TSTP Solution File: KLE039+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE039+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 17:23:58 EDT 2022
% Result : Theorem 110.46s 70.02s
% Output : Proof 110.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE039+2 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n029.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 08:09:58 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.
% 110.46/70.02 % SZS status Theorem
% 110.46/70.02 % SZS output start Proof
% 110.46/70.02 tff(leq_type, type, (
% 110.46/70.02 leq: ( $i * $i ) > $o)).
% 110.46/70.02 tff(star_type, type, (
% 110.46/70.02 star: $i > $i)).
% 110.46/70.02 tff(tptp_fun_X0_0_type, type, (
% 110.46/70.02 tptp_fun_X0_0: $i)).
% 110.46/70.02 tff(addition_type, type, (
% 110.46/70.02 addition: ( $i * $i ) > $i)).
% 110.46/70.02 tff(multiplication_type, type, (
% 110.46/70.02 multiplication: ( $i * $i ) > $i)).
% 110.46/70.02 tff(one_type, type, (
% 110.46/70.02 one: $i)).
% 110.46/70.02 tff(1,plain,
% 110.46/70.02 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 110.46/70.02 inference(bind,[status(th)],[])).
% 110.46/70.02 tff(2,plain,
% 110.46/70.02 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 110.46/70.02 inference(quant_intro,[status(thm)],[1])).
% 110.46/70.02 tff(3,plain,
% 110.46/70.02 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 110.46/70.02 inference(rewrite,[status(thm)],[])).
% 110.46/70.02 tff(4,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','additive_idempotence')).
% 110.46/70.02 tff(5,plain,
% 110.46/70.02 (![A: $i] : (addition(A, A) = A)),
% 110.46/70.02 inference(modus_ponens,[status(thm)],[4, 3])).
% 110.46/70.02 tff(6,plain,(
% 110.46/70.02 ![A: $i] : (addition(A, A) = A)),
% 110.46/70.02 inference(skolemize,[status(sab)],[5])).
% 110.46/70.02 tff(7,plain,
% 110.46/70.02 (![A: $i] : (addition(A, A) = A)),
% 110.46/70.02 inference(modus_ponens,[status(thm)],[6, 2])).
% 110.46/70.02 tff(8,plain,
% 110.46/70.02 ((~![A: $i] : (addition(A, A) = A)) | (addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(X0!0))) = multiplication(star(X0!0), star(X0!0)))),
% 110.46/70.02 inference(quant_inst,[status(thm)],[])).
% 110.46/70.02 tff(9,plain,
% 110.46/70.02 (addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(X0!0))) = multiplication(star(X0!0), star(X0!0))),
% 110.46/70.02 inference(unit_resolution,[status(thm)],[8, 7])).
% 110.46/70.02 tff(10,plain,
% 110.46/70.02 (leq(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(X0!0))), star(X0!0)) <=> leq(multiplication(star(X0!0), star(X0!0)), star(X0!0))),
% 110.46/70.02 inference(monotonicity,[status(thm)],[9])).
% 110.46/70.02 tff(11,plain,
% 110.46/70.02 (leq(multiplication(star(X0!0), star(X0!0)), star(X0!0)) <=> leq(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(X0!0))), star(X0!0))),
% 110.46/70.02 inference(symmetry,[status(thm)],[10])).
% 110.46/70.02 tff(12,plain,
% 110.46/70.02 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 110.46/70.02 inference(bind,[status(th)],[])).
% 110.46/70.02 tff(13,plain,
% 110.46/70.02 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 110.46/70.02 inference(quant_intro,[status(thm)],[12])).
% 110.46/70.02 tff(14,plain,
% 110.46/70.02 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 110.46/70.02 inference(rewrite,[status(thm)],[])).
% 110.46/70.02 tff(15,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','order')).
% 110.46/70.02 tff(16,plain,
% 110.46/70.02 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 110.46/70.02 inference(modus_ponens,[status(thm)],[15, 14])).
% 110.46/70.02 tff(17,plain,(
% 110.46/70.02 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 110.46/70.02 inference(skolemize,[status(sab)],[16])).
% 110.46/70.02 tff(18,plain,
% 110.46/70.02 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 110.46/70.02 inference(modus_ponens,[status(thm)],[17, 13])).
% 110.46/70.02 tff(19,plain,
% 110.46/70.02 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) <=> (addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) = star(X0!0)))),
% 110.46/70.02 inference(quant_inst,[status(thm)],[])).
% 110.46/70.02 tff(20,plain,
% 110.46/70.02 (leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) <=> (addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) = star(X0!0))),
% 110.46/70.02 inference(unit_resolution,[status(thm)],[19, 18])).
% 110.46/70.02 tff(21,plain,
% 110.46/70.02 (^[A: $i] : refl(leq(addition(one, multiplication(A, star(A))), star(A)) <=> leq(addition(one, multiplication(A, star(A))), star(A)))),
% 110.46/70.02 inference(bind,[status(th)],[])).
% 110.46/70.02 tff(22,plain,
% 110.46/70.02 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 110.46/70.02 inference(quant_intro,[status(thm)],[21])).
% 110.46/70.02 tff(23,plain,
% 110.46/70.02 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 110.46/70.02 inference(rewrite,[status(thm)],[])).
% 110.46/70.02 tff(24,axiom,(![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','star_unfold_right')).
% 110.46/70.02 tff(25,plain,
% 110.46/70.02 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 110.46/70.02 inference(modus_ponens,[status(thm)],[24, 23])).
% 110.46/70.02 tff(26,plain,(
% 110.46/70.02 ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 110.46/70.02 inference(skolemize,[status(sab)],[25])).
% 110.46/70.02 tff(27,plain,
% 110.46/70.02 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 110.46/70.02 inference(modus_ponens,[status(thm)],[26, 22])).
% 110.46/70.02 tff(28,plain,
% 110.46/70.02 ((~![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))) | leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))),
% 110.46/70.02 inference(quant_inst,[status(thm)],[])).
% 110.46/70.02 tff(29,plain,
% 110.46/70.02 (leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))),
% 110.46/70.02 inference(unit_resolution,[status(thm)],[28, 27])).
% 110.46/70.02 tff(30,plain,
% 110.46/70.02 ((~(leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) <=> (addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) = star(X0!0)))) | (~leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))) | (addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) = star(X0!0))),
% 110.46/70.02 inference(tautology,[status(thm)],[])).
% 110.46/70.02 tff(31,plain,
% 110.46/70.02 ((~(leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) <=> (addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) = star(X0!0)))) | (addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) = star(X0!0))),
% 110.46/70.02 inference(unit_resolution,[status(thm)],[30, 29])).
% 110.46/70.02 tff(32,plain,
% 110.46/70.02 (addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) = star(X0!0)),
% 110.46/70.02 inference(unit_resolution,[status(thm)],[31, 20])).
% 110.46/70.02 tff(33,plain,
% 110.46/70.02 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 110.46/70.02 inference(bind,[status(th)],[])).
% 110.46/70.02 tff(34,plain,
% 110.46/70.02 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 110.46/70.02 inference(quant_intro,[status(thm)],[33])).
% 110.46/70.02 tff(35,plain,
% 110.46/70.02 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 110.46/70.02 inference(rewrite,[status(thm)],[])).
% 110.46/70.02 tff(36,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','additive_commutativity')).
% 110.46/70.02 tff(37,plain,
% 110.46/70.02 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 110.46/70.02 inference(modus_ponens,[status(thm)],[36, 35])).
% 110.46/70.02 tff(38,plain,(
% 110.46/70.02 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 110.46/70.02 inference(skolemize,[status(sab)],[37])).
% 110.46/70.02 tff(39,plain,
% 110.46/70.02 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 110.46/70.02 inference(modus_ponens,[status(thm)],[38, 34])).
% 110.46/70.02 tff(40,plain,
% 110.46/70.02 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, multiplication(X0!0, star(X0!0))) = addition(multiplication(X0!0, star(X0!0)), one))),
% 110.46/70.02 inference(quant_inst,[status(thm)],[])).
% 110.46/70.02 tff(41,plain,
% 110.46/70.02 (addition(one, multiplication(X0!0, star(X0!0))) = addition(multiplication(X0!0, star(X0!0)), one)),
% 110.46/70.02 inference(unit_resolution,[status(thm)],[40, 39])).
% 110.46/70.02 tff(42,plain,
% 110.46/70.02 (addition(multiplication(X0!0, star(X0!0)), one) = addition(one, multiplication(X0!0, star(X0!0)))),
% 110.46/70.02 inference(symmetry,[status(thm)],[41])).
% 110.46/70.02 tff(43,plain,
% 110.46/70.02 (addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)) = addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))),
% 110.46/70.02 inference(monotonicity,[status(thm)],[42])).
% 110.46/70.02 tff(44,plain,
% 110.46/70.02 (^[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)))),
% 110.46/70.02 inference(bind,[status(th)],[])).
% 110.46/70.02 tff(45,plain,
% 110.46/70.02 (![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))),
% 110.46/70.02 inference(quant_intro,[status(thm)],[44])).
% 110.46/70.02 tff(46,plain,
% 110.46/70.02 (![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))),
% 110.46/70.02 inference(rewrite,[status(thm)],[])).
% 110.46/70.02 tff(47,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')).
% 110.46/70.02 tff(48,plain,
% 110.46/70.02 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 110.46/70.02 inference(modus_ponens,[status(thm)],[47, 46])).
% 110.46/70.02 tff(49,plain,(
% 110.46/70.02 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 110.46/70.02 inference(skolemize,[status(sab)],[48])).
% 110.46/70.02 tff(50,plain,
% 110.46/70.02 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 110.46/70.02 inference(modus_ponens,[status(thm)],[49, 45])).
% 110.46/70.02 tff(51,plain,
% 110.46/70.02 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0))) = addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)))),
% 110.46/70.02 inference(quant_inst,[status(thm)],[])).
% 110.46/70.02 tff(52,plain,
% 110.46/70.02 (addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0))) = addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))),
% 110.46/70.02 inference(unit_resolution,[status(thm)],[51, 50])).
% 110.46/70.02 tff(53,plain,
% 110.46/70.02 ((~![A: $i] : (addition(A, A) = A)) | (addition(star(X0!0), star(X0!0)) = star(X0!0))),
% 110.46/70.02 inference(quant_inst,[status(thm)],[])).
% 110.46/70.02 tff(54,plain,
% 110.46/70.02 (addition(star(X0!0), star(X0!0)) = star(X0!0)),
% 110.46/70.02 inference(unit_resolution,[status(thm)],[53, 7])).
% 110.46/70.02 tff(55,plain,
% 110.46/70.02 (multiplication(X0!0, addition(star(X0!0), star(X0!0))) = multiplication(X0!0, star(X0!0))),
% 110.46/70.02 inference(monotonicity,[status(thm)],[54])).
% 110.46/70.02 tff(56,plain,
% 110.46/70.02 (^[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))))),
% 110.46/70.02 inference(bind,[status(th)],[])).
% 110.46/70.02 tff(57,plain,
% 110.46/70.02 (![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)))),
% 110.46/70.02 inference(quant_intro,[status(thm)],[56])).
% 110.46/70.02 tff(58,plain,
% 110.46/70.02 (![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)))),
% 110.46/70.02 inference(rewrite,[status(thm)],[])).
% 110.46/70.02 tff(59,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')).
% 110.46/70.02 tff(60,plain,
% 110.46/70.02 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 110.46/70.02 inference(modus_ponens,[status(thm)],[59, 58])).
% 110.46/70.02 tff(61,plain,(
% 110.46/70.02 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 110.46/70.02 inference(skolemize,[status(sab)],[60])).
% 110.46/70.02 tff(62,plain,
% 110.46/70.02 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 110.46/70.02 inference(modus_ponens,[status(thm)],[61, 57])).
% 110.46/70.02 tff(63,plain,
% 110.46/70.02 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!0, addition(star(X0!0), star(X0!0))) = addition(multiplication(X0!0, star(X0!0)), multiplication(X0!0, star(X0!0))))),
% 110.46/70.02 inference(quant_inst,[status(thm)],[])).
% 110.46/70.02 tff(64,plain,
% 110.46/70.02 (multiplication(X0!0, addition(star(X0!0), star(X0!0))) = addition(multiplication(X0!0, star(X0!0)), multiplication(X0!0, star(X0!0)))),
% 110.46/70.02 inference(unit_resolution,[status(thm)],[63, 62])).
% 110.46/70.02 tff(65,plain,
% 110.46/70.02 (addition(multiplication(X0!0, star(X0!0)), multiplication(X0!0, star(X0!0))) = multiplication(X0!0, addition(star(X0!0), star(X0!0)))),
% 110.46/70.02 inference(symmetry,[status(thm)],[64])).
% 110.46/70.02 tff(66,plain,
% 110.46/70.02 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, multiplication(star(X0!0), X0!0)) = addition(multiplication(star(X0!0), X0!0), one))),
% 110.46/70.02 inference(quant_inst,[status(thm)],[])).
% 110.46/70.02 tff(67,plain,
% 110.46/70.02 (addition(one, multiplication(star(X0!0), X0!0)) = addition(multiplication(star(X0!0), X0!0), one)),
% 110.46/70.02 inference(unit_resolution,[status(thm)],[66, 39])).
% 110.46/70.02 tff(68,plain,
% 110.46/70.02 (addition(multiplication(star(X0!0), X0!0), one) = addition(one, multiplication(star(X0!0), X0!0))),
% 110.46/70.02 inference(symmetry,[status(thm)],[67])).
% 110.46/70.02 tff(69,plain,
% 110.46/70.02 (addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)) = addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 110.46/70.02 inference(monotonicity,[status(thm)],[68])).
% 110.46/70.03 tff(70,plain,
% 110.46/70.03 (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))),
% 110.46/70.03 inference(symmetry,[status(thm)],[69])).
% 110.46/70.03 tff(71,plain,
% 110.46/70.03 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) <=> (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = star(X0!0)))),
% 110.46/70.03 inference(quant_inst,[status(thm)],[])).
% 110.46/70.03 tff(72,plain,
% 110.46/70.03 (leq(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) <=> (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = star(X0!0))),
% 110.46/70.03 inference(unit_resolution,[status(thm)],[71, 18])).
% 110.46/70.03 tff(73,plain,
% 110.46/70.03 (^[A: $i] : refl(leq(addition(one, multiplication(star(A), A)), star(A)) <=> leq(addition(one, multiplication(star(A), A)), star(A)))),
% 110.46/70.03 inference(bind,[status(th)],[])).
% 110.46/70.03 tff(74,plain,
% 110.46/70.03 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 110.46/70.03 inference(quant_intro,[status(thm)],[73])).
% 110.46/70.03 tff(75,plain,
% 110.46/70.03 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 110.46/70.03 inference(rewrite,[status(thm)],[])).
% 110.46/70.03 tff(76,axiom,(![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','star_unfold_left')).
% 110.46/70.03 tff(77,plain,
% 110.46/70.03 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 110.46/70.03 inference(modus_ponens,[status(thm)],[76, 75])).
% 110.46/70.03 tff(78,plain,(
% 110.46/70.03 ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 110.46/70.03 inference(skolemize,[status(sab)],[77])).
% 110.46/70.03 tff(79,plain,
% 110.46/70.03 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 110.46/70.03 inference(modus_ponens,[status(thm)],[78, 74])).
% 110.46/70.03 tff(80,plain,
% 110.46/70.03 ((~![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))) | leq(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 110.46/70.03 inference(quant_inst,[status(thm)],[])).
% 110.46/70.03 tff(81,plain,
% 110.46/70.03 (leq(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 110.46/70.03 inference(unit_resolution,[status(thm)],[80, 79])).
% 110.46/70.03 tff(82,plain,
% 110.46/70.03 ((~(leq(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) <=> (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = star(X0!0)))) | (~leq(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))) | (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = star(X0!0))),
% 110.46/70.03 inference(tautology,[status(thm)],[])).
% 110.46/70.03 tff(83,plain,
% 110.46/70.03 ((~(leq(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) <=> (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = star(X0!0)))) | (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = star(X0!0))),
% 110.46/70.03 inference(unit_resolution,[status(thm)],[82, 81])).
% 110.46/70.03 tff(84,plain,
% 110.46/70.03 (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = star(X0!0)),
% 110.46/70.03 inference(unit_resolution,[status(thm)],[83, 72])).
% 110.46/70.03 tff(85,plain,
% 110.46/70.03 (star(X0!0) = addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 110.46/70.03 inference(symmetry,[status(thm)],[84])).
% 110.46/70.03 tff(86,plain,
% 110.46/70.03 (star(X0!0) = addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))),
% 110.46/70.03 inference(transitivity,[status(thm)],[85, 70])).
% 110.46/70.03 tff(87,plain,
% 110.46/70.03 (multiplication(X0!0, star(X0!0)) = multiplication(X0!0, addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)))),
% 110.46/70.03 inference(monotonicity,[status(thm)],[86])).
% 110.46/70.03 tff(88,plain,
% 110.46/70.03 (multiplication(X0!0, addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))) = multiplication(X0!0, star(X0!0))),
% 110.46/70.03 inference(symmetry,[status(thm)],[87])).
% 110.46/70.03 tff(89,plain,
% 110.46/70.03 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!0, addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))) = addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))),
% 110.46/70.03 inference(quant_inst,[status(thm)],[])).
% 110.46/70.03 tff(90,plain,
% 110.46/70.03 (multiplication(X0!0, addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))) = addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))),
% 110.46/70.03 inference(unit_resolution,[status(thm)],[89, 62])).
% 110.46/70.03 tff(91,plain,
% 110.46/70.03 (addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))) = multiplication(X0!0, addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)))),
% 110.46/70.03 inference(symmetry,[status(thm)],[90])).
% 110.46/70.03 tff(92,plain,
% 110.46/70.03 (addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))) = multiplication(X0!0, star(X0!0))),
% 110.46/70.03 inference(transitivity,[status(thm)],[91, 88])).
% 110.46/70.03 tff(93,plain,
% 110.46/70.03 (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))) = addition(multiplication(X0!0, star(X0!0)), multiplication(X0!0, star(X0!0)))),
% 110.46/70.03 inference(monotonicity,[status(thm)],[92, 92])).
% 110.46/70.03 tff(94,plain,
% 110.46/70.03 (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))) = multiplication(X0!0, star(X0!0))),
% 110.46/70.03 inference(transitivity,[status(thm)],[93, 65, 55])).
% 110.46/70.03 tff(95,plain,
% 110.46/70.03 (addition(addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), addition(one, star(X0!0))) = addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0)))),
% 110.46/70.03 inference(monotonicity,[status(thm)],[94])).
% 110.46/70.03 tff(96,plain,
% 110.46/70.03 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0)))) = addition(addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), addition(one, star(X0!0))))),
% 110.46/70.03 inference(quant_inst,[status(thm)],[])).
% 110.46/70.03 tff(97,plain,
% 110.46/70.03 (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0)))) = addition(addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), addition(one, star(X0!0)))),
% 110.46/70.03 inference(unit_resolution,[status(thm)],[96, 50])).
% 110.46/70.03 tff(98,plain,
% 110.46/70.03 (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0))) = addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0)))),
% 110.46/70.03 inference(monotonicity,[status(thm)],[92])).
% 110.46/70.03 tff(99,plain,
% 110.46/70.03 (addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0))) = addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0)))),
% 110.46/70.03 inference(symmetry,[status(thm)],[98])).
% 110.46/70.03 tff(100,plain,
% 110.46/70.03 (addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)) = addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0)))),
% 110.46/70.03 inference(symmetry,[status(thm)],[52])).
% 110.46/70.03 tff(101,plain,
% 110.46/70.03 (addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) = addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))),
% 110.46/70.03 inference(symmetry,[status(thm)],[43])).
% 110.46/70.03 tff(102,plain,
% 110.46/70.03 (star(X0!0) = addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))),
% 110.46/70.03 inference(symmetry,[status(thm)],[32])).
% 110.46/70.03 tff(103,plain,
% 110.46/70.03 (star(X0!0) = addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0)))),
% 110.46/70.03 inference(transitivity,[status(thm)],[102, 101, 100, 99])).
% 110.46/70.03 tff(104,plain,
% 110.46/70.03 (multiplication(X0!0, star(X0!0)) = addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))),
% 110.46/70.03 inference(transitivity,[status(thm)],[87, 90])).
% 110.46/70.03 tff(105,plain,
% 110.46/70.03 (addition(multiplication(X0!0, star(X0!0)), star(X0!0)) = addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0))))),
% 110.46/70.03 inference(monotonicity,[status(thm)],[104, 103])).
% 110.46/70.03 tff(106,plain,
% 110.46/70.03 (addition(multiplication(X0!0, star(X0!0)), star(X0!0)) = star(X0!0)),
% 110.46/70.03 inference(transitivity,[status(thm)],[105, 97, 95, 52, 43, 32])).
% 110.46/70.03 tff(107,plain,
% 110.46/70.03 (leq(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), star(X0!0)) <=> leq(star(X0!0), star(X0!0))),
% 110.46/70.03 inference(monotonicity,[status(thm)],[106])).
% 110.46/70.03 tff(108,plain,
% 110.46/70.03 (leq(star(X0!0), star(X0!0)) <=> leq(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), star(X0!0))),
% 110.46/70.03 inference(symmetry,[status(thm)],[107])).
% 110.46/70.03 tff(109,plain,
% 110.46/70.03 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(star(X0!0), star(X0!0)) <=> (addition(star(X0!0), star(X0!0)) = star(X0!0)))),
% 110.46/70.03 inference(quant_inst,[status(thm)],[])).
% 110.46/70.03 tff(110,plain,
% 110.46/70.03 (leq(star(X0!0), star(X0!0)) <=> (addition(star(X0!0), star(X0!0)) = star(X0!0))),
% 110.46/70.03 inference(unit_resolution,[status(thm)],[109, 18])).
% 110.46/70.03 tff(111,plain,
% 110.46/70.03 ((~(leq(star(X0!0), star(X0!0)) <=> (addition(star(X0!0), star(X0!0)) = star(X0!0)))) | leq(star(X0!0), star(X0!0)) | (~(addition(star(X0!0), star(X0!0)) = star(X0!0)))),
% 110.46/70.03 inference(tautology,[status(thm)],[])).
% 110.46/70.03 tff(112,plain,
% 110.46/70.03 (leq(star(X0!0), star(X0!0))),
% 110.46/70.03 inference(unit_resolution,[status(thm)],[111, 54, 110])).
% 110.46/70.03 tff(113,plain,
% 110.46/70.03 (leq(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), star(X0!0))),
% 110.46/70.03 inference(modus_ponens,[status(thm)],[112, 108])).
% 110.46/70.03 tff(114,plain,
% 110.46/70.03 (^[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)))),
% 110.46/70.03 inference(bind,[status(th)],[])).
% 110.46/70.03 tff(115,plain,
% 110.46/70.03 (![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))),
% 110.46/70.03 inference(quant_intro,[status(thm)],[114])).
% 110.46/70.03 tff(116,plain,
% 110.46/70.03 (![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))),
% 110.46/70.03 inference(rewrite,[status(thm)],[])).
% 110.46/70.03 tff(117,plain,
% 110.46/70.03 (^[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)))),
% 110.46/70.03 inference(bind,[status(th)],[])).
% 110.46/70.03 tff(118,plain,
% 110.46/70.03 (![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))),
% 110.46/70.03 inference(quant_intro,[status(thm)],[117])).
% 110.46/70.03 tff(119,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')).
% 110.46/70.03 tff(120,plain,
% 110.46/70.03 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 110.46/70.03 inference(modus_ponens,[status(thm)],[119, 118])).
% 110.46/70.03 tff(121,plain,
% 110.46/70.03 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 110.46/70.03 inference(modus_ponens,[status(thm)],[120, 116])).
% 110.46/70.03 tff(122,plain,(
% 110.46/70.03 ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 110.46/70.03 inference(skolemize,[status(sab)],[121])).
% 110.46/70.03 tff(123,plain,
% 110.46/70.03 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 110.46/70.03 inference(modus_ponens,[status(thm)],[122, 115])).
% 110.46/70.03 tff(124,plain,
% 110.46/70.03 (((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | ((~leq(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), star(X0!0))) | leq(multiplication(star(X0!0), star(X0!0)), star(X0!0)))) <=> ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | (~leq(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), star(X0!0))) | leq(multiplication(star(X0!0), star(X0!0)), star(X0!0)))),
% 110.46/70.03 inference(rewrite,[status(thm)],[])).
% 110.46/70.03 tff(125,plain,
% 110.46/70.03 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | ((~leq(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), star(X0!0))) | leq(multiplication(star(X0!0), star(X0!0)), star(X0!0)))),
% 110.46/70.03 inference(quant_inst,[status(thm)],[])).
% 110.46/70.03 tff(126,plain,
% 110.46/70.03 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | (~leq(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), star(X0!0))) | leq(multiplication(star(X0!0), star(X0!0)), star(X0!0))),
% 110.46/70.03 inference(modus_ponens,[status(thm)],[125, 124])).
% 110.46/70.03 tff(127,plain,
% 110.46/70.03 ((~leq(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), star(X0!0))) | leq(multiplication(star(X0!0), star(X0!0)), star(X0!0))),
% 110.46/70.03 inference(unit_resolution,[status(thm)],[126, 123])).
% 110.46/70.03 tff(128,plain,
% 110.46/70.03 (leq(multiplication(star(X0!0), star(X0!0)), star(X0!0))),
% 110.46/70.03 inference(unit_resolution,[status(thm)],[127, 113])).
% 110.46/70.03 tff(129,plain,
% 110.46/70.03 (leq(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(X0!0))), star(X0!0))),
% 110.46/70.03 inference(modus_ponens,[status(thm)],[128, 11])).
% 110.46/70.03 tff(130,plain,
% 110.46/70.03 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(star(X0!0), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0))) = addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)), multiplication(star(X0!0), star(X0!0))))),
% 110.46/70.03 inference(quant_inst,[status(thm)],[])).
% 110.46/70.03 tff(131,plain,
% 110.46/70.03 (multiplication(star(X0!0), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0))) = addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)), multiplication(star(X0!0), star(X0!0)))),
% 110.46/70.03 inference(unit_resolution,[status(thm)],[130, 62])).
% 110.46/70.03 tff(132,plain,
% 110.46/70.03 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)) = addition(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 110.46/70.03 inference(quant_inst,[status(thm)],[])).
% 110.46/70.03 tff(133,plain,
% 110.46/70.03 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)) = addition(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.46/70.03 inference(unit_resolution,[status(thm)],[132, 39])).
% 110.46/70.03 tff(134,plain,
% 110.46/70.03 (addition(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0))),
% 110.46/70.03 inference(symmetry,[status(thm)],[133])).
% 110.46/70.03 tff(135,plain,
% 110.46/70.03 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(star(X0!0), star(star(X0!0))) <=> (addition(star(X0!0), star(star(X0!0))) = star(star(X0!0))))),
% 110.46/70.03 inference(quant_inst,[status(thm)],[])).
% 110.46/70.03 tff(136,plain,
% 110.46/70.03 (leq(star(X0!0), star(star(X0!0))) <=> (addition(star(X0!0), star(star(X0!0))) = star(star(X0!0)))),
% 110.46/70.03 inference(unit_resolution,[status(thm)],[135, 18])).
% 110.46/70.03 tff(137,plain,
% 110.46/70.03 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) <=> (addition(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = star(star(X0!0))))),
% 110.46/70.03 inference(quant_inst,[status(thm)],[])).
% 110.46/70.03 tff(138,plain,
% 110.46/70.03 (leq(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) <=> (addition(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = star(star(X0!0)))),
% 110.46/70.03 inference(unit_resolution,[status(thm)],[137, 18])).
% 110.46/70.03 tff(139,plain,
% 110.46/70.03 ((~![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))) | leq(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0)))),
% 110.46/70.03 inference(quant_inst,[status(thm)],[])).
% 110.46/70.03 tff(140,plain,
% 110.46/70.03 (leq(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0)))),
% 110.46/70.03 inference(unit_resolution,[status(thm)],[139, 27])).
% 110.46/70.03 tff(141,plain,
% 110.46/70.03 ((~(leq(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) <=> (addition(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = star(star(X0!0))))) | (~leq(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0)))) | (addition(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = star(star(X0!0)))),
% 110.46/70.03 inference(tautology,[status(thm)],[])).
% 110.46/70.03 tff(142,plain,
% 110.46/70.03 ((~(leq(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) <=> (addition(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = star(star(X0!0))))) | (addition(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = star(star(X0!0)))),
% 110.46/70.03 inference(unit_resolution,[status(thm)],[141, 140])).
% 110.46/70.03 tff(143,plain,
% 110.46/70.03 (addition(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = star(star(X0!0))),
% 110.46/70.03 inference(unit_resolution,[status(thm)],[142, 138])).
% 110.46/70.03 tff(144,plain,
% 110.46/70.03 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, multiplication(star(X0!0), star(star(X0!0)))) = addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.46/70.03 inference(quant_inst,[status(thm)],[])).
% 110.46/70.03 tff(145,plain,
% 110.46/70.03 (addition(one, multiplication(star(X0!0), star(star(X0!0)))) = addition(multiplication(star(X0!0), star(star(X0!0))), one)),
% 110.46/70.03 inference(unit_resolution,[status(thm)],[144, 39])).
% 110.46/70.03 tff(146,plain,
% 110.46/70.03 (addition(multiplication(star(X0!0), star(star(X0!0))), one) = addition(one, multiplication(star(X0!0), star(star(X0!0))))),
% 110.46/70.03 inference(symmetry,[status(thm)],[145])).
% 110.46/70.03 tff(147,plain,
% 110.46/70.03 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0))) = addition(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0)))),
% 110.46/70.03 inference(monotonicity,[status(thm)],[146])).
% 110.46/70.03 tff(148,plain,
% 110.46/70.03 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(star(X0!0), star(star(X0!0))), addition(one, star(star(X0!0)))) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0))))),
% 110.46/70.03 inference(quant_inst,[status(thm)],[])).
% 110.46/70.03 tff(149,plain,
% 110.46/70.03 (addition(multiplication(star(X0!0), star(star(X0!0))), addition(one, star(star(X0!0)))) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0)))),
% 110.46/70.03 inference(unit_resolution,[status(thm)],[148, 50])).
% 110.46/70.03 tff(150,plain,
% 110.46/70.03 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))) <=> (addition(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))) = star(star(X0!0))))),
% 110.46/70.03 inference(quant_inst,[status(thm)],[])).
% 110.46/70.03 tff(151,plain,
% 110.46/70.03 (leq(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))) <=> (addition(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))) = star(star(X0!0)))),
% 110.46/70.03 inference(unit_resolution,[status(thm)],[150, 18])).
% 110.46/70.03 tff(152,plain,
% 110.46/70.03 ((~![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))) | leq(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0)))),
% 110.46/70.03 inference(quant_inst,[status(thm)],[])).
% 110.46/70.03 tff(153,plain,
% 110.46/70.03 (leq(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0)))),
% 110.46/70.03 inference(unit_resolution,[status(thm)],[152, 79])).
% 110.46/70.03 tff(154,plain,
% 110.46/70.03 ((~(leq(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))) <=> (addition(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))) = star(star(X0!0))))) | (~leq(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0)))) | (addition(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))) = star(star(X0!0)))),
% 110.46/70.03 inference(tautology,[status(thm)],[])).
% 110.46/70.03 tff(155,plain,
% 110.46/70.03 ((~(leq(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))) <=> (addition(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))) = star(star(X0!0))))) | (addition(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))) = star(star(X0!0)))),
% 110.46/70.03 inference(unit_resolution,[status(thm)],[154, 153])).
% 110.46/70.03 tff(156,plain,
% 110.46/70.03 (addition(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))) = star(star(X0!0))),
% 110.46/70.03 inference(unit_resolution,[status(thm)],[155, 151])).
% 110.46/70.03 tff(157,plain,
% 110.46/70.03 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, multiplication(star(star(X0!0)), star(X0!0))) = addition(multiplication(star(star(X0!0)), star(X0!0)), one))),
% 110.46/70.03 inference(quant_inst,[status(thm)],[])).
% 110.46/70.03 tff(158,plain,
% 110.46/70.03 (addition(one, multiplication(star(star(X0!0)), star(X0!0))) = addition(multiplication(star(star(X0!0)), star(X0!0)), one)),
% 110.46/70.03 inference(unit_resolution,[status(thm)],[157, 39])).
% 110.46/70.03 tff(159,plain,
% 110.46/70.03 (addition(multiplication(star(star(X0!0)), star(X0!0)), one) = addition(one, multiplication(star(star(X0!0)), star(X0!0)))),
% 110.46/70.03 inference(symmetry,[status(thm)],[158])).
% 110.46/70.03 tff(160,plain,
% 110.46/70.03 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))) = addition(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0)))),
% 110.46/70.03 inference(monotonicity,[status(thm)],[159])).
% 110.46/70.03 tff(161,plain,
% 110.46/70.03 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))) = star(star(X0!0))),
% 110.46/70.03 inference(transitivity,[status(thm)],[160, 156])).
% 110.46/70.03 tff(162,plain,
% 110.46/70.03 (multiplication(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0)))) = multiplication(star(X0!0), star(star(X0!0)))),
% 110.46/70.03 inference(monotonicity,[status(thm)],[161])).
% 110.46/70.03 tff(163,plain,
% 110.46/70.03 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0)))) = addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.46/70.03 inference(quant_inst,[status(thm)],[])).
% 110.46/70.03 tff(164,plain,
% 110.46/70.03 (multiplication(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0)))) = addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))),
% 110.46/70.03 inference(unit_resolution,[status(thm)],[163, 62])).
% 110.46/70.03 tff(165,plain,
% 110.46/70.03 (addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))) = multiplication(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))))),
% 110.46/70.03 inference(symmetry,[status(thm)],[164])).
% 110.46/70.03 tff(166,plain,
% 110.46/70.03 ((~![A: $i] : (addition(A, A) = A)) | (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))) = addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.46/70.03 inference(quant_inst,[status(thm)],[])).
% 110.46/70.03 tff(167,plain,
% 110.46/70.03 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))) = addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))),
% 110.46/70.03 inference(unit_resolution,[status(thm)],[166, 7])).
% 110.46/70.03 tff(168,plain,
% 110.46/70.03 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))) = multiplication(star(X0!0), star(star(X0!0)))),
% 110.46/70.03 inference(transitivity,[status(thm)],[167, 165, 162])).
% 110.46/70.03 tff(169,plain,
% 110.46/70.03 (addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, star(star(X0!0)))) = addition(multiplication(star(X0!0), star(star(X0!0))), addition(one, star(star(X0!0))))),
% 110.46/70.03 inference(monotonicity,[status(thm)],[168])).
% 110.46/70.03 tff(170,plain,
% 110.46/70.03 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0))))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, star(star(X0!0)))))),
% 110.46/70.04 inference(quant_inst,[status(thm)],[])).
% 110.46/70.04 tff(171,plain,
% 110.46/70.04 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0))))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, star(star(X0!0))))),
% 110.46/70.04 inference(unit_resolution,[status(thm)],[170, 50])).
% 110.46/70.04 tff(172,plain,
% 110.46/70.04 (addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))) = multiplication(star(X0!0), star(star(X0!0)))),
% 110.46/70.04 inference(transitivity,[status(thm)],[165, 162])).
% 110.46/70.04 tff(173,plain,
% 110.46/70.04 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0)))) = addition(multiplication(star(X0!0), star(star(X0!0))), addition(one, star(star(X0!0))))),
% 110.46/70.04 inference(monotonicity,[status(thm)],[172])).
% 110.46/70.04 tff(174,plain,
% 110.46/70.04 (addition(multiplication(star(X0!0), star(star(X0!0))), addition(one, star(star(X0!0)))) = addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0))))),
% 110.46/70.04 inference(symmetry,[status(thm)],[173])).
% 110.46/70.04 tff(175,plain,
% 110.46/70.04 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0))) = addition(multiplication(star(X0!0), star(star(X0!0))), addition(one, star(star(X0!0))))),
% 110.46/70.04 inference(symmetry,[status(thm)],[149])).
% 110.46/70.04 tff(176,plain,
% 110.46/70.04 (addition(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0)))),
% 110.46/70.04 inference(symmetry,[status(thm)],[147])).
% 110.46/70.04 tff(177,plain,
% 110.46/70.04 (star(star(X0!0)) = addition(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0)))),
% 110.46/70.04 inference(symmetry,[status(thm)],[143])).
% 110.46/70.04 tff(178,plain,
% 110.46/70.04 (star(star(X0!0)) = addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0))))),
% 110.46/70.04 inference(transitivity,[status(thm)],[177, 176, 175, 174])).
% 110.46/70.04 tff(179,plain,
% 110.46/70.04 (multiplication(star(X0!0), star(star(X0!0))) = multiplication(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))))),
% 110.46/70.04 inference(symmetry,[status(thm)],[162])).
% 110.46/70.04 tff(180,plain,
% 110.46/70.04 (multiplication(star(X0!0), star(star(X0!0))) = addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))),
% 110.46/70.04 inference(transitivity,[status(thm)],[179, 164])).
% 110.46/70.04 tff(181,plain,
% 110.46/70.04 (addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0))) = addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0)))))),
% 110.46/70.04 inference(monotonicity,[status(thm)],[180, 178])).
% 110.46/70.04 tff(182,plain,
% 110.46/70.04 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0)))) = addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0)))),
% 110.46/70.04 inference(monotonicity,[status(thm)],[172, 161])).
% 110.46/70.04 tff(183,plain,
% 110.46/70.04 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0)))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), star(star(X0!0))))),
% 110.46/70.04 inference(quant_inst,[status(thm)],[])).
% 110.46/70.04 tff(184,plain,
% 110.46/70.04 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0)))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), star(star(X0!0)))),
% 110.46/70.04 inference(unit_resolution,[status(thm)],[183, 50])).
% 110.46/70.04 tff(185,plain,
% 110.46/70.04 (addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), star(star(X0!0))) = addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))))),
% 110.46/70.04 inference(symmetry,[status(thm)],[184])).
% 110.46/70.04 tff(186,plain,
% 110.46/70.04 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), star(star(X0!0))) = addition(star(star(X0!0)), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(star(X0!0)), star(X0!0)), one))))),
% 110.46/70.04 inference(quant_inst,[status(thm)],[])).
% 110.46/70.04 tff(187,plain,
% 110.46/70.04 (addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), star(star(X0!0))) = addition(star(star(X0!0)), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)))),
% 110.46/70.04 inference(unit_resolution,[status(thm)],[186, 39])).
% 110.46/70.04 tff(188,plain,
% 110.46/70.04 (addition(star(star(X0!0)), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(star(X0!0)), star(X0!0)), one))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), star(star(X0!0)))),
% 110.46/70.04 inference(symmetry,[status(thm)],[187])).
% 110.46/70.04 tff(189,plain,
% 110.46/70.04 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(star(star(X0!0)), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(star(X0!0)), star(X0!0)), one))) = addition(addition(star(star(X0!0)), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)))),
% 110.46/70.04 inference(quant_inst,[status(thm)],[])).
% 110.46/70.04 tff(190,plain,
% 110.46/70.04 (addition(star(star(X0!0)), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(star(X0!0)), star(X0!0)), one))) = addition(addition(star(star(X0!0)), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(multiplication(star(star(X0!0)), star(X0!0)), one))),
% 110.46/70.04 inference(unit_resolution,[status(thm)],[189, 50])).
% 110.46/70.04 tff(191,plain,
% 110.46/70.04 (addition(addition(star(star(X0!0)), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(star(star(X0!0)), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)))),
% 110.46/70.04 inference(symmetry,[status(thm)],[190])).
% 110.46/70.04 tff(192,plain,
% 110.46/70.04 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(star(star(X0!0)), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(star(star(X0!0)), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))))),
% 110.46/70.04 inference(quant_inst,[status(thm)],[])).
% 110.46/70.04 tff(193,plain,
% 110.46/70.04 (addition(addition(star(star(X0!0)), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(star(star(X0!0)), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.46/70.04 inference(unit_resolution,[status(thm)],[192, 39])).
% 110.46/70.04 tff(194,plain,
% 110.46/70.04 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(star(star(X0!0)), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(addition(star(star(X0!0)), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(multiplication(star(star(X0!0)), star(X0!0)), one))),
% 110.46/70.04 inference(symmetry,[status(thm)],[193])).
% 110.46/70.04 tff(195,plain,
% 110.46/70.04 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = addition(star(star(X0!0)), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.46/70.04 inference(quant_inst,[status(thm)],[])).
% 110.46/70.04 tff(196,plain,
% 110.46/70.04 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = addition(star(star(X0!0)), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.46/70.04 inference(unit_resolution,[status(thm)],[195, 39])).
% 110.46/70.04 tff(197,plain,
% 110.46/70.04 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0)))),
% 110.46/70.04 inference(monotonicity,[status(thm)],[172])).
% 110.46/70.04 tff(198,plain,
% 110.46/70.04 (addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0))) = addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0)))),
% 110.46/70.04 inference(symmetry,[status(thm)],[197])).
% 110.46/70.04 tff(199,plain,
% 110.46/70.04 (addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0))) = addition(star(star(X0!0)), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.46/70.04 inference(transitivity,[status(thm)],[198, 196])).
% 110.46/70.04 tff(200,plain,
% 110.46/70.04 (multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))), star(X0!0)) = multiplication(star(star(X0!0)), star(X0!0))),
% 110.46/70.04 inference(monotonicity,[status(thm)],[161])).
% 110.46/70.04 tff(201,plain,
% 110.46/70.04 (^[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))))),
% 110.46/70.04 inference(bind,[status(th)],[])).
% 110.46/70.04 tff(202,plain,
% 110.46/70.04 (![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)))),
% 110.46/70.04 inference(quant_intro,[status(thm)],[201])).
% 110.46/70.04 tff(203,plain,
% 110.46/70.04 (![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)))),
% 110.46/70.04 inference(rewrite,[status(thm)],[])).
% 110.46/70.04 tff(204,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')).
% 110.46/70.04 tff(205,plain,
% 110.46/70.04 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 110.46/70.04 inference(modus_ponens,[status(thm)],[204, 203])).
% 110.46/70.04 tff(206,plain,(
% 110.46/70.04 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 110.46/70.04 inference(skolemize,[status(sab)],[205])).
% 110.46/70.04 tff(207,plain,
% 110.46/70.04 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 110.46/70.04 inference(modus_ponens,[status(thm)],[206, 202])).
% 110.46/70.04 tff(208,plain,
% 110.46/70.04 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))), star(X0!0)) = addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))),
% 110.46/70.04 inference(quant_inst,[status(thm)],[])).
% 110.46/70.04 tff(209,plain,
% 110.46/70.04 (multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))), star(X0!0)) = addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))),
% 110.46/70.04 inference(unit_resolution,[status(thm)],[208, 207])).
% 110.46/70.04 tff(210,plain,
% 110.46/70.04 (addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))) = multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))), star(X0!0))),
% 110.46/70.04 inference(symmetry,[status(thm)],[209])).
% 110.46/70.04 tff(211,plain,
% 110.46/70.04 (addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))) = multiplication(star(star(X0!0)), star(X0!0))),
% 110.46/70.04 inference(transitivity,[status(thm)],[210, 200])).
% 110.46/70.04 tff(212,plain,
% 110.46/70.04 (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), one) = addition(multiplication(star(star(X0!0)), star(X0!0)), one)),
% 110.46/70.04 inference(monotonicity,[status(thm)],[211])).
% 110.46/70.04 tff(213,plain,
% 110.46/70.04 (addition(addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), one), addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0)))) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(star(star(X0!0)), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.46/70.04 inference(monotonicity,[status(thm)],[212, 199])).
% 110.46/70.04 tff(214,plain,
% 110.46/70.04 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0))))) = addition(addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), one), addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0)))))),
% 110.46/70.04 inference(quant_inst,[status(thm)],[])).
% 110.46/70.04 tff(215,plain,
% 110.46/70.04 (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0))))) = addition(addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), one), addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0))))),
% 110.46/70.04 inference(unit_resolution,[status(thm)],[214, 50])).
% 110.46/70.04 tff(216,plain,
% 110.46/70.04 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0)))) = addition(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))))),
% 110.46/70.04 inference(quant_inst,[status(thm)],[])).
% 110.46/70.04 tff(217,plain,
% 110.46/70.04 (addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0)))) = addition(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0)))),
% 110.46/70.04 inference(unit_resolution,[status(thm)],[216, 50])).
% 110.46/70.04 tff(218,plain,
% 110.46/70.04 (addition(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0))))),
% 110.46/70.04 inference(symmetry,[status(thm)],[217])).
% 110.46/70.04 tff(219,plain,
% 110.46/70.04 (star(star(X0!0)) = addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0))))),
% 110.46/70.04 inference(transitivity,[status(thm)],[177, 218])).
% 110.46/70.04 tff(220,plain,
% 110.46/70.04 (multiplication(star(star(X0!0)), star(X0!0)) = multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))), star(X0!0))),
% 110.46/70.04 inference(symmetry,[status(thm)],[200])).
% 110.46/70.04 tff(221,plain,
% 110.46/70.04 (multiplication(star(star(X0!0)), star(X0!0)) = addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))),
% 110.46/70.04 inference(transitivity,[status(thm)],[220, 209])).
% 110.46/70.04 tff(222,plain,
% 110.46/70.04 (addition(multiplication(star(star(X0!0)), star(X0!0)), star(star(X0!0))) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0)))))),
% 110.46/70.04 inference(monotonicity,[status(thm)],[221, 219])).
% 110.46/70.04 tff(223,plain,
% 110.46/70.04 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 110.46/70.04 inference(bind,[status(th)],[])).
% 110.46/70.04 tff(224,plain,
% 110.46/70.04 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 110.46/70.04 inference(quant_intro,[status(thm)],[223])).
% 110.46/70.04 tff(225,plain,
% 110.46/70.04 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 110.46/70.04 inference(rewrite,[status(thm)],[])).
% 110.46/70.04 tff(226,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','multiplicative_right_identity')).
% 110.46/70.04 tff(227,plain,
% 110.46/70.04 (![A: $i] : (multiplication(A, one) = A)),
% 110.46/70.04 inference(modus_ponens,[status(thm)],[226, 225])).
% 110.46/70.04 tff(228,plain,(
% 110.46/70.04 ![A: $i] : (multiplication(A, one) = A)),
% 110.46/70.04 inference(skolemize,[status(sab)],[227])).
% 110.46/70.04 tff(229,plain,
% 110.46/70.04 (![A: $i] : (multiplication(A, one) = A)),
% 110.46/70.04 inference(modus_ponens,[status(thm)],[228, 224])).
% 110.46/70.04 tff(230,plain,
% 110.46/70.04 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(star(star(X0!0)), one) = star(star(X0!0)))),
% 110.46/70.04 inference(quant_inst,[status(thm)],[])).
% 110.46/70.04 tff(231,plain,
% 110.46/70.04 (multiplication(star(star(X0!0)), one) = star(star(X0!0))),
% 110.46/70.04 inference(unit_resolution,[status(thm)],[230, 229])).
% 110.46/70.04 tff(232,plain,
% 110.46/70.04 (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), multiplication(star(star(X0!0)), one)) = addition(multiplication(star(star(X0!0)), star(X0!0)), star(star(X0!0)))),
% 110.46/70.04 inference(monotonicity,[status(thm)],[211, 231])).
% 110.46/70.04 tff(233,plain,
% 110.46/70.04 (addition(multiplication(star(star(X0!0)), star(X0!0)), multiplication(star(star(X0!0)), one)) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), multiplication(star(star(X0!0)), one))),
% 110.46/70.04 inference(monotonicity,[status(thm)],[221])).
% 110.46/70.04 tff(234,plain,
% 110.46/70.04 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(star(star(X0!0)), addition(star(X0!0), one)) = addition(multiplication(star(star(X0!0)), star(X0!0)), multiplication(star(star(X0!0)), one)))),
% 110.46/70.04 inference(quant_inst,[status(thm)],[])).
% 110.46/70.04 tff(235,plain,
% 110.46/70.04 (multiplication(star(star(X0!0)), addition(star(X0!0), one)) = addition(multiplication(star(star(X0!0)), star(X0!0)), multiplication(star(star(X0!0)), one))),
% 110.46/70.04 inference(unit_resolution,[status(thm)],[234, 62])).
% 110.46/70.04 tff(236,plain,
% 110.46/70.04 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, star(X0!0)) = addition(star(X0!0), one))),
% 110.46/70.04 inference(quant_inst,[status(thm)],[])).
% 110.46/70.04 tff(237,plain,
% 110.46/70.04 (addition(one, star(X0!0)) = addition(star(X0!0), one)),
% 110.46/70.04 inference(unit_resolution,[status(thm)],[236, 39])).
% 110.46/70.04 tff(238,plain,
% 110.46/70.04 (multiplication(star(star(X0!0)), addition(one, star(X0!0))) = multiplication(star(star(X0!0)), addition(star(X0!0), one))),
% 110.46/70.04 inference(monotonicity,[status(thm)],[237])).
% 110.46/70.04 tff(239,plain,
% 110.46/70.04 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0))) = addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)))),
% 110.46/70.04 inference(quant_inst,[status(thm)],[])).
% 110.46/70.04 tff(240,plain,
% 110.46/70.04 (addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0))) = addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 110.46/70.04 inference(unit_resolution,[status(thm)],[239, 50])).
% 110.46/70.04 tff(241,plain,
% 110.46/70.04 (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0)))),
% 110.46/70.04 inference(symmetry,[status(thm)],[240])).
% 110.46/70.04 tff(242,plain,
% 110.46/70.04 (star(X0!0) = addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0)))),
% 110.46/70.04 inference(transitivity,[status(thm)],[85, 241])).
% 110.46/70.04 tff(243,plain,
% 110.46/70.04 (addition(one, star(X0!0)) = addition(one, addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0))))),
% 110.46/70.04 inference(monotonicity,[status(thm)],[242])).
% 110.46/70.04 tff(244,plain,
% 110.46/70.04 (addition(one, addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0)))) = addition(one, star(X0!0))),
% 110.46/70.04 inference(symmetry,[status(thm)],[243])).
% 110.46/70.04 tff(245,plain,
% 110.46/70.04 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0)))) = addition(addition(one, one), addition(multiplication(star(X0!0), X0!0), star(X0!0))))),
% 110.46/70.04 inference(quant_inst,[status(thm)],[])).
% 110.46/70.04 tff(246,plain,
% 110.46/70.04 (addition(one, addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0)))) = addition(addition(one, one), addition(multiplication(star(X0!0), X0!0), star(X0!0)))),
% 110.46/70.04 inference(unit_resolution,[status(thm)],[245, 50])).
% 110.46/70.04 tff(247,plain,
% 110.46/70.04 (addition(addition(one, one), addition(multiplication(star(X0!0), X0!0), star(X0!0))) = addition(one, addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0))))),
% 110.46/70.04 inference(symmetry,[status(thm)],[246])).
% 110.46/70.04 tff(248,plain,
% 110.46/70.04 ((~![A: $i] : (addition(A, A) = A)) | (addition(one, one) = one)),
% 110.46/70.04 inference(quant_inst,[status(thm)],[])).
% 110.46/70.04 tff(249,plain,
% 110.46/70.04 (addition(one, one) = one),
% 110.46/70.04 inference(unit_resolution,[status(thm)],[248, 7])).
% 110.46/70.04 tff(250,plain,
% 110.46/70.04 (addition(addition(one, one), addition(multiplication(star(X0!0), X0!0), star(X0!0))) = addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0)))),
% 110.46/70.04 inference(monotonicity,[status(thm)],[249])).
% 110.46/70.04 tff(251,plain,
% 110.46/70.04 (addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0))) = addition(addition(one, one), addition(multiplication(star(X0!0), X0!0), star(X0!0)))),
% 110.46/70.04 inference(symmetry,[status(thm)],[250])).
% 110.46/70.04 tff(252,plain,
% 110.46/70.04 (star(X0!0) = addition(one, star(X0!0))),
% 110.46/70.04 inference(transitivity,[status(thm)],[85, 241, 251, 247, 244])).
% 110.46/70.04 tff(253,plain,
% 110.46/70.04 (multiplication(star(star(X0!0)), star(X0!0)) = multiplication(star(star(X0!0)), addition(one, star(X0!0)))),
% 110.46/70.04 inference(monotonicity,[status(thm)],[252])).
% 110.46/70.04 tff(254,plain,
% 110.46/70.04 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), star(star(X0!0)))) = addition(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))))),
% 110.46/70.04 inference(quant_inst,[status(thm)],[])).
% 110.46/70.04 tff(255,plain,
% 110.46/70.04 (addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), star(star(X0!0)))) = addition(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0)))),
% 110.46/70.04 inference(unit_resolution,[status(thm)],[254, 50])).
% 110.46/70.04 tff(256,plain,
% 110.46/70.04 (addition(addition(one, one), addition(multiplication(star(star(X0!0)), star(X0!0)), star(star(X0!0)))) = addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), star(star(X0!0))))),
% 110.46/70.04 inference(monotonicity,[status(thm)],[249])).
% 110.46/70.04 tff(257,plain,
% 110.46/70.04 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), star(star(X0!0))))) = addition(addition(one, one), addition(multiplication(star(star(X0!0)), star(X0!0)), star(star(X0!0)))))),
% 110.46/70.04 inference(quant_inst,[status(thm)],[])).
% 110.46/70.04 tff(258,plain,
% 110.46/70.04 (addition(one, addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), star(star(X0!0))))) = addition(addition(one, one), addition(multiplication(star(star(X0!0)), star(X0!0)), star(star(X0!0))))),
% 110.46/70.04 inference(unit_resolution,[status(thm)],[257, 50])).
% 110.46/70.04 tff(259,plain,
% 110.46/70.04 (addition(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))) = addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), star(star(X0!0))))),
% 110.46/70.04 inference(symmetry,[status(thm)],[255])).
% 110.46/70.04 tff(260,plain,
% 110.46/70.04 (star(star(X0!0)) = addition(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0)))),
% 110.46/70.04 inference(symmetry,[status(thm)],[156])).
% 110.46/70.04 tff(261,plain,
% 110.46/70.04 (star(star(X0!0)) = addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), star(star(X0!0))))),
% 110.46/70.04 inference(transitivity,[status(thm)],[260, 259])).
% 110.46/70.04 tff(262,plain,
% 110.46/70.04 (addition(one, star(star(X0!0))) = addition(one, addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), star(star(X0!0)))))),
% 110.46/70.04 inference(monotonicity,[status(thm)],[261])).
% 110.46/70.04 tff(263,plain,
% 110.46/70.04 (addition(one, star(star(X0!0))) = star(star(X0!0))),
% 110.46/70.04 inference(transitivity,[status(thm)],[262, 258, 256, 255, 156])).
% 110.46/70.04 tff(264,plain,
% 110.46/70.04 (multiplication(addition(one, star(star(X0!0))), star(X0!0)) = multiplication(star(star(X0!0)), star(X0!0))),
% 110.46/70.04 inference(monotonicity,[status(thm)],[263])).
% 110.46/70.04 tff(265,plain,
% 110.46/70.04 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, star(star(X0!0))) = addition(star(star(X0!0)), one))),
% 110.46/70.04 inference(quant_inst,[status(thm)],[])).
% 110.46/70.04 tff(266,plain,
% 110.46/70.04 (addition(one, star(star(X0!0))) = addition(star(star(X0!0)), one)),
% 110.46/70.04 inference(unit_resolution,[status(thm)],[265, 39])).
% 110.46/70.04 tff(267,plain,
% 110.46/70.04 (addition(star(star(X0!0)), one) = addition(one, star(star(X0!0)))),
% 110.46/70.04 inference(symmetry,[status(thm)],[266])).
% 110.46/70.04 tff(268,plain,
% 110.46/70.04 (multiplication(addition(star(star(X0!0)), one), star(X0!0)) = multiplication(addition(one, star(star(X0!0))), star(X0!0))),
% 110.46/70.04 inference(monotonicity,[status(thm)],[267])).
% 110.46/70.04 tff(269,plain,
% 110.46/70.04 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(star(star(X0!0)), one), star(X0!0)) = addition(multiplication(star(star(X0!0)), star(X0!0)), multiplication(one, star(X0!0))))),
% 110.46/70.04 inference(quant_inst,[status(thm)],[])).
% 110.46/70.04 tff(270,plain,
% 110.46/70.04 (multiplication(addition(star(star(X0!0)), one), star(X0!0)) = addition(multiplication(star(star(X0!0)), star(X0!0)), multiplication(one, star(X0!0)))),
% 110.46/70.04 inference(unit_resolution,[status(thm)],[269, 207])).
% 110.46/70.04 tff(271,plain,
% 110.46/70.04 (addition(multiplication(star(star(X0!0)), star(X0!0)), multiplication(one, star(X0!0))) = multiplication(addition(star(star(X0!0)), one), star(X0!0))),
% 110.46/70.04 inference(symmetry,[status(thm)],[270])).
% 110.46/70.04 tff(272,plain,
% 110.46/70.04 (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), multiplication(one, star(X0!0))) = addition(multiplication(star(star(X0!0)), star(X0!0)), multiplication(one, star(X0!0)))),
% 110.46/70.04 inference(monotonicity,[status(thm)],[211])).
% 110.46/70.04 tff(273,plain,
% 110.46/70.04 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 110.46/70.04 inference(bind,[status(th)],[])).
% 110.46/70.04 tff(274,plain,
% 110.46/70.04 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 110.46/70.04 inference(quant_intro,[status(thm)],[273])).
% 110.46/70.04 tff(275,plain,
% 110.46/70.04 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 110.46/70.04 inference(rewrite,[status(thm)],[])).
% 110.46/70.04 tff(276,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','multiplicative_left_identity')).
% 110.46/70.04 tff(277,plain,
% 110.46/70.04 (![A: $i] : (multiplication(one, A) = A)),
% 110.46/70.04 inference(modus_ponens,[status(thm)],[276, 275])).
% 110.46/70.04 tff(278,plain,(
% 110.46/70.04 ![A: $i] : (multiplication(one, A) = A)),
% 110.46/70.04 inference(skolemize,[status(sab)],[277])).
% 110.46/70.04 tff(279,plain,
% 110.46/70.04 (![A: $i] : (multiplication(one, A) = A)),
% 110.46/70.04 inference(modus_ponens,[status(thm)],[278, 274])).
% 110.46/70.04 tff(280,plain,
% 110.46/70.04 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, star(X0!0)) = star(X0!0))),
% 110.46/70.04 inference(quant_inst,[status(thm)],[])).
% 110.46/70.04 tff(281,plain,
% 110.46/70.04 (multiplication(one, star(X0!0)) = star(X0!0)),
% 110.46/70.04 inference(unit_resolution,[status(thm)],[280, 279])).
% 110.46/70.04 tff(282,plain,
% 110.46/70.04 (star(X0!0) = multiplication(one, star(X0!0))),
% 110.46/70.04 inference(symmetry,[status(thm)],[281])).
% 110.46/70.04 tff(283,plain,
% 110.46/70.04 (addition(multiplication(star(star(X0!0)), star(X0!0)), star(X0!0)) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), multiplication(one, star(X0!0)))),
% 110.46/70.04 inference(monotonicity,[status(thm)],[221, 282])).
% 110.46/70.04 tff(284,plain,
% 110.46/70.04 (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), star(X0!0)) = addition(multiplication(star(star(X0!0)), star(X0!0)), star(X0!0))),
% 110.46/70.05 inference(monotonicity,[status(thm)],[211])).
% 110.46/70.05 tff(285,plain,
% 110.46/70.05 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(star(X0!0), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), star(X0!0)))),
% 110.46/70.05 inference(quant_inst,[status(thm)],[])).
% 110.46/70.05 tff(286,plain,
% 110.46/70.05 (addition(star(X0!0), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), star(X0!0))),
% 110.46/70.05 inference(unit_resolution,[status(thm)],[285, 39])).
% 110.46/70.05 tff(287,plain,
% 110.46/70.05 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)) = addition(star(X0!0), addition(multiplication(star(X0!0), X0!0), one)))),
% 110.46/70.05 inference(quant_inst,[status(thm)],[])).
% 110.46/70.05 tff(288,plain,
% 110.46/70.05 (addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)) = addition(star(X0!0), addition(multiplication(star(X0!0), X0!0), one))),
% 110.46/70.05 inference(unit_resolution,[status(thm)],[287, 39])).
% 110.46/70.05 tff(289,plain,
% 110.46/70.05 (addition(star(X0!0), addition(multiplication(star(X0!0), X0!0), one)) = addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))),
% 110.46/70.05 inference(symmetry,[status(thm)],[288])).
% 110.46/70.05 tff(290,plain,
% 110.46/70.05 (multiplication(star(X0!0), X0!0) = multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)), X0!0)),
% 110.46/70.05 inference(monotonicity,[status(thm)],[86])).
% 110.46/70.05 tff(291,plain,
% 110.46/70.05 (multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)), X0!0) = multiplication(star(X0!0), X0!0)),
% 110.46/70.05 inference(symmetry,[status(thm)],[290])).
% 110.46/70.05 tff(292,plain,
% 110.46/70.05 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)), X0!0) = addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)))),
% 110.46/70.05 inference(quant_inst,[status(thm)],[])).
% 110.46/70.05 tff(293,plain,
% 110.46/70.05 (multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)), X0!0) = addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))),
% 110.46/70.05 inference(unit_resolution,[status(thm)],[292, 207])).
% 110.46/70.05 tff(294,plain,
% 110.46/70.05 (addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)) = multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)), X0!0)),
% 110.46/70.05 inference(symmetry,[status(thm)],[293])).
% 110.46/70.05 tff(295,plain,
% 110.46/70.05 (addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)) = multiplication(star(X0!0), X0!0)),
% 110.46/70.05 inference(transitivity,[status(thm)],[294, 291])).
% 110.46/70.05 tff(296,plain,
% 110.46/70.05 (addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), one) = addition(multiplication(star(X0!0), X0!0), one)),
% 110.46/70.05 inference(monotonicity,[status(thm)],[295])).
% 110.46/70.05 tff(297,plain,
% 110.46/70.05 (addition(star(X0!0), addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), one)) = addition(star(X0!0), addition(multiplication(star(X0!0), X0!0), one))),
% 110.46/70.05 inference(monotonicity,[status(thm)],[296])).
% 110.46/70.05 tff(298,plain,
% 110.46/70.05 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(star(X0!0), addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), one)) = addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), one))),
% 110.46/70.05 inference(quant_inst,[status(thm)],[])).
% 110.46/70.05 tff(299,plain,
% 110.46/70.05 (addition(star(X0!0), addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), one)) = addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), one)),
% 110.46/70.05 inference(unit_resolution,[status(thm)],[298, 50])).
% 110.46/70.05 tff(300,plain,
% 110.46/70.05 (addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), one) = addition(star(X0!0), addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), one))),
% 110.46/70.05 inference(symmetry,[status(thm)],[299])).
% 110.46/70.05 tff(301,plain,
% 110.46/70.05 (addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), one) = star(X0!0)),
% 110.46/70.05 inference(transitivity,[status(thm)],[300, 297, 289, 69, 84])).
% 110.46/70.05 tff(302,plain,
% 110.46/70.05 (addition(addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(star(X0!0), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))),
% 110.46/70.05 inference(monotonicity,[status(thm)],[301])).
% 110.46/70.05 tff(303,plain,
% 110.46/70.05 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))) = addition(addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))))),
% 110.46/70.05 inference(quant_inst,[status(thm)],[])).
% 110.46/70.05 tff(304,plain,
% 110.46/70.05 (addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))) = addition(addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))),
% 110.46/70.05 inference(unit_resolution,[status(thm)],[303, 50])).
% 110.46/70.05 tff(305,plain,
% 110.46/70.05 (addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(one, multiplication(star(star(X0!0)), star(X0!0)))),
% 110.46/70.05 inference(monotonicity,[status(thm)],[211])).
% 110.46/70.05 tff(306,plain,
% 110.46/70.05 (addition(one, multiplication(star(star(X0!0)), star(X0!0))) = addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))),
% 110.46/70.05 inference(symmetry,[status(thm)],[305])).
% 110.46/70.05 tff(307,plain,
% 110.46/70.05 (addition(multiplication(star(star(X0!0)), star(X0!0)), one) = addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))),
% 110.46/70.05 inference(transitivity,[status(thm)],[159, 306])).
% 110.46/70.05 tff(308,plain,
% 110.46/70.05 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(X0!0)) = addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))))),
% 110.46/70.05 inference(quant_inst,[status(thm)],[])).
% 110.46/70.05 tff(309,plain,
% 110.46/70.05 (addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(X0!0)) = addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)))),
% 110.46/70.05 inference(unit_resolution,[status(thm)],[308, 39])).
% 110.46/70.05 tff(310,plain,
% 110.46/70.05 (addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(X0!0)) = addition(multiplication(star(X0!0), X0!0), star(X0!0))),
% 110.46/70.05 inference(monotonicity,[status(thm)],[295])).
% 110.46/70.05 tff(311,plain,
% 110.46/70.05 (addition(multiplication(star(X0!0), X0!0), star(X0!0)) = addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(X0!0))),
% 110.46/70.05 inference(symmetry,[status(thm)],[310])).
% 110.46/70.05 tff(312,plain,
% 110.46/70.05 (addition(multiplication(star(X0!0), X0!0), star(X0!0)) = addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)))),
% 110.46/70.05 inference(transitivity,[status(thm)],[311, 309])).
% 110.46/70.05 tff(313,plain,
% 110.46/70.05 (addition(addition(multiplication(star(X0!0), X0!0), star(X0!0)), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))))),
% 110.46/70.05 inference(monotonicity,[status(thm)],[312, 307])).
% 110.46/70.05 tff(314,plain,
% 110.46/70.05 ((~![A: $i] : (addition(A, A) = A)) | (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(multiplication(star(star(X0!0)), star(X0!0)), one))),
% 110.46/70.05 inference(quant_inst,[status(thm)],[])).
% 110.46/70.05 tff(315,plain,
% 110.46/70.05 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(multiplication(star(star(X0!0)), star(X0!0)), one)),
% 110.46/70.05 inference(unit_resolution,[status(thm)],[314, 7])).
% 110.46/70.05 tff(316,plain,
% 110.46/70.05 (addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(multiplication(star(star(X0!0)), star(X0!0)), one)),
% 110.46/70.05 inference(transitivity,[status(thm)],[305, 158])).
% 110.46/70.05 tff(317,plain,
% 110.46/70.05 (addition(addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(star(X0!0)), star(X0!0)), one))),
% 110.46/70.05 inference(monotonicity,[status(thm)],[316])).
% 110.46/70.05 tff(318,plain,
% 110.46/70.05 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), star(X0!0)), one))) = addition(addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)))),
% 110.46/70.05 inference(quant_inst,[status(thm)],[])).
% 110.46/70.05 tff(319,plain,
% 110.46/70.05 (addition(one, addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), star(X0!0)), one))) = addition(addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), addition(multiplication(star(star(X0!0)), star(X0!0)), one))),
% 110.46/70.05 inference(unit_resolution,[status(thm)],[318, 50])).
% 110.46/70.05 tff(320,plain,
% 110.46/70.05 (addition(one, addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), star(X0!0)), one))) = addition(multiplication(star(star(X0!0)), star(X0!0)), one)),
% 110.46/70.05 inference(transitivity,[status(thm)],[319, 317, 315])).
% 110.46/70.05 tff(321,plain,
% 110.46/70.05 (addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))) = addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(X0!0))),
% 110.46/70.05 inference(symmetry,[status(thm)],[309])).
% 110.46/70.05 tff(322,plain,
% 110.46/70.05 (addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))) = addition(multiplication(star(X0!0), X0!0), star(X0!0))),
% 110.46/70.05 inference(transitivity,[status(thm)],[321, 310])).
% 110.46/70.05 tff(323,plain,
% 110.46/70.05 (addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), addition(one, addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)))) = addition(addition(multiplication(star(X0!0), X0!0), star(X0!0)), addition(multiplication(star(star(X0!0)), star(X0!0)), one))),
% 110.46/70.05 inference(monotonicity,[status(thm)],[322, 320])).
% 110.46/70.05 tff(324,plain,
% 110.46/70.05 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), addition(one, addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)))) = addition(addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), one), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), star(X0!0)), one))))),
% 110.46/70.05 inference(quant_inst,[status(thm)],[])).
% 110.46/70.05 tff(325,plain,
% 110.46/70.05 (addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), addition(one, addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)))) = addition(addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), one), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)))),
% 110.46/70.05 inference(unit_resolution,[status(thm)],[324, 50])).
% 110.46/70.05 tff(326,plain,
% 110.46/70.05 (addition(addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), one), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), star(X0!0)), one))) = addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), addition(one, addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), star(X0!0)), one))))),
% 110.46/70.05 inference(symmetry,[status(thm)],[325])).
% 110.46/70.05 tff(327,plain,
% 110.46/70.05 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))))),
% 110.46/70.05 inference(quant_inst,[status(thm)],[])).
% 110.46/70.05 tff(328,plain,
% 110.46/70.05 (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))),
% 110.46/70.05 inference(unit_resolution,[status(thm)],[327, 39])).
% 110.46/70.05 tff(329,plain,
% 110.46/70.05 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), star(X0!0)), one))),
% 110.46/70.05 inference(symmetry,[status(thm)],[328])).
% 110.46/70.05 tff(330,plain,
% 110.46/70.05 (addition(star(X0!0), addition(multiplication(star(X0!0), X0!0), one)) = addition(star(X0!0), addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), one))),
% 110.46/70.05 inference(symmetry,[status(thm)],[297])).
% 110.46/70.05 tff(331,plain,
% 110.46/70.05 (star(X0!0) = addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), one)),
% 110.46/70.05 inference(transitivity,[status(thm)],[85, 70, 288, 330, 299])).
% 110.46/70.05 tff(332,plain,
% 110.46/70.05 (addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))) = addition(addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), one), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)))),
% 110.46/70.05 inference(monotonicity,[status(thm)],[331, 329])).
% 110.46/70.05 tff(333,plain,
% 110.46/70.05 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))) = addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))))),
% 110.46/70.05 inference(quant_inst,[status(thm)],[])).
% 110.46/70.05 tff(334,plain,
% 110.46/70.05 (addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))) = addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))),
% 110.46/70.05 inference(unit_resolution,[status(thm)],[333, 50])).
% 110.46/70.05 tff(335,plain,
% 110.46/70.05 (addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))))),
% 110.46/70.05 inference(symmetry,[status(thm)],[334])).
% 110.46/70.05 tff(336,plain,
% 110.46/70.05 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0))) = addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)))),
% 110.46/70.05 inference(quant_inst,[status(thm)],[])).
% 110.46/70.05 tff(337,plain,
% 110.46/70.05 (addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0))) = addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))),
% 110.46/70.05 inference(unit_resolution,[status(thm)],[336, 50])).
% 110.46/70.05 tff(338,plain,
% 110.46/70.05 (addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0))) = star(X0!0)),
% 110.46/70.05 inference(transitivity,[status(thm)],[337, 32])).
% 110.46/70.05 tff(339,plain,
% 110.46/70.05 (multiplication(star(star(X0!0)), addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0)))) = multiplication(star(star(X0!0)), star(X0!0))),
% 110.46/70.05 inference(monotonicity,[status(thm)],[338])).
% 110.46/70.05 tff(340,plain,
% 110.46/70.05 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(star(star(X0!0)), addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0)))) = addition(multiplication(star(star(X0!0)), one), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0)))))),
% 110.46/70.05 inference(quant_inst,[status(thm)],[])).
% 110.46/70.05 tff(341,plain,
% 110.46/70.05 (multiplication(star(star(X0!0)), addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0)))) = addition(multiplication(star(star(X0!0)), one), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0))))),
% 110.46/70.05 inference(unit_resolution,[status(thm)],[340, 62])).
% 110.46/70.05 tff(342,plain,
% 110.46/70.05 (addition(multiplication(star(star(X0!0)), one), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0)))) = multiplication(star(star(X0!0)), addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0))))),
% 110.46/70.05 inference(symmetry,[status(thm)],[341])).
% 110.46/70.05 tff(343,plain,
% 110.46/70.05 (addition(multiplication(star(star(X0!0)), one), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0)))) = addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))),
% 110.46/70.05 inference(transitivity,[status(thm)],[342, 339, 220, 209])).
% 110.46/70.05 tff(344,plain,
% 110.46/70.05 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)))),
% 110.46/70.05 inference(quant_inst,[status(thm)],[])).
% 110.46/70.05 tff(345,plain,
% 110.46/70.05 (addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0))),
% 110.46/70.05 inference(unit_resolution,[status(thm)],[344, 39])).
% 110.46/70.05 tff(346,plain,
% 110.46/70.05 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)) = addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one))),
% 110.46/70.05 inference(symmetry,[status(thm)],[345])).
% 110.46/70.05 tff(347,plain,
% 110.46/70.05 (addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), addition(multiplication(star(star(X0!0)), one), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0))))) = addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))),
% 110.46/70.05 inference(monotonicity,[status(thm)],[346, 343])).
% 110.46/70.05 tff(348,plain,
% 110.46/70.05 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), addition(multiplication(star(star(X0!0)), one), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0))))) = addition(addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0)))))),
% 110.46/70.05 inference(quant_inst,[status(thm)],[])).
% 110.46/70.05 tff(349,plain,
% 110.46/70.05 (addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), addition(multiplication(star(star(X0!0)), one), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0))))) = addition(addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0))))),
% 110.46/70.05 inference(unit_resolution,[status(thm)],[348, 50])).
% 110.46/70.05 tff(350,plain,
% 110.46/70.05 (addition(addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0)))) = addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), addition(multiplication(star(star(X0!0)), one), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0)))))),
% 110.46/70.06 inference(symmetry,[status(thm)],[349])).
% 110.46/70.06 tff(351,plain,
% 110.46/70.06 (addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), one)) = addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), star(star(X0!0)))),
% 110.46/70.06 inference(monotonicity,[status(thm)],[231])).
% 110.46/70.06 tff(352,plain,
% 110.46/70.06 (addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), star(star(X0!0))) = addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), one))),
% 110.46/70.06 inference(symmetry,[status(thm)],[351])).
% 110.46/70.06 tff(353,plain,
% 110.46/70.06 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(star(X0!0), star(star(X0!0)))) = addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), star(star(X0!0))))),
% 110.46/70.06 inference(quant_inst,[status(thm)],[])).
% 110.46/70.06 tff(354,plain,
% 110.46/70.06 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(star(X0!0), star(star(X0!0)))) = addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), star(star(X0!0)))),
% 110.46/70.06 inference(unit_resolution,[status(thm)],[353, 50])).
% 110.46/70.06 tff(355,plain,
% 110.46/70.06 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(star(X0!0), star(star(X0!0))) = addition(star(star(X0!0)), star(X0!0)))),
% 110.46/70.06 inference(quant_inst,[status(thm)],[])).
% 110.46/70.06 tff(356,plain,
% 110.46/70.06 (addition(star(X0!0), star(star(X0!0))) = addition(star(star(X0!0)), star(X0!0))),
% 110.46/70.06 inference(unit_resolution,[status(thm)],[355, 39])).
% 110.46/70.06 tff(357,plain,
% 110.46/70.06 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(star(X0!0), star(star(X0!0)))) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(star(star(X0!0)), star(X0!0)))),
% 110.46/70.06 inference(monotonicity,[status(thm)],[356])).
% 110.46/70.06 tff(358,plain,
% 110.46/70.06 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(star(star(X0!0)), star(X0!0))) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(star(X0!0), star(star(X0!0))))),
% 110.46/70.06 inference(symmetry,[status(thm)],[357])).
% 110.46/70.06 tff(359,plain,
% 110.46/70.06 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(star(star(X0!0)), star(X0!0))) = addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))), star(X0!0)))),
% 110.46/70.06 inference(quant_inst,[status(thm)],[])).
% 110.46/70.06 tff(360,plain,
% 110.46/70.06 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(star(star(X0!0)), star(X0!0))) = addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))), star(X0!0))),
% 110.46/70.06 inference(unit_resolution,[status(thm)],[359, 50])).
% 110.46/70.06 tff(361,plain,
% 110.46/70.06 (addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))), star(X0!0)) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(star(star(X0!0)), star(X0!0)))),
% 110.46/70.06 inference(symmetry,[status(thm)],[360])).
% 110.46/70.06 tff(362,plain,
% 110.46/70.06 (addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))), star(X0!0)) = addition(star(star(X0!0)), star(X0!0))),
% 110.46/70.06 inference(monotonicity,[status(thm)],[161])).
% 110.46/70.06 tff(363,plain,
% 110.46/70.06 (addition(star(star(X0!0)), star(X0!0)) = addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))), star(X0!0))),
% 110.46/70.06 inference(symmetry,[status(thm)],[362])).
% 110.46/70.06 tff(364,plain,
% 110.46/70.06 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0))) = star(star(X0!0))),
% 110.46/70.06 inference(transitivity,[status(thm)],[147, 143])).
% 110.46/70.06 tff(365,plain,
% 110.46/70.06 (addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0))), star(X0!0)) = addition(star(star(X0!0)), star(X0!0))),
% 110.46/70.06 inference(monotonicity,[status(thm)],[364])).
% 110.46/70.06 tff(366,plain,
% 110.46/70.06 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(star(star(X0!0)), star(X0!0))) = addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0))), star(X0!0)))),
% 110.46/70.06 inference(quant_inst,[status(thm)],[])).
% 110.46/70.06 tff(367,plain,
% 110.46/70.06 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(star(star(X0!0)), star(X0!0))) = addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0))), star(X0!0))),
% 110.46/70.06 inference(unit_resolution,[status(thm)],[366, 50])).
% 110.46/70.06 tff(368,plain,
% 110.46/70.06 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(star(X0!0), star(star(X0!0)))) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(star(star(X0!0)), star(X0!0)))),
% 110.46/70.06 inference(monotonicity,[status(thm)],[356])).
% 110.46/70.06 tff(369,plain,
% 110.46/70.06 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(star(X0!0), star(star(X0!0)))) = addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)), star(star(X0!0))))),
% 110.46/70.06 inference(quant_inst,[status(thm)],[])).
% 110.46/70.06 tff(370,plain,
% 110.46/70.06 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(star(X0!0), star(star(X0!0)))) = addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)), star(star(X0!0)))),
% 110.46/70.06 inference(unit_resolution,[status(thm)],[369, 50])).
% 110.46/70.06 tff(371,plain,
% 110.46/70.06 (addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)), star(star(X0!0))) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(star(X0!0), star(star(X0!0))))),
% 110.46/70.06 inference(symmetry,[status(thm)],[370])).
% 110.46/70.06 tff(372,plain,
% 110.46/70.06 (addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)), multiplication(star(star(X0!0)), one)) = addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)), star(star(X0!0)))),
% 110.46/70.06 inference(monotonicity,[status(thm)],[231])).
% 110.46/70.06 tff(373,plain,
% 110.46/70.06 (addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)), multiplication(star(star(X0!0)), one)) = addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), one))),
% 110.46/70.06 inference(transitivity,[status(thm)],[372, 371, 368, 367, 365, 363, 361, 358, 354, 352])).
% 110.46/70.06 tff(374,plain,
% 110.46/70.06 (addition(addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)), multiplication(star(star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0)))) = addition(addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0))))),
% 110.46/70.06 inference(monotonicity,[status(thm)],[373])).
% 110.46/70.06 tff(375,plain,
% 110.46/70.06 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)), addition(multiplication(star(star(X0!0)), one), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0))))) = addition(addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)), multiplication(star(star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0)))))),
% 110.46/70.06 inference(quant_inst,[status(thm)],[])).
% 110.46/70.06 tff(376,plain,
% 110.46/70.06 (addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)), addition(multiplication(star(star(X0!0)), one), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0))))) = addition(addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)), multiplication(star(star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0))))),
% 110.46/70.06 inference(unit_resolution,[status(thm)],[375, 50])).
% 110.46/70.06 tff(377,plain,
% 110.46/70.06 (multiplication(star(star(X0!0)), star(X0!0)) = multiplication(star(star(X0!0)), addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0))))),
% 110.46/70.06 inference(symmetry,[status(thm)],[339])).
% 110.46/70.06 tff(378,plain,
% 110.46/70.06 (addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))) = addition(multiplication(star(star(X0!0)), one), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0))))),
% 110.46/70.06 inference(transitivity,[status(thm)],[210, 200, 377, 341])).
% 110.46/70.06 tff(379,plain,
% 110.46/70.06 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)))),
% 110.46/70.06 inference(quant_inst,[status(thm)],[])).
% 110.46/70.06 tff(380,plain,
% 110.46/70.06 (addition(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0))),
% 110.46/70.06 inference(unit_resolution,[status(thm)],[379, 39])).
% 110.46/70.06 tff(381,plain,
% 110.46/70.06 (addition(addition(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)), addition(multiplication(star(star(X0!0)), one), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0)))))),
% 110.46/70.06 inference(monotonicity,[status(thm)],[380, 378])).
% 110.46/70.06 tff(382,plain,
% 110.46/70.06 (addition(one, addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))) = addition(one, multiplication(star(X0!0), star(star(X0!0))))),
% 110.46/70.06 inference(monotonicity,[status(thm)],[172])).
% 110.46/70.06 tff(383,plain,
% 110.46/70.06 (addition(one, multiplication(star(X0!0), star(star(X0!0)))) = addition(one, addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.46/70.06 inference(symmetry,[status(thm)],[382])).
% 110.46/70.06 tff(384,plain,
% 110.46/70.06 (addition(multiplication(star(X0!0), star(star(X0!0))), one) = addition(one, addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.46/70.06 inference(transitivity,[status(thm)],[146, 383])).
% 110.46/70.06 tff(385,plain,
% 110.46/70.06 (addition(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(star(X0!0), addition(one, addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.46/70.06 inference(monotonicity,[status(thm)],[384])).
% 110.46/70.06 tff(386,plain,
% 110.46/70.06 (addition(star(X0!0), addition(one, addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.46/70.06 inference(symmetry,[status(thm)],[385])).
% 110.46/70.06 tff(387,plain,
% 110.46/70.06 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(star(X0!0), addition(one, addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(addition(star(X0!0), one), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.46/70.06 inference(quant_inst,[status(thm)],[])).
% 110.46/70.06 tff(388,plain,
% 110.46/70.06 (addition(star(X0!0), addition(one, addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(addition(star(X0!0), one), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.46/70.06 inference(unit_resolution,[status(thm)],[387, 50])).
% 110.46/70.06 tff(389,plain,
% 110.46/70.06 (addition(addition(star(X0!0), one), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))) = addition(star(X0!0), addition(one, addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.46/70.06 inference(symmetry,[status(thm)],[388])).
% 110.46/70.06 tff(390,plain,
% 110.46/70.06 (addition(addition(star(X0!0), one), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))) = addition(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.46/70.06 inference(transitivity,[status(thm)],[389, 386])).
% 110.46/70.06 tff(391,plain,
% 110.46/70.06 (addition(addition(addition(star(X0!0), one), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(addition(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))),
% 110.46/70.06 inference(monotonicity,[status(thm)],[390])).
% 110.46/70.06 tff(392,plain,
% 110.46/70.06 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(star(X0!0), one), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))) = addition(addition(addition(star(X0!0), one), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))))),
% 110.46/70.06 inference(quant_inst,[status(thm)],[])).
% 110.46/70.06 tff(393,plain,
% 110.46/70.06 (addition(addition(star(X0!0), one), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))) = addition(addition(addition(star(X0!0), one), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))),
% 110.46/70.06 inference(unit_resolution,[status(thm)],[392, 50])).
% 110.46/70.06 tff(394,plain,
% 110.46/70.06 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.46/70.06 inference(quant_inst,[status(thm)],[])).
% 110.46/70.06 tff(395,plain,
% 110.46/70.06 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.46/70.06 inference(unit_resolution,[status(thm)],[394, 39])).
% 110.46/70.06 tff(396,plain,
% 110.46/70.06 (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))) = addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))),
% 110.46/70.06 inference(symmetry,[status(thm)],[395])).
% 110.46/70.06 tff(397,plain,
% 110.46/70.06 (addition(addition(star(X0!0), one), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(addition(star(X0!0), one), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))))),
% 110.46/70.06 inference(monotonicity,[status(thm)],[396])).
% 110.46/70.06 tff(398,plain,
% 110.46/70.06 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(star(X0!0), one), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(addition(addition(star(X0!0), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.46/70.06 inference(quant_inst,[status(thm)],[])).
% 110.46/70.06 tff(399,plain,
% 110.46/70.06 (addition(addition(star(X0!0), one), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(addition(addition(star(X0!0), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.46/70.06 inference(unit_resolution,[status(thm)],[398, 50])).
% 110.46/70.06 tff(400,plain,
% 110.46/70.06 (addition(addition(addition(star(X0!0), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))) = addition(addition(star(X0!0), one), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.46/70.06 inference(symmetry,[status(thm)],[399])).
% 110.46/70.06 tff(401,plain,
% 110.46/70.06 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(star(X0!0), addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))) = addition(addition(star(X0!0), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))))),
% 110.46/70.06 inference(quant_inst,[status(thm)],[])).
% 110.46/70.06 tff(402,plain,
% 110.46/70.06 (addition(star(X0!0), addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))) = addition(addition(star(X0!0), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))),
% 110.46/70.06 inference(unit_resolution,[status(thm)],[401, 50])).
% 110.46/70.06 tff(403,plain,
% 110.46/70.06 (addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(star(X0!0), addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))))),
% 110.46/70.06 inference(monotonicity,[status(thm)],[307])).
% 110.46/70.06 tff(404,plain,
% 110.46/70.06 (addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(addition(star(X0!0), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))),
% 110.46/70.06 inference(transitivity,[status(thm)],[403, 402])).
% 110.46/70.06 tff(405,plain,
% 110.46/70.06 (addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))) = addition(addition(addition(star(X0!0), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.46/70.06 inference(monotonicity,[status(thm)],[404])).
% 110.46/70.06 tff(406,plain,
% 110.46/70.06 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.46/70.06 inference(quant_inst,[status(thm)],[])).
% 110.46/70.06 tff(407,plain,
% 110.46/70.06 (addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.46/70.06 inference(unit_resolution,[status(thm)],[406, 50])).
% 110.46/70.06 tff(408,plain,
% 110.46/70.06 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.46/70.06 inference(quant_inst,[status(thm)],[])).
% 110.46/70.06 tff(409,plain,
% 110.46/70.06 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.46/70.06 inference(unit_resolution,[status(thm)],[408, 39])).
% 110.46/70.06 tff(410,plain,
% 110.46/70.06 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))) = addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(star(X0!0)), star(X0!0)), one))),
% 110.46/70.06 inference(monotonicity,[status(thm)],[316])).
% 110.46/70.06 tff(411,plain,
% 110.46/70.06 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))))),
% 110.46/70.07 inference(quant_inst,[status(thm)],[])).
% 110.46/70.07 tff(412,plain,
% 110.46/70.07 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))),
% 110.46/70.07 inference(unit_resolution,[status(thm)],[411, 50])).
% 110.46/70.07 tff(413,plain,
% 110.46/70.07 (addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))))),
% 110.46/70.07 inference(symmetry,[status(thm)],[412])).
% 110.46/70.07 tff(414,plain,
% 110.46/70.07 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), one) = addition(multiplication(star(X0!0), star(star(X0!0))), one)),
% 110.46/70.07 inference(monotonicity,[status(thm)],[172])).
% 110.46/70.07 tff(415,plain,
% 110.46/70.07 (addition(multiplication(star(X0!0), star(star(X0!0))), one) = addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), one)),
% 110.46/70.07 inference(symmetry,[status(thm)],[414])).
% 110.46/70.07 tff(416,plain,
% 110.46/70.07 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))),
% 110.46/70.07 inference(monotonicity,[status(thm)],[415])).
% 110.46/70.07 tff(417,plain,
% 110.46/70.07 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 110.46/70.07 inference(quant_inst,[status(thm)],[])).
% 110.46/70.07 tff(418,plain,
% 110.46/70.07 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.46/70.07 inference(unit_resolution,[status(thm)],[417, 39])).
% 110.46/70.07 tff(419,plain,
% 110.46/70.07 (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))),
% 110.46/70.07 inference(symmetry,[status(thm)],[418])).
% 110.46/70.07 tff(420,plain,
% 110.46/70.07 ((~![A: $i] : (addition(A, A) = A)) | (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.46/70.07 inference(quant_inst,[status(thm)],[])).
% 110.46/70.07 tff(421,plain,
% 110.46/70.07 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(multiplication(star(X0!0), star(star(X0!0))), one)),
% 110.46/70.07 inference(unit_resolution,[status(thm)],[420, 7])).
% 110.46/70.07 tff(422,plain,
% 110.46/70.07 (addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.46/70.07 inference(monotonicity,[status(thm)],[414])).
% 110.46/70.07 tff(423,plain,
% 110.46/70.07 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 110.46/70.07 inference(quant_inst,[status(thm)],[])).
% 110.46/70.07 tff(424,plain,
% 110.46/70.07 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), one), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.46/70.07 inference(unit_resolution,[status(thm)],[423, 50])).
% 110.46/70.07 tff(425,plain,
% 110.46/70.07 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(multiplication(star(X0!0), star(star(X0!0))), one)),
% 110.46/70.07 inference(transitivity,[status(thm)],[424, 422, 421])).
% 110.46/70.07 tff(426,plain,
% 110.46/70.07 (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one)))) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.46/70.07 inference(monotonicity,[status(thm)],[425])).
% 110.46/70.07 tff(427,plain,
% 110.46/70.07 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one)))) = addition(addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one))))),
% 110.46/70.07 inference(quant_inst,[status(thm)],[])).
% 110.46/70.07 tff(428,plain,
% 110.46/70.07 (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one)))) = addition(addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 110.46/70.07 inference(unit_resolution,[status(thm)],[427, 50])).
% 110.46/70.07 tff(429,plain,
% 110.46/70.07 (addition(addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one))))),
% 110.46/70.07 inference(symmetry,[status(thm)],[428])).
% 110.46/70.07 tff(430,plain,
% 110.46/70.07 (addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 110.46/70.07 inference(monotonicity,[status(thm)],[395])).
% 110.46/70.07 tff(431,plain,
% 110.46/70.07 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one)))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one))))),
% 110.46/70.07 inference(quant_inst,[status(thm)],[])).
% 110.46/70.07 tff(432,plain,
% 110.46/70.07 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one)))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 110.46/70.07 inference(unit_resolution,[status(thm)],[431, 50])).
% 110.46/70.07 tff(433,plain,
% 110.46/70.07 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 110.46/70.07 inference(quant_inst,[status(thm)],[])).
% 110.46/70.07 tff(434,plain,
% 110.46/70.07 (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), one), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.46/70.07 inference(unit_resolution,[status(thm)],[433, 50])).
% 110.46/70.07 tff(435,plain,
% 110.46/70.07 (addition(addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 110.46/70.07 inference(symmetry,[status(thm)],[434])).
% 110.46/70.07 tff(436,plain,
% 110.46/70.07 (addition(addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.46/70.07 inference(monotonicity,[status(thm)],[212])).
% 110.46/70.07 tff(437,plain,
% 110.46/70.07 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), one), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.46/70.07 inference(symmetry,[status(thm)],[436])).
% 110.46/70.07 tff(438,plain,
% 110.46/70.07 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 110.46/70.07 inference(transitivity,[status(thm)],[437, 435])).
% 110.46/70.07 tff(439,plain,
% 110.46/70.07 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one))))),
% 110.46/70.07 inference(monotonicity,[status(thm)],[438])).
% 110.46/70.07 tff(440,plain,
% 110.46/70.07 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 110.46/70.07 inference(quant_inst,[status(thm)],[])).
% 110.46/70.07 tff(441,plain,
% 110.46/70.07 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.46/70.07 inference(unit_resolution,[status(thm)],[440, 39])).
% 110.46/70.07 tff(442,plain,
% 110.46/70.07 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), one), addition(multiplication(star(star(X0!0)), star(X0!0)), one))),
% 110.46/70.07 inference(monotonicity,[status(thm)],[415])).
% 110.46/70.07 tff(443,plain,
% 110.46/70.07 (addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), one), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(star(X0!0)), star(X0!0)), one))),
% 110.46/70.07 inference(symmetry,[status(thm)],[442])).
% 110.46/70.07 tff(444,plain,
% 110.46/70.07 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), one))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), one), addition(multiplication(star(star(X0!0)), star(X0!0)), one)))),
% 110.46/70.07 inference(quant_inst,[status(thm)],[])).
% 110.46/70.07 tff(445,plain,
% 110.46/70.07 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), one))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), one), addition(multiplication(star(star(X0!0)), star(X0!0)), one))),
% 110.46/70.07 inference(unit_resolution,[status(thm)],[444, 50])).
% 110.46/70.07 tff(446,plain,
% 110.46/70.07 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), one))) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.46/70.07 inference(transitivity,[status(thm)],[445, 443, 441])).
% 110.46/70.07 tff(447,plain,
% 110.46/70.07 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), one)))) = addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 110.46/70.07 inference(monotonicity,[status(thm)],[446])).
% 110.46/70.07 tff(448,plain,
% 110.46/70.07 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), one)))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), one))))),
% 110.46/70.07 inference(quant_inst,[status(thm)],[])).
% 110.46/70.07 tff(449,plain,
% 110.46/70.07 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), one)))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), one)))),
% 110.46/70.07 inference(unit_resolution,[status(thm)],[448, 50])).
% 110.46/70.07 tff(450,plain,
% 110.46/70.07 (addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), one))) = addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), one))))),
% 110.46/70.07 inference(symmetry,[status(thm)],[449])).
% 110.46/70.07 tff(451,plain,
% 110.46/70.07 (addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))) = addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.46/70.07 inference(symmetry,[status(thm)],[167])).
% 110.46/70.07 tff(452,plain,
% 110.46/70.07 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), one))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), one)))),
% 110.46/70.07 inference(monotonicity,[status(thm)],[451])).
% 110.46/70.07 tff(453,plain,
% 110.46/70.07 (addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), one), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), one)))),
% 110.46/70.07 inference(symmetry,[status(thm)],[445])).
% 110.46/70.07 tff(454,plain,
% 110.46/70.07 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(star(X0!0)), star(X0!0)), one))),
% 110.46/70.07 inference(symmetry,[status(thm)],[441])).
% 110.46/70.07 tff(455,plain,
% 110.46/70.07 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.46/70.07 inference(transitivity,[status(thm)],[454, 442, 453, 452, 450, 447, 439, 432, 430, 429, 426, 419, 416, 413, 410, 409])).
% 110.46/70.07 tff(456,plain,
% 110.46/70.07 (addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.46/70.07 inference(monotonicity,[status(thm)],[455])).
% 110.46/70.07 tff(457,plain,
% 110.46/70.07 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(X0!0)))),
% 110.46/70.07 inference(quant_inst,[status(thm)],[])).
% 110.46/70.07 tff(458,plain,
% 110.46/70.07 (addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(X0!0))),
% 110.46/70.07 inference(unit_resolution,[status(thm)],[457, 39])).
% 110.46/70.07 tff(459,plain,
% 110.46/70.07 (addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(X0!0)) = addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 110.46/70.07 inference(symmetry,[status(thm)],[458])).
% 110.46/70.07 tff(460,plain,
% 110.46/70.07 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0))) = addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(X0!0)))),
% 110.46/70.07 inference(quant_inst,[status(thm)],[])).
% 110.46/70.07 tff(461,plain,
% 110.46/70.07 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0))) = addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(X0!0))),
% 110.46/70.07 inference(unit_resolution,[status(thm)],[460, 50])).
% 110.46/70.07 tff(462,plain,
% 110.46/70.07 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)))),
% 110.46/70.07 inference(monotonicity,[status(thm)],[380])).
% 110.46/70.07 tff(463,plain,
% 110.46/70.07 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)) = addition(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.46/70.08 inference(symmetry,[status(thm)],[380])).
% 110.46/70.08 tff(464,plain,
% 110.46/70.08 (addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)) = star(X0!0)),
% 110.46/70.08 inference(transitivity,[status(thm)],[43, 32])).
% 110.46/70.08 tff(465,plain,
% 110.46/70.08 (multiplication(star(star(X0!0)), addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) = multiplication(star(star(X0!0)), star(X0!0))),
% 110.46/70.08 inference(monotonicity,[status(thm)],[464])).
% 110.46/70.08 tff(466,plain,
% 110.46/70.08 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(star(star(X0!0)), addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) = addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))))),
% 110.46/70.08 inference(quant_inst,[status(thm)],[])).
% 110.46/70.08 tff(467,plain,
% 110.46/70.08 (multiplication(star(star(X0!0)), addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) = addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0)))),
% 110.46/70.08 inference(unit_resolution,[status(thm)],[466, 62])).
% 110.46/70.08 tff(468,plain,
% 110.46/70.08 (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))) = multiplication(star(star(X0!0)), addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)))),
% 110.46/70.08 inference(symmetry,[status(thm)],[467])).
% 110.46/70.08 tff(469,plain,
% 110.46/70.08 (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0)))),
% 110.46/70.08 inference(monotonicity,[status(thm)],[211])).
% 110.46/70.08 tff(470,plain,
% 110.46/70.08 (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))) = multiplication(star(star(X0!0)), star(X0!0))),
% 110.46/70.08 inference(transitivity,[status(thm)],[469, 468, 465])).
% 110.46/70.08 tff(471,plain,
% 110.46/70.08 (addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), one) = addition(multiplication(star(star(X0!0)), star(X0!0)), one)),
% 110.46/70.08 inference(monotonicity,[status(thm)],[470])).
% 110.46/70.08 tff(472,plain,
% 110.46/70.08 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), one)) = addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), one))),
% 110.46/70.08 inference(quant_inst,[status(thm)],[])).
% 110.46/70.08 tff(473,plain,
% 110.46/70.08 (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), one)) = addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), one)),
% 110.46/70.08 inference(unit_resolution,[status(thm)],[472, 50])).
% 110.46/70.08 tff(474,plain,
% 110.46/70.08 (addition(multiplication(star(star(X0!0)), star(X0!0)), one) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), one)),
% 110.46/70.08 inference(symmetry,[status(thm)],[212])).
% 110.46/70.08 tff(475,plain,
% 110.46/70.08 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0)))) = addition(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0)))),
% 110.46/70.08 inference(monotonicity,[status(thm)],[159, 364])).
% 110.46/70.08 tff(476,plain,
% 110.46/70.08 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0)))) = addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(star(X0!0))))),
% 110.46/70.08 inference(quant_inst,[status(thm)],[])).
% 110.46/70.08 tff(477,plain,
% 110.46/70.08 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0)))) = addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(star(X0!0)))),
% 110.46/70.08 inference(unit_resolution,[status(thm)],[476, 50])).
% 110.46/70.08 tff(478,plain,
% 110.46/70.08 (addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(star(X0!0))) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0))))),
% 110.46/70.08 inference(symmetry,[status(thm)],[477])).
% 110.46/70.08 tff(479,plain,
% 110.46/70.08 (addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(star(X0!0))) = star(star(X0!0))),
% 110.46/70.08 inference(transitivity,[status(thm)],[478, 475, 156])).
% 110.46/70.08 tff(480,plain,
% 110.46/70.08 (multiplication(addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(star(X0!0))), addition(multiplication(X0!0, star(X0!0)), one)) = multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))),
% 110.46/70.08 inference(monotonicity,[status(thm)],[479])).
% 110.46/70.08 tff(481,plain,
% 110.46/70.08 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(star(X0!0))), addition(multiplication(X0!0, star(X0!0)), one)) = addition(multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))))),
% 110.46/70.08 inference(quant_inst,[status(thm)],[])).
% 110.46/70.08 tff(482,plain,
% 110.46/70.08 (multiplication(addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(star(X0!0))), addition(multiplication(X0!0, star(X0!0)), one)) = addition(multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)))),
% 110.46/70.08 inference(unit_resolution,[status(thm)],[481, 207])).
% 110.46/70.08 tff(483,plain,
% 110.46/70.08 (addition(multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))) = multiplication(addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(star(X0!0))), addition(multiplication(X0!0, star(X0!0)), one))),
% 110.46/70.08 inference(symmetry,[status(thm)],[482])).
% 110.46/70.08 tff(484,plain,
% 110.46/70.08 (addition(multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))) = multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))),
% 110.46/70.08 inference(transitivity,[status(thm)],[483, 480])).
% 110.46/70.08 tff(485,plain,
% 110.46/70.08 (addition(addition(multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), one))),
% 110.46/70.08 inference(monotonicity,[status(thm)],[484, 474])).
% 110.46/70.08 tff(486,plain,
% 110.46/70.08 (addition(addition(multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(multiplication(star(star(X0!0)), star(X0!0)), one)),
% 110.46/70.08 inference(transitivity,[status(thm)],[485, 473, 471])).
% 110.46/70.08 tff(487,plain,
% 110.46/70.08 (addition(addition(addition(multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0))) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 110.46/70.08 inference(monotonicity,[status(thm)],[486, 463])).
% 110.46/70.08 tff(488,plain,
% 110.46/70.08 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)))) = addition(addition(addition(multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0))))),
% 110.46/70.08 inference(quant_inst,[status(thm)],[])).
% 110.46/70.08 tff(489,plain,
% 110.46/70.08 (addition(addition(multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)))) = addition(addition(addition(multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)))),
% 110.46/70.08 inference(unit_resolution,[status(thm)],[488, 50])).
% 110.46/70.08 tff(490,plain,
% 110.46/70.08 (addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(X0!0)) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)))),
% 110.46/70.08 inference(symmetry,[status(thm)],[461])).
% 110.46/70.08 tff(491,plain,
% 110.46/70.08 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 110.46/70.08 inference(quant_inst,[status(thm)],[])).
% 110.46/70.08 tff(492,plain,
% 110.46/70.08 (addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.46/70.08 inference(unit_resolution,[status(thm)],[491, 50])).
% 110.46/70.08 tff(493,plain,
% 110.46/70.08 (addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 110.46/70.08 inference(symmetry,[status(thm)],[492])).
% 110.46/70.08 tff(494,plain,
% 110.46/70.08 (addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)))),
% 110.46/70.08 inference(transitivity,[status(thm)],[493, 458, 490])).
% 110.46/70.08 tff(495,plain,
% 110.46/70.08 (multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)) = multiplication(addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(star(X0!0))), addition(multiplication(X0!0, star(X0!0)), one))),
% 110.46/70.08 inference(symmetry,[status(thm)],[480])).
% 110.46/70.08 tff(496,plain,
% 110.46/70.08 (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), one) = addition(multiplication(X0!0, star(X0!0)), one)),
% 110.46/70.08 inference(monotonicity,[status(thm)],[92])).
% 110.46/70.08 tff(497,plain,
% 110.46/70.08 (addition(multiplication(X0!0, star(X0!0)), one) = addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), one)),
% 110.46/70.08 inference(symmetry,[status(thm)],[496])).
% 110.46/70.08 tff(498,plain,
% 110.46/70.08 (multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)) = multiplication(star(star(X0!0)), addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), one))),
% 110.46/70.08 inference(monotonicity,[status(thm)],[497])).
% 110.46/70.08 tff(499,plain,
% 110.46/70.08 (multiplication(star(star(X0!0)), addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), one)) = multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))),
% 110.46/70.08 inference(symmetry,[status(thm)],[498])).
% 110.46/70.08 tff(500,plain,
% 110.46/70.08 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(star(star(X0!0)), addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), one)) = addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), multiplication(star(star(X0!0)), one)))),
% 110.46/70.08 inference(quant_inst,[status(thm)],[])).
% 110.46/70.08 tff(501,plain,
% 110.46/70.08 (multiplication(star(star(X0!0)), addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), one)) = addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), multiplication(star(star(X0!0)), one))),
% 110.46/70.08 inference(unit_resolution,[status(thm)],[500, 62])).
% 110.46/70.08 tff(502,plain,
% 110.46/70.08 (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), multiplication(star(star(X0!0)), one)) = multiplication(star(star(X0!0)), addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), one))),
% 110.46/70.08 inference(symmetry,[status(thm)],[501])).
% 110.46/70.08 tff(503,plain,
% 110.46/70.08 (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), multiplication(star(star(X0!0)), one)) = addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), star(star(X0!0)))),
% 110.46/70.08 inference(monotonicity,[status(thm)],[231])).
% 110.46/70.08 tff(504,plain,
% 110.46/70.08 (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), star(star(X0!0))) = addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), multiplication(star(star(X0!0)), one))),
% 110.46/70.08 inference(symmetry,[status(thm)],[503])).
% 110.46/70.08 tff(505,plain,
% 110.46/70.08 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(multiplication(star(star(X0!0)), one), star(star(X0!0))) <=> (addition(multiplication(star(star(X0!0)), one), star(star(X0!0))) = star(star(X0!0))))),
% 110.46/70.08 inference(quant_inst,[status(thm)],[])).
% 110.46/70.08 tff(506,plain,
% 110.46/70.08 (leq(multiplication(star(star(X0!0)), one), star(star(X0!0))) <=> (addition(multiplication(star(star(X0!0)), one), star(star(X0!0))) = star(star(X0!0)))),
% 110.46/70.08 inference(unit_resolution,[status(thm)],[505, 18])).
% 110.46/70.08 tff(507,plain,
% 110.46/70.08 (leq(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0))) <=> leq(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0)))),
% 110.46/70.08 inference(monotonicity,[status(thm)],[146])).
% 110.46/70.08 tff(508,plain,
% 110.46/70.08 (leq(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) <=> leq(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0)))),
% 110.46/70.08 inference(symmetry,[status(thm)],[507])).
% 110.46/70.08 tff(509,plain,
% 110.46/70.08 (leq(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0)))),
% 110.46/70.08 inference(modus_ponens,[status(thm)],[140, 508])).
% 110.46/70.08 tff(510,plain,
% 110.46/70.08 (((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | ((~leq(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0)))) | leq(multiplication(star(star(X0!0)), one), star(star(X0!0))))) <=> ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | (~leq(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0)))) | leq(multiplication(star(star(X0!0)), one), star(star(X0!0))))),
% 110.46/70.08 inference(rewrite,[status(thm)],[])).
% 110.46/70.08 tff(511,plain,
% 110.46/70.08 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | ((~leq(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0)))) | leq(multiplication(star(star(X0!0)), one), star(star(X0!0))))),
% 110.46/70.08 inference(quant_inst,[status(thm)],[])).
% 110.46/70.08 tff(512,plain,
% 110.46/70.08 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | (~leq(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0)))) | leq(multiplication(star(star(X0!0)), one), star(star(X0!0)))),
% 110.46/70.08 inference(modus_ponens,[status(thm)],[511, 510])).
% 110.46/70.08 tff(513,plain,
% 110.46/70.08 ((~leq(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0)))) | leq(multiplication(star(star(X0!0)), one), star(star(X0!0)))),
% 110.46/70.08 inference(unit_resolution,[status(thm)],[512, 123])).
% 110.46/70.08 tff(514,plain,
% 110.46/70.08 (leq(multiplication(star(star(X0!0)), one), star(star(X0!0)))),
% 110.46/70.08 inference(unit_resolution,[status(thm)],[513, 509])).
% 110.46/70.08 tff(515,plain,
% 110.46/70.08 ((~(leq(multiplication(star(star(X0!0)), one), star(star(X0!0))) <=> (addition(multiplication(star(star(X0!0)), one), star(star(X0!0))) = star(star(X0!0))))) | (~leq(multiplication(star(star(X0!0)), one), star(star(X0!0)))) | (addition(multiplication(star(star(X0!0)), one), star(star(X0!0))) = star(star(X0!0)))),
% 110.46/70.08 inference(tautology,[status(thm)],[])).
% 110.46/70.08 tff(516,plain,
% 110.46/70.08 ((~(leq(multiplication(star(star(X0!0)), one), star(star(X0!0))) <=> (addition(multiplication(star(star(X0!0)), one), star(star(X0!0))) = star(star(X0!0))))) | (addition(multiplication(star(star(X0!0)), one), star(star(X0!0))) = star(star(X0!0)))),
% 110.46/70.08 inference(unit_resolution,[status(thm)],[515, 514])).
% 110.46/70.08 tff(517,plain,
% 110.46/70.08 (addition(multiplication(star(star(X0!0)), one), star(star(X0!0))) = star(star(X0!0))),
% 110.46/70.08 inference(unit_resolution,[status(thm)],[516, 506])).
% 110.46/70.08 tff(518,plain,
% 110.46/70.08 (star(star(X0!0)) = addition(multiplication(star(star(X0!0)), one), star(star(X0!0)))),
% 110.46/70.08 inference(symmetry,[status(thm)],[517])).
% 110.46/70.08 tff(519,plain,
% 110.46/70.08 (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), star(star(X0!0))) = addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), addition(multiplication(star(star(X0!0)), one), star(star(X0!0))))),
% 110.46/70.08 inference(monotonicity,[status(thm)],[518])).
% 110.46/70.08 tff(520,plain,
% 110.46/70.08 (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), addition(multiplication(star(star(X0!0)), one), star(star(X0!0)))) = addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), star(star(X0!0)))),
% 110.46/70.08 inference(symmetry,[status(thm)],[519])).
% 110.46/70.08 tff(521,plain,
% 110.46/70.08 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), addition(multiplication(star(star(X0!0)), one), star(star(X0!0)))) = addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), multiplication(star(star(X0!0)), one)), star(star(X0!0))))),
% 110.46/70.08 inference(quant_inst,[status(thm)],[])).
% 110.46/70.08 tff(522,plain,
% 110.46/70.08 (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), addition(multiplication(star(star(X0!0)), one), star(star(X0!0)))) = addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), multiplication(star(star(X0!0)), one)), star(star(X0!0)))),
% 110.46/70.08 inference(unit_resolution,[status(thm)],[521, 50])).
% 110.46/70.09 tff(523,plain,
% 110.46/70.09 (addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), multiplication(star(star(X0!0)), one)), star(star(X0!0))) = addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), addition(multiplication(star(star(X0!0)), one), star(star(X0!0))))),
% 110.46/70.09 inference(symmetry,[status(thm)],[522])).
% 110.46/70.09 tff(524,plain,
% 110.46/70.09 (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, star(star(X0!0)))) = addition(multiplication(star(star(X0!0)), star(X0!0)), addition(one, star(star(X0!0))))),
% 110.46/70.09 inference(monotonicity,[status(thm)],[211])).
% 110.46/70.09 tff(525,plain,
% 110.46/70.09 (addition(multiplication(star(star(X0!0)), star(X0!0)), addition(one, star(star(X0!0)))) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, star(star(X0!0))))),
% 110.46/70.09 inference(symmetry,[status(thm)],[524])).
% 110.46/70.09 tff(526,plain,
% 110.46/70.09 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(star(star(X0!0)), star(X0!0)), addition(one, star(star(X0!0)))) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))))),
% 110.46/70.09 inference(quant_inst,[status(thm)],[])).
% 110.46/70.09 tff(527,plain,
% 110.46/70.09 (addition(multiplication(star(star(X0!0)), star(X0!0)), addition(one, star(star(X0!0)))) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0)))),
% 110.46/70.09 inference(unit_resolution,[status(thm)],[526, 50])).
% 110.46/70.09 tff(528,plain,
% 110.46/70.09 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))) = addition(multiplication(star(star(X0!0)), star(X0!0)), addition(one, star(star(X0!0))))),
% 110.46/70.09 inference(symmetry,[status(thm)],[527])).
% 110.46/70.09 tff(529,plain,
% 110.46/70.09 (addition(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0)))),
% 110.46/70.09 inference(symmetry,[status(thm)],[160])).
% 110.46/70.09 tff(530,plain,
% 110.46/70.09 (star(star(X0!0)) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, star(star(X0!0))))),
% 110.46/70.09 inference(transitivity,[status(thm)],[260, 529, 528, 525])).
% 110.46/70.09 tff(531,plain,
% 110.46/70.09 (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), multiplication(star(star(X0!0)), one)) = multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))),
% 110.46/70.09 inference(transitivity,[status(thm)],[502, 499])).
% 110.46/70.09 tff(532,plain,
% 110.46/70.09 (addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), multiplication(star(star(X0!0)), one)), star(star(X0!0))) = addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, star(star(X0!0)))))),
% 110.46/70.09 inference(monotonicity,[status(thm)],[531, 530])).
% 110.46/70.09 tff(533,plain,
% 110.46/70.09 (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, star(star(X0!0))))) = addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), multiplication(star(star(X0!0)), one)), star(star(X0!0)))),
% 110.46/70.09 inference(symmetry,[status(thm)],[532])).
% 110.46/70.09 tff(534,plain,
% 110.46/70.09 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, star(star(X0!0))))) = addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), addition(one, star(star(X0!0)))))),
% 110.46/70.09 inference(quant_inst,[status(thm)],[])).
% 110.46/70.09 tff(535,plain,
% 110.46/70.09 (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, star(star(X0!0))))) = addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), addition(one, star(star(X0!0))))),
% 110.46/70.09 inference(unit_resolution,[status(thm)],[534, 50])).
% 110.46/70.09 tff(536,plain,
% 110.46/70.09 (addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), addition(one, star(star(X0!0)))) = addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, star(star(X0!0)))))),
% 110.46/70.09 inference(symmetry,[status(thm)],[535])).
% 110.46/70.09 tff(537,plain,
% 110.46/70.09 (addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), addition(one, star(star(X0!0)))) = addition(multiplication(star(star(X0!0)), star(X0!0)), addition(one, star(star(X0!0))))),
% 110.46/70.09 inference(monotonicity,[status(thm)],[470])).
% 110.46/70.09 tff(538,plain,
% 110.46/70.09 (addition(multiplication(star(star(X0!0)), star(X0!0)), addition(one, star(star(X0!0)))) = addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), addition(one, star(star(X0!0))))),
% 110.46/70.09 inference(symmetry,[status(thm)],[537])).
% 110.46/70.09 tff(539,plain,
% 110.46/70.09 (star(star(X0!0)) = addition(multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)))),
% 110.46/70.09 inference(transitivity,[status(thm)],[260, 529, 528, 538, 536, 533, 523, 520, 504, 502, 499, 495, 482])).
% 110.46/70.09 tff(540,plain,
% 110.46/70.09 (addition(star(star(X0!0)), addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0))))),
% 110.46/70.09 inference(monotonicity,[status(thm)],[539, 494])).
% 110.46/70.09 tff(541,plain,
% 110.46/70.09 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(star(X0!0))) = addition(star(star(X0!0)), addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(star(X0!0), star(star(X0!0))), one))))),
% 110.46/70.09 inference(quant_inst,[status(thm)],[])).
% 110.46/70.09 tff(542,plain,
% 110.46/70.09 (addition(addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(star(X0!0))) = addition(star(star(X0!0)), addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 110.46/70.09 inference(unit_resolution,[status(thm)],[541, 39])).
% 110.46/70.09 tff(543,plain,
% 110.46/70.09 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0)))) = addition(addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(star(X0!0))))),
% 110.46/70.09 inference(quant_inst,[status(thm)],[])).
% 110.46/70.09 tff(544,plain,
% 110.46/70.09 (addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0)))) = addition(addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(star(X0!0)))),
% 110.46/70.09 inference(unit_resolution,[status(thm)],[543, 50])).
% 110.46/70.09 tff(545,plain,
% 110.46/70.09 (star(star(X0!0)) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0)))),
% 110.46/70.09 inference(transitivity,[status(thm)],[177, 176])).
% 110.46/70.09 tff(546,plain,
% 110.46/70.09 (addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), star(star(X0!0))) = addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0))))),
% 110.46/70.09 inference(monotonicity,[status(thm)],[545])).
% 110.46/70.09 tff(547,plain,
% 110.46/70.09 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0)))) = addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), star(star(X0!0))))),
% 110.46/70.09 inference(quant_inst,[status(thm)],[])).
% 110.46/70.09 tff(548,plain,
% 110.46/70.09 (addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0)))) = addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), star(star(X0!0)))),
% 110.46/70.09 inference(unit_resolution,[status(thm)],[547, 50])).
% 110.46/70.09 tff(549,plain,
% 110.46/70.09 (star(star(X0!0)) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0)))),
% 110.46/70.09 inference(transitivity,[status(thm)],[260, 529])).
% 110.46/70.09 tff(550,plain,
% 110.46/70.09 (addition(star(X0!0), star(star(X0!0))) = addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))))),
% 110.46/70.09 inference(monotonicity,[status(thm)],[549])).
% 110.46/70.09 tff(551,plain,
% 110.46/70.09 (addition(star(X0!0), star(star(X0!0))) = star(star(X0!0))),
% 110.46/70.09 inference(transitivity,[status(thm)],[550, 548, 546, 544, 542, 540, 489, 487, 462, 461, 459, 456, 407, 405, 400, 397, 393, 391, 381, 376, 374, 350, 347, 335, 332, 326, 323, 313, 304, 302, 286, 284, 283, 272, 271, 268, 264, 253, 238, 235, 233, 232, 222, 215, 213, 194, 191, 188, 185, 182, 181, 171, 169, 149, 147, 143])).
% 110.46/70.09 tff(552,assumption,(~leq(star(X0!0), star(star(X0!0)))), introduced(assumption)).
% 110.46/70.09 tff(553,plain,
% 110.46/70.09 ((~(leq(star(X0!0), star(star(X0!0))) <=> (addition(star(X0!0), star(star(X0!0))) = star(star(X0!0))))) | leq(star(X0!0), star(star(X0!0))) | (~(addition(star(X0!0), star(star(X0!0))) = star(star(X0!0))))),
% 110.57/70.09 inference(tautology,[status(thm)],[])).
% 110.57/70.09 tff(554,plain,
% 110.57/70.09 ((~(leq(star(X0!0), star(star(X0!0))) <=> (addition(star(X0!0), star(star(X0!0))) = star(star(X0!0))))) | (~(addition(star(X0!0), star(star(X0!0))) = star(star(X0!0))))),
% 110.57/70.09 inference(unit_resolution,[status(thm)],[553, 552])).
% 110.57/70.09 tff(555,plain,
% 110.57/70.09 (~(addition(star(X0!0), star(star(X0!0))) = star(star(X0!0)))),
% 110.57/70.09 inference(unit_resolution,[status(thm)],[554, 136])).
% 110.57/70.09 tff(556,plain,
% 110.57/70.09 ($false),
% 110.57/70.09 inference(unit_resolution,[status(thm)],[555, 551])).
% 110.57/70.09 tff(557,plain,(leq(star(X0!0), star(star(X0!0)))), inference(lemma,lemma(discharge,[]))).
% 110.57/70.09 tff(558,plain,
% 110.57/70.09 ((~(leq(star(X0!0), star(star(X0!0))) <=> (addition(star(X0!0), star(star(X0!0))) = star(star(X0!0))))) | (~leq(star(X0!0), star(star(X0!0)))) | (addition(star(X0!0), star(star(X0!0))) = star(star(X0!0)))),
% 110.57/70.09 inference(tautology,[status(thm)],[])).
% 110.57/70.09 tff(559,plain,
% 110.57/70.09 ((~(leq(star(X0!0), star(star(X0!0))) <=> (addition(star(X0!0), star(star(X0!0))) = star(star(X0!0))))) | (addition(star(X0!0), star(star(X0!0))) = star(star(X0!0)))),
% 110.57/70.09 inference(unit_resolution,[status(thm)],[558, 557])).
% 110.57/70.09 tff(560,plain,
% 110.57/70.09 (addition(star(X0!0), star(star(X0!0))) = star(star(X0!0))),
% 110.57/70.09 inference(unit_resolution,[status(thm)],[559, 136])).
% 110.57/70.09 tff(561,plain,
% 110.57/70.09 (multiplication(star(X0!0), addition(star(X0!0), star(star(X0!0)))) = multiplication(star(X0!0), star(star(X0!0)))),
% 110.57/70.09 inference(monotonicity,[status(thm)],[560])).
% 110.57/70.09 tff(562,plain,
% 110.57/70.09 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(star(X0!0), addition(star(X0!0), star(star(X0!0)))) = addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.57/70.09 inference(quant_inst,[status(thm)],[])).
% 110.57/70.09 tff(563,plain,
% 110.57/70.09 (multiplication(star(X0!0), addition(star(X0!0), star(star(X0!0)))) = addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))),
% 110.57/70.09 inference(unit_resolution,[status(thm)],[562, 62])).
% 110.57/70.09 tff(564,plain,
% 110.57/70.09 (addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))) = multiplication(star(X0!0), addition(star(X0!0), star(star(X0!0))))),
% 110.57/70.09 inference(symmetry,[status(thm)],[563])).
% 110.57/70.09 tff(565,plain,
% 110.57/70.09 (addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))) = multiplication(star(X0!0), star(star(X0!0)))),
% 110.57/70.09 inference(transitivity,[status(thm)],[564, 561])).
% 110.57/70.09 tff(566,plain,
% 110.57/70.09 (addition(one, addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = addition(one, multiplication(star(X0!0), star(star(X0!0))))),
% 110.57/70.09 inference(monotonicity,[status(thm)],[565])).
% 110.57/70.09 tff(567,plain,
% 110.57/70.09 (addition(one, multiplication(star(X0!0), star(star(X0!0)))) = addition(one, addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.57/70.09 inference(symmetry,[status(thm)],[566])).
% 110.57/70.09 tff(568,plain,
% 110.57/70.09 (addition(multiplication(star(X0!0), star(star(X0!0))), one) = addition(one, addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.57/70.09 inference(transitivity,[status(thm)],[146, 567])).
% 110.57/70.09 tff(569,plain,
% 110.57/70.09 (addition(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(star(X0!0), addition(one, addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.57/70.09 inference(monotonicity,[status(thm)],[568])).
% 110.57/70.09 tff(570,plain,
% 110.57/70.09 (addition(star(X0!0), addition(one, addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.57/70.09 inference(symmetry,[status(thm)],[569])).
% 110.57/70.09 tff(571,plain,
% 110.57/70.09 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(star(X0!0), addition(one, addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(addition(star(X0!0), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.57/70.09 inference(quant_inst,[status(thm)],[])).
% 110.57/70.09 tff(572,plain,
% 110.57/70.09 (addition(star(X0!0), addition(one, addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(addition(star(X0!0), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.57/70.09 inference(unit_resolution,[status(thm)],[571, 50])).
% 110.57/70.09 tff(573,plain,
% 110.57/70.09 (addition(addition(star(X0!0), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = addition(star(X0!0), addition(one, addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.57/70.09 inference(symmetry,[status(thm)],[572])).
% 110.57/70.09 tff(574,plain,
% 110.57/70.09 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)) = addition(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)))),
% 110.57/70.09 inference(quant_inst,[status(thm)],[])).
% 110.57/70.09 tff(575,plain,
% 110.57/70.09 (addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)) = addition(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))),
% 110.57/70.09 inference(unit_resolution,[status(thm)],[574, 39])).
% 110.57/70.09 tff(576,plain,
% 110.57/70.09 (addition(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)) = addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))),
% 110.57/70.09 inference(symmetry,[status(thm)],[575])).
% 110.57/70.09 tff(577,plain,
% 110.57/70.09 (addition(star(X0!0), addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), one)) = addition(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))),
% 110.57/70.09 inference(monotonicity,[status(thm)],[496])).
% 110.57/70.09 tff(578,plain,
% 110.57/70.09 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(star(X0!0), addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), one)) = addition(addition(star(X0!0), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), one))),
% 110.57/70.09 inference(quant_inst,[status(thm)],[])).
% 110.57/70.09 tff(579,plain,
% 110.57/70.09 (addition(star(X0!0), addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), one)) = addition(addition(star(X0!0), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), one)),
% 110.57/70.09 inference(unit_resolution,[status(thm)],[578, 50])).
% 110.57/70.09 tff(580,plain,
% 110.57/70.09 (addition(addition(star(X0!0), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), one) = addition(star(X0!0), addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), one))),
% 110.57/70.09 inference(symmetry,[status(thm)],[579])).
% 110.57/70.09 tff(581,plain,
% 110.57/70.09 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), star(X0!0)) = addition(star(X0!0), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))))),
% 110.57/70.09 inference(quant_inst,[status(thm)],[])).
% 110.57/70.09 tff(582,plain,
% 110.57/70.09 (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), star(X0!0)) = addition(star(X0!0), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))),
% 110.57/70.09 inference(unit_resolution,[status(thm)],[581, 39])).
% 110.57/70.09 tff(583,plain,
% 110.57/70.09 (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), star(X0!0)) = addition(multiplication(X0!0, star(X0!0)), star(X0!0))),
% 110.57/70.09 inference(monotonicity,[status(thm)],[92])).
% 110.57/70.09 tff(584,plain,
% 110.57/70.09 (addition(multiplication(X0!0, star(X0!0)), star(X0!0)) = addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), star(X0!0))),
% 110.57/70.09 inference(symmetry,[status(thm)],[583])).
% 110.57/70.09 tff(585,plain,
% 110.57/70.09 (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0)))) = addition(multiplication(X0!0, star(X0!0)), star(X0!0))),
% 110.57/70.09 inference(symmetry,[status(thm)],[105])).
% 110.57/70.09 tff(586,plain,
% 110.57/70.09 (addition(addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), addition(one, star(X0!0))) = addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0))))),
% 110.57/70.09 inference(symmetry,[status(thm)],[97])).
% 110.57/70.09 tff(587,plain,
% 110.57/70.09 (addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0))) = addition(addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), addition(one, star(X0!0)))),
% 110.57/70.09 inference(symmetry,[status(thm)],[95])).
% 110.57/70.09 tff(588,plain,
% 110.57/70.09 (star(X0!0) = addition(star(X0!0), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))),
% 110.57/70.09 inference(transitivity,[status(thm)],[102, 101, 100, 587, 586, 585, 584, 582])).
% 110.57/70.09 tff(589,plain,
% 110.57/70.09 (addition(star(X0!0), one) = addition(addition(star(X0!0), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), one)),
% 110.57/70.09 inference(monotonicity,[status(thm)],[588])).
% 110.57/70.09 tff(590,plain,
% 110.57/70.09 (addition(star(X0!0), one) = star(X0!0)),
% 110.57/70.09 inference(transitivity,[status(thm)],[589, 580, 577, 576, 43, 32])).
% 110.57/70.09 tff(591,plain,
% 110.57/70.09 (addition(addition(star(X0!0), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = addition(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.57/70.09 inference(monotonicity,[status(thm)],[590])).
% 110.57/70.09 tff(592,plain,
% 110.57/70.09 (addition(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = addition(addition(star(X0!0), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.57/70.09 inference(symmetry,[status(thm)],[591])).
% 110.57/70.09 tff(593,plain,
% 110.57/70.09 (multiplication(addition(star(X0!0), star(star(X0!0))), star(X0!0)) = multiplication(star(star(X0!0)), star(X0!0))),
% 110.57/70.09 inference(monotonicity,[status(thm)],[560])).
% 110.57/70.09 tff(594,plain,
% 110.57/70.09 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(star(X0!0), star(star(X0!0))), star(X0!0)) = addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))),
% 110.57/70.09 inference(quant_inst,[status(thm)],[])).
% 110.57/70.09 tff(595,plain,
% 110.57/70.09 (multiplication(addition(star(X0!0), star(star(X0!0))), star(X0!0)) = addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))),
% 110.57/70.09 inference(unit_resolution,[status(thm)],[594, 207])).
% 110.57/70.09 tff(596,plain,
% 110.57/70.09 (addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))) = multiplication(addition(star(X0!0), star(star(X0!0))), star(X0!0))),
% 110.57/70.09 inference(symmetry,[status(thm)],[595])).
% 110.57/70.09 tff(597,plain,
% 110.57/70.09 (addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))) = multiplication(star(star(X0!0)), star(X0!0))),
% 110.57/70.09 inference(transitivity,[status(thm)],[596, 593])).
% 110.57/70.09 tff(598,plain,
% 110.57/70.09 (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), one) = addition(multiplication(star(star(X0!0)), star(X0!0)), one)),
% 110.57/70.09 inference(monotonicity,[status(thm)],[597])).
% 110.57/70.09 tff(599,plain,
% 110.57/70.09 (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), one) = addition(one, multiplication(star(star(X0!0)), star(X0!0)))),
% 110.57/70.09 inference(transitivity,[status(thm)],[598, 159])).
% 110.57/70.09 tff(600,plain,
% 110.57/70.09 (addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), one), star(star(X0!0))) = addition(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0)))),
% 110.57/70.09 inference(monotonicity,[status(thm)],[599])).
% 110.57/70.09 tff(601,plain,
% 110.57/70.09 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, star(star(X0!0)))) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), one), star(star(X0!0))))),
% 110.57/70.09 inference(quant_inst,[status(thm)],[])).
% 110.57/70.09 tff(602,plain,
% 110.57/70.09 (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, star(star(X0!0)))) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), one), star(star(X0!0)))),
% 110.57/70.09 inference(unit_resolution,[status(thm)],[601, 50])).
% 110.57/70.09 tff(603,plain,
% 110.57/70.09 (multiplication(star(star(X0!0)), star(X0!0)) = multiplication(addition(star(X0!0), star(star(X0!0))), star(X0!0))),
% 110.57/70.09 inference(symmetry,[status(thm)],[593])).
% 110.57/70.09 tff(604,plain,
% 110.57/70.09 (multiplication(star(star(X0!0)), addition(star(X0!0), star(X0!0))) = multiplication(star(star(X0!0)), star(X0!0))),
% 110.57/70.09 inference(monotonicity,[status(thm)],[54])).
% 110.57/70.09 tff(605,plain,
% 110.57/70.09 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(star(star(X0!0)), addition(star(X0!0), star(X0!0))) = addition(multiplication(star(star(X0!0)), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))),
% 110.57/70.09 inference(quant_inst,[status(thm)],[])).
% 110.57/70.09 tff(606,plain,
% 110.57/70.09 (multiplication(star(star(X0!0)), addition(star(X0!0), star(X0!0))) = addition(multiplication(star(star(X0!0)), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))),
% 110.57/70.09 inference(unit_resolution,[status(thm)],[605, 62])).
% 110.57/70.09 tff(607,plain,
% 110.57/70.09 (addition(multiplication(star(star(X0!0)), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))) = multiplication(star(star(X0!0)), addition(star(X0!0), star(X0!0)))),
% 110.57/70.09 inference(symmetry,[status(thm)],[606])).
% 110.57/70.09 tff(608,plain,
% 110.57/70.09 (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(multiplication(star(star(X0!0)), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))),
% 110.57/70.09 inference(monotonicity,[status(thm)],[597, 597])).
% 110.57/70.09 tff(609,plain,
% 110.57/70.09 (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))),
% 110.57/70.09 inference(transitivity,[status(thm)],[608, 607, 604, 603, 595])).
% 110.57/70.09 tff(610,plain,
% 110.57/70.09 (addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), addition(one, star(star(X0!0)))) = addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, star(star(X0!0))))),
% 110.57/70.10 inference(monotonicity,[status(thm)],[609])).
% 110.57/70.10 tff(611,plain,
% 110.57/70.10 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, star(star(X0!0))))) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), addition(one, star(star(X0!0)))))),
% 110.57/70.10 inference(quant_inst,[status(thm)],[])).
% 110.57/70.10 tff(612,plain,
% 110.57/70.10 (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, star(star(X0!0))))) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), addition(one, star(star(X0!0))))),
% 110.57/70.10 inference(unit_resolution,[status(thm)],[611, 50])).
% 110.57/70.10 tff(613,plain,
% 110.57/70.10 (addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), one), star(star(X0!0))) = addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, star(star(X0!0))))),
% 110.57/70.10 inference(symmetry,[status(thm)],[602])).
% 110.57/70.10 tff(614,plain,
% 110.57/70.10 (addition(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), one), star(star(X0!0)))),
% 110.57/70.10 inference(symmetry,[status(thm)],[600])).
% 110.57/70.10 tff(615,plain,
% 110.57/70.10 (star(star(X0!0)) = addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, star(star(X0!0))))),
% 110.57/70.10 inference(transitivity,[status(thm)],[260, 614, 613])).
% 110.57/70.10 tff(616,plain,
% 110.57/70.10 (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))) = addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, star(star(X0!0)))))),
% 110.57/70.10 inference(monotonicity,[status(thm)],[615])).
% 110.57/70.10 tff(617,plain,
% 110.57/70.10 (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))) = star(star(X0!0))),
% 110.57/70.10 inference(transitivity,[status(thm)],[616, 612, 610, 602, 600, 156])).
% 110.57/70.10 tff(618,plain,
% 110.57/70.10 (multiplication(star(X0!0), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0)))) = multiplication(star(X0!0), star(star(X0!0)))),
% 110.57/70.10 inference(monotonicity,[status(thm)],[617])).
% 110.57/70.10 tff(619,plain,
% 110.57/70.10 (multiplication(star(X0!0), star(star(X0!0))) = multiplication(star(X0!0), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))))),
% 110.57/70.10 inference(symmetry,[status(thm)],[618])).
% 110.57/70.10 tff(620,plain,
% 110.57/70.10 (addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))) = multiplication(star(X0!0), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))))),
% 110.57/70.10 inference(transitivity,[status(thm)],[564, 561, 619])).
% 110.57/70.10 tff(621,plain,
% 110.57/70.10 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(star(X0!0), one) = star(X0!0))),
% 110.57/70.10 inference(quant_inst,[status(thm)],[])).
% 110.57/70.10 tff(622,plain,
% 110.57/70.10 (multiplication(star(X0!0), one) = star(X0!0)),
% 110.57/70.10 inference(unit_resolution,[status(thm)],[621, 229])).
% 110.57/70.10 tff(623,plain,
% 110.57/70.10 (star(X0!0) = multiplication(star(X0!0), one)),
% 110.57/70.10 inference(symmetry,[status(thm)],[622])).
% 110.57/70.10 tff(624,plain,
% 110.57/70.10 (addition(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = addition(multiplication(star(X0!0), one), multiplication(star(X0!0), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0)))))),
% 110.57/70.10 inference(monotonicity,[status(thm)],[623, 620])).
% 110.57/70.10 tff(625,plain,
% 110.57/70.10 (addition(multiplication(star(X0!0), one), multiplication(star(X0!0), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))))) = addition(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.57/70.10 inference(symmetry,[status(thm)],[624])).
% 110.57/70.10 tff(626,plain,
% 110.57/70.10 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(star(X0!0), addition(one, addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))))) = addition(multiplication(star(X0!0), one), multiplication(star(X0!0), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))))))),
% 110.57/70.10 inference(quant_inst,[status(thm)],[])).
% 110.57/70.10 tff(627,plain,
% 110.57/70.10 (multiplication(star(X0!0), addition(one, addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))))) = addition(multiplication(star(X0!0), one), multiplication(star(X0!0), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0)))))),
% 110.57/70.10 inference(unit_resolution,[status(thm)],[626, 62])).
% 110.57/70.10 tff(628,plain,
% 110.57/70.10 (addition(one, addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(one, multiplication(star(star(X0!0)), star(X0!0)))),
% 110.57/70.10 inference(monotonicity,[status(thm)],[597])).
% 110.57/70.10 tff(629,plain,
% 110.57/70.10 (addition(addition(one, addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), star(star(X0!0))) = addition(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0)))),
% 110.57/70.10 inference(monotonicity,[status(thm)],[628])).
% 110.57/70.10 tff(630,plain,
% 110.57/70.10 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0)))) = addition(addition(one, addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), star(star(X0!0))))),
% 110.57/70.10 inference(quant_inst,[status(thm)],[])).
% 110.57/70.10 tff(631,plain,
% 110.57/70.10 (addition(one, addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0)))) = addition(addition(one, addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), star(star(X0!0)))),
% 110.57/70.10 inference(unit_resolution,[status(thm)],[630, 50])).
% 110.57/70.10 tff(632,plain,
% 110.57/70.10 (addition(one, addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0)))) = star(star(X0!0))),
% 110.57/70.10 inference(transitivity,[status(thm)],[631, 629, 156])).
% 110.57/70.10 tff(633,plain,
% 110.57/70.10 (multiplication(star(X0!0), addition(one, addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))))) = multiplication(star(X0!0), star(star(X0!0)))),
% 110.57/70.10 inference(monotonicity,[status(thm)],[632])).
% 110.57/70.10 tff(634,plain,
% 110.57/70.10 (multiplication(star(X0!0), star(star(X0!0))) = multiplication(star(X0!0), addition(one, addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0)))))),
% 110.57/70.10 inference(symmetry,[status(thm)],[633])).
% 110.57/70.10 tff(635,plain,
% 110.57/70.10 (addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0))),
% 110.57/70.10 inference(transitivity,[status(thm)],[564, 561, 634, 627, 625, 592, 573, 570, 134])).
% 110.57/70.10 tff(636,plain,
% 110.57/70.10 (multiplication(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = multiplication(star(X0!0), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)))),
% 110.57/70.10 inference(monotonicity,[status(thm)],[635])).
% 110.57/70.10 tff(637,plain,
% 110.57/70.10 (multiplication(star(X0!0), star(star(X0!0))) = multiplication(star(X0!0), addition(star(X0!0), star(star(X0!0))))),
% 110.57/70.10 inference(symmetry,[status(thm)],[561])).
% 110.57/70.10 tff(638,plain,
% 110.57/70.10 (multiplication(star(X0!0), star(star(X0!0))) = addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))),
% 110.57/70.10 inference(transitivity,[status(thm)],[637, 563])).
% 110.57/70.10 tff(639,plain,
% 110.57/70.10 (multiplication(star(X0!0), multiplication(star(X0!0), star(star(X0!0)))) = multiplication(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.57/70.10 inference(monotonicity,[status(thm)],[638])).
% 110.57/70.10 tff(640,plain,
% 110.57/70.10 (^[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)))),
% 110.57/70.10 inference(bind,[status(th)],[])).
% 110.57/70.10 tff(641,plain,
% 110.57/70.10 (![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))),
% 110.57/70.10 inference(quant_intro,[status(thm)],[640])).
% 110.57/70.10 tff(642,plain,
% 110.57/70.10 (![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))),
% 110.57/70.10 inference(rewrite,[status(thm)],[])).
% 110.57/70.10 tff(643,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')).
% 110.57/70.10 tff(644,plain,
% 110.57/70.10 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 110.57/70.10 inference(modus_ponens,[status(thm)],[643, 642])).
% 110.57/70.10 tff(645,plain,(
% 110.57/70.10 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 110.57/70.10 inference(skolemize,[status(sab)],[644])).
% 110.57/70.10 tff(646,plain,
% 110.57/70.10 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 110.57/70.10 inference(modus_ponens,[status(thm)],[645, 641])).
% 110.57/70.10 tff(647,plain,
% 110.57/70.10 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(star(X0!0), multiplication(star(X0!0), star(star(X0!0)))) = multiplication(multiplication(star(X0!0), star(X0!0)), star(star(X0!0))))),
% 110.57/70.10 inference(quant_inst,[status(thm)],[])).
% 110.57/70.10 tff(648,plain,
% 110.57/70.10 (multiplication(star(X0!0), multiplication(star(X0!0), star(star(X0!0)))) = multiplication(multiplication(star(X0!0), star(X0!0)), star(star(X0!0)))),
% 110.57/70.10 inference(unit_resolution,[status(thm)],[647, 646])).
% 110.57/70.10 tff(649,plain,
% 110.57/70.10 (multiplication(multiplication(star(X0!0), star(X0!0)), star(star(X0!0))) = multiplication(star(X0!0), multiplication(star(X0!0), star(star(X0!0))))),
% 110.57/70.10 inference(symmetry,[status(thm)],[648])).
% 110.57/70.10 tff(650,plain,
% 110.57/70.10 (multiplication(multiplication(star(X0!0), star(X0!0)), star(star(X0!0))) = addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)), multiplication(star(X0!0), star(X0!0)))),
% 110.57/70.10 inference(transitivity,[status(thm)],[649, 639, 636, 131])).
% 110.57/70.10 tff(651,plain,
% 110.57/70.10 (leq(multiplication(multiplication(star(X0!0), star(X0!0)), star(star(X0!0))), star(X0!0)) <=> leq(addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)), multiplication(star(X0!0), star(X0!0))), star(X0!0))),
% 110.57/70.10 inference(monotonicity,[status(thm)],[650])).
% 110.57/70.10 tff(652,plain,
% 110.57/70.10 (leq(addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)), multiplication(star(X0!0), star(X0!0))), star(X0!0)) <=> leq(multiplication(multiplication(star(X0!0), star(X0!0)), star(star(X0!0))), star(X0!0))),
% 110.57/70.10 inference(symmetry,[status(thm)],[651])).
% 110.57/70.10 tff(653,plain,
% 110.57/70.10 (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one) = addition(multiplication(star(X0!0), star(star(X0!0))), one)),
% 110.57/70.10 inference(monotonicity,[status(thm)],[565])).
% 110.57/70.10 tff(654,plain,
% 110.57/70.10 (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one) = addition(one, multiplication(star(X0!0), star(star(X0!0))))),
% 110.57/70.10 inference(transitivity,[status(thm)],[653, 146])).
% 110.57/70.10 tff(655,plain,
% 110.57/70.10 (addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one), star(star(X0!0))) = addition(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0)))),
% 110.57/70.10 inference(monotonicity,[status(thm)],[654])).
% 110.57/70.10 tff(656,plain,
% 110.57/70.10 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0)))) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one), star(star(X0!0))))),
% 110.57/70.10 inference(quant_inst,[status(thm)],[])).
% 110.57/70.10 tff(657,plain,
% 110.57/70.10 (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0)))) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one), star(star(X0!0)))),
% 110.57/70.10 inference(unit_resolution,[status(thm)],[656, 50])).
% 110.57/70.10 tff(658,plain,
% 110.57/70.10 (multiplication(addition(star(X0!0), star(X0!0)), star(star(X0!0))) = multiplication(star(X0!0), star(star(X0!0)))),
% 110.57/70.10 inference(monotonicity,[status(thm)],[54])).
% 110.57/70.10 tff(659,plain,
% 110.57/70.10 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(star(X0!0), star(X0!0)), star(star(X0!0))) = addition(multiplication(star(X0!0), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.57/70.10 inference(quant_inst,[status(thm)],[])).
% 110.57/70.10 tff(660,plain,
% 110.57/70.10 (multiplication(addition(star(X0!0), star(X0!0)), star(star(X0!0))) = addition(multiplication(star(X0!0), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0))))),
% 110.57/70.10 inference(unit_resolution,[status(thm)],[659, 207])).
% 110.57/70.10 tff(661,plain,
% 110.57/70.10 (addition(multiplication(star(X0!0), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))) = multiplication(addition(star(X0!0), star(X0!0)), star(star(X0!0)))),
% 110.57/70.10 inference(symmetry,[status(thm)],[660])).
% 110.57/70.10 tff(662,plain,
% 110.57/70.10 (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = addition(multiplication(star(X0!0), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0))))),
% 110.57/70.10 inference(monotonicity,[status(thm)],[565, 565])).
% 110.57/70.10 tff(663,plain,
% 110.57/70.10 (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))),
% 110.57/70.10 inference(transitivity,[status(thm)],[662, 661, 658, 637, 563])).
% 110.57/70.10 tff(664,plain,
% 110.57/70.10 (addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, star(star(X0!0)))) = addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0))))),
% 110.57/70.10 inference(monotonicity,[status(thm)],[663])).
% 110.57/70.10 tff(665,plain,
% 110.57/70.10 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0))))) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, star(star(X0!0)))))),
% 110.57/70.10 inference(quant_inst,[status(thm)],[])).
% 110.57/70.10 tff(666,plain,
% 110.57/70.10 (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0))))) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, star(star(X0!0))))),
% 110.57/70.10 inference(unit_resolution,[status(thm)],[665, 50])).
% 110.57/70.10 tff(667,plain,
% 110.57/70.10 (addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one), star(star(X0!0))) = addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0))))),
% 110.57/70.10 inference(symmetry,[status(thm)],[657])).
% 110.57/70.10 tff(668,plain,
% 110.57/70.10 (addition(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one), star(star(X0!0)))),
% 110.57/70.10 inference(symmetry,[status(thm)],[655])).
% 110.57/70.10 tff(669,plain,
% 110.57/70.10 (star(star(X0!0)) = addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0))))),
% 110.57/70.10 inference(transitivity,[status(thm)],[177, 668, 667])).
% 110.57/70.10 tff(670,plain,
% 110.57/70.10 (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0)))))),
% 110.57/70.10 inference(monotonicity,[status(thm)],[669])).
% 110.57/70.10 tff(671,plain,
% 110.57/70.10 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = addition(star(star(X0!0)), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.57/70.10 inference(quant_inst,[status(thm)],[])).
% 110.57/70.10 tff(672,plain,
% 110.57/70.10 (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = addition(star(star(X0!0)), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.57/70.10 inference(unit_resolution,[status(thm)],[671, 39])).
% 110.57/70.10 tff(673,plain,
% 110.57/70.10 (addition(star(star(X0!0)), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0)))),
% 110.57/70.10 inference(symmetry,[status(thm)],[672])).
% 110.57/70.10 tff(674,plain,
% 110.57/70.10 (multiplication(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), star(star(X0!0))) = multiplication(star(X0!0), star(star(X0!0)))),
% 110.57/70.10 inference(monotonicity,[status(thm)],[106])).
% 110.57/70.10 tff(675,plain,
% 110.57/70.10 (multiplication(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), star(star(X0!0))) = addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))),
% 110.57/70.10 inference(transitivity,[status(thm)],[674, 637, 563])).
% 110.57/70.10 tff(676,plain,
% 110.57/70.10 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, star(star(X0!0))) = star(star(X0!0)))),
% 110.57/70.10 inference(quant_inst,[status(thm)],[])).
% 110.57/70.10 tff(677,plain,
% 110.57/70.10 (multiplication(one, star(star(X0!0))) = star(star(X0!0))),
% 110.57/70.10 inference(unit_resolution,[status(thm)],[676, 279])).
% 110.57/70.10 tff(678,plain,
% 110.57/70.10 (addition(multiplication(one, star(star(X0!0))), multiplication(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), star(star(X0!0)))) = addition(star(star(X0!0)), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.57/70.10 inference(monotonicity,[status(thm)],[677, 675])).
% 110.57/70.10 tff(679,plain,
% 110.57/70.10 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0))), star(star(X0!0))) = addition(multiplication(one, star(star(X0!0))), multiplication(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), star(star(X0!0)))))),
% 110.57/70.10 inference(quant_inst,[status(thm)],[])).
% 110.57/70.10 tff(680,plain,
% 110.57/70.10 (multiplication(addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0))), star(star(X0!0))) = addition(multiplication(one, star(star(X0!0))), multiplication(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), star(star(X0!0))))),
% 110.57/70.10 inference(unit_resolution,[status(thm)],[679, 207])).
% 110.57/70.10 tff(681,plain,
% 110.57/70.10 (addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) = addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0)))),
% 110.57/70.10 inference(symmetry,[status(thm)],[337])).
% 110.57/70.10 tff(682,plain,
% 110.57/70.10 (star(X0!0) = addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0)))),
% 110.57/70.10 inference(transitivity,[status(thm)],[102, 681])).
% 110.57/70.10 tff(683,plain,
% 110.57/70.10 (multiplication(star(X0!0), star(star(X0!0))) = multiplication(addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0))), star(star(X0!0)))),
% 110.57/70.10 inference(monotonicity,[status(thm)],[682])).
% 110.57/70.10 tff(684,plain,
% 110.57/70.10 (multiplication(star(X0!0), addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) = multiplication(star(X0!0), star(X0!0))),
% 110.57/70.10 inference(monotonicity,[status(thm)],[464])).
% 110.57/70.10 tff(685,plain,
% 110.57/70.10 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(star(X0!0), addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) = addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0))))),
% 110.57/70.10 inference(quant_inst,[status(thm)],[])).
% 110.57/70.10 tff(686,plain,
% 110.57/70.10 (multiplication(star(X0!0), addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) = addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0)))),
% 110.57/70.10 inference(unit_resolution,[status(thm)],[685, 62])).
% 110.57/70.10 tff(687,plain,
% 110.57/70.10 (addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0))) = multiplication(star(X0!0), addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)))),
% 110.57/70.10 inference(symmetry,[status(thm)],[686])).
% 110.57/70.10 tff(688,plain,
% 110.57/70.10 (addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0))) = multiplication(star(X0!0), star(X0!0))),
% 110.57/70.10 inference(transitivity,[status(thm)],[687, 684])).
% 110.57/70.10 tff(689,plain,
% 110.57/70.10 (addition(addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))),
% 110.57/70.10 inference(monotonicity,[status(thm)],[688, 565])).
% 110.57/70.10 tff(690,plain,
% 110.57/70.10 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.57/70.10 inference(quant_inst,[status(thm)],[])).
% 110.57/70.10 tff(691,plain,
% 110.57/70.10 (addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.57/70.10 inference(unit_resolution,[status(thm)],[690, 50])).
% 110.57/70.10 tff(692,plain,
% 110.57/70.10 (addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))),
% 110.57/70.10 inference(monotonicity,[status(thm)],[565])).
% 110.57/70.10 tff(693,plain,
% 110.57/70.10 (addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))) = addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.57/70.10 inference(symmetry,[status(thm)],[692])).
% 110.57/70.10 tff(694,plain,
% 110.57/70.10 (multiplication(star(X0!0), star(star(X0!0))) = addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.57/70.10 inference(transitivity,[status(thm)],[637, 563, 693])).
% 110.57/70.10 tff(695,plain,
% 110.57/70.10 (addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))) = addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.57/70.10 inference(monotonicity,[status(thm)],[694])).
% 110.57/70.10 tff(696,plain,
% 110.57/70.10 (multiplication(addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0))), addition(multiplication(X0!0, star(X0!0)), one)) = multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))),
% 110.57/70.10 inference(monotonicity,[status(thm)],[338])).
% 110.57/70.10 tff(697,plain,
% 110.57/70.10 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0))), addition(multiplication(X0!0, star(X0!0)), one)) = addition(multiplication(one, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))))),
% 110.57/70.10 inference(quant_inst,[status(thm)],[])).
% 110.57/70.10 tff(698,plain,
% 110.57/70.10 (multiplication(addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0))), addition(multiplication(X0!0, star(X0!0)), one)) = addition(multiplication(one, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)))),
% 110.57/70.10 inference(unit_resolution,[status(thm)],[697, 207])).
% 110.57/70.10 tff(699,plain,
% 110.57/70.10 (addition(multiplication(one, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))) = multiplication(addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0))), addition(multiplication(X0!0, star(X0!0)), one))),
% 110.57/70.10 inference(symmetry,[status(thm)],[698])).
% 110.57/70.10 tff(700,plain,
% 110.57/70.10 (multiplication(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)) = multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))),
% 110.57/70.11 inference(monotonicity,[status(thm)],[106])).
% 110.57/70.11 tff(701,plain,
% 110.57/70.11 (multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)) = multiplication(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))),
% 110.57/70.11 inference(symmetry,[status(thm)],[700])).
% 110.57/70.11 tff(702,plain,
% 110.57/70.11 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(X0!0), X0!0), one), addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) = addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), star(X0!0)))),
% 110.57/70.11 inference(quant_inst,[status(thm)],[])).
% 110.57/70.11 tff(703,plain,
% 110.57/70.11 (addition(addition(multiplication(star(X0!0), X0!0), one), addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) = addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), star(X0!0))),
% 110.57/70.11 inference(unit_resolution,[status(thm)],[702, 50])).
% 110.57/70.11 tff(704,plain,
% 110.57/70.11 (addition(addition(multiplication(star(X0!0), X0!0), one), addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) = addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 110.57/70.11 inference(monotonicity,[status(thm)],[68, 464])).
% 110.57/70.11 tff(705,plain,
% 110.57/70.11 (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = addition(addition(multiplication(star(X0!0), X0!0), one), addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)))),
% 110.57/70.11 inference(symmetry,[status(thm)],[704])).
% 110.57/70.11 tff(706,plain,
% 110.57/70.11 (star(X0!0) = addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), star(X0!0))),
% 110.57/70.11 inference(transitivity,[status(thm)],[85, 705, 703])).
% 110.57/70.11 tff(707,plain,
% 110.57/70.11 (multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)) = multiplication(addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))),
% 110.57/70.11 inference(monotonicity,[status(thm)],[706])).
% 110.57/70.11 tff(708,plain,
% 110.57/70.11 (multiplication(addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)) = multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))),
% 110.57/70.11 inference(symmetry,[status(thm)],[707])).
% 110.57/70.11 tff(709,plain,
% 110.57/70.11 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)) = addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))))),
% 110.57/70.11 inference(quant_inst,[status(thm)],[])).
% 110.57/70.11 tff(710,plain,
% 110.57/70.11 (multiplication(addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)) = addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)))),
% 110.57/70.11 inference(unit_resolution,[status(thm)],[709, 207])).
% 110.57/70.11 tff(711,plain,
% 110.57/70.11 (addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))) = multiplication(addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))),
% 110.57/70.11 inference(symmetry,[status(thm)],[710])).
% 110.57/70.11 tff(712,plain,
% 110.57/70.11 (addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))) = multiplication(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))),
% 110.57/70.11 inference(transitivity,[status(thm)],[711, 708, 701])).
% 110.57/70.11 tff(713,plain,
% 110.57/70.11 (addition(multiplication(one, addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)))) = addition(multiplication(one, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)))),
% 110.57/70.11 inference(monotonicity,[status(thm)],[712])).
% 110.57/70.11 tff(714,plain,
% 110.57/70.11 (addition(multiplication(one, addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)))) = multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))),
% 110.57/70.11 inference(transitivity,[status(thm)],[713, 699, 696])).
% 110.57/70.11 tff(715,plain,
% 110.57/70.11 (addition(addition(multiplication(one, addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))),
% 110.57/70.11 inference(monotonicity,[status(thm)],[714, 565])).
% 110.57/70.11 tff(716,plain,
% 110.57/70.11 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(one, addition(multiplication(X0!0, star(X0!0)), one)), addition(addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(addition(multiplication(one, addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.57/70.11 inference(quant_inst,[status(thm)],[])).
% 110.57/70.11 tff(717,plain,
% 110.57/70.11 (addition(multiplication(one, addition(multiplication(X0!0, star(X0!0)), one)), addition(addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(addition(multiplication(one, addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.57/70.11 inference(unit_resolution,[status(thm)],[716, 50])).
% 110.57/70.11 tff(718,plain,
% 110.57/70.11 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, addition(multiplication(X0!0, star(X0!0)), one)) = addition(multiplication(X0!0, star(X0!0)), one))),
% 110.57/70.11 inference(quant_inst,[status(thm)],[])).
% 110.57/70.11 tff(719,plain,
% 110.57/70.11 (multiplication(one, addition(multiplication(X0!0, star(X0!0)), one)) = addition(multiplication(X0!0, star(X0!0)), one)),
% 110.57/70.11 inference(unit_resolution,[status(thm)],[718, 279])).
% 110.57/70.11 tff(720,plain,
% 110.57/70.11 (addition(multiplication(X0!0, star(X0!0)), one) = multiplication(one, addition(multiplication(X0!0, star(X0!0)), one))),
% 110.57/70.11 inference(symmetry,[status(thm)],[719])).
% 110.57/70.11 tff(721,plain,
% 110.57/70.11 (addition(addition(multiplication(X0!0, star(X0!0)), one), addition(addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(multiplication(one, addition(multiplication(X0!0, star(X0!0)), one)), addition(addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.57/70.11 inference(monotonicity,[status(thm)],[720])).
% 110.57/70.11 tff(722,plain,
% 110.57/70.11 (addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))) = multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))),
% 110.57/70.11 inference(transitivity,[status(thm)],[711, 708])).
% 110.57/70.11 tff(723,plain,
% 110.57/70.11 (addition(addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))),
% 110.57/70.11 inference(monotonicity,[status(thm)],[722, 565])).
% 110.57/70.11 tff(724,plain,
% 110.57/70.11 (addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))) = addition(addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.57/70.11 inference(symmetry,[status(thm)],[723])).
% 110.57/70.11 tff(725,plain,
% 110.57/70.11 (addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))),
% 110.57/70.11 inference(symmetry,[status(thm)],[695])).
% 110.57/70.11 tff(726,plain,
% 110.57/70.11 (addition(addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.57/70.11 inference(symmetry,[status(thm)],[691])).
% 110.57/70.11 tff(727,plain,
% 110.57/70.11 (addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))) = addition(addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.57/70.11 inference(symmetry,[status(thm)],[689])).
% 110.57/70.11 tff(728,plain,
% 110.57/70.11 (addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))) = addition(addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.57/70.11 inference(transitivity,[status(thm)],[727, 726, 725, 724])).
% 110.57/70.11 tff(729,plain,
% 110.57/70.11 (addition(addition(multiplication(X0!0, star(X0!0)), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = addition(addition(multiplication(X0!0, star(X0!0)), one), addition(addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.57/70.11 inference(monotonicity,[status(thm)],[728])).
% 110.57/70.11 tff(730,plain,
% 110.57/70.11 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(X0!0, star(X0!0)), one)) = addition(addition(multiplication(X0!0, star(X0!0)), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.57/70.11 inference(quant_inst,[status(thm)],[])).
% 110.57/70.11 tff(731,plain,
% 110.57/70.11 (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(X0!0, star(X0!0)), one)) = addition(addition(multiplication(X0!0, star(X0!0)), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.57/70.11 inference(unit_resolution,[status(thm)],[730, 39])).
% 110.57/70.11 tff(732,plain,
% 110.57/70.11 (addition(one, addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))) = addition(one, multiplication(X0!0, star(X0!0)))),
% 110.57/70.11 inference(monotonicity,[status(thm)],[92])).
% 110.57/70.11 tff(733,plain,
% 110.57/70.11 (addition(one, addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))) = addition(multiplication(X0!0, star(X0!0)), one)),
% 110.57/70.11 inference(transitivity,[status(thm)],[732, 41])).
% 110.57/70.11 tff(734,plain,
% 110.57/70.11 (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))) = addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(X0!0, star(X0!0)), one))),
% 110.57/70.11 inference(monotonicity,[status(thm)],[733])).
% 110.57/70.11 tff(735,plain,
% 110.57/70.11 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))))),
% 110.57/70.11 inference(quant_inst,[status(thm)],[])).
% 110.57/70.11 tff(736,plain,
% 110.57/70.11 (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))),
% 110.57/70.11 inference(unit_resolution,[status(thm)],[735, 50])).
% 110.57/70.11 tff(737,plain,
% 110.57/70.11 (addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))) = addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))))),
% 110.57/70.11 inference(symmetry,[status(thm)],[736])).
% 110.57/70.11 tff(738,plain,
% 110.57/70.11 (addition(multiplication(star(X0!0), star(star(X0!0))), one) = addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one)),
% 110.57/70.11 inference(symmetry,[status(thm)],[653])).
% 110.57/70.11 tff(739,plain,
% 110.57/70.11 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))),
% 110.57/70.11 inference(monotonicity,[status(thm)],[738])).
% 110.57/70.11 tff(740,plain,
% 110.57/70.11 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one)) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.57/70.11 inference(monotonicity,[status(thm)],[653])).
% 110.57/70.11 tff(741,plain,
% 110.57/70.11 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one)) = addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), one))),
% 110.57/70.11 inference(quant_inst,[status(thm)],[])).
% 110.57/70.11 tff(742,plain,
% 110.57/70.11 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one)) = addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), one)),
% 110.57/70.11 inference(unit_resolution,[status(thm)],[741, 50])).
% 110.57/70.11 tff(743,plain,
% 110.57/70.11 (addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), one) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one))),
% 110.57/70.11 inference(symmetry,[status(thm)],[742])).
% 110.57/70.11 tff(744,plain,
% 110.57/70.11 (addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), one) = addition(multiplication(star(X0!0), star(star(X0!0))), one)),
% 110.57/70.11 inference(transitivity,[status(thm)],[743, 740, 421])).
% 110.57/70.11 tff(745,plain,
% 110.57/70.11 (addition(addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), one), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))),
% 110.57/70.11 inference(monotonicity,[status(thm)],[744])).
% 110.57/70.11 tff(746,plain,
% 110.57/70.11 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))) = addition(addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), one), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))))),
% 110.57/70.11 inference(quant_inst,[status(thm)],[])).
% 110.57/70.11 tff(747,plain,
% 110.57/70.11 (addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))) = addition(addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), one), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))),
% 110.57/70.11 inference(unit_resolution,[status(thm)],[746, 50])).
% 110.57/70.11 tff(748,plain,
% 110.57/70.11 (addition(one, multiplication(X0!0, star(X0!0))) = addition(one, addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))),
% 110.57/70.11 inference(symmetry,[status(thm)],[732])).
% 110.57/70.11 tff(749,plain,
% 110.57/70.11 (addition(multiplication(X0!0, star(X0!0)), one) = addition(one, addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))),
% 110.57/70.11 inference(transitivity,[status(thm)],[42, 748])).
% 110.57/70.11 tff(750,plain,
% 110.57/70.11 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.57/70.11 inference(quant_inst,[status(thm)],[])).
% 110.57/70.11 tff(751,plain,
% 110.57/70.11 (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.57/70.11 inference(unit_resolution,[status(thm)],[750, 39])).
% 110.57/70.11 tff(752,plain,
% 110.57/70.11 (addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(X0!0, star(X0!0)), one)) = addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))))),
% 110.59/70.11 inference(monotonicity,[status(thm)],[751, 749])).
% 110.59/70.11 tff(753,plain,
% 110.59/70.11 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.59/70.11 inference(symmetry,[status(thm)],[751])).
% 110.59/70.11 tff(754,plain,
% 110.59/70.11 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(star(X0!0), star(X0!0)), addition(one, addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(addition(multiplication(star(X0!0), star(X0!0)), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.59/70.11 inference(quant_inst,[status(thm)],[])).
% 110.59/70.11 tff(755,plain,
% 110.59/70.11 (addition(multiplication(star(X0!0), star(X0!0)), addition(one, addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(addition(multiplication(star(X0!0), star(X0!0)), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.59/70.11 inference(unit_resolution,[status(thm)],[754, 50])).
% 110.59/70.11 tff(756,plain,
% 110.59/70.11 (addition(one, addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one)),
% 110.59/70.11 inference(transitivity,[status(thm)],[566, 145, 738])).
% 110.59/70.11 tff(757,plain,
% 110.59/70.11 (addition(multiplication(star(X0!0), star(X0!0)), addition(one, addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(multiplication(star(X0!0), star(X0!0)), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one))),
% 110.59/70.11 inference(monotonicity,[status(thm)],[756])).
% 110.59/70.11 tff(758,plain,
% 110.59/70.11 (addition(multiplication(star(X0!0), star(X0!0)), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one)) = addition(multiplication(star(X0!0), star(X0!0)), addition(one, addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.59/70.11 inference(symmetry,[status(thm)],[757])).
% 110.59/70.11 tff(759,plain,
% 110.59/70.11 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(star(X0!0), star(X0!0)), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one)) = addition(addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), one))),
% 110.59/70.11 inference(quant_inst,[status(thm)],[])).
% 110.59/70.11 tff(760,plain,
% 110.59/70.11 (addition(multiplication(star(X0!0), star(X0!0)), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one)) = addition(addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), one)),
% 110.59/70.12 inference(unit_resolution,[status(thm)],[759, 50])).
% 110.59/70.12 tff(761,plain,
% 110.59/70.12 (addition(addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), one) = addition(multiplication(star(X0!0), star(X0!0)), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one))),
% 110.59/70.12 inference(symmetry,[status(thm)],[760])).
% 110.59/70.12 tff(762,plain,
% 110.59/70.12 (addition(multiplication(star(X0!0), star(star(X0!0))), one) = addition(addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), one)),
% 110.59/70.12 inference(monotonicity,[status(thm)],[694])).
% 110.59/70.12 tff(763,plain,
% 110.59/70.12 (addition(multiplication(star(X0!0), star(star(X0!0))), one) = addition(addition(multiplication(star(X0!0), star(X0!0)), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.59/70.12 inference(transitivity,[status(thm)],[762, 761, 758, 755])).
% 110.59/70.12 tff(764,plain,
% 110.59/70.12 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.59/70.12 inference(monotonicity,[status(thm)],[763])).
% 110.59/70.12 tff(765,plain,
% 110.59/70.12 (addition(addition(addition(multiplication(star(X0!0), star(X0!0)), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.59/70.12 inference(symmetry,[status(thm)],[764])).
% 110.59/70.12 tff(766,plain,
% 110.59/70.12 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(X0!0), star(X0!0)), one), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.59/70.12 inference(quant_inst,[status(thm)],[])).
% 110.59/70.12 tff(767,plain,
% 110.59/70.12 (addition(addition(multiplication(star(X0!0), star(X0!0)), one), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.59/70.12 inference(unit_resolution,[status(thm)],[766, 50])).
% 110.59/70.12 tff(768,plain,
% 110.59/70.12 (addition(addition(multiplication(star(X0!0), star(X0!0)), one), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(addition(multiplication(star(X0!0), star(X0!0)), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.59/70.12 inference(monotonicity,[status(thm)],[663])).
% 110.59/70.12 tff(769,plain,
% 110.59/70.12 (addition(addition(multiplication(star(X0!0), star(X0!0)), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = addition(addition(multiplication(star(X0!0), star(X0!0)), one), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.59/70.12 inference(symmetry,[status(thm)],[768])).
% 110.59/70.12 tff(770,plain,
% 110.59/70.12 (addition(multiplication(star(X0!0), star(star(X0!0))), one) = addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.59/70.12 inference(transitivity,[status(thm)],[762, 761, 758, 755, 769, 767, 765, 753])).
% 110.59/70.12 tff(771,plain,
% 110.59/70.12 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(X0!0, star(X0!0)), one)) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(X0!0, star(X0!0)), one))),
% 110.59/70.12 inference(monotonicity,[status(thm)],[770])).
% 110.59/70.12 tff(772,plain,
% 110.59/70.12 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(X0!0, star(X0!0)), one)) = addition(addition(multiplication(X0!0, star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 110.59/70.12 inference(quant_inst,[status(thm)],[])).
% 110.59/70.12 tff(773,plain,
% 110.59/70.12 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(X0!0, star(X0!0)), one)) = addition(addition(multiplication(X0!0, star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.59/70.12 inference(unit_resolution,[status(thm)],[772, 39])).
% 110.59/70.12 tff(774,plain,
% 110.59/70.12 (addition(addition(multiplication(X0!0, star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(X0!0, star(X0!0)), one))),
% 110.60/70.12 inference(symmetry,[status(thm)],[773])).
% 110.60/70.12 tff(775,plain,
% 110.60/70.12 (addition(addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), one) = addition(multiplication(star(X0!0), star(star(X0!0))), one)),
% 110.60/70.12 inference(symmetry,[status(thm)],[762])).
% 110.60/70.12 tff(776,plain,
% 110.60/70.12 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)), star(X0!0)) = addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)), multiplication(star(X0!0), star(X0!0))))),
% 110.60/70.12 inference(quant_inst,[status(thm)],[])).
% 110.60/70.12 tff(777,plain,
% 110.60/70.12 (multiplication(addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)), star(X0!0)) = addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)), multiplication(star(X0!0), star(X0!0)))),
% 110.60/70.12 inference(unit_resolution,[status(thm)],[776, 207])).
% 110.60/70.12 tff(778,plain,
% 110.60/70.12 (multiplication(addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)), star(X0!0)) = multiplication(star(X0!0), star(X0!0))),
% 110.60/70.12 inference(monotonicity,[status(thm)],[464])).
% 110.60/70.12 tff(779,plain,
% 110.60/70.12 (multiplication(star(X0!0), star(X0!0)) = multiplication(addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)), star(X0!0))),
% 110.60/70.12 inference(symmetry,[status(thm)],[778])).
% 110.60/70.12 tff(780,plain,
% 110.60/70.12 (multiplication(star(X0!0), star(X0!0)) = addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)), multiplication(star(X0!0), star(X0!0)))),
% 110.60/70.12 inference(transitivity,[status(thm)],[779, 777])).
% 110.60/70.12 tff(781,plain,
% 110.60/70.12 (addition(multiplication(star(X0!0), star(X0!0)), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one)) = addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)), multiplication(star(X0!0), star(X0!0))), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.60/70.12 inference(monotonicity,[status(thm)],[780, 653])).
% 110.60/70.12 tff(782,plain,
% 110.60/70.12 (addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)), multiplication(star(X0!0), star(X0!0))), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(multiplication(star(X0!0), star(X0!0)), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one))),
% 110.60/70.12 inference(symmetry,[status(thm)],[781])).
% 110.60/70.12 tff(783,plain,
% 110.60/70.12 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)), addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)), multiplication(star(X0!0), star(X0!0))), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 110.60/70.12 inference(quant_inst,[status(thm)],[])).
% 110.60/70.12 tff(784,plain,
% 110.60/70.12 (addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)), addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)), multiplication(star(X0!0), star(X0!0))), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.60/70.12 inference(unit_resolution,[status(thm)],[783, 50])).
% 110.60/70.12 tff(785,plain,
% 110.60/70.12 (addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(multiplication(star(X0!0), star(X0!0)), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one))),
% 110.60/70.12 inference(monotonicity,[status(thm)],[738])).
% 110.60/70.12 tff(786,plain,
% 110.60/70.12 (addition(multiplication(star(X0!0), star(X0!0)), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one)) = addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.60/70.12 inference(symmetry,[status(thm)],[785])).
% 110.60/70.12 tff(787,plain,
% 110.60/70.12 (addition(multiplication(star(X0!0), star(star(X0!0))), one) = addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.60/70.12 inference(transitivity,[status(thm)],[762, 761, 786])).
% 110.60/70.12 tff(788,plain,
% 110.60/70.12 (multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)) = multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), star(X0!0)))),
% 110.60/70.12 inference(monotonicity,[status(thm)],[706])).
% 110.60/70.12 tff(789,plain,
% 110.60/70.12 (multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), star(X0!0))) = multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))),
% 110.60/70.12 inference(symmetry,[status(thm)],[788])).
% 110.60/70.12 tff(790,plain,
% 110.60/70.12 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), star(X0!0))) = addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))), multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))))),
% 110.60/70.12 inference(quant_inst,[status(thm)],[])).
% 110.60/70.12 tff(791,plain,
% 110.60/70.12 (multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), star(X0!0))) = addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))), multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)))),
% 110.60/70.12 inference(unit_resolution,[status(thm)],[790, 62])).
% 110.60/70.12 tff(792,plain,
% 110.60/70.12 (addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))), multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) = multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), star(X0!0)))),
% 110.60/70.12 inference(symmetry,[status(thm)],[791])).
% 110.60/70.12 tff(793,plain,
% 110.60/70.12 (addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))), multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) = multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))),
% 110.60/70.12 inference(transitivity,[status(thm)],[792, 789])).
% 110.60/70.12 tff(794,plain,
% 110.60/70.12 (addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))), multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)), addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 110.60/70.12 inference(monotonicity,[status(thm)],[793, 787])).
% 110.60/70.12 tff(795,plain,
% 110.60/70.12 (addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))), multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(multiplication(star(X0!0), star(star(X0!0))), one)),
% 110.60/70.12 inference(transitivity,[status(thm)],[794, 784, 782, 760, 775])).
% 110.60/70.12 tff(796,plain,
% 110.60/70.12 (addition(addition(multiplication(X0!0, star(X0!0)), one), addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))), multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))), addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(multiplication(X0!0, star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.60/70.12 inference(monotonicity,[status(thm)],[795])).
% 110.60/70.12 tff(797,plain,
% 110.60/70.12 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(addition(multiplication(X0!0, star(X0!0)), one), one) = addition(multiplication(X0!0, star(X0!0)), one))),
% 110.60/70.12 inference(quant_inst,[status(thm)],[])).
% 110.60/70.12 tff(798,plain,
% 110.60/70.12 (multiplication(addition(multiplication(X0!0, star(X0!0)), one), one) = addition(multiplication(X0!0, star(X0!0)), one)),
% 110.60/70.12 inference(unit_resolution,[status(thm)],[797, 229])).
% 110.60/70.12 tff(799,plain,
% 110.60/70.12 (addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), one), addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))), multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))), addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(multiplication(X0!0, star(X0!0)), one), addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))), multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 110.60/70.12 inference(monotonicity,[status(thm)],[798])).
% 110.60/70.12 tff(800,plain,
% 110.60/70.12 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), one), addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))), multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))), addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), one), addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))), multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)))), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 110.60/70.12 inference(quant_inst,[status(thm)],[])).
% 110.60/70.12 tff(801,plain,
% 110.60/70.12 (addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), one), addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))), multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))), addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), one), addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))), multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)))), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.60/70.12 inference(unit_resolution,[status(thm)],[800, 50])).
% 110.60/70.12 tff(802,plain,
% 110.60/70.12 (addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), one), addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))), multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)))), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), one), addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))), multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 110.60/70.12 inference(symmetry,[status(thm)],[801])).
% 110.60/70.12 tff(803,plain,
% 110.60/70.12 (addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(multiplication(star(X0!0), star(star(X0!0))), one)),
% 110.60/70.12 inference(transitivity,[status(thm)],[785, 760, 775])).
% 110.60/70.12 tff(804,plain,
% 110.60/70.12 (multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(multiplication(X0!0, star(X0!0)), star(X0!0))) = multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))),
% 110.60/70.12 inference(monotonicity,[status(thm)],[106])).
% 110.60/70.12 tff(805,plain,
% 110.60/70.12 (multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)) = multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(multiplication(X0!0, star(X0!0)), star(X0!0)))),
% 110.60/70.12 inference(symmetry,[status(thm)],[804])).
% 110.60/70.12 tff(806,plain,
% 110.60/70.12 (addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))), multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) = multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(multiplication(X0!0, star(X0!0)), star(X0!0)))),
% 110.60/70.12 inference(transitivity,[status(thm)],[792, 789, 805])).
% 110.60/70.12 tff(807,plain,
% 110.60/70.12 (addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), one), addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))), multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)))) = addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), one), multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(multiplication(X0!0, star(X0!0)), star(X0!0))))),
% 110.60/70.12 inference(monotonicity,[status(thm)],[806])).
% 110.60/70.12 tff(808,plain,
% 110.60/70.12 (addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), one), multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(multiplication(X0!0, star(X0!0)), star(X0!0)))) = addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), one), addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))), multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))))),
% 110.60/70.12 inference(symmetry,[status(thm)],[807])).
% 110.60/70.12 tff(809,plain,
% 110.60/70.12 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0)))) = addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), one), multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(multiplication(X0!0, star(X0!0)), star(X0!0)))))),
% 110.60/70.12 inference(quant_inst,[status(thm)],[])).
% 110.60/70.12 tff(810,plain,
% 110.60/70.12 (multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0)))) = addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), one), multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(multiplication(X0!0, star(X0!0)), star(X0!0))))),
% 110.60/70.12 inference(unit_resolution,[status(thm)],[809, 62])).
% 110.60/70.12 tff(811,plain,
% 110.60/70.12 (multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0)))) = multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))),
% 110.60/70.12 inference(monotonicity,[status(thm)],[338])).
% 110.60/70.12 tff(812,plain,
% 110.60/70.12 (multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)) = multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0))))),
% 110.60/70.12 inference(symmetry,[status(thm)],[811])).
% 110.60/70.12 tff(813,plain,
% 110.60/70.12 (multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)) = addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), one), addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))), multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))))),
% 110.60/70.12 inference(transitivity,[status(thm)],[812, 810, 808])).
% 110.60/70.12 tff(814,plain,
% 110.60/70.12 (addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)), addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), one), addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))), multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)))), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.60/70.12 inference(monotonicity,[status(thm)],[813, 803])).
% 110.60/70.12 tff(815,plain,
% 110.60/70.12 (addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)), multiplication(star(X0!0), star(X0!0))), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)), addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 110.60/70.12 inference(symmetry,[status(thm)],[784])).
% 110.60/70.12 tff(816,plain,
% 110.60/70.12 (addition(one, addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = addition(multiplication(star(X0!0), star(star(X0!0))), one)),
% 110.60/70.12 inference(transitivity,[status(thm)],[566, 145])).
% 110.60/70.12 tff(817,plain,
% 110.60/70.12 (addition(addition(one, addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.60/70.12 inference(monotonicity,[status(thm)],[816])).
% 110.60/70.13 tff(818,plain,
% 110.60/70.13 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(one, addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 110.60/70.13 inference(quant_inst,[status(thm)],[])).
% 110.60/70.13 tff(819,plain,
% 110.60/70.13 (addition(one, addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(one, addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.60/70.13 inference(unit_resolution,[status(thm)],[818, 50])).
% 110.60/70.13 tff(820,plain,
% 110.60/70.13 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), star(star(X0!0))), one)), one))),
% 110.60/70.13 inference(quant_inst,[status(thm)],[])).
% 110.60/70.13 tff(821,plain,
% 110.60/70.13 (addition(one, addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), star(star(X0!0))), one)), one)),
% 110.60/70.13 inference(unit_resolution,[status(thm)],[820, 39])).
% 110.60/70.13 tff(822,plain,
% 110.60/70.13 (addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), star(star(X0!0))), one)), one) = addition(one, addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 110.60/70.13 inference(symmetry,[status(thm)],[821])).
% 110.60/70.13 tff(823,plain,
% 110.60/70.13 (addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(one, one)) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), star(star(X0!0))), one)), one)),
% 110.60/70.13 inference(monotonicity,[status(thm)],[249])).
% 110.60/70.13 tff(824,plain,
% 110.60/70.13 (addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, one)) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(one, one))),
% 110.60/70.13 inference(monotonicity,[status(thm)],[753])).
% 110.60/70.13 tff(825,plain,
% 110.60/70.13 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, one)) = addition(addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), one), one))),
% 110.60/70.13 inference(quant_inst,[status(thm)],[])).
% 110.60/70.13 tff(826,plain,
% 110.60/70.13 (addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, one)) = addition(addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), one), one)),
% 110.60/70.13 inference(unit_resolution,[status(thm)],[825, 50])).
% 110.60/70.13 tff(827,plain,
% 110.60/70.13 (addition(addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), one), one) = addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, one))),
% 110.60/70.13 inference(symmetry,[status(thm)],[826])).
% 110.60/70.13 tff(828,plain,
% 110.60/70.13 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one))),
% 110.60/70.13 inference(symmetry,[status(thm)],[740])).
% 110.60/70.13 tff(829,plain,
% 110.60/70.13 (addition(multiplication(star(X0!0), star(star(X0!0))), one) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.60/70.13 inference(symmetry,[status(thm)],[421])).
% 110.60/70.13 tff(830,plain,
% 110.60/70.13 (addition(multiplication(star(X0!0), star(star(X0!0))), one) = addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), one)),
% 110.60/70.13 inference(transitivity,[status(thm)],[829, 828, 742])).
% 110.60/70.13 tff(831,plain,
% 110.60/70.13 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), one) = addition(addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), one), one)),
% 110.60/70.13 inference(monotonicity,[status(thm)],[830])).
% 110.60/70.13 tff(832,plain,
% 110.60/70.13 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), one))),
% 110.60/70.13 inference(quant_inst,[status(thm)],[])).
% 110.60/70.13 tff(833,plain,
% 110.60/70.13 (addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), one)),
% 110.60/70.13 inference(unit_resolution,[status(thm)],[832, 39])).
% 110.60/70.13 tff(834,plain,
% 110.60/70.13 (addition(one, addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.60/70.13 inference(monotonicity,[status(thm)],[803])).
% 110.60/70.13 tff(835,plain,
% 110.60/70.13 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(one, multiplication(star(X0!0), star(X0!0))), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 110.60/70.13 inference(quant_inst,[status(thm)],[])).
% 110.60/70.13 tff(836,plain,
% 110.60/70.13 (addition(one, addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(one, multiplication(star(X0!0), star(X0!0))), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.60/70.13 inference(unit_resolution,[status(thm)],[835, 50])).
% 110.60/70.13 tff(837,plain,
% 110.60/70.13 (addition(addition(one, multiplication(star(X0!0), star(X0!0))), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(one, addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 110.60/70.13 inference(symmetry,[status(thm)],[836])).
% 110.60/70.13 tff(838,plain,
% 110.60/70.13 (multiplication(star(X0!0), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0)))) = multiplication(star(X0!0), star(star(X0!0)))),
% 110.60/70.13 inference(monotonicity,[status(thm)],[364])).
% 110.60/70.13 tff(839,plain,
% 110.60/70.13 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(star(X0!0), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0)))) = addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.60/70.13 inference(quant_inst,[status(thm)],[])).
% 110.60/70.13 tff(840,plain,
% 110.60/70.13 (multiplication(star(X0!0), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0)))) = addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)), multiplication(star(X0!0), star(star(X0!0))))),
% 110.60/70.13 inference(unit_resolution,[status(thm)],[839, 62])).
% 110.60/70.13 tff(841,plain,
% 110.60/70.13 (addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)), multiplication(star(X0!0), star(star(X0!0)))) = multiplication(star(X0!0), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0))))),
% 110.60/70.13 inference(symmetry,[status(thm)],[840])).
% 110.60/70.13 tff(842,plain,
% 110.60/70.13 (addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)), multiplication(star(X0!0), star(star(X0!0))))),
% 110.60/70.13 inference(monotonicity,[status(thm)],[565])).
% 110.60/70.13 tff(843,plain,
% 110.60/70.13 (addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = multiplication(star(X0!0), star(star(X0!0)))),
% 110.60/70.13 inference(transitivity,[status(thm)],[842, 841, 838])).
% 110.60/70.13 tff(844,plain,
% 110.60/70.13 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), one) = addition(multiplication(star(X0!0), star(star(X0!0))), one)),
% 110.60/70.13 inference(monotonicity,[status(thm)],[843])).
% 110.60/70.13 tff(845,plain,
% 110.60/70.13 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one)) = addition(addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), one))),
% 110.60/70.13 inference(quant_inst,[status(thm)],[])).
% 110.60/70.13 tff(846,plain,
% 110.60/70.13 (addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one)) = addition(addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), one)),
% 110.60/70.13 inference(unit_resolution,[status(thm)],[845, 50])).
% 110.60/70.13 tff(847,plain,
% 110.60/70.13 (multiplication(star(X0!0), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one)) = multiplication(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.60/70.13 inference(monotonicity,[status(thm)],[653])).
% 110.60/70.13 tff(848,plain,
% 110.60/70.13 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(star(X0!0), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one)) = addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), multiplication(star(X0!0), one)))),
% 110.60/70.13 inference(quant_inst,[status(thm)],[])).
% 110.60/70.13 tff(849,plain,
% 110.60/70.13 (multiplication(star(X0!0), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one)) = addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), multiplication(star(X0!0), one))),
% 110.60/70.13 inference(unit_resolution,[status(thm)],[848, 62])).
% 110.60/70.13 tff(850,plain,
% 110.60/70.13 (addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), multiplication(star(X0!0), one)) = multiplication(star(X0!0), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one))),
% 110.60/70.13 inference(symmetry,[status(thm)],[849])).
% 110.60/70.13 tff(851,plain,
% 110.60/70.13 (addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), multiplication(star(X0!0), one)) = multiplication(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.60/70.13 inference(transitivity,[status(thm)],[850, 847])).
% 110.60/70.13 tff(852,plain,
% 110.60/70.13 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), multiplication(star(X0!0), one)), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one))),
% 110.60/70.13 inference(monotonicity,[status(thm)],[851, 738])).
% 110.60/70.13 tff(853,plain,
% 110.60/70.13 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), multiplication(star(X0!0), one)), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), multiplication(star(X0!0), one))))),
% 110.60/70.13 inference(quant_inst,[status(thm)],[])).
% 110.60/70.13 tff(854,plain,
% 110.60/70.13 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), multiplication(star(X0!0), one)), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), multiplication(star(X0!0), one)))),
% 110.60/70.13 inference(unit_resolution,[status(thm)],[853, 39])).
% 110.60/70.13 tff(855,plain,
% 110.60/70.13 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), multiplication(star(X0!0), one))) = addition(addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), multiplication(star(X0!0), one)), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.60/70.13 inference(symmetry,[status(thm)],[854])).
% 110.60/70.13 tff(856,plain,
% 110.60/70.13 (addition(addition(multiplication(star(X0!0), star(X0!0)), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = addition(multiplication(star(X0!0), star(X0!0)), addition(one, addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.60/70.13 inference(symmetry,[status(thm)],[755])).
% 110.60/70.13 tff(857,plain,
% 110.60/70.13 (addition(addition(multiplication(star(X0!0), star(X0!0)), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = addition(multiplication(star(X0!0), star(star(X0!0))), one)),
% 110.60/70.13 inference(transitivity,[status(thm)],[856, 757, 760, 775])).
% 110.60/70.13 tff(858,plain,
% 110.60/70.13 (addition(addition(addition(multiplication(star(X0!0), star(X0!0)), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), multiplication(star(X0!0), one))) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), multiplication(star(X0!0), one)))),
% 110.60/70.13 inference(monotonicity,[status(thm)],[857])).
% 110.60/70.13 tff(859,plain,
% 110.60/70.13 (multiplication(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = multiplication(star(X0!0), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one))),
% 110.60/70.13 inference(symmetry,[status(thm)],[847])).
% 110.60/70.13 tff(860,plain,
% 110.60/70.13 (multiplication(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = multiplication(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.60/70.13 inference(monotonicity,[status(thm)],[106])).
% 110.60/70.13 tff(861,plain,
% 110.60/70.13 (multiplication(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), multiplication(star(X0!0), one))),
% 110.60/70.13 inference(transitivity,[status(thm)],[860, 859, 849])).
% 110.60/70.13 tff(862,plain,
% 110.60/70.13 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.60/70.13 inference(quant_inst,[status(thm)],[])).
% 110.60/70.13 tff(863,plain,
% 110.60/70.13 (multiplication(one, addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(multiplication(star(X0!0), star(star(X0!0))), one)),
% 110.60/70.13 inference(unit_resolution,[status(thm)],[862, 279])).
% 110.60/70.13 tff(864,plain,
% 110.60/70.13 (multiplication(one, addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(addition(multiplication(star(X0!0), star(X0!0)), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.60/70.13 inference(transitivity,[status(thm)],[863, 762, 761, 758, 755])).
% 110.60/70.13 tff(865,plain,
% 110.60/70.13 (addition(multiplication(one, addition(multiplication(star(X0!0), star(star(X0!0))), one)), multiplication(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), multiplication(star(X0!0), one)))),
% 110.60/70.13 inference(monotonicity,[status(thm)],[864, 861])).
% 110.60/70.13 tff(866,plain,
% 110.60/70.13 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(multiplication(one, addition(multiplication(star(X0!0), star(star(X0!0))), one)), multiplication(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), addition(multiplication(star(X0!0), star(star(X0!0))), one))))),
% 110.60/70.13 inference(quant_inst,[status(thm)],[])).
% 110.60/70.13 tff(867,plain,
% 110.60/70.13 (multiplication(addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(multiplication(one, addition(multiplication(star(X0!0), star(star(X0!0))), one)), multiplication(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 110.60/70.13 inference(unit_resolution,[status(thm)],[866, 207])).
% 110.60/70.13 tff(868,plain,
% 110.60/70.13 (multiplication(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = multiplication(addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.60/70.13 inference(monotonicity,[status(thm)],[682])).
% 110.60/70.13 tff(869,plain,
% 110.60/70.13 (multiplication(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(multiplication(star(X0!0), star(star(X0!0))), one)),
% 110.60/70.13 inference(transitivity,[status(thm)],[868, 867, 865, 858, 855, 852, 846, 844])).
% 110.60/70.13 tff(870,plain,
% 110.60/70.13 (addition(addition(one, multiplication(star(X0!0), star(X0!0))), multiplication(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(one, multiplication(star(X0!0), star(X0!0))), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.60/70.13 inference(monotonicity,[status(thm)],[869])).
% 110.60/70.13 tff(871,plain,
% 110.60/70.13 (multiplication(star(X0!0), addition(one, addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))) = multiplication(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.60/70.13 inference(monotonicity,[status(thm)],[816])).
% 110.60/70.13 tff(872,plain,
% 110.60/70.13 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(star(X0!0), addition(one, addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(multiplication(star(X0!0), one), multiplication(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))))),
% 110.60/70.13 inference(quant_inst,[status(thm)],[])).
% 110.60/70.13 tff(873,plain,
% 110.60/70.13 (multiplication(star(X0!0), addition(one, addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(multiplication(star(X0!0), one), multiplication(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.60/70.13 inference(unit_resolution,[status(thm)],[872, 62])).
% 110.60/70.13 tff(874,plain,
% 110.60/70.13 (addition(multiplication(star(X0!0), one), multiplication(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))) = multiplication(star(X0!0), addition(one, addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.60/70.13 inference(symmetry,[status(thm)],[873])).
% 110.60/70.13 tff(875,plain,
% 110.60/70.13 (addition(multiplication(star(X0!0), one), multiplication(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))) = multiplication(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 110.60/70.13 inference(transitivity,[status(thm)],[874, 871])).
% 110.60/70.13 tff(876,plain,
% 110.60/70.13 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, multiplication(star(X0!0), star(X0!0))) = addition(multiplication(star(X0!0), star(X0!0)), one))),
% 110.60/70.13 inference(quant_inst,[status(thm)],[])).
% 110.60/70.13 tff(877,plain,
% 110.60/70.13 (addition(one, multiplication(star(X0!0), star(X0!0))) = addition(multiplication(star(X0!0), star(X0!0)), one)),
% 110.60/70.13 inference(unit_resolution,[status(thm)],[876, 39])).
% 110.60/70.13 tff(878,plain,
% 110.60/70.13 (addition(multiplication(star(X0!0), star(X0!0)), one) = addition(one, multiplication(star(X0!0), star(X0!0)))),
% 110.60/70.13 inference(symmetry,[status(thm)],[877])).
% 110.60/70.13 tff(879,plain,
% 110.60/70.13 (addition(addition(multiplication(star(X0!0), star(X0!0)), one), addition(multiplication(star(X0!0), one), multiplication(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))))) = addition(addition(one, multiplication(star(X0!0), star(X0!0))), multiplication(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 110.60/70.13 inference(monotonicity,[status(thm)],[878, 875])).
% 110.60/70.13 tff(880,plain,
% 110.60/70.13 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(X0!0), star(X0!0)), one), addition(multiplication(star(X0!0), one), multiplication(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))))) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), one), multiplication(star(X0!0), one)), multiplication(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))))),
% 110.60/70.13 inference(quant_inst,[status(thm)],[])).
% 110.60/70.13 tff(881,plain,
% 110.60/70.13 (addition(addition(multiplication(star(X0!0), star(X0!0)), one), addition(multiplication(star(X0!0), one), multiplication(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))))) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), one), multiplication(star(X0!0), one)), multiplication(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.60/70.13 inference(unit_resolution,[status(thm)],[880, 50])).
% 110.60/70.13 tff(882,plain,
% 110.60/70.13 (addition(addition(addition(multiplication(star(X0!0), star(X0!0)), one), multiplication(star(X0!0), one)), multiplication(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(addition(multiplication(star(X0!0), star(X0!0)), one), addition(multiplication(star(X0!0), one), multiplication(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))))),
% 110.60/70.13 inference(symmetry,[status(thm)],[881])).
% 110.60/70.13 tff(883,plain,
% 110.60/70.13 (addition(addition(multiplication(star(X0!0), star(X0!0)), one), multiplication(star(X0!0), one)) = addition(addition(multiplication(star(X0!0), star(X0!0)), one), star(X0!0))),
% 110.60/70.13 inference(monotonicity,[status(thm)],[622])).
% 110.60/70.13 tff(884,plain,
% 110.60/70.13 (addition(addition(multiplication(star(X0!0), star(X0!0)), one), star(X0!0)) = addition(addition(multiplication(star(X0!0), star(X0!0)), one), multiplication(star(X0!0), one))),
% 110.60/70.13 inference(symmetry,[status(thm)],[883])).
% 110.60/70.13 tff(885,plain,
% 110.60/70.13 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), one)) = addition(addition(multiplication(star(X0!0), star(X0!0)), one), star(X0!0)))),
% 110.60/70.13 inference(quant_inst,[status(thm)],[])).
% 110.60/70.13 tff(886,plain,
% 110.60/70.13 (addition(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), one)) = addition(addition(multiplication(star(X0!0), star(X0!0)), one), star(X0!0))),
% 110.60/70.13 inference(unit_resolution,[status(thm)],[885, 39])).
% 110.60/70.13 tff(887,plain,
% 110.60/70.13 (addition(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), one)) = addition(star(X0!0), addition(one, multiplication(star(X0!0), star(X0!0))))),
% 110.60/70.13 inference(monotonicity,[status(thm)],[878])).
% 110.60/70.13 tff(888,plain,
% 110.60/70.13 (addition(star(X0!0), addition(one, multiplication(star(X0!0), star(X0!0)))) = addition(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), one))),
% 110.60/70.13 inference(symmetry,[status(thm)],[887])).
% 110.60/70.13 tff(889,plain,
% 110.60/70.13 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(star(X0!0), addition(one, multiplication(star(X0!0), star(X0!0)))) = addition(addition(star(X0!0), one), multiplication(star(X0!0), star(X0!0))))),
% 110.60/70.13 inference(quant_inst,[status(thm)],[])).
% 110.60/70.13 tff(890,plain,
% 110.60/70.13 (addition(star(X0!0), addition(one, multiplication(star(X0!0), star(X0!0)))) = addition(addition(star(X0!0), one), multiplication(star(X0!0), star(X0!0)))),
% 110.60/70.13 inference(unit_resolution,[status(thm)],[889, 50])).
% 110.60/70.13 tff(891,plain,
% 110.60/70.13 (addition(addition(star(X0!0), one), multiplication(star(X0!0), star(X0!0))) = addition(star(X0!0), addition(one, multiplication(star(X0!0), star(X0!0))))),
% 110.60/70.13 inference(symmetry,[status(thm)],[890])).
% 110.60/70.13 tff(892,plain,
% 110.60/70.13 (addition(addition(star(X0!0), one), multiplication(star(X0!0), star(X0!0))) = addition(star(X0!0), multiplication(star(X0!0), star(X0!0)))),
% 110.60/70.13 inference(monotonicity,[status(thm)],[590])).
% 110.60/70.13 tff(893,plain,
% 110.60/70.13 (addition(star(X0!0), multiplication(star(X0!0), star(X0!0))) = addition(addition(star(X0!0), one), multiplication(star(X0!0), star(X0!0)))),
% 110.60/70.13 inference(symmetry,[status(thm)],[892])).
% 110.60/70.13 tff(894,plain,
% 110.60/70.13 (multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), star(X0!0))) = multiplication(star(X0!0), star(X0!0))),
% 110.60/70.14 inference(monotonicity,[status(thm)],[106])).
% 110.60/70.14 tff(895,plain,
% 110.60/70.14 (multiplication(star(X0!0), star(X0!0)) = multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), star(X0!0)))),
% 110.60/70.14 inference(symmetry,[status(thm)],[894])).
% 110.60/70.14 tff(896,plain,
% 110.60/70.14 (addition(star(X0!0), multiplication(star(X0!0), star(X0!0))) = addition(multiplication(star(X0!0), one), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), star(X0!0))))),
% 110.60/70.14 inference(monotonicity,[status(thm)],[623, 895])).
% 110.60/70.14 tff(897,plain,
% 110.60/70.14 (addition(multiplication(star(X0!0), one), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), star(X0!0)))) = addition(star(X0!0), multiplication(star(X0!0), star(X0!0)))),
% 110.60/70.14 inference(symmetry,[status(thm)],[896])).
% 110.60/70.14 tff(898,plain,
% 110.60/70.14 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(star(X0!0), addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0)))) = addition(multiplication(star(X0!0), one), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), star(X0!0)))))),
% 110.60/70.14 inference(quant_inst,[status(thm)],[])).
% 110.60/70.14 tff(899,plain,
% 110.60/70.14 (multiplication(star(X0!0), addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0)))) = addition(multiplication(star(X0!0), one), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), star(X0!0))))),
% 110.60/70.14 inference(unit_resolution,[status(thm)],[898, 62])).
% 110.60/70.14 tff(900,plain,
% 110.60/70.14 (multiplication(star(X0!0), addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0)))) = multiplication(star(X0!0), star(X0!0))),
% 110.60/70.14 inference(monotonicity,[status(thm)],[338])).
% 110.60/70.14 tff(901,plain,
% 110.60/70.14 (multiplication(star(X0!0), star(X0!0)) = multiplication(star(X0!0), addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0))))),
% 110.60/70.14 inference(symmetry,[status(thm)],[900])).
% 110.60/70.14 tff(902,plain,
% 110.60/70.14 (multiplication(star(X0!0), star(X0!0)) = addition(addition(multiplication(star(X0!0), star(X0!0)), one), multiplication(star(X0!0), one))),
% 110.60/70.14 inference(transitivity,[status(thm)],[901, 899, 897, 893, 891, 888, 886, 884])).
% 110.60/70.14 tff(903,plain,
% 110.60/70.14 (addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), one), multiplication(star(X0!0), one)), multiplication(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.60/70.14 inference(monotonicity,[status(thm)],[902])).
% 110.60/70.14 tff(904,plain,
% 110.60/70.14 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(star(X0!0), addition(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))))),
% 110.60/70.14 inference(quant_inst,[status(thm)],[])).
% 110.60/70.14 tff(905,plain,
% 110.60/70.14 (multiplication(star(X0!0), addition(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.60/70.14 inference(unit_resolution,[status(thm)],[904, 62])).
% 110.60/70.14 tff(906,plain,
% 110.60/70.14 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)) = addition(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))),
% 110.60/70.14 inference(transitivity,[status(thm)],[133, 569, 572, 591])).
% 110.60/70.14 tff(907,plain,
% 110.60/70.14 (multiplication(star(X0!0), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0))) = multiplication(star(X0!0), addition(star(X0!0), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))))),
% 110.60/70.14 inference(monotonicity,[status(thm)],[906])).
% 110.60/70.14 tff(908,plain,
% 110.60/70.14 (addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)), multiplication(star(X0!0), star(X0!0))) = multiplication(star(X0!0), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)))),
% 110.60/70.14 inference(symmetry,[status(thm)],[131])).
% 110.60/70.14 tff(909,plain,
% 110.60/70.14 (addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)), multiplication(star(X0!0), star(X0!0))) = star(star(X0!0))),
% 110.60/70.14 inference(transitivity,[status(thm)],[908, 907, 905, 903, 882, 879, 870, 837, 834, 833, 831, 827, 824, 823, 822, 819, 817, 421, 762, 761, 781, 815, 814, 802, 799, 796, 774, 771, 752, 747, 745, 739, 737, 734, 731, 729, 721, 717, 715, 695, 691, 689, 564, 561, 683, 680, 678, 673, 670, 666, 664, 657, 655, 143])).
% 110.60/70.14 tff(910,plain,
% 110.60/70.14 (leq(addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)), multiplication(star(X0!0), star(X0!0))), star(X0!0)) <=> leq(star(star(X0!0)), star(X0!0))),
% 110.60/70.14 inference(monotonicity,[status(thm)],[909])).
% 110.60/70.14 tff(911,plain,
% 110.60/70.14 (leq(star(star(X0!0)), star(X0!0)) <=> leq(addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)), multiplication(star(X0!0), star(X0!0))), star(X0!0))),
% 110.60/70.14 inference(symmetry,[status(thm)],[910])).
% 110.60/70.14 tff(912,plain,
% 110.60/70.14 (leq(star(star(X0!0)), star(X0!0)) <=> leq(multiplication(multiplication(star(X0!0), star(X0!0)), star(star(X0!0))), star(X0!0))),
% 110.60/70.14 inference(transitivity,[status(thm)],[911, 652])).
% 110.60/70.14 tff(913,plain,
% 110.60/70.14 ((~leq(star(star(X0!0)), star(X0!0))) <=> (~leq(multiplication(multiplication(star(X0!0), star(X0!0)), star(star(X0!0))), star(X0!0)))),
% 110.60/70.14 inference(monotonicity,[status(thm)],[912])).
% 110.60/70.14 tff(914,plain,
% 110.60/70.14 ((~(~((~leq(star(star(X0!0)), star(X0!0))) | (~leq(star(X0!0), star(star(X0!0))))))) <=> ((~leq(star(star(X0!0)), star(X0!0))) | (~leq(star(X0!0), star(star(X0!0)))))),
% 110.60/70.14 inference(rewrite,[status(thm)],[])).
% 110.60/70.14 tff(915,plain,
% 110.60/70.14 ((leq(star(star(X0!0)), star(X0!0)) & leq(star(X0!0), star(star(X0!0)))) <=> (~((~leq(star(star(X0!0)), star(X0!0))) | (~leq(star(X0!0), star(star(X0!0))))))),
% 110.60/70.14 inference(rewrite,[status(thm)],[])).
% 110.60/70.14 tff(916,plain,
% 110.60/70.14 ((~(leq(star(star(X0!0)), star(X0!0)) & leq(star(X0!0), star(star(X0!0))))) <=> (~(~((~leq(star(star(X0!0)), star(X0!0))) | (~leq(star(X0!0), star(star(X0!0)))))))),
% 110.60/70.14 inference(monotonicity,[status(thm)],[915])).
% 110.60/70.14 tff(917,plain,
% 110.60/70.14 ((~(leq(star(star(X0!0)), star(X0!0)) & leq(star(X0!0), star(star(X0!0))))) <=> ((~leq(star(star(X0!0)), star(X0!0))) | (~leq(star(X0!0), star(star(X0!0)))))),
% 110.60/70.14 inference(transitivity,[status(thm)],[916, 914])).
% 110.60/70.14 tff(918,plain,
% 110.60/70.14 ((~![X0: $i] : (leq(star(star(X0)), star(X0)) & leq(star(X0), star(star(X0))))) <=> (~![X0: $i] : (leq(star(star(X0)), star(X0)) & leq(star(X0), star(star(X0)))))),
% 110.60/70.14 inference(rewrite,[status(thm)],[])).
% 110.60/70.14 tff(919,axiom,(~![X0: $i] : (leq(star(star(X0)), star(X0)) & leq(star(X0), star(star(X0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 110.60/70.14 tff(920,plain,
% 110.60/70.14 (~![X0: $i] : (leq(star(star(X0)), star(X0)) & leq(star(X0), star(star(X0))))),
% 110.60/70.14 inference(modus_ponens,[status(thm)],[919, 918])).
% 110.60/70.14 tff(921,plain,
% 110.60/70.14 (~![X0: $i] : (leq(star(star(X0)), star(X0)) & leq(star(X0), star(star(X0))))),
% 110.60/70.14 inference(modus_ponens,[status(thm)],[920, 918])).
% 110.60/70.14 tff(922,plain,
% 110.60/70.14 (~![X0: $i] : (leq(star(star(X0)), star(X0)) & leq(star(X0), star(star(X0))))),
% 110.60/70.14 inference(modus_ponens,[status(thm)],[921, 918])).
% 110.60/70.14 tff(923,plain,
% 110.60/70.14 (~![X0: $i] : (leq(star(star(X0)), star(X0)) & leq(star(X0), star(star(X0))))),
% 110.60/70.14 inference(modus_ponens,[status(thm)],[922, 918])).
% 110.60/70.14 tff(924,plain,
% 110.60/70.14 (~![X0: $i] : (leq(star(star(X0)), star(X0)) & leq(star(X0), star(star(X0))))),
% 110.60/70.14 inference(modus_ponens,[status(thm)],[923, 918])).
% 110.60/70.14 tff(925,plain,
% 110.60/70.14 (~![X0: $i] : (leq(star(star(X0)), star(X0)) & leq(star(X0), star(star(X0))))),
% 110.60/70.14 inference(modus_ponens,[status(thm)],[924, 918])).
% 110.60/70.14 tff(926,plain,
% 110.60/70.14 (~![X0: $i] : (leq(star(star(X0)), star(X0)) & leq(star(X0), star(star(X0))))),
% 110.60/70.14 inference(modus_ponens,[status(thm)],[925, 918])).
% 110.60/70.14 tff(927,plain,(
% 110.60/70.14 ~(leq(star(star(X0!0)), star(X0!0)) & leq(star(X0!0), star(star(X0!0))))),
% 110.60/70.14 inference(skolemize,[status(sab)],[926])).
% 110.60/70.14 tff(928,plain,
% 110.60/70.14 ((~leq(star(star(X0!0)), star(X0!0))) | (~leq(star(X0!0), star(star(X0!0))))),
% 110.60/70.14 inference(modus_ponens,[status(thm)],[927, 917])).
% 110.60/70.14 tff(929,plain,
% 110.60/70.14 (~leq(star(star(X0!0)), star(X0!0))),
% 110.60/70.14 inference(unit_resolution,[status(thm)],[928, 557])).
% 110.60/70.14 tff(930,plain,
% 110.60/70.14 (~leq(multiplication(multiplication(star(X0!0), star(X0!0)), star(star(X0!0))), star(X0!0))),
% 110.60/70.14 inference(modus_ponens,[status(thm)],[929, 913])).
% 110.60/70.14 tff(931,plain,
% 110.60/70.14 (^[A: $i, B: $i, C: $i] : refl(((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A)) <=> ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A)))),
% 110.60/70.14 inference(bind,[status(th)],[])).
% 110.60/70.14 tff(932,plain,
% 110.60/70.14 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 110.60/70.14 inference(quant_intro,[status(thm)],[931])).
% 110.60/70.14 tff(933,plain,
% 110.60/70.14 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 110.60/70.14 inference(rewrite,[status(thm)],[])).
% 110.60/70.14 tff(934,plain,
% 110.60/70.14 (^[A: $i, B: $i, C: $i] : rewrite((leq(addition(multiplication(A, B), C), A) => leq(multiplication(C, star(B)), A)) <=> ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A)))),
% 110.60/70.14 inference(bind,[status(th)],[])).
% 110.60/70.14 tff(935,plain,
% 110.60/70.14 (![A: $i, B: $i, C: $i] : (leq(addition(multiplication(A, B), C), A) => leq(multiplication(C, star(B)), A)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 110.60/70.14 inference(quant_intro,[status(thm)],[934])).
% 110.60/70.14 tff(936,axiom,(![A: $i, B: $i, C: $i] : (leq(addition(multiplication(A, B), C), A) => leq(multiplication(C, star(B)), A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','star_induction_right')).
% 110.60/70.14 tff(937,plain,
% 110.60/70.14 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 110.60/70.14 inference(modus_ponens,[status(thm)],[936, 935])).
% 110.60/70.14 tff(938,plain,
% 110.60/70.14 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 110.60/70.14 inference(modus_ponens,[status(thm)],[937, 933])).
% 110.60/70.14 tff(939,plain,(
% 110.60/70.14 ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 110.60/70.14 inference(skolemize,[status(sab)],[938])).
% 110.60/70.14 tff(940,plain,
% 110.60/70.14 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 110.60/70.14 inference(modus_ponens,[status(thm)],[939, 932])).
% 110.60/70.14 tff(941,plain,
% 110.60/70.14 (((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))) | ((~leq(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(X0!0))), star(X0!0))) | leq(multiplication(multiplication(star(X0!0), star(X0!0)), star(star(X0!0))), star(X0!0)))) <=> ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))) | (~leq(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(X0!0))), star(X0!0))) | leq(multiplication(multiplication(star(X0!0), star(X0!0)), star(star(X0!0))), star(X0!0)))),
% 110.60/70.14 inference(rewrite,[status(thm)],[])).
% 110.60/70.14 tff(942,plain,
% 110.60/70.14 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))) | ((~leq(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(X0!0))), star(X0!0))) | leq(multiplication(multiplication(star(X0!0), star(X0!0)), star(star(X0!0))), star(X0!0)))),
% 110.60/70.14 inference(quant_inst,[status(thm)],[])).
% 110.60/70.15 tff(943,plain,
% 110.60/70.15 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))) | (~leq(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(X0!0))), star(X0!0))) | leq(multiplication(multiplication(star(X0!0), star(X0!0)), star(star(X0!0))), star(X0!0))),
% 110.60/70.15 inference(modus_ponens,[status(thm)],[942, 941])).
% 110.60/70.15 tff(944,plain,
% 110.60/70.15 ((~leq(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(X0!0))), star(X0!0))) | leq(multiplication(multiplication(star(X0!0), star(X0!0)), star(star(X0!0))), star(X0!0))),
% 110.60/70.15 inference(unit_resolution,[status(thm)],[943, 940])).
% 110.60/70.15 tff(945,plain,
% 110.60/70.15 ($false),
% 110.60/70.15 inference(unit_resolution,[status(thm)],[944, 930, 129])).
% 110.60/70.15 % SZS output end Proof
%------------------------------------------------------------------------------