12.30/8.13 tff(124,plain,
% 12.30/8.13 (multiplication(addition(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1)), star(X1!1)) = multiplication(multiplication(X2!0, X1!1), star(X1!1))),
% 12.30/8.13 inference(monotonicity,[status(thm)],[123])).
% 12.30/8.13 tff(125,plain,
% 12.30/8.13 (multiplication(multiplication(X2!0, X1!1), star(X1!1)) = multiplication(addition(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1)), star(X1!1))),
% 12.30/8.13 inference(symmetry,[status(thm)],[124])).
% 12.30/8.13 tff(126,plain,
% 12.30/8.13 (^[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)))),
% 12.30/8.13 inference(bind,[status(th)],[])).
% 12.30/8.13 tff(127,plain,
% 12.30/8.13 (![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))),
% 12.30/8.13 inference(quant_intro,[status(thm)],[126])).
% 12.30/8.13 tff(128,plain,
% 12.30/8.13 (![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))),
% 12.30/8.13 inference(rewrite,[status(thm)],[])).
% 12.30/8.13 tff(129,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','multiplicative_associativity')).
% 12.30/8.13 tff(130,plain,
% 12.30/8.13 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 12.30/8.13 inference(modus_ponens,[status(thm)],[129, 128])).
% 12.30/8.13 tff(131,plain,(
% 12.30/8.13 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 12.30/8.13 inference(skolemize,[status(sab)],[130])).
% 12.30/8.13 tff(132,plain,
% 12.30/8.13 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 12.30/8.13 inference(modus_ponens,[status(thm)],[131, 127])).
% 12.30/8.13 tff(133,plain,
% 12.30/8.13 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X2!0, multiplication(X1!1, star(X1!1))) = multiplication(multiplication(X2!0, X1!1), star(X1!1)))),
% 12.30/8.13 inference(quant_inst,[status(thm)],[])).
% 12.30/8.13 tff(134,plain,
% 12.30/8.13 (multiplication(X2!0, multiplication(X1!1, star(X1!1))) = multiplication(multiplication(X2!0, X1!1), star(X1!1))),
% 12.30/8.13 inference(unit_resolution,[status(thm)],[133, 132])).
% 12.30/8.13 tff(135,plain,
% 12.30/8.13 (multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))) = multiplication(X2!0, multiplication(X1!1, star(X1!1)))),
% 12.30/8.13 inference(monotonicity,[status(thm)],[48])).
% 12.30/8.13 tff(136,plain,
% 12.30/8.13 (multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))) = addition(multiplication(multiplication(X2!0, X1!1), star(X1!1)), multiplication(multiplication(X0!2, X2!0), star(X1!1)))),
% 12.30/8.13 inference(transitivity,[status(thm)],[135, 134, 125, 106, 97])).
% 12.30/8.13 tff(137,plain,
% 12.30/8.13 (addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), multiplication(X2!0, star(X1!1))) = addition(addition(multiplication(multiplication(X2!0, X1!1), star(X1!1)), multiplication(multiplication(X0!2, X2!0), star(X1!1))), addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))))),
% 12.30/8.13 inference(monotonicity,[status(thm)],[136, 95])).
% 12.30/8.13 tff(138,plain,
% 12.30/8.13 (addition(addition(multiplication(multiplication(X2!0, X1!1), star(X1!1)), multiplication(multiplication(X0!2, X2!0), star(X1!1))), addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1)))) = addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), multiplication(X2!0, star(X1!1)))),
% 12.30/8.13 inference(symmetry,[status(thm)],[137])).
% 12.30/8.13 tff(139,plain,
% 12.30/8.13 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(multiplication(X2!0, X1!1), star(X1!1)), addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))))) = addition(addition(multiplication(multiplication(X2!0, X1!1), star(X1!1)), multiplication(multiplication(X0!2, X2!0), star(X1!1))), addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1)))))),
% 12.30/8.13 inference(quant_inst,[status(thm)],[])).
% 12.30/8.13 tff(140,plain,
% 12.30/8.13 (addition(multiplication(multiplication(X2!0, X1!1), star(X1!1)), addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))))) = addition(addition(multiplication(multiplication(X2!0, X1!1), star(X1!1)), multiplication(multiplication(X0!2, X2!0), star(X1!1))), addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))))),
% 12.30/8.13 inference(unit_resolution,[status(thm)],[139, 57])).
% 12.30/8.13 tff(141,plain,
% 12.30/8.13 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))), multiplication(X2!0, star(X1!1))) = addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1))))))),
% 12.30/8.13 inference(quant_inst,[status(thm)],[])).
% 12.30/8.13 tff(142,plain,
% 12.30/8.13 (addition(addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))), multiplication(X2!0, star(X1!1))) = addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))))),
% 12.30/8.13 inference(unit_resolution,[status(thm)],[141, 7])).
% 12.30/8.13 tff(143,plain,
% 12.30/8.13 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0) = addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))))),
% 12.30/8.13 inference(quant_inst,[status(thm)],[])).
% 12.30/8.13 tff(144,plain,
% 12.30/8.13 (addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0) = addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1))))),
% 12.30/8.13 inference(unit_resolution,[status(thm)],[143, 7])).
% 12.30/8.13 tff(145,plain,
% 12.30/8.13 (addition(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1))) = addition(addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))), multiplication(X2!0, star(X1!1)))),
% 12.30/8.13 inference(monotonicity,[status(thm)],[144])).
% 12.30/8.13 tff(146,plain,
% 12.30/8.13 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(multiplication(X1!1, star(X1!1)), star(X1!1))) = addition(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1)))),
% 12.30/8.13 inference(quant_inst,[status(thm)],[])).
% 12.30/8.13 tff(147,plain,
% 12.30/8.13 (addition(one, addition(multiplication(X1!1, star(X1!1)), star(X1!1))) = addition(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1))),
% 12.30/8.13 inference(unit_resolution,[status(thm)],[146, 57])).
% 12.30/8.13 tff(148,plain,
% 12.30/8.13 (addition(one, addition(multiplication(X1!1, star(X1!1)), star(X1!1))) = star(X1!1)),
% 12.30/8.13 inference(transitivity,[status(thm)],[147, 33])).
% 12.30/8.13 tff(149,plain,
% 12.30/8.13 (multiplication(X2!0, addition(one, addition(multiplication(X1!1, star(X1!1)), star(X1!1)))) = multiplication(X2!0, star(X1!1))),
% 12.30/8.13 inference(monotonicity,[status(thm)],[148])).
% 12.30/8.13 tff(150,plain,
% 12.30/8.13 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X2!0, addition(one, addition(multiplication(X1!1, star(X1!1)), star(X1!1)))) = addition(multiplication(X2!0, one), multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), star(X1!1)))))),
% 12.30/8.13 inference(quant_inst,[status(thm)],[])).
% 12.30/8.13 tff(151,plain,
% 12.30/8.13 (multiplication(X2!0, addition(one, addition(multiplication(X1!1, star(X1!1)), star(X1!1)))) = addition(multiplication(X2!0, one), multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), star(X1!1))))),
% 12.30/8.13 inference(unit_resolution,[status(thm)],[150, 44])).
% 12.30/8.13 tff(152,plain,
% 12.30/8.13 (addition(multiplication(X2!0, one), multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), star(X1!1)))) = multiplication(X2!0, addition(one, addition(multiplication(X1!1, star(X1!1)), star(X1!1))))),
% 12.30/8.13 inference(symmetry,[status(thm)],[151])).
% 12.30/8.13 tff(153,plain,
% 12.30/8.13 (addition(multiplication(X2!0, one), multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), star(X1!1)))) = multiplication(X2!0, star(X1!1))),
% 12.30/8.13 inference(transitivity,[status(thm)],[152, 149])).
% 12.30/8.13 tff(154,plain,
% 12.30/8.13 (addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))) = addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0)),
% 12.30/8.13 inference(symmetry,[status(thm)],[144])).
% 12.30/8.13 tff(155,plain,
% 12.30/8.13 (addition(addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))), addition(multiplication(X2!0, one), multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), star(X1!1))))) = addition(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1)))),
% 12.30/8.13 inference(monotonicity,[status(thm)],[154, 153])).
% 12.30/8.13 tff(156,plain,
% 12.30/8.13 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))), addition(multiplication(X2!0, one), multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), star(X1!1))))) = addition(addition(addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))), multiplication(X2!0, one)), multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), star(X1!1)))))),
% 12.30/8.13 inference(quant_inst,[status(thm)],[])).
% 12.30/8.13 tff(157,plain,
% 12.30/8.13 (addition(addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))), addition(multiplication(X2!0, one), multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), star(X1!1))))) = addition(addition(addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))), multiplication(X2!0, one)), multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), star(X1!1))))),
% 12.30/8.13 inference(unit_resolution,[status(thm)],[156, 57])).
% 12.30/8.13 tff(158,plain,
% 12.30/8.13 (addition(addition(addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))), multiplication(X2!0, one)), multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), star(X1!1)))) = addition(addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))), addition(multiplication(X2!0, one), multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), star(X1!1)))))),
% 12.30/8.13 inference(symmetry,[status(thm)],[157])).
% 12.30/8.13 tff(159,plain,
% 12.30/8.13 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 12.30/8.13 inference(bind,[status(th)],[])).
% 12.30/8.13 tff(160,plain,
% 12.30/8.13 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 12.30/8.13 inference(quant_intro,[status(thm)],[159])).
% 12.30/8.13 tff(161,plain,
% 12.30/8.13 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 12.30/8.13 inference(rewrite,[status(thm)],[])).
% 12.30/8.13 tff(162,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','multiplicative_right_identity')).
% 12.30/8.13 tff(163,plain,
% 12.30/8.13 (![A: $i] : (multiplication(A, one) = A)),
% 12.30/8.13 inference(modus_ponens,[status(thm)],[162, 161])).
% 12.30/8.13 tff(164,plain,(
% 12.30/8.13 ![A: $i] : (multiplication(A, one) = A)),
% 12.30/8.13 inference(skolemize,[status(sab)],[163])).
% 12.30/8.13 tff(165,plain,
% 12.30/8.13 (![A: $i] : (multiplication(A, one) = A)),
% 12.30/8.13 inference(modus_ponens,[status(thm)],[164, 160])).
% 12.30/8.13 tff(166,plain,
% 12.30/8.13 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(X2!0, one) = X2!0)),
% 12.30/8.13 inference(quant_inst,[status(thm)],[])).
% 12.30/8.13 tff(167,plain,
% 12.30/8.13 (multiplication(X2!0, one) = X2!0),
% 12.30/8.13 inference(unit_resolution,[status(thm)],[166, 165])).
% 12.30/8.13 tff(168,plain,
% 12.30/8.13 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X0!2, multiplication(X2!0, star(X1!1))) = multiplication(multiplication(X0!2, X2!0), star(X1!1)))),
% 12.30/8.13 inference(quant_inst,[status(thm)],[])).
% 12.30/8.13 tff(169,plain,
% 12.30/8.13 (multiplication(X0!2, multiplication(X2!0, star(X1!1))) = multiplication(multiplication(X0!2, X2!0), star(X1!1))),
% 12.30/8.13 inference(unit_resolution,[status(thm)],[168, 132])).
% 12.30/8.13 tff(170,plain,
% 12.30/8.13 (multiplication(multiplication(X0!2, X2!0), star(X1!1)) = multiplication(X0!2, multiplication(X2!0, star(X1!1)))),
% 12.30/8.13 inference(symmetry,[status(thm)],[169])).
% 12.30/8.13 tff(171,plain,
% 12.30/8.13 (addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), X2!0) = addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0)),
% 12.30/8.13 inference(monotonicity,[status(thm)],[170])).
% 12.30/8.13 tff(172,plain,
% 12.30/8.13 (addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0) = addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), X2!0)),
% 12.30/8.13 inference(symmetry,[status(thm)],[171])).
% 12.30/8.13 tff(173,plain,
% 12.30/8.13 (addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))) = addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), X2!0)),
% 12.30/8.13 inference(transitivity,[status(thm)],[154, 172])).
% 12.30/8.13 tff(174,plain,
% 12.30/8.13 (addition(addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))), multiplication(X2!0, one)) = addition(addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), X2!0), X2!0)),
% 12.30/8.13 inference(monotonicity,[status(thm)],[173, 167])).
% 12.30/8.13 tff(175,plain,
% 12.30/8.13 (addition(addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), X2!0), X2!0) = addition(addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))), multiplication(X2!0, one))),
% 12.30/8.13 inference(symmetry,[status(thm)],[174])).
% 12.30/8.13 tff(176,plain,
% 12.30/8.13 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), addition(X2!0, X2!0)) = addition(addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), X2!0), X2!0))),
% 12.30/8.13 inference(quant_inst,[status(thm)],[])).
% 12.30/8.13 tff(177,plain,
% 12.30/8.13 (addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), addition(X2!0, X2!0)) = addition(addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), X2!0), X2!0)),
% 12.30/8.13 inference(unit_resolution,[status(thm)],[176, 57])).
% 12.30/8.13 tff(178,plain,
% 12.30/8.13 ((~![A: $i] : (addition(A, A) = A)) | (addition(X2!0, X2!0) = X2!0)),
% 12.30/8.13 inference(quant_inst,[status(thm)],[])).
% 12.30/8.13 tff(179,plain,
% 12.30/8.13 (addition(X2!0, X2!0) = X2!0),
% 12.30/8.13 inference(unit_resolution,[status(thm)],[178, 74])).
% 12.30/8.13 tff(180,plain,
% 12.30/8.13 (addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), addition(X2!0, X2!0)) = addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0)),
% 12.30/8.13 inference(monotonicity,[status(thm)],[170, 179])).
% 12.30/8.13 tff(181,plain,
% 12.30/8.13 (addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0) = addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), addition(X2!0, X2!0))),
% 12.30/8.13 inference(symmetry,[status(thm)],[180])).
% 12.30/8.13 tff(182,plain,
% 12.30/8.13 (addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), multiplication(X2!0, one)) = addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0)),
% 12.30/8.13 inference(monotonicity,[status(thm)],[170, 167])).
% 12.30/8.13 tff(183,plain,
% 12.30/8.13 (addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), multiplication(X2!0, one)) = addition(addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))), multiplication(X2!0, one))),
% 12.30/8.13 inference(transitivity,[status(thm)],[182, 181, 177, 175])).
% 12.30/8.13 tff(184,plain,
% 12.30/8.13 (addition(addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), multiplication(X2!0, one)), multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), star(X1!1)))) = addition(addition(addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))), multiplication(X2!0, one)), multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), star(X1!1))))),
% 12.30/8.13 inference(monotonicity,[status(thm)],[183])).
% 12.30/8.13 tff(185,plain,
% 12.30/8.13 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), addition(multiplication(X2!0, one), multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), star(X1!1))))) = addition(addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), multiplication(X2!0, one)), multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), star(X1!1)))))),
% 12.30/8.13 inference(quant_inst,[status(thm)],[])).
% 12.30/8.13 tff(186,plain,
% 12.30/8.13 (addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), addition(multiplication(X2!0, one), multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), star(X1!1))))) = addition(addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), multiplication(X2!0, one)), multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), star(X1!1))))),
% 12.30/8.13 inference(unit_resolution,[status(thm)],[185, 57])).
% 12.30/8.13 tff(187,plain,
% 12.30/8.13 (multiplication(X2!0, star(X1!1)) = multiplication(X2!0, addition(one, addition(multiplication(X1!1, star(X1!1)), star(X1!1))))),
% 12.30/8.13 inference(symmetry,[status(thm)],[149])).
% 12.30/8.13 tff(188,plain,
% 12.30/8.13 (multiplication(X2!0, star(X1!1)) = addition(multiplication(X2!0, one), multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), star(X1!1))))),
% 12.30/8.13 inference(transitivity,[status(thm)],[187, 151])).
% 12.30/8.13 tff(189,plain,
% 12.30/8.13 (addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), multiplication(X2!0, star(X1!1))) = addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), addition(multiplication(X2!0, one), multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), star(X1!1)))))),
% 12.30/8.13 inference(monotonicity,[status(thm)],[188])).
% 12.30/8.13 tff(190,plain,
% 12.30/8.13 (addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))) = multiplication(X2!0, addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1)))),
% 12.30/8.13 inference(symmetry,[status(thm)],[91])).
% 12.30/8.13 tff(191,plain,
% 12.30/8.13 (addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))) = multiplication(X2!0, star(X1!1))),
% 12.30/8.13 inference(transitivity,[status(thm)],[190, 93])).
% 12.30/8.13 tff(192,plain,
% 12.30/8.13 (addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1)))) = addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), multiplication(X2!0, star(X1!1)))),
% 12.30/8.13 inference(monotonicity,[status(thm)],[191])).
% 12.30/8.13 tff(193,plain,
% 12.30/8.13 (addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1)))) = addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))))),
% 12.30/8.13 inference(transitivity,[status(thm)],[192, 189, 186, 184, 158, 155, 145, 142])).
% 12.30/8.13 tff(194,plain,
% 12.30/8.13 (multiplication(X2!0, multiplication(X1!1, star(X1!1))) = multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))))),
% 12.30/8.13 inference(symmetry,[status(thm)],[135])).
% 12.30/8.13 tff(195,plain,
% 12.30/8.13 (multiplication(multiplication(X2!0, X1!1), star(X1!1)) = multiplication(X2!0, multiplication(X1!1, star(X1!1)))),
% 12.30/8.13 inference(symmetry,[status(thm)],[134])).
% 12.30/8.13 tff(196,plain,
% 12.30/8.13 (multiplication(multiplication(X2!0, X1!1), star(X1!1)) = multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))))),
% 12.30/8.13 inference(transitivity,[status(thm)],[195, 194])).
% 12.30/8.13 tff(197,plain,
% 12.30/8.13 (addition(multiplication(multiplication(X2!0, X1!1), star(X1!1)), addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))))) = addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1))))))),
% 12.30/8.13 inference(monotonicity,[status(thm)],[196, 193])).
% 12.30/8.13 tff(198,plain,
% 12.30/8.13 (addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))))) = addition(multiplication(multiplication(X2!0, X1!1), star(X1!1)), addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1)))))),
% 12.30/8.13 inference(symmetry,[status(thm)],[197])).
% 12.30/8.13 tff(199,plain,
% 12.30/8.13 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X2!0, addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), multiplication(X2!0, star(X1!1)))) = addition(addition(X2!0, multiplication(multiplication(X0!2, X2!0), star(X1!1))), multiplication(X2!0, star(X1!1))))),
% 12.30/8.13 inference(quant_inst,[status(thm)],[])).
% 12.30/8.13 tff(200,plain,
% 12.30/8.13 (addition(X2!0, addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), multiplication(X2!0, star(X1!1)))) = addition(addition(X2!0, multiplication(multiplication(X0!2, X2!0), star(X1!1))), multiplication(X2!0, star(X1!1)))),
% 12.30/8.13 inference(unit_resolution,[status(thm)],[199, 57])).
% 12.30/8.13 tff(201,plain,
% 12.30/8.13 (addition(addition(X2!0, multiplication(multiplication(X0!2, X2!0), star(X1!1))), multiplication(X2!0, star(X1!1))) = addition(X2!0, addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), multiplication(X2!0, star(X1!1))))),
% 12.30/8.13 inference(symmetry,[status(thm)],[200])).
% 12.30/8.13 tff(202,plain,
% 12.30/8.13 (addition(X2!0, multiplication(multiplication(X0!2, X2!0), star(X1!1))) = addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1))))),
% 12.30/8.13 inference(monotonicity,[status(thm)],[170])).
% 12.30/8.13 tff(203,plain,
% 12.30/8.13 (addition(X2!0, multiplication(multiplication(X0!2, X2!0), star(X1!1))) = addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0)),
% 12.30/8.13 inference(transitivity,[status(thm)],[202, 154])).
% 12.30/8.14 tff(204,plain,
% 12.30/8.14 (addition(addition(X2!0, multiplication(multiplication(X0!2, X2!0), star(X1!1))), multiplication(X2!0, star(X1!1))) = addition(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1)))),
% 12.30/8.14 inference(monotonicity,[status(thm)],[203])).
% 12.30/8.14 tff(205,plain,
% 12.30/8.14 (addition(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1))) = addition(addition(X2!0, multiplication(multiplication(X0!2, X2!0), star(X1!1))), multiplication(X2!0, star(X1!1)))),
% 12.30/8.14 inference(symmetry,[status(thm)],[204])).
% 12.30/8.14 tff(206,plain,
% 12.30/8.14 (addition(addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))), multiplication(X2!0, star(X1!1))) = addition(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1)))),
% 12.30/8.14 inference(symmetry,[status(thm)],[145])).
% 12.30/8.14 tff(207,plain,
% 12.30/8.14 (addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1))))) = addition(addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))), multiplication(X2!0, star(X1!1)))),
% 12.30/8.14 inference(symmetry,[status(thm)],[142])).
% 12.30/8.14 tff(208,plain,
% 12.30/8.14 (addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1))))) = addition(X2!0, addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), multiplication(X2!0, star(X1!1))))),
% 12.30/8.14 inference(transitivity,[status(thm)],[207, 206, 205, 201])).
% 12.30/8.14 tff(209,plain,
% 12.30/8.14 (addition(multiplication(X2!0, one), addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))))) = addition(X2!0, addition(X2!0, addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), multiplication(X2!0, star(X1!1)))))),
% 12.30/8.14 inference(monotonicity,[status(thm)],[167, 208])).
% 12.30/8.14 tff(210,plain,
% 12.30/8.14 (addition(X2!0, addition(X2!0, addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), multiplication(X2!0, star(X1!1))))) = addition(multiplication(X2!0, one), addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1))))))),
% 12.30/8.14 inference(symmetry,[status(thm)],[209])).
% 12.30/8.14 tff(211,plain,
% 12.30/8.14 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X2!0, addition(X2!0, addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), multiplication(X2!0, star(X1!1))))) = addition(addition(X2!0, X2!0), addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), multiplication(X2!0, star(X1!1)))))),
% 12.30/8.14 inference(quant_inst,[status(thm)],[])).
% 12.30/8.14 tff(212,plain,
% 12.30/8.14 (addition(X2!0, addition(X2!0, addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), multiplication(X2!0, star(X1!1))))) = addition(addition(X2!0, X2!0), addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), multiplication(X2!0, star(X1!1))))),
% 12.30/8.14 inference(unit_resolution,[status(thm)],[211, 57])).
% 12.30/8.14 tff(213,plain,
% 12.30/8.14 (addition(addition(X2!0, X2!0), addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), multiplication(X2!0, star(X1!1)))) = addition(X2!0, addition(X2!0, addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), multiplication(X2!0, star(X1!1)))))),
% 12.30/8.14 inference(symmetry,[status(thm)],[212])).
% 12.30/8.14 tff(214,plain,
% 12.30/8.14 (addition(addition(X2!0, X2!0), addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), multiplication(X2!0, star(X1!1)))) = addition(X2!0, addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), multiplication(X2!0, star(X1!1))))),
% 12.30/8.14 inference(monotonicity,[status(thm)],[179])).
% 12.30/8.14 tff(215,plain,
% 12.30/8.14 (addition(X2!0, addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), multiplication(X2!0, star(X1!1)))) = addition(addition(X2!0, X2!0), addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), multiplication(X2!0, star(X1!1))))),
% 12.30/8.14 inference(symmetry,[status(thm)],[214])).
% 12.30/8.14 tff(216,plain,
% 12.30/8.14 (addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1))))) = addition(multiplication(X2!0, one), addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1))))))),
% 12.30/8.14 inference(transitivity,[status(thm)],[207, 206, 205, 201, 215, 213, 210])).
% 12.30/8.14 tff(217,plain,
% 12.30/8.14 (addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))))) = addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), addition(multiplication(X2!0, one), addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))))))),
% 12.30/8.14 inference(monotonicity,[status(thm)],[216])).
% 12.30/8.14 tff(218,plain,
% 12.30/8.14 (addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), addition(multiplication(X2!0, one), addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1))))))) = addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1))))))),
% 12.30/8.14 inference(symmetry,[status(thm)],[217])).
% 12.30/8.14 tff(219,plain,
% 12.30/8.14 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), addition(multiplication(X2!0, one), addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1))))))) = addition(addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), multiplication(X2!0, one)), addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))))))),
% 12.30/8.14 inference(quant_inst,[status(thm)],[])).
% 12.30/8.14 tff(220,plain,
% 12.30/8.14 (addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), addition(multiplication(X2!0, one), addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1))))))) = addition(addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), multiplication(X2!0, one)), addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1))))))),
% 12.30/8.14 inference(unit_resolution,[status(thm)],[219, 57])).
% 12.30/8.14 tff(221,plain,
% 12.30/8.14 (addition(addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), multiplication(X2!0, one)), addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))))) = addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), addition(multiplication(X2!0, one), addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))))))),
% 12.30/8.14 inference(symmetry,[status(thm)],[220])).
% 12.30/8.14 tff(222,plain,
% 12.30/8.14 (addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1))))) = addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))))),
% 12.30/8.14 inference(monotonicity,[status(thm)],[191])).
% 12.30/8.14 tff(223,plain,
% 12.30/8.14 (addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1))))) = addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))))),
% 12.30/8.14 inference(symmetry,[status(thm)],[222])).
% 12.30/8.14 tff(224,plain,
% 12.30/8.14 (addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), one) = addition(multiplication(X1!1, star(X1!1)), one)),
% 12.30/8.14 inference(monotonicity,[status(thm)],[48])).
% 12.30/8.14 tff(225,plain,
% 12.30/8.14 (multiplication(X2!0, addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), one)) = multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one))),
% 12.30/8.14 inference(monotonicity,[status(thm)],[224])).
% 12.30/8.14 tff(226,plain,
% 12.30/8.14 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X2!0, addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), one)) = addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), multiplication(X2!0, one)))),
% 12.30/8.14 inference(quant_inst,[status(thm)],[])).
% 12.30/8.14 tff(227,plain,
% 12.30/8.14 (multiplication(X2!0, addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), one)) = addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), multiplication(X2!0, one))),
% 12.30/8.14 inference(unit_resolution,[status(thm)],[226, 44])).
% 12.30/8.14 tff(228,plain,
% 12.30/8.14 (addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), multiplication(X2!0, one)) = multiplication(X2!0, addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), one))),
% 12.30/8.14 inference(symmetry,[status(thm)],[227])).
% 12.30/8.14 tff(229,plain,
% 12.30/8.14 (addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), multiplication(X2!0, one)) = multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one))),
% 12.30/8.14 inference(transitivity,[status(thm)],[228, 225])).
% 12.30/8.14 tff(230,plain,
% 12.30/8.14 (addition(addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), multiplication(X2!0, one)), addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))))) = addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1))))))),
% 12.30/8.14 inference(monotonicity,[status(thm)],[229, 223])).
% 12.30/8.14 tff(231,plain,
% 12.30/8.14 (addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))))) = addition(addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), multiplication(X2!0, one)), addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1))))))),
% 12.30/8.14 inference(symmetry,[status(thm)],[230])).
% 12.30/8.14 tff(232,plain,
% 12.30/8.14 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))))) = addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1)))), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1))))))),
% 12.30/8.14 inference(quant_inst,[status(thm)],[])).
% 12.30/8.14 tff(233,plain,
% 12.30/8.14 (addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))))) = addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1)))), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))))),
% 12.30/8.14 inference(unit_resolution,[status(thm)],[232, 57])).
% 12.30/8.14 tff(234,plain,
% 12.30/8.14 (addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1)))), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1))))) = addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1))))))),
% 12.30/8.14 inference(symmetry,[status(thm)],[233])).
% 12.30/8.14 tff(235,plain,
% 12.30/8.14 (addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1)))) = addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1)))),
% 12.30/8.14 inference(monotonicity,[status(thm)],[191])).
% 12.30/8.14 tff(236,plain,
% 12.30/8.14 (addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1)))) = multiplication(X2!0, star(X1!1))),
% 12.30/8.14 inference(transitivity,[status(thm)],[235, 190, 93])).
% 12.30/8.14 tff(237,plain,
% 12.30/8.14 (addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1)))), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1))))) = addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))))),
% 12.30/8.14 inference(monotonicity,[status(thm)],[236])).
% 12.30/8.14 tff(238,plain,
% 12.30/8.14 (addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1))))) = addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1)))), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))))),
% 12.30/8.14 inference(symmetry,[status(thm)],[237])).
% 12.30/8.14 tff(239,plain,
% 12.30/8.14 (addition(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1))) = multiplication(X2!0, star(X1!1))),
% 12.30/8.14 inference(transitivity,[status(thm)],[145, 142, 238, 234, 231, 221, 218, 198, 140, 138, 89, 86, 82])).
% 12.30/8.14 tff(240,plain,
% 12.30/8.14 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1))) <=> (addition(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1))) = multiplication(X2!0, star(X1!1))))),
% 12.30/8.14 inference(quant_inst,[status(thm)],[])).
% 12.30/8.14 tff(241,plain,
% 12.30/8.14 (leq(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1))) <=> (addition(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1))) = multiplication(X2!0, star(X1!1)))),
% 12.30/8.14 inference(unit_resolution,[status(thm)],[240, 19])).
% 12.30/8.14 tff(242,plain,
% 12.30/8.14 (~leq(multiplication(star(X0!2), X2!0), multiplication(X2!0, star(X1!1)))),
% 12.30/8.14 inference(or_elim,[status(thm)],[119])).
% 12.30/8.14 tff(243,plain,
% 12.30/8.14 (^[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)))),
% 12.30/8.14 inference(bind,[status(th)],[])).
% 12.30/8.14 tff(244,plain,
% 12.30/8.14 (![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))),
% 12.30/8.14 inference(quant_intro,[status(thm)],[243])).
% 12.30/8.14 tff(245,plain,
% 12.30/8.14 (![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))),
% 12.30/8.14 inference(rewrite,[status(thm)],[])).
% 12.30/8.14 tff(246,plain,
% 12.30/8.14 (^[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)))),
% 12.30/8.14 inference(bind,[status(th)],[])).
% 12.30/8.14 tff(247,plain,
% 12.30/8.14 (![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))),
% 12.30/8.14 inference(quant_intro,[status(thm)],[246])).
% 12.30/8.14 tff(248,axiom,(![A: $i, B: $i, C: $i] : (leq(addition(multiplication(A, B), C), B) => leq(multiplication(star(A), C), B))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','star_induction_left')).
% 12.30/8.14 tff(249,plain,
% 12.30/8.14 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 12.30/8.14 inference(modus_ponens,[status(thm)],[248, 247])).
% 12.30/8.14 tff(250,plain,
% 12.30/8.14 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 12.30/8.14 inference(modus_ponens,[status(thm)],[249, 245])).
% 12.30/8.14 tff(251,plain,(
% 12.30/8.14 ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 12.30/8.14 inference(skolemize,[status(sab)],[250])).
% 12.30/8.14 tff(252,plain,
% 12.30/8.14 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 12.30/8.14 inference(modus_ponens,[status(thm)],[251, 244])).
% 12.30/8.14 tff(253,plain,
% 12.30/8.14 (((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | ((~leq(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1)))) | leq(multiplication(star(X0!2), X2!0), multiplication(X2!0, star(X1!1))))) <=> ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | (~leq(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1)))) | leq(multiplication(star(X0!2), X2!0), multiplication(X2!0, star(X1!1))))),
% 12.30/8.14 inference(rewrite,[status(thm)],[])).
% 12.30/8.14 tff(254,plain,
% 12.30/8.14 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | ((~leq(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1)))) | leq(multiplication(star(X0!2), X2!0), multiplication(X2!0, star(X1!1))))),
% 12.30/8.14 inference(quant_inst,[status(thm)],[])).
% 12.30/8.14 tff(255,plain,
% 12.30/8.14 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | (~leq(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1)))) | leq(multiplication(star(X0!2), X2!0), multiplication(X2!0, star(X1!1)))),
% 12.30/8.14 inference(modus_ponens,[status(thm)],[254, 253])).
% 12.30/8.16 tff(256,plain,
% 12.30/8.16 (~leq(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1)))),
% 12.30/8.16 inference(unit_resolution,[status(thm)],[255, 252, 242])).
% 12.30/8.16 tff(257,plain,
% 12.30/8.16 ((~(leq(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1))) <=> (addition(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1))) = multiplication(X2!0, star(X1!1))))) | leq(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1))) | (~(addition(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1))) = multiplication(X2!0, star(X1!1))))),
% 12.30/8.16 inference(tautology,[status(thm)],[])).
% 12.30/8.16 tff(258,plain,
% 12.30/8.16 ((~(leq(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1))) <=> (addition(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1))) = multiplication(X2!0, star(X1!1))))) | (~(addition(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1))) = multiplication(X2!0, star(X1!1))))),
% 12.30/8.16 inference(unit_resolution,[status(thm)],[257, 256])).
% 12.30/8.16 tff(259,plain,
% 12.30/8.16 (~(addition(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1))) = multiplication(X2!0, star(X1!1)))),
% 12.30/8.16 inference(unit_resolution,[status(thm)],[258, 241])).
% 12.30/8.16 tff(260,plain,
% 12.30/8.16 ($false),
% 12.30/8.16 inference(unit_resolution,[status(thm)],[259, 239])).
% 12.30/8.16 % SZS output end Proof
%------------------------------------------------------------------------------