TSTP Solution File: KLE036+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE036+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 17:23:57 EDT 2022
% Result : Theorem 17.40s 11.49s
% Output : Proof 17.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE036+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 07:56:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 17.40/11.49 % SZS status Theorem
% 17.40/11.49 % SZS output start Proof
% 17.40/11.49 tff(leq_type, type, (
% 17.40/11.49 leq: ( $i * $i ) > $o)).
% 17.40/11.49 tff(addition_type, type, (
% 17.40/11.49 addition: ( $i * $i ) > $i)).
% 17.40/11.49 tff(one_type, type, (
% 17.40/11.49 one: $i)).
% 17.40/11.49 tff(multiplication_type, type, (
% 17.40/11.49 multiplication: ( $i * $i ) > $i)).
% 17.40/11.49 tff(star_type, type, (
% 17.40/11.49 star: $i > $i)).
% 17.40/11.49 tff(tptp_fun_X0_0_type, type, (
% 17.40/11.49 tptp_fun_X0_0: $i)).
% 17.40/11.49 tff(1,plain,
% 17.40/11.49 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 17.40/11.49 inference(bind,[status(th)],[])).
% 17.40/11.49 tff(2,plain,
% 17.40/11.49 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 17.40/11.49 inference(quant_intro,[status(thm)],[1])).
% 17.40/11.49 tff(3,plain,
% 17.40/11.49 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 17.40/11.49 inference(rewrite,[status(thm)],[])).
% 17.40/11.49 tff(4,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','additive_commutativity')).
% 17.40/11.49 tff(5,plain,
% 17.40/11.49 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 17.40/11.49 inference(modus_ponens,[status(thm)],[4, 3])).
% 17.40/11.49 tff(6,plain,(
% 17.40/11.49 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 17.40/11.49 inference(skolemize,[status(sab)],[5])).
% 17.40/11.49 tff(7,plain,
% 17.40/11.49 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 17.40/11.49 inference(modus_ponens,[status(thm)],[6, 2])).
% 17.40/11.49 tff(8,plain,
% 17.40/11.49 ((~![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))),
% 17.40/11.49 inference(quant_inst,[status(thm)],[])).
% 17.40/11.49 tff(9,plain,
% 17.40/11.49 (addition(one, multiplication(star(X0!0), X0!0)) = addition(multiplication(star(X0!0), X0!0), one)),
% 17.40/11.49 inference(unit_resolution,[status(thm)],[8, 7])).
% 17.40/11.49 tff(10,plain,
% 17.40/11.49 (addition(multiplication(star(X0!0), X0!0), one) = addition(one, multiplication(star(X0!0), X0!0))),
% 17.40/11.49 inference(symmetry,[status(thm)],[9])).
% 17.40/11.49 tff(11,plain,
% 17.40/11.49 (addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)) = addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 17.40/11.49 inference(monotonicity,[status(thm)],[10])).
% 17.40/11.49 tff(12,plain,
% 17.40/11.49 (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))),
% 17.40/11.49 inference(symmetry,[status(thm)],[11])).
% 17.40/11.49 tff(13,plain,
% 17.40/11.49 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 17.40/11.49 inference(bind,[status(th)],[])).
% 17.40/11.49 tff(14,plain,
% 17.40/11.49 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 17.40/11.49 inference(quant_intro,[status(thm)],[13])).
% 17.40/11.49 tff(15,plain,
% 17.40/11.49 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 17.40/11.49 inference(rewrite,[status(thm)],[])).
% 17.40/11.49 tff(16,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','order')).
% 17.40/11.49 tff(17,plain,
% 17.40/11.49 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 17.40/11.49 inference(modus_ponens,[status(thm)],[16, 15])).
% 17.40/11.49 tff(18,plain,(
% 17.40/11.49 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 17.40/11.49 inference(skolemize,[status(sab)],[17])).
% 17.40/11.49 tff(19,plain,
% 17.40/11.49 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 17.40/11.49 inference(modus_ponens,[status(thm)],[18, 14])).
% 17.40/11.49 tff(20,plain,
% 17.40/11.49 ((~![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)))),
% 17.40/11.49 inference(quant_inst,[status(thm)],[])).
% 17.40/11.49 tff(21,plain,
% 17.40/11.49 (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))),
% 17.40/11.49 inference(unit_resolution,[status(thm)],[20, 19])).
% 17.40/11.49 tff(22,plain,
% 17.40/11.49 (^[A: $i] : refl(leq(addition(one, multiplication(star(A), A)), star(A)) <=> leq(addition(one, multiplication(star(A), A)), star(A)))),
% 17.40/11.49 inference(bind,[status(th)],[])).
% 17.40/11.49 tff(23,plain,
% 17.40/11.49 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 17.40/11.49 inference(quant_intro,[status(thm)],[22])).
% 17.40/11.49 tff(24,plain,
% 17.40/11.49 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 17.40/11.49 inference(rewrite,[status(thm)],[])).
% 17.40/11.49 tff(25,axiom,(![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','star_unfold_left')).
% 17.40/11.49 tff(26,plain,
% 17.40/11.49 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 17.40/11.49 inference(modus_ponens,[status(thm)],[25, 24])).
% 17.40/11.49 tff(27,plain,(
% 17.40/11.49 ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 17.40/11.49 inference(skolemize,[status(sab)],[26])).
% 17.40/11.49 tff(28,plain,
% 17.40/11.49 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 17.40/11.49 inference(modus_ponens,[status(thm)],[27, 23])).
% 17.40/11.49 tff(29,plain,
% 17.40/11.49 ((~![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))) | leq(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 17.40/11.49 inference(quant_inst,[status(thm)],[])).
% 17.40/11.49 tff(30,plain,
% 17.40/11.49 (leq(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 17.40/11.49 inference(unit_resolution,[status(thm)],[29, 28])).
% 17.40/11.49 tff(31,plain,
% 17.40/11.49 ((~(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))),
% 17.40/11.49 inference(tautology,[status(thm)],[])).
% 17.40/11.49 tff(32,plain,
% 17.40/11.49 ((~(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))),
% 17.40/11.49 inference(unit_resolution,[status(thm)],[31, 30])).
% 17.40/11.49 tff(33,plain,
% 17.40/11.49 (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = star(X0!0)),
% 17.40/11.49 inference(unit_resolution,[status(thm)],[32, 21])).
% 17.40/11.49 tff(34,plain,
% 17.40/11.49 (star(X0!0) = addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 17.40/11.49 inference(symmetry,[status(thm)],[33])).
% 17.40/11.49 tff(35,plain,
% 17.40/11.49 (star(X0!0) = addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))),
% 17.40/11.49 inference(transitivity,[status(thm)],[34, 12])).
% 17.40/11.49 tff(36,plain,
% 17.40/11.49 (multiplication(star(X0!0), X0!0) = multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)), X0!0)),
% 17.40/11.49 inference(monotonicity,[status(thm)],[35])).
% 17.40/11.49 tff(37,plain,
% 17.40/11.49 (multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)), X0!0) = multiplication(star(X0!0), X0!0)),
% 17.40/11.49 inference(symmetry,[status(thm)],[36])).
% 17.40/11.49 tff(38,plain,
% 17.40/11.49 (^[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))))),
% 17.40/11.49 inference(bind,[status(th)],[])).
% 17.40/11.49 tff(39,plain,
% 17.40/11.49 (![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)))),
% 17.40/11.49 inference(quant_intro,[status(thm)],[38])).
% 17.40/11.49 tff(40,plain,
% 17.40/11.49 (![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)))),
% 17.40/11.49 inference(rewrite,[status(thm)],[])).
% 17.40/11.49 tff(41,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')).
% 17.40/11.49 tff(42,plain,
% 17.40/11.49 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 17.40/11.49 inference(modus_ponens,[status(thm)],[41, 40])).
% 17.40/11.49 tff(43,plain,(
% 17.40/11.49 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 17.40/11.49 inference(skolemize,[status(sab)],[42])).
% 17.40/11.49 tff(44,plain,
% 17.40/11.49 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 17.40/11.49 inference(modus_ponens,[status(thm)],[43, 39])).
% 17.40/11.49 tff(45,plain,
% 17.40/11.49 ((~![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)))),
% 17.40/11.49 inference(quant_inst,[status(thm)],[])).
% 17.40/11.49 tff(46,plain,
% 17.40/11.49 (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))),
% 17.40/11.49 inference(unit_resolution,[status(thm)],[45, 44])).
% 17.40/11.49 tff(47,plain,
% 17.40/11.49 (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)),
% 17.40/11.49 inference(symmetry,[status(thm)],[46])).
% 17.40/11.49 tff(48,plain,
% 17.40/11.49 (addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)) = multiplication(star(X0!0), X0!0)),
% 17.40/11.49 inference(transitivity,[status(thm)],[47, 37])).
% 17.40/11.49 tff(49,plain,
% 17.40/11.49 (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)),
% 17.40/11.49 inference(monotonicity,[status(thm)],[48])).
% 17.40/11.49 tff(50,plain,
% 17.40/11.49 (multiplication(X0!0, addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), one)) = multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one))),
% 17.40/11.49 inference(monotonicity,[status(thm)],[49])).
% 17.40/11.49 tff(51,plain,
% 17.40/11.49 (^[A: $i, B: $i, C: $i] : refl((multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))))),
% 17.40/11.49 inference(bind,[status(th)],[])).
% 17.40/11.49 tff(52,plain,
% 17.40/11.49 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 17.40/11.49 inference(quant_intro,[status(thm)],[51])).
% 17.40/11.49 tff(53,plain,
% 17.40/11.49 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 17.40/11.49 inference(rewrite,[status(thm)],[])).
% 17.40/11.49 tff(54,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')).
% 17.40/11.49 tff(55,plain,
% 17.40/11.49 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 17.40/11.49 inference(modus_ponens,[status(thm)],[54, 53])).
% 17.40/11.49 tff(56,plain,(
% 17.40/11.49 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 17.40/11.49 inference(skolemize,[status(sab)],[55])).
% 17.40/11.49 tff(57,plain,
% 17.40/11.49 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 17.40/11.49 inference(modus_ponens,[status(thm)],[56, 52])).
% 17.40/11.49 tff(58,plain,
% 17.40/11.49 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!0, addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), one)) = addition(multiplication(X0!0, addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), multiplication(X0!0, one)))),
% 17.40/11.49 inference(quant_inst,[status(thm)],[])).
% 17.40/11.49 tff(59,plain,
% 17.40/11.49 (multiplication(X0!0, addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), one)) = addition(multiplication(X0!0, addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), multiplication(X0!0, one))),
% 17.40/11.49 inference(unit_resolution,[status(thm)],[58, 57])).
% 17.40/11.49 tff(60,plain,
% 17.40/11.49 (addition(multiplication(X0!0, addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), multiplication(X0!0, one)) = multiplication(X0!0, addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), one))),
% 17.40/11.49 inference(symmetry,[status(thm)],[59])).
% 17.40/11.49 tff(61,plain,
% 17.40/11.49 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 17.40/11.49 inference(bind,[status(th)],[])).
% 17.40/11.49 tff(62,plain,
% 17.40/11.49 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 17.40/11.49 inference(quant_intro,[status(thm)],[61])).
% 17.40/11.49 tff(63,plain,
% 17.40/11.49 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 17.40/11.49 inference(rewrite,[status(thm)],[])).
% 17.40/11.49 tff(64,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','multiplicative_right_identity')).
% 17.40/11.49 tff(65,plain,
% 17.40/11.49 (![A: $i] : (multiplication(A, one) = A)),
% 17.40/11.49 inference(modus_ponens,[status(thm)],[64, 63])).
% 17.40/11.49 tff(66,plain,(
% 17.40/11.49 ![A: $i] : (multiplication(A, one) = A)),
% 17.40/11.49 inference(skolemize,[status(sab)],[65])).
% 17.40/11.49 tff(67,plain,
% 17.40/11.49 (![A: $i] : (multiplication(A, one) = A)),
% 17.40/11.49 inference(modus_ponens,[status(thm)],[66, 62])).
% 17.40/11.49 tff(68,plain,
% 17.40/11.49 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(X0!0, one) = X0!0)),
% 17.40/11.49 inference(quant_inst,[status(thm)],[])).
% 17.40/11.49 tff(69,plain,
% 17.40/11.49 (multiplication(X0!0, one) = X0!0),
% 17.40/11.49 inference(unit_resolution,[status(thm)],[68, 67])).
% 17.40/11.49 tff(70,plain,
% 17.40/11.49 (X0!0 = multiplication(X0!0, one)),
% 17.40/11.49 inference(symmetry,[status(thm)],[69])).
% 17.40/11.49 tff(71,plain,
% 17.40/11.49 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 17.40/11.49 inference(bind,[status(th)],[])).
% 17.40/11.49 tff(72,plain,
% 17.40/11.49 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 17.40/11.49 inference(quant_intro,[status(thm)],[71])).
% 17.40/11.49 tff(73,plain,
% 17.40/11.49 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 17.40/11.49 inference(rewrite,[status(thm)],[])).
% 17.40/11.49 tff(74,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','multiplicative_left_identity')).
% 17.40/11.49 tff(75,plain,
% 17.40/11.49 (![A: $i] : (multiplication(one, A) = A)),
% 17.40/11.49 inference(modus_ponens,[status(thm)],[74, 73])).
% 17.40/11.49 tff(76,plain,(
% 17.40/11.49 ![A: $i] : (multiplication(one, A) = A)),
% 17.40/11.49 inference(skolemize,[status(sab)],[75])).
% 17.40/11.49 tff(77,plain,
% 17.40/11.49 (![A: $i] : (multiplication(one, A) = A)),
% 17.40/11.49 inference(modus_ponens,[status(thm)],[76, 72])).
% 17.40/11.49 tff(78,plain,
% 17.40/11.49 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X0!0) = X0!0)),
% 17.40/11.49 inference(quant_inst,[status(thm)],[])).
% 17.40/11.49 tff(79,plain,
% 17.40/11.49 (multiplication(one, X0!0) = X0!0),
% 17.40/11.49 inference(unit_resolution,[status(thm)],[78, 77])).
% 17.40/11.49 tff(80,plain,
% 17.40/11.49 (multiplication(one, X0!0) = multiplication(X0!0, one)),
% 17.40/11.49 inference(transitivity,[status(thm)],[79, 70])).
% 17.40/11.49 tff(81,plain,
% 17.40/11.49 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)) <=> (addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)) = star(X0!0)))),
% 17.40/11.49 inference(quant_inst,[status(thm)],[])).
% 17.40/11.49 tff(82,plain,
% 17.40/11.49 (leq(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)) <=> (addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)) = star(X0!0))),
% 17.40/11.50 inference(unit_resolution,[status(thm)],[81, 19])).
% 17.40/11.50 tff(83,plain,
% 17.40/11.50 ((~![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))),
% 17.40/11.50 inference(quant_inst,[status(thm)],[])).
% 17.40/11.50 tff(84,plain,
% 17.40/11.50 (addition(one, multiplication(X0!0, star(X0!0))) = addition(multiplication(X0!0, star(X0!0)), one)),
% 17.40/11.50 inference(unit_resolution,[status(thm)],[83, 7])).
% 17.40/11.50 tff(85,plain,
% 17.40/11.50 (addition(multiplication(X0!0, star(X0!0)), one) = addition(one, multiplication(X0!0, star(X0!0)))),
% 17.40/11.50 inference(symmetry,[status(thm)],[84])).
% 17.40/11.50 tff(86,plain,
% 17.40/11.50 (leq(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)) <=> leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))),
% 17.40/11.50 inference(monotonicity,[status(thm)],[85])).
% 17.40/11.50 tff(87,plain,
% 17.40/11.50 (leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) <=> leq(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))),
% 17.40/11.50 inference(symmetry,[status(thm)],[86])).
% 17.40/11.50 tff(88,plain,
% 17.40/11.50 (^[A: $i] : refl(leq(addition(one, multiplication(A, star(A))), star(A)) <=> leq(addition(one, multiplication(A, star(A))), star(A)))),
% 17.40/11.50 inference(bind,[status(th)],[])).
% 17.40/11.50 tff(89,plain,
% 17.40/11.50 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 17.40/11.50 inference(quant_intro,[status(thm)],[88])).
% 17.40/11.50 tff(90,plain,
% 17.40/11.50 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 17.40/11.50 inference(rewrite,[status(thm)],[])).
% 17.40/11.50 tff(91,axiom,(![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','star_unfold_right')).
% 17.40/11.50 tff(92,plain,
% 17.40/11.50 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 17.40/11.50 inference(modus_ponens,[status(thm)],[91, 90])).
% 17.40/11.50 tff(93,plain,(
% 17.40/11.50 ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 17.40/11.50 inference(skolemize,[status(sab)],[92])).
% 17.40/11.50 tff(94,plain,
% 17.40/11.50 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 17.40/11.50 inference(modus_ponens,[status(thm)],[93, 89])).
% 17.40/11.50 tff(95,plain,
% 17.40/11.50 ((~![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))) | leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))),
% 17.40/11.50 inference(quant_inst,[status(thm)],[])).
% 17.40/11.50 tff(96,plain,
% 17.40/11.50 (leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))),
% 17.40/11.50 inference(unit_resolution,[status(thm)],[95, 94])).
% 17.40/11.50 tff(97,plain,
% 17.40/11.50 (leq(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))),
% 17.40/11.50 inference(modus_ponens,[status(thm)],[96, 87])).
% 17.40/11.50 tff(98,plain,
% 17.40/11.50 ((~(leq(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)) <=> (addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)) = star(X0!0)))) | (~leq(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) | (addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)) = star(X0!0))),
% 17.40/11.50 inference(tautology,[status(thm)],[])).
% 17.40/11.50 tff(99,plain,
% 17.40/11.50 (addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)) = star(X0!0)),
% 17.40/11.50 inference(unit_resolution,[status(thm)],[98, 97, 82])).
% 17.40/11.50 tff(100,plain,
% 17.40/11.50 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)) = addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)))),
% 17.40/11.50 inference(quant_inst,[status(thm)],[])).
% 17.40/11.50 tff(101,plain,
% 17.40/11.50 (addition(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)) = addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))),
% 17.40/11.50 inference(unit_resolution,[status(thm)],[100, 7])).
% 17.40/11.50 tff(102,plain,
% 17.40/11.50 (^[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)))),
% 17.40/11.50 inference(bind,[status(th)],[])).
% 17.40/11.50 tff(103,plain,
% 17.40/11.50 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C)) <=> ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 17.40/11.50 inference(quant_intro,[status(thm)],[102])).
% 17.40/11.50 tff(104,plain,
% 17.40/11.50 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C)) <=> ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 17.40/11.50 inference(rewrite,[status(thm)],[])).
% 17.40/11.50 tff(105,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')).
% 17.40/11.50 tff(106,plain,
% 17.40/11.50 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 17.40/11.50 inference(modus_ponens,[status(thm)],[105, 104])).
% 17.40/11.50 tff(107,plain,(
% 17.40/11.50 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 17.40/11.50 inference(skolemize,[status(sab)],[106])).
% 17.40/11.50 tff(108,plain,
% 17.40/11.50 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 17.40/11.50 inference(modus_ponens,[status(thm)],[107, 103])).
% 17.40/11.50 tff(109,plain,
% 17.40/11.50 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)) = addition(addition(star(X0!0), multiplication(X0!0, star(X0!0))), one))),
% 17.40/11.50 inference(quant_inst,[status(thm)],[])).
% 17.40/11.50 tff(110,plain,
% 17.40/11.50 (addition(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)) = addition(addition(star(X0!0), multiplication(X0!0, star(X0!0))), one)),
% 17.40/11.50 inference(unit_resolution,[status(thm)],[109, 108])).
% 17.40/11.50 tff(111,plain,
% 17.40/11.50 (addition(addition(star(X0!0), multiplication(X0!0, star(X0!0))), one) = addition(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))),
% 17.40/11.50 inference(symmetry,[status(thm)],[110])).
% 17.40/11.50 tff(112,plain,
% 17.40/11.50 (addition(addition(star(X0!0), multiplication(X0!0, star(X0!0))), one) = star(X0!0)),
% 17.40/11.50 inference(transitivity,[status(thm)],[111, 101, 99])).
% 17.40/11.50 tff(113,plain,
% 17.40/11.50 (multiplication(addition(addition(star(X0!0), multiplication(X0!0, star(X0!0))), one), X0!0) = multiplication(star(X0!0), X0!0)),
% 17.40/11.50 inference(monotonicity,[status(thm)],[112])).
% 17.40/11.50 tff(114,plain,
% 17.40/11.50 (multiplication(star(X0!0), X0!0) = multiplication(addition(addition(star(X0!0), multiplication(X0!0, star(X0!0))), one), X0!0)),
% 17.40/11.50 inference(symmetry,[status(thm)],[113])).
% 17.40/11.50 tff(115,plain,
% 17.40/11.50 (addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)) = multiplication(addition(addition(star(X0!0), multiplication(X0!0, star(X0!0))), one), X0!0)),
% 17.40/11.50 inference(transitivity,[status(thm)],[47, 37, 114])).
% 17.40/11.50 tff(116,plain,
% 17.40/11.50 (multiplication(X0!0, addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))) = multiplication(X0!0, multiplication(addition(addition(star(X0!0), multiplication(X0!0, star(X0!0))), one), X0!0))),
% 17.40/11.50 inference(monotonicity,[status(thm)],[115])).
% 17.40/11.50 tff(117,plain,
% 17.40/11.50 (multiplication(X0!0, multiplication(addition(addition(star(X0!0), multiplication(X0!0, star(X0!0))), one), X0!0)) = multiplication(X0!0, addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)))),
% 17.40/11.50 inference(symmetry,[status(thm)],[116])).
% 17.40/11.50 tff(118,plain,
% 17.40/11.50 (^[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)))),
% 17.40/11.50 inference(bind,[status(th)],[])).
% 17.40/11.50 tff(119,plain,
% 17.40/11.50 (![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))),
% 17.40/11.50 inference(quant_intro,[status(thm)],[118])).
% 17.40/11.50 tff(120,plain,
% 17.40/11.50 (![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))),
% 17.40/11.50 inference(rewrite,[status(thm)],[])).
% 17.40/11.50 tff(121,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')).
% 17.40/11.50 tff(122,plain,
% 17.40/11.50 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 17.40/11.50 inference(modus_ponens,[status(thm)],[121, 120])).
% 17.40/11.50 tff(123,plain,(
% 17.40/11.50 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 17.40/11.50 inference(skolemize,[status(sab)],[122])).
% 17.40/11.50 tff(124,plain,
% 17.40/11.50 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 17.40/11.50 inference(modus_ponens,[status(thm)],[123, 119])).
% 17.40/11.50 tff(125,plain,
% 17.40/11.50 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X0!0, multiplication(addition(addition(star(X0!0), multiplication(X0!0, star(X0!0))), one), X0!0)) = multiplication(multiplication(X0!0, addition(addition(star(X0!0), multiplication(X0!0, star(X0!0))), one)), X0!0))),
% 17.40/11.50 inference(quant_inst,[status(thm)],[])).
% 17.40/11.50 tff(126,plain,
% 17.40/11.50 (multiplication(X0!0, multiplication(addition(addition(star(X0!0), multiplication(X0!0, star(X0!0))), one), X0!0)) = multiplication(multiplication(X0!0, addition(addition(star(X0!0), multiplication(X0!0, star(X0!0))), one)), X0!0)),
% 17.40/11.50 inference(unit_resolution,[status(thm)],[125, 124])).
% 17.40/11.50 tff(127,plain,
% 17.40/11.50 (multiplication(multiplication(X0!0, addition(addition(star(X0!0), multiplication(X0!0, star(X0!0))), one)), X0!0) = multiplication(X0!0, multiplication(addition(addition(star(X0!0), multiplication(X0!0, star(X0!0))), one), X0!0))),
% 17.40/11.50 inference(symmetry,[status(thm)],[126])).
% 17.40/11.50 tff(128,plain,
% 17.40/11.50 (multiplication(X0!0, addition(addition(star(X0!0), multiplication(X0!0, star(X0!0))), one)) = multiplication(X0!0, star(X0!0))),
% 17.40/11.50 inference(monotonicity,[status(thm)],[112])).
% 17.40/11.50 tff(129,plain,
% 17.40/11.50 (multiplication(X0!0, star(X0!0)) = multiplication(X0!0, addition(addition(star(X0!0), multiplication(X0!0, star(X0!0))), one))),
% 17.40/11.50 inference(symmetry,[status(thm)],[128])).
% 17.40/11.50 tff(130,plain,
% 17.40/11.50 (multiplication(X0!0, star(X0!0)) = multiplication(X0!0, addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)))),
% 17.40/11.50 inference(monotonicity,[status(thm)],[35])).
% 17.40/11.50 tff(131,plain,
% 17.40/11.50 (multiplication(X0!0, addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))) = multiplication(X0!0, star(X0!0))),
% 17.40/11.50 inference(symmetry,[status(thm)],[130])).
% 17.40/11.50 tff(132,plain,
% 17.40/11.50 ((~![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))))),
% 17.40/11.50 inference(quant_inst,[status(thm)],[])).
% 17.40/11.50 tff(133,plain,
% 17.40/11.50 (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)))),
% 17.40/11.50 inference(unit_resolution,[status(thm)],[132, 57])).
% 17.40/11.50 tff(134,plain,
% 17.40/11.50 (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)))),
% 17.40/11.50 inference(symmetry,[status(thm)],[133])).
% 17.40/11.50 tff(135,plain,
% 17.40/11.50 (addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))) = multiplication(X0!0, addition(addition(star(X0!0), multiplication(X0!0, star(X0!0))), one))),
% 17.40/11.50 inference(transitivity,[status(thm)],[134, 131, 129])).
% 17.40/11.50 tff(136,plain,
% 17.40/11.50 (multiplication(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), X0!0) = multiplication(multiplication(X0!0, addition(addition(star(X0!0), multiplication(X0!0, star(X0!0))), one)), X0!0)),
% 17.40/11.50 inference(monotonicity,[status(thm)],[135])).
% 17.50/11.50 tff(137,plain,
% 17.50/11.50 (multiplication(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), X0!0) = multiplication(X0!0, addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)))),
% 17.50/11.50 inference(transitivity,[status(thm)],[136, 127, 117])).
% 17.50/11.50 tff(138,plain,
% 17.50/11.50 (addition(multiplication(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), X0!0), multiplication(one, X0!0)) = addition(multiplication(X0!0, addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), multiplication(X0!0, one))),
% 17.50/11.50 inference(monotonicity,[status(thm)],[137, 80])).
% 17.50/11.50 tff(139,plain,
% 17.50/11.50 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), one), X0!0) = addition(multiplication(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), X0!0), multiplication(one, X0!0)))),
% 17.50/11.50 inference(quant_inst,[status(thm)],[])).
% 17.50/11.50 tff(140,plain,
% 17.50/11.50 (multiplication(addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), one), X0!0) = addition(multiplication(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), X0!0), multiplication(one, X0!0))),
% 17.50/11.50 inference(unit_resolution,[status(thm)],[139, 44])).
% 17.50/11.50 tff(141,plain,
% 17.50/11.50 (addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))) = multiplication(X0!0, star(X0!0))),
% 17.50/11.50 inference(transitivity,[status(thm)],[134, 131])).
% 17.50/11.50 tff(142,plain,
% 17.50/11.50 (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)),
% 17.50/11.50 inference(monotonicity,[status(thm)],[141])).
% 17.50/11.50 tff(143,plain,
% 17.50/11.50 (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)),
% 17.50/11.50 inference(symmetry,[status(thm)],[142])).
% 17.50/11.50 tff(144,plain,
% 17.50/11.50 (multiplication(addition(multiplication(X0!0, star(X0!0)), one), X0!0) = multiplication(addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), one), X0!0)),
% 17.50/11.50 inference(monotonicity,[status(thm)],[143])).
% 17.50/11.50 tff(145,plain,
% 17.50/11.50 (multiplication(addition(multiplication(X0!0, star(X0!0)), one), X0!0) = multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one))),
% 17.50/11.50 inference(transitivity,[status(thm)],[144, 140, 138, 60, 50])).
% 17.50/11.50 tff(146,plain,
% 17.50/11.50 (addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), X0!0), one) = addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), one)),
% 17.50/11.50 inference(monotonicity,[status(thm)],[145])).
% 17.50/11.50 tff(147,plain,
% 17.50/11.50 (addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), one) = addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), X0!0), one)),
% 17.50/11.50 inference(symmetry,[status(thm)],[146])).
% 17.50/11.50 tff(148,plain,
% 17.50/11.50 (leq(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), one), addition(multiplication(X0!0, star(X0!0)), one)) <=> leq(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))),
% 17.50/11.50 inference(monotonicity,[status(thm)],[147])).
% 17.50/11.50 tff(149,plain,
% 17.50/11.50 (leq(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)) <=> leq(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), one), addition(multiplication(X0!0, star(X0!0)), one))),
% 17.50/11.50 inference(symmetry,[status(thm)],[148])).
% 17.50/11.50 tff(150,plain,
% 17.50/11.50 ((~leq(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))) <=> (~leq(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), one), addition(multiplication(X0!0, star(X0!0)), one)))),
% 17.50/11.50 inference(monotonicity,[status(thm)],[149])).
% 17.50/11.50 tff(151,plain,
% 17.50/11.50 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, addition(addition(star(X0!0), multiplication(X0!0, star(X0!0))), one)) = addition(addition(star(X0!0), multiplication(X0!0, star(X0!0))), one))),
% 17.50/11.50 inference(quant_inst,[status(thm)],[])).
% 17.50/11.50 tff(152,plain,
% 17.50/11.50 (multiplication(one, addition(addition(star(X0!0), multiplication(X0!0, star(X0!0))), one)) = addition(addition(star(X0!0), multiplication(X0!0, star(X0!0))), one)),
% 17.50/11.50 inference(unit_resolution,[status(thm)],[151, 77])).
% 17.50/11.50 tff(153,plain,
% 17.50/11.50 (addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)) = addition(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))),
% 17.50/11.50 inference(symmetry,[status(thm)],[101])).
% 17.50/11.50 tff(154,plain,
% 17.50/11.50 (star(X0!0) = addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))),
% 17.50/11.50 inference(symmetry,[status(thm)],[99])).
% 17.50/11.50 tff(155,plain,
% 17.50/11.50 (star(X0!0) = addition(addition(star(X0!0), multiplication(X0!0, star(X0!0))), one)),
% 17.50/11.50 inference(transitivity,[status(thm)],[154, 153, 110])).
% 17.50/11.50 tff(156,plain,
% 17.50/11.50 (multiplication(one, star(X0!0)) = multiplication(one, addition(addition(star(X0!0), multiplication(X0!0, star(X0!0))), one))),
% 17.50/11.50 inference(monotonicity,[status(thm)],[155])).
% 17.50/11.50 tff(157,plain,
% 17.50/11.50 (multiplication(one, star(X0!0)) = star(X0!0)),
% 17.50/11.50 inference(transitivity,[status(thm)],[156, 152, 111, 101, 99])).
% 17.50/11.50 tff(158,plain,
% 17.50/11.50 (leq(multiplication(one, star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)) <=> leq(star(X0!0), addition(one, multiplication(X0!0, star(X0!0))))),
% 17.50/11.50 inference(monotonicity,[status(thm)],[157, 85])).
% 17.50/11.50 tff(159,plain,
% 17.50/11.50 (leq(star(X0!0), addition(one, multiplication(X0!0, star(X0!0)))) <=> leq(multiplication(one, star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))),
% 17.50/11.50 inference(symmetry,[status(thm)],[158])).
% 17.50/11.50 tff(160,plain,
% 17.50/11.50 ((~leq(star(X0!0), addition(one, multiplication(X0!0, star(X0!0))))) <=> (~leq(multiplication(one, star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)))),
% 17.50/11.50 inference(monotonicity,[status(thm)],[159])).
% 17.50/11.50 tff(161,plain,
% 17.50/11.50 ((~![X0: $i] : leq(star(X0), addition(one, multiplication(X0, star(X0))))) <=> (~![X0: $i] : leq(star(X0), addition(one, multiplication(X0, star(X0)))))),
% 17.50/11.50 inference(rewrite,[status(thm)],[])).
% 17.50/11.50 tff(162,axiom,(~![X0: $i] : leq(star(X0), addition(one, multiplication(X0, star(X0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 17.50/11.50 tff(163,plain,
% 17.50/11.50 (~![X0: $i] : leq(star(X0), addition(one, multiplication(X0, star(X0))))),
% 17.50/11.50 inference(modus_ponens,[status(thm)],[162, 161])).
% 17.50/11.50 tff(164,plain,
% 17.50/11.50 (~![X0: $i] : leq(star(X0), addition(one, multiplication(X0, star(X0))))),
% 17.50/11.50 inference(modus_ponens,[status(thm)],[163, 161])).
% 17.50/11.50 tff(165,plain,
% 17.50/11.50 (~![X0: $i] : leq(star(X0), addition(one, multiplication(X0, star(X0))))),
% 17.50/11.50 inference(modus_ponens,[status(thm)],[164, 161])).
% 17.50/11.50 tff(166,plain,
% 17.50/11.50 (~![X0: $i] : leq(star(X0), addition(one, multiplication(X0, star(X0))))),
% 17.50/11.50 inference(modus_ponens,[status(thm)],[165, 161])).
% 17.50/11.50 tff(167,plain,
% 17.50/11.50 (~![X0: $i] : leq(star(X0), addition(one, multiplication(X0, star(X0))))),
% 17.50/11.50 inference(modus_ponens,[status(thm)],[166, 161])).
% 17.50/11.50 tff(168,plain,
% 17.50/11.50 (~![X0: $i] : leq(star(X0), addition(one, multiplication(X0, star(X0))))),
% 17.50/11.50 inference(modus_ponens,[status(thm)],[167, 161])).
% 17.50/11.50 tff(169,plain,
% 17.50/11.50 (~![X0: $i] : leq(star(X0), addition(one, multiplication(X0, star(X0))))),
% 17.50/11.50 inference(modus_ponens,[status(thm)],[168, 161])).
% 17.50/11.50 tff(170,plain,(
% 17.50/11.50 ~leq(star(X0!0), addition(one, multiplication(X0!0, star(X0!0))))),
% 17.50/11.50 inference(skolemize,[status(sab)],[169])).
% 17.50/11.50 tff(171,plain,
% 17.50/11.50 (~leq(multiplication(one, star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))),
% 17.50/11.50 inference(modus_ponens,[status(thm)],[170, 160])).
% 17.50/11.50 tff(172,plain,
% 17.50/11.50 (^[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)))),
% 17.50/11.50 inference(bind,[status(th)],[])).
% 17.50/11.50 tff(173,plain,
% 17.50/11.50 (![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))),
% 17.50/11.50 inference(quant_intro,[status(thm)],[172])).
% 17.50/11.50 tff(174,plain,
% 17.50/11.50 (![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))),
% 17.50/11.50 inference(rewrite,[status(thm)],[])).
% 17.50/11.50 tff(175,plain,
% 17.50/11.50 (^[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)))),
% 17.50/11.50 inference(bind,[status(th)],[])).
% 17.50/11.50 tff(176,plain,
% 17.50/11.50 (![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))),
% 17.50/11.50 inference(quant_intro,[status(thm)],[175])).
% 17.50/11.50 tff(177,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')).
% 17.50/11.50 tff(178,plain,
% 17.50/11.50 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 17.50/11.50 inference(modus_ponens,[status(thm)],[177, 176])).
% 17.50/11.50 tff(179,plain,
% 17.50/11.50 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 17.50/11.50 inference(modus_ponens,[status(thm)],[178, 174])).
% 17.50/11.50 tff(180,plain,(
% 17.50/11.50 ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 17.50/11.50 inference(skolemize,[status(sab)],[179])).
% 17.50/11.50 tff(181,plain,
% 17.50/11.50 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 17.50/11.50 inference(modus_ponens,[status(thm)],[180, 173])).
% 17.50/11.50 tff(182,plain,
% 17.50/11.50 (((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))) | ((~leq(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))) | leq(multiplication(one, star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)))) <=> ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))) | (~leq(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))) | leq(multiplication(one, star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)))),
% 17.50/11.50 inference(rewrite,[status(thm)],[])).
% 17.50/11.50 tff(183,plain,
% 17.50/11.50 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))) | ((~leq(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))) | leq(multiplication(one, star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)))),
% 17.50/11.50 inference(quant_inst,[status(thm)],[])).
% 17.50/11.50 tff(184,plain,
% 17.50/11.50 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))) | (~leq(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))) | leq(multiplication(one, star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))),
% 17.50/11.50 inference(modus_ponens,[status(thm)],[183, 182])).
% 17.50/11.50 tff(185,plain,
% 17.50/11.50 ((~leq(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))) | leq(multiplication(one, star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))),
% 17.50/11.50 inference(unit_resolution,[status(thm)],[184, 181])).
% 17.50/11.50 tff(186,plain,
% 17.50/11.50 (~leq(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))),
% 17.50/11.50 inference(unit_resolution,[status(thm)],[185, 171])).
% 17.50/11.50 tff(187,plain,
% 17.50/11.50 (~leq(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), one), addition(multiplication(X0!0, star(X0!0)), one))),
% 17.50/11.50 inference(modus_ponens,[status(thm)],[186, 150])).
% 17.50/11.50 tff(188,plain,
% 17.50/11.50 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), one), addition(multiplication(X0!0, star(X0!0)), one)) <=> (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), one), addition(multiplication(X0!0, star(X0!0)), one)) = addition(multiplication(X0!0, star(X0!0)), one)))),
% 17.50/11.50 inference(quant_inst,[status(thm)],[])).
% 17.50/11.50 tff(189,plain,
% 17.50/11.50 (leq(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), one), addition(multiplication(X0!0, star(X0!0)), one)) <=> (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), one), addition(multiplication(X0!0, star(X0!0)), one)) = addition(multiplication(X0!0, star(X0!0)), one))),
% 17.50/11.50 inference(unit_resolution,[status(thm)],[188, 19])).
% 17.50/11.50 tff(190,plain,
% 17.50/11.50 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 17.50/11.50 inference(bind,[status(th)],[])).
% 17.50/11.50 tff(191,plain,
% 17.50/11.50 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 17.50/11.50 inference(quant_intro,[status(thm)],[190])).
% 17.50/11.50 tff(192,plain,
% 17.50/11.50 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 17.50/11.50 inference(rewrite,[status(thm)],[])).
% 17.50/11.50 tff(193,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','additive_idempotence')).
% 17.50/11.50 tff(194,plain,
% 17.50/11.50 (![A: $i] : (addition(A, A) = A)),
% 17.50/11.50 inference(modus_ponens,[status(thm)],[193, 192])).
% 17.50/11.50 tff(195,plain,(
% 17.50/11.50 ![A: $i] : (addition(A, A) = A)),
% 17.50/11.50 inference(skolemize,[status(sab)],[194])).
% 17.50/11.50 tff(196,plain,
% 17.50/11.50 (![A: $i] : (addition(A, A) = A)),
% 17.50/11.50 inference(modus_ponens,[status(thm)],[195, 191])).
% 17.50/11.50 tff(197,plain,
% 17.50/11.50 ((~![A: $i] : (addition(A, A) = A)) | (addition(one, one) = one)),
% 17.50/11.50 inference(quant_inst,[status(thm)],[])).
% 17.50/11.50 tff(198,plain,
% 17.50/11.50 (addition(one, one) = one),
% 17.50/11.50 inference(unit_resolution,[status(thm)],[197, 196])).
% 17.50/11.50 tff(199,plain,
% 17.50/11.50 (addition(addition(one, 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)))),
% 17.50/11.50 inference(monotonicity,[status(thm)],[198, 141])).
% 17.50/11.50 tff(200,plain,
% 17.50/11.50 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(one, addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))) = addition(addition(one, one), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))))),
% 17.50/11.50 inference(quant_inst,[status(thm)],[])).
% 17.50/11.50 tff(201,plain,
% 17.50/11.50 (addition(one, addition(one, addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))) = addition(addition(one, one), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))),
% 17.50/11.50 inference(unit_resolution,[status(thm)],[200, 108])).
% 17.50/11.50 tff(202,plain,
% 17.50/11.50 (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)))),
% 17.50/11.50 inference(monotonicity,[status(thm)],[141])).
% 17.50/11.50 tff(203,plain,
% 17.50/11.50 (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))))),
% 17.50/11.51 inference(symmetry,[status(thm)],[202])).
% 17.50/11.51 tff(204,plain,
% 17.50/11.51 (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))))),
% 17.50/11.51 inference(transitivity,[status(thm)],[85, 203])).
% 17.50/11.51 tff(205,plain,
% 17.50/11.51 (addition(one, addition(multiplication(X0!0, star(X0!0)), one)) = addition(one, addition(one, addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))))),
% 17.50/11.51 inference(monotonicity,[status(thm)],[204])).
% 17.50/11.51 tff(206,plain,
% 17.50/11.51 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, addition(multiplication(X0!0, star(X0!0)), one)) = addition(addition(multiplication(X0!0, star(X0!0)), one), one))),
% 17.50/11.51 inference(quant_inst,[status(thm)],[])).
% 17.50/11.51 tff(207,plain,
% 17.50/11.51 (addition(one, addition(multiplication(X0!0, star(X0!0)), one)) = addition(addition(multiplication(X0!0, star(X0!0)), one), one)),
% 17.50/11.51 inference(unit_resolution,[status(thm)],[206, 7])).
% 17.50/11.51 tff(208,plain,
% 17.50/11.51 (addition(addition(multiplication(X0!0, star(X0!0)), one), one) = addition(one, addition(multiplication(X0!0, star(X0!0)), one))),
% 17.50/11.51 inference(symmetry,[status(thm)],[207])).
% 17.50/11.51 tff(209,plain,
% 17.50/11.51 (addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), 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)))),
% 17.50/11.51 inference(monotonicity,[status(thm)],[141])).
% 17.50/11.51 tff(210,plain,
% 17.50/11.51 (addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))) = multiplication(X0!0, star(X0!0))),
% 17.50/11.51 inference(transitivity,[status(thm)],[209, 134, 131])).
% 17.50/11.51 tff(211,plain,
% 17.50/11.51 (addition(one, addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), 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)))),
% 17.50/11.51 inference(monotonicity,[status(thm)],[210])).
% 17.50/11.51 tff(212,plain,
% 17.50/11.51 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))) = addition(addition(one, multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one))), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))))),
% 17.50/11.51 inference(quant_inst,[status(thm)],[])).
% 17.50/11.51 tff(213,plain,
% 17.50/11.51 (addition(one, addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))) = addition(addition(one, multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one))), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))),
% 17.50/11.51 inference(unit_resolution,[status(thm)],[212, 108])).
% 17.50/11.51 tff(214,plain,
% 17.50/11.51 (addition(addition(one, multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one))), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))) = addition(one, addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))))),
% 17.50/11.51 inference(symmetry,[status(thm)],[213])).
% 17.50/11.51 tff(215,plain,
% 17.50/11.51 (addition(addition(one, multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), 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)),
% 17.50/11.51 inference(transitivity,[status(thm)],[214, 211, 84])).
% 17.50/11.51 tff(216,plain,
% 17.50/11.51 (addition(addition(addition(one, multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one))), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), one) = addition(addition(multiplication(X0!0, star(X0!0)), one), one)),
% 17.50/11.51 inference(monotonicity,[status(thm)],[215])).
% 17.50/11.51 tff(217,plain,
% 17.50/11.51 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(one, multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one))), addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), one)) = addition(addition(addition(one, multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one))), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), one))),
% 17.50/11.51 inference(quant_inst,[status(thm)],[])).
% 17.50/11.51 tff(218,plain,
% 17.50/11.51 (addition(addition(one, multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one))), addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), one)) = addition(addition(addition(one, multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one))), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), one)),
% 17.50/11.51 inference(unit_resolution,[status(thm)],[217, 108])).
% 17.50/11.51 tff(219,plain,
% 17.50/11.51 (addition(addition(one, multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one))), addition(multiplication(X0!0, star(X0!0)), one)) = addition(addition(one, multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one))), addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), one))),
% 17.50/11.51 inference(monotonicity,[status(thm)],[143])).
% 17.50/11.51 tff(220,plain,
% 17.50/11.51 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one))) = addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), one))),
% 17.50/11.51 inference(quant_inst,[status(thm)],[])).
% 17.50/11.51 tff(221,plain,
% 17.50/11.51 (addition(one, multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one))) = addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), one)),
% 17.50/11.51 inference(unit_resolution,[status(thm)],[220, 7])).
% 17.50/11.51 tff(222,plain,
% 17.50/11.51 (addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), one) = addition(one, multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)))),
% 17.50/11.51 inference(symmetry,[status(thm)],[221])).
% 17.50/11.51 tff(223,plain,
% 17.50/11.51 (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), one), addition(multiplication(X0!0, star(X0!0)), one)) = addition(addition(one, multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one))), addition(multiplication(X0!0, star(X0!0)), one))),
% 17.50/11.51 inference(monotonicity,[status(thm)],[222])).
% 17.50/11.51 tff(224,plain,
% 17.50/11.51 (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), one), addition(multiplication(X0!0, star(X0!0)), one)) = addition(multiplication(X0!0, star(X0!0)), one)),
% 17.50/11.51 inference(transitivity,[status(thm)],[223, 219, 218, 216, 208, 205, 201, 199, 84])).
% 17.50/11.51 tff(225,plain,
% 17.50/11.51 ((~(leq(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), one), addition(multiplication(X0!0, star(X0!0)), one)) <=> (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), one), addition(multiplication(X0!0, star(X0!0)), one)) = addition(multiplication(X0!0, star(X0!0)), one)))) | leq(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), one), addition(multiplication(X0!0, star(X0!0)), one)) | (~(addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), one), addition(multiplication(X0!0, star(X0!0)), one)) = addition(multiplication(X0!0, star(X0!0)), one)))),
% 17.50/11.53 inference(tautology,[status(thm)],[])).
% 17.50/11.53 tff(226,plain,
% 17.50/11.53 (leq(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), one), addition(multiplication(X0!0, star(X0!0)), one))),
% 17.50/11.53 inference(unit_resolution,[status(thm)],[225, 224, 189])).
% 17.50/11.53 tff(227,plain,
% 17.50/11.53 ($false),
% 17.50/11.53 inference(unit_resolution,[status(thm)],[226, 187])).
% 17.50/11.53 % SZS output end Proof
%------------------------------------------------------------------------------