TSTP Solution File: KLE159+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE159+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 17:24:24 EDT 2022
% Result : Theorem 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KLE159+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n002.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 09:11:30 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.
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 % SZS output start Proof
% 0.19/0.44 tff(multiplication_type, type, (
% 0.19/0.44 multiplication: ( $i * $i ) > $i)).
% 0.19/0.44 tff(tptp_fun_X0_2_type, type, (
% 0.19/0.44 tptp_fun_X0_2: $i)).
% 0.19/0.44 tff(star_type, type, (
% 0.19/0.44 star: $i > $i)).
% 0.19/0.44 tff(tptp_fun_X2_0_type, type, (
% 0.19/0.44 tptp_fun_X2_0: $i)).
% 0.19/0.44 tff(addition_type, type, (
% 0.19/0.44 addition: ( $i * $i ) > $i)).
% 0.19/0.44 tff(tptp_fun_X1_1_type, type, (
% 0.19/0.44 tptp_fun_X1_1: $i)).
% 0.19/0.44 tff(one_type, type, (
% 0.19/0.44 one: $i)).
% 0.19/0.44 tff(leq_type, type, (
% 0.19/0.44 leq: ( $i * $i ) > $o)).
% 0.19/0.44 tff(1,plain,
% 0.19/0.44 (^[A: $i] : refl((addition(one, multiplication(A, star(A))) = star(A)) <=> (addition(one, multiplication(A, star(A))) = star(A)))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(2,plain,
% 0.19/0.44 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A)) <=> ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.44 tff(3,plain,
% 0.19/0.44 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A)) <=> ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(4,axiom,(![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','star_unfold1')).
% 0.19/0.44 tff(5,plain,
% 0.19/0.44 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.44 tff(6,plain,(
% 0.19/0.44 ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.19/0.44 inference(skolemize,[status(sab)],[5])).
% 0.19/0.44 tff(7,plain,
% 0.19/0.44 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.44 tff(8,plain,
% 0.19/0.44 ((~![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))) | (addition(one, multiplication(X2!0, star(X2!0))) = star(X2!0))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(9,plain,
% 0.19/0.44 (addition(one, multiplication(X2!0, star(X2!0))) = star(X2!0)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.44 tff(10,plain,
% 0.19/0.44 (multiplication(addition(one, multiplication(X2!0, star(X2!0))), X0!2) = multiplication(star(X2!0), X0!2)),
% 0.19/0.44 inference(monotonicity,[status(thm)],[9])).
% 0.19/0.44 tff(11,plain,
% 0.19/0.44 (^[A: $i, B: $i, C: $i] : refl((multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))) <=> (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(12,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.44 tff(13,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(14,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/KLE004+0.ax','distributivity2')).
% 0.19/0.44 tff(15,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.19/0.44 tff(16,plain,(
% 0.19/0.44 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[15])).
% 0.19/0.44 tff(17,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.44 tff(18,plain,
% 0.19/0.44 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(one, multiplication(X2!0, star(X2!0))), X0!2) = addition(multiplication(one, X0!2), multiplication(multiplication(X2!0, star(X2!0)), X0!2)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(19,plain,
% 0.19/0.44 (multiplication(addition(one, multiplication(X2!0, star(X2!0))), X0!2) = addition(multiplication(one, X0!2), multiplication(multiplication(X2!0, star(X2!0)), X0!2))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.19/0.44 tff(20,plain,
% 0.19/0.44 (addition(multiplication(one, X0!2), multiplication(multiplication(X2!0, star(X2!0)), X0!2)) = multiplication(addition(one, multiplication(X2!0, star(X2!0))), X0!2)),
% 0.19/0.44 inference(symmetry,[status(thm)],[19])).
% 0.19/0.44 tff(21,plain,
% 0.19/0.44 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(22,plain,
% 0.19/0.44 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[21])).
% 0.19/0.44 tff(23,plain,
% 0.19/0.44 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(24,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','additive_commutativity')).
% 0.19/0.44 tff(25,plain,
% 0.19/0.44 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.44 tff(26,plain,(
% 0.19/0.44 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.19/0.44 inference(skolemize,[status(sab)],[25])).
% 0.19/0.44 tff(27,plain,
% 0.19/0.44 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.19/0.44 tff(28,plain,
% 0.19/0.44 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(one, X0!2), multiplication(multiplication(X2!0, star(X2!0)), X0!2)) = addition(multiplication(multiplication(X2!0, star(X2!0)), X0!2), multiplication(one, X0!2)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(29,plain,
% 0.19/0.44 (addition(multiplication(one, X0!2), multiplication(multiplication(X2!0, star(X2!0)), X0!2)) = addition(multiplication(multiplication(X2!0, star(X2!0)), X0!2), multiplication(one, X0!2))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.19/0.44 tff(30,plain,
% 0.19/0.44 (addition(multiplication(multiplication(X2!0, star(X2!0)), X0!2), multiplication(one, X0!2)) = addition(multiplication(one, X0!2), multiplication(multiplication(X2!0, star(X2!0)), X0!2))),
% 0.19/0.44 inference(symmetry,[status(thm)],[29])).
% 0.19/0.44 tff(31,plain,
% 0.19/0.44 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(32,plain,
% 0.19/0.44 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.19/0.44 inference(quant_intro,[status(thm)],[31])).
% 0.19/0.44 tff(33,plain,
% 0.19/0.44 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(34,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','multiplicative_left_identity')).
% 0.19/0.44 tff(35,plain,
% 0.19/0.44 (![A: $i] : (multiplication(one, A) = A)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.44 tff(36,plain,(
% 0.19/0.44 ![A: $i] : (multiplication(one, A) = A)),
% 0.19/0.44 inference(skolemize,[status(sab)],[35])).
% 0.19/0.44 tff(37,plain,
% 0.19/0.44 (![A: $i] : (multiplication(one, A) = A)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.19/0.44 tff(38,plain,
% 0.19/0.44 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X0!2) = X0!2)),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(39,plain,
% 0.19/0.44 (multiplication(one, X0!2) = X0!2),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.19/0.44 tff(40,plain,
% 0.19/0.44 (X0!2 = multiplication(one, X0!2)),
% 0.19/0.44 inference(symmetry,[status(thm)],[39])).
% 0.19/0.44 tff(41,plain,
% 0.19/0.44 (^[A: $i] : refl((addition(one, multiplication(star(A), A)) = star(A)) <=> (addition(one, multiplication(star(A), A)) = star(A)))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(42,plain,
% 0.19/0.44 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A)) <=> ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[41])).
% 0.19/0.44 tff(43,plain,
% 0.19/0.44 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A)) <=> ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(44,axiom,(![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','star_unfold2')).
% 0.19/0.44 tff(45,plain,
% 0.19/0.44 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.44 tff(46,plain,(
% 0.19/0.44 ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.19/0.44 inference(skolemize,[status(sab)],[45])).
% 0.19/0.44 tff(47,plain,
% 0.19/0.44 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.19/0.44 tff(48,plain,
% 0.19/0.44 ((~![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))) | (addition(one, multiplication(star(X2!0), X2!0)) = star(X2!0))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(49,plain,
% 0.19/0.44 (addition(one, multiplication(star(X2!0), X2!0)) = star(X2!0)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.19/0.44 tff(50,plain,
% 0.19/0.44 (star(X2!0) = addition(one, multiplication(star(X2!0), X2!0))),
% 0.19/0.44 inference(symmetry,[status(thm)],[49])).
% 0.19/0.44 tff(51,plain,
% 0.19/0.44 (multiplication(X2!0, star(X2!0)) = multiplication(X2!0, addition(one, multiplication(star(X2!0), X2!0)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[50])).
% 0.19/0.44 tff(52,plain,
% 0.19/0.44 (multiplication(X2!0, addition(one, multiplication(star(X2!0), X2!0))) = multiplication(X2!0, star(X2!0))),
% 0.19/0.44 inference(symmetry,[status(thm)],[51])).
% 0.19/0.44 tff(53,plain,
% 0.19/0.44 (^[A: $i, B: $i, C: $i] : refl((multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(54,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.44 tff(55,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(56,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/KLE004+0.ax','distributivity1')).
% 0.19/0.44 tff(57,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.44 tff(58,plain,(
% 0.19/0.44 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[57])).
% 0.19/0.44 tff(59,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.19/0.44 tff(60,plain,
% 0.19/0.44 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X2!0, addition(one, multiplication(star(X2!0), X2!0))) = addition(multiplication(X2!0, one), multiplication(X2!0, multiplication(star(X2!0), X2!0))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(61,plain,
% 0.19/0.44 (multiplication(X2!0, addition(one, multiplication(star(X2!0), X2!0))) = addition(multiplication(X2!0, one), multiplication(X2!0, multiplication(star(X2!0), X2!0)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.19/0.44 tff(62,plain,
% 0.19/0.44 (addition(multiplication(X2!0, one), multiplication(X2!0, multiplication(star(X2!0), X2!0))) = multiplication(X2!0, addition(one, multiplication(star(X2!0), X2!0)))),
% 0.19/0.44 inference(symmetry,[status(thm)],[61])).
% 0.19/0.44 tff(63,plain,
% 0.19/0.44 (^[A: $i, B: $i, C: $i] : refl((multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(64,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[63])).
% 0.19/0.44 tff(65,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(66,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','multiplicative_associativity')).
% 0.19/0.44 tff(67,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.19/0.44 tff(68,plain,(
% 0.19/0.44 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.19/0.44 inference(skolemize,[status(sab)],[67])).
% 0.19/0.44 tff(69,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.19/0.44 tff(70,plain,
% 0.19/0.44 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X2!0, multiplication(star(X2!0), X2!0)) = multiplication(multiplication(X2!0, star(X2!0)), X2!0))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(71,plain,
% 0.19/0.44 (multiplication(X2!0, multiplication(star(X2!0), X2!0)) = multiplication(multiplication(X2!0, star(X2!0)), X2!0)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.19/0.44 tff(72,plain,
% 0.19/0.44 (multiplication(multiplication(X2!0, star(X2!0)), X2!0) = multiplication(X2!0, multiplication(star(X2!0), X2!0))),
% 0.19/0.44 inference(symmetry,[status(thm)],[71])).
% 0.19/0.44 tff(73,plain,
% 0.19/0.44 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(74,plain,
% 0.19/0.44 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.19/0.44 inference(quant_intro,[status(thm)],[73])).
% 0.19/0.44 tff(75,plain,
% 0.19/0.44 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(76,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','multiplicative_right_identity')).
% 0.19/0.44 tff(77,plain,
% 0.19/0.44 (![A: $i] : (multiplication(A, one) = A)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.19/0.44 tff(78,plain,(
% 0.19/0.44 ![A: $i] : (multiplication(A, one) = A)),
% 0.19/0.44 inference(skolemize,[status(sab)],[77])).
% 0.19/0.44 tff(79,plain,
% 0.19/0.44 (![A: $i] : (multiplication(A, one) = A)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.19/0.44 tff(80,plain,
% 0.19/0.44 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(X2!0, one) = X2!0)),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(81,plain,
% 0.19/0.44 (multiplication(X2!0, one) = X2!0),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.19/0.44 tff(82,plain,
% 0.19/0.44 (X2!0 = multiplication(X2!0, one)),
% 0.19/0.44 inference(symmetry,[status(thm)],[81])).
% 0.19/0.44 tff(83,plain,
% 0.19/0.44 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X2!0) = X2!0)),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(84,plain,
% 0.19/0.44 (multiplication(one, X2!0) = X2!0),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[83, 37])).
% 0.19/0.44 tff(85,plain,
% 0.19/0.44 (multiplication(one, X2!0) = multiplication(X2!0, one)),
% 0.19/0.44 inference(transitivity,[status(thm)],[84, 82])).
% 0.19/0.44 tff(86,plain,
% 0.19/0.44 (addition(multiplication(one, X2!0), multiplication(multiplication(X2!0, star(X2!0)), X2!0)) = addition(multiplication(X2!0, one), multiplication(X2!0, multiplication(star(X2!0), X2!0)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[85, 72])).
% 0.19/0.44 tff(87,plain,
% 0.19/0.44 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(one, multiplication(X2!0, star(X2!0))), X2!0) = addition(multiplication(one, X2!0), multiplication(multiplication(X2!0, star(X2!0)), X2!0)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(88,plain,
% 0.19/0.44 (multiplication(addition(one, multiplication(X2!0, star(X2!0))), X2!0) = addition(multiplication(one, X2!0), multiplication(multiplication(X2!0, star(X2!0)), X2!0))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[87, 17])).
% 0.19/0.44 tff(89,plain,
% 0.19/0.44 (star(X2!0) = addition(one, multiplication(X2!0, star(X2!0)))),
% 0.19/0.44 inference(symmetry,[status(thm)],[9])).
% 0.19/0.44 tff(90,plain,
% 0.19/0.44 (multiplication(star(X2!0), X2!0) = multiplication(addition(one, multiplication(X2!0, star(X2!0))), X2!0)),
% 0.19/0.44 inference(monotonicity,[status(thm)],[89])).
% 0.19/0.44 tff(91,plain,
% 0.19/0.44 (multiplication(star(X2!0), X2!0) = multiplication(X2!0, star(X2!0))),
% 0.19/0.44 inference(transitivity,[status(thm)],[90, 88, 86, 62, 52])).
% 0.19/0.44 tff(92,plain,
% 0.19/0.44 (multiplication(multiplication(star(X2!0), X2!0), X0!2) = multiplication(multiplication(X2!0, star(X2!0)), X0!2)),
% 0.19/0.44 inference(monotonicity,[status(thm)],[91])).
% 0.19/0.44 tff(93,plain,
% 0.19/0.44 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(star(X2!0), multiplication(X2!0, X0!2)) = multiplication(multiplication(star(X2!0), X2!0), X0!2))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(94,plain,
% 0.19/0.44 (multiplication(star(X2!0), multiplication(X2!0, X0!2)) = multiplication(multiplication(star(X2!0), X2!0), X0!2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[93, 69])).
% 0.19/0.44 tff(95,plain,
% 0.19/0.44 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(96,plain,
% 0.19/0.44 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[95])).
% 0.19/0.44 tff(97,plain,
% 0.19/0.44 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(98,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','order')).
% 0.19/0.44 tff(99,plain,
% 0.19/0.44 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.19/0.44 tff(100,plain,(
% 0.19/0.44 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.19/0.44 inference(skolemize,[status(sab)],[99])).
% 0.19/0.44 tff(101,plain,
% 0.19/0.44 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.19/0.44 tff(102,plain,
% 0.19/0.44 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) <=> (addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) = multiplication(X2!0, X0!2)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(103,plain,
% 0.19/0.44 (leq(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) <=> (addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) = multiplication(X2!0, X0!2))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.19/0.44 tff(104,plain,
% 0.19/0.44 ((~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, star(X1)), multiplication(star(X2), X0)))) <=> (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, star(X1)), multiplication(star(X2), X0))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(105,plain,
% 0.19/0.44 ((~![X0: $i, X1: $i, X2: $i] : (leq(multiplication(X0, X1), multiplication(X2, X0)) => leq(multiplication(X0, star(X1)), multiplication(star(X2), X0)))) <=> (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, star(X1)), multiplication(star(X2), X0))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(106,axiom,(~![X0: $i, X1: $i, X2: $i] : (leq(multiplication(X0, X1), multiplication(X2, X0)) => leq(multiplication(X0, star(X1)), multiplication(star(X2), X0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 0.19/0.45 tff(107,plain,
% 0.19/0.45 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, star(X1)), multiplication(star(X2), X0)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.19/0.45 tff(108,plain,
% 0.19/0.45 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, star(X1)), multiplication(star(X2), X0)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[107, 104])).
% 0.19/0.45 tff(109,plain,
% 0.19/0.45 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, star(X1)), multiplication(star(X2), X0)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.19/0.45 tff(110,plain,
% 0.19/0.45 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, star(X1)), multiplication(star(X2), X0)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[109, 104])).
% 0.19/0.45 tff(111,plain,
% 0.19/0.45 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, star(X1)), multiplication(star(X2), X0)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[110, 104])).
% 0.19/0.45 tff(112,plain,
% 0.19/0.45 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, star(X1)), multiplication(star(X2), X0)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.19/0.45 tff(113,plain,
% 0.19/0.45 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, star(X1)), multiplication(star(X2), X0)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[112, 104])).
% 0.19/0.45 tff(114,plain,(
% 0.19/0.45 ~((~leq(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2))) | leq(multiplication(X0!2, star(X1!1)), multiplication(star(X2!0), X0!2)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[113])).
% 0.19/0.45 tff(115,plain,
% 0.19/0.45 (leq(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2))),
% 0.19/0.45 inference(or_elim,[status(thm)],[114])).
% 0.19/0.45 tff(116,plain,
% 0.19/0.45 ((~(leq(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) <=> (addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) = multiplication(X2!0, X0!2)))) | (~leq(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2))) | (addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) = multiplication(X2!0, X0!2))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(117,plain,
% 0.19/0.45 ((~(leq(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) <=> (addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) = multiplication(X2!0, X0!2)))) | (addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) = multiplication(X2!0, X0!2))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.19/0.45 tff(118,plain,
% 0.19/0.45 (addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) = multiplication(X2!0, X0!2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[117, 103])).
% 0.19/0.45 tff(119,plain,
% 0.19/0.45 (multiplication(star(X2!0), addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2))) = multiplication(star(X2!0), multiplication(X2!0, X0!2))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[118])).
% 0.19/0.45 tff(120,plain,
% 0.19/0.45 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(star(X2!0), addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2))) = addition(multiplication(star(X2!0), multiplication(X0!2, X1!1)), multiplication(star(X2!0), multiplication(X2!0, X0!2))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(121,plain,
% 0.19/0.45 (multiplication(star(X2!0), addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2))) = addition(multiplication(star(X2!0), multiplication(X0!2, X1!1)), multiplication(star(X2!0), multiplication(X2!0, X0!2)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[120, 59])).
% 0.19/0.45 tff(122,plain,
% 0.19/0.45 (addition(multiplication(star(X2!0), multiplication(X0!2, X1!1)), multiplication(star(X2!0), multiplication(X2!0, X0!2))) = multiplication(star(X2!0), addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)))),
% 0.19/0.45 inference(symmetry,[status(thm)],[121])).
% 0.19/0.45 tff(123,plain,
% 0.19/0.45 (multiplication(multiplication(star(X2!0), X2!0), X0!2) = multiplication(star(X2!0), multiplication(X2!0, X0!2))),
% 0.19/0.45 inference(symmetry,[status(thm)],[94])).
% 0.19/0.45 tff(124,plain,
% 0.19/0.45 (multiplication(multiplication(X2!0, star(X2!0)), X0!2) = multiplication(multiplication(star(X2!0), X2!0), X0!2)),
% 0.19/0.45 inference(symmetry,[status(thm)],[92])).
% 0.19/0.45 tff(125,plain,
% 0.19/0.45 (multiplication(multiplication(X2!0, star(X2!0)), X0!2) = multiplication(star(X2!0), multiplication(X2!0, X0!2))),
% 0.19/0.45 inference(transitivity,[status(thm)],[124, 123])).
% 0.19/0.45 tff(126,plain,
% 0.19/0.45 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(star(X2!0), multiplication(X0!2, X1!1)) = multiplication(multiplication(star(X2!0), X0!2), X1!1))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(127,plain,
% 0.19/0.45 (multiplication(star(X2!0), multiplication(X0!2, X1!1)) = multiplication(multiplication(star(X2!0), X0!2), X1!1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[126, 69])).
% 0.19/0.45 tff(128,plain,
% 0.19/0.45 (multiplication(multiplication(star(X2!0), X0!2), X1!1) = multiplication(star(X2!0), multiplication(X0!2, X1!1))),
% 0.19/0.45 inference(symmetry,[status(thm)],[127])).
% 0.19/0.45 tff(129,plain,
% 0.19/0.45 (addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), multiplication(multiplication(X2!0, star(X2!0)), X0!2)) = addition(multiplication(star(X2!0), multiplication(X0!2, X1!1)), multiplication(star(X2!0), multiplication(X2!0, X0!2)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[128, 125])).
% 0.19/0.45 tff(130,plain,
% 0.19/0.45 (addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), multiplication(multiplication(X2!0, star(X2!0)), X0!2)) = multiplication(multiplication(X2!0, star(X2!0)), X0!2)),
% 0.19/0.45 inference(transitivity,[status(thm)],[129, 122, 119, 94, 92])).
% 0.19/0.45 tff(131,plain,
% 0.19/0.45 (addition(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), multiplication(multiplication(X2!0, star(X2!0)), X0!2)), X0!2) = addition(multiplication(multiplication(X2!0, star(X2!0)), X0!2), multiplication(one, X0!2))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[130, 40])).
% 0.19/0.45 tff(132,plain,
% 0.19/0.45 (^[C: $i, B: $i, A: $i] : refl((addition(A, addition(B, C)) = addition(addition(A, B), C)) <=> (addition(A, addition(B, C)) = addition(addition(A, B), C)))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(133,plain,
% 0.19/0.45 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C)) <=> ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[132])).
% 0.19/0.45 tff(134,plain,
% 0.19/0.45 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C)) <=> ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(135,axiom,(![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','additive_associativity')).
% 0.19/0.45 tff(136,plain,
% 0.19/0.45 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.19/0.45 tff(137,plain,(
% 0.19/0.45 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.19/0.45 inference(skolemize,[status(sab)],[136])).
% 0.19/0.45 tff(138,plain,
% 0.19/0.45 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.19/0.45 tff(139,plain,
% 0.19/0.45 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), addition(multiplication(multiplication(X2!0, star(X2!0)), X0!2), X0!2)) = addition(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), multiplication(multiplication(X2!0, star(X2!0)), X0!2)), X0!2))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(140,plain,
% 0.19/0.45 (addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), addition(multiplication(multiplication(X2!0, star(X2!0)), X0!2), X0!2)) = addition(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), multiplication(multiplication(X2!0, star(X2!0)), X0!2)), X0!2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.19/0.45 tff(141,plain,
% 0.19/0.45 (addition(multiplication(multiplication(X2!0, star(X2!0)), X0!2), X0!2) = addition(multiplication(multiplication(X2!0, star(X2!0)), X0!2), multiplication(one, X0!2))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[40])).
% 0.19/0.45 tff(142,plain,
% 0.19/0.45 (addition(multiplication(multiplication(X2!0, star(X2!0)), X0!2), multiplication(one, X0!2)) = addition(multiplication(multiplication(X2!0, star(X2!0)), X0!2), X0!2)),
% 0.19/0.45 inference(symmetry,[status(thm)],[141])).
% 0.19/0.45 tff(143,plain,
% 0.19/0.45 (multiplication(star(X2!0), X0!2) = multiplication(addition(one, multiplication(X2!0, star(X2!0))), X0!2)),
% 0.19/0.45 inference(symmetry,[status(thm)],[10])).
% 0.19/0.45 tff(144,plain,
% 0.19/0.45 (multiplication(star(X2!0), X0!2) = multiplication(addition(one, multiplication(star(X2!0), X2!0)), X0!2)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[50])).
% 0.19/0.45 tff(145,plain,
% 0.19/0.45 (multiplication(addition(one, multiplication(star(X2!0), X2!0)), X0!2) = multiplication(star(X2!0), X0!2)),
% 0.19/0.45 inference(symmetry,[status(thm)],[144])).
% 0.19/0.45 tff(146,plain,
% 0.19/0.45 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(one, multiplication(star(X2!0), X2!0)), X0!2) = addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(147,plain,
% 0.19/0.45 (multiplication(addition(one, multiplication(star(X2!0), X2!0)), X0!2) = addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[146, 17])).
% 0.19/0.45 tff(148,plain,
% 0.19/0.45 (addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2)) = multiplication(addition(one, multiplication(star(X2!0), X2!0)), X0!2)),
% 0.19/0.45 inference(symmetry,[status(thm)],[147])).
% 0.19/0.45 tff(149,plain,
% 0.19/0.45 (addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2)) = addition(multiplication(multiplication(X2!0, star(X2!0)), X0!2), X0!2)),
% 0.19/0.45 inference(transitivity,[status(thm)],[148, 145, 143, 19, 29, 142])).
% 0.19/0.45 tff(150,plain,
% 0.19/0.45 (addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2))) = addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), addition(multiplication(multiplication(X2!0, star(X2!0)), X0!2), X0!2))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[149])).
% 0.19/0.45 tff(151,plain,
% 0.19/0.45 (addition(X0!2, multiplication(multiplication(X2!0, star(X2!0)), X0!2)) = addition(multiplication(one, X0!2), multiplication(multiplication(X2!0, star(X2!0)), X0!2))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[40])).
% 0.19/0.45 tff(152,plain,
% 0.19/0.45 (addition(X0!2, multiplication(multiplication(X2!0, star(X2!0)), X0!2)) = addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2))),
% 0.19/0.45 inference(transitivity,[status(thm)],[151, 20, 10, 144, 147])).
% 0.19/0.45 tff(153,plain,
% 0.19/0.45 (addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), addition(X0!2, multiplication(multiplication(X2!0, star(X2!0)), X0!2))) = addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[152])).
% 0.19/0.45 tff(154,plain,
% 0.19/0.45 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), addition(X0!2, multiplication(multiplication(X2!0, star(X2!0)), X0!2))) = addition(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(multiplication(X2!0, star(X2!0)), X0!2)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(155,plain,
% 0.19/0.45 (addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), addition(X0!2, multiplication(multiplication(X2!0, star(X2!0)), X0!2))) = addition(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(multiplication(X2!0, star(X2!0)), X0!2))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[154, 138])).
% 0.19/0.45 tff(156,plain,
% 0.19/0.45 (addition(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(multiplication(X2!0, star(X2!0)), X0!2)) = addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), addition(X0!2, multiplication(multiplication(X2!0, star(X2!0)), X0!2)))),
% 0.19/0.45 inference(symmetry,[status(thm)],[155])).
% 0.19/0.45 tff(157,plain,
% 0.19/0.45 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(158,plain,
% 0.19/0.45 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.19/0.45 inference(quant_intro,[status(thm)],[157])).
% 0.19/0.45 tff(159,plain,
% 0.19/0.45 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(160,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','idempotence')).
% 0.19/0.45 tff(161,plain,
% 0.19/0.45 (![A: $i] : (addition(A, A) = A)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.19/0.45 tff(162,plain,(
% 0.19/0.45 ![A: $i] : (addition(A, A) = A)),
% 0.19/0.45 inference(skolemize,[status(sab)],[161])).
% 0.19/0.45 tff(163,plain,
% 0.19/0.45 (![A: $i] : (addition(A, A) = A)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[162, 158])).
% 0.19/0.45 tff(164,plain,
% 0.19/0.45 ((~![A: $i] : (addition(A, A) = A)) | (addition(X0!2, X0!2) = X0!2)),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(165,plain,
% 0.19/0.45 (addition(X0!2, X0!2) = X0!2),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.19/0.45 tff(166,plain,
% 0.19/0.45 (addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), addition(X0!2, X0!2)) = addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[165])).
% 0.19/0.45 tff(167,plain,
% 0.19/0.45 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), addition(X0!2, X0!2)) = addition(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), X0!2))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(168,plain,
% 0.19/0.45 (addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), addition(X0!2, X0!2)) = addition(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), X0!2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[167, 138])).
% 0.19/0.45 tff(169,plain,
% 0.19/0.45 (addition(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), X0!2) = addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), addition(X0!2, X0!2))),
% 0.19/0.45 inference(symmetry,[status(thm)],[168])).
% 0.19/0.45 tff(170,plain,
% 0.19/0.45 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2) = addition(X0!2, multiplication(multiplication(star(X2!0), X0!2), X1!1)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(171,plain,
% 0.19/0.45 (addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2) = addition(X0!2, multiplication(multiplication(star(X2!0), X0!2), X1!1))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[170, 27])).
% 0.19/0.45 tff(172,plain,
% 0.19/0.45 (addition(X0!2, multiplication(multiplication(star(X2!0), X0!2), X1!1)) = addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2)),
% 0.19/0.45 inference(symmetry,[status(thm)],[171])).
% 0.19/0.45 tff(173,plain,
% 0.19/0.45 (addition(addition(X0!2, multiplication(multiplication(star(X2!0), X0!2), X1!1)), multiplication(one, X0!2)) = addition(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), X0!2)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[172, 39])).
% 0.19/0.45 tff(174,plain,
% 0.19/0.45 (addition(addition(X0!2, multiplication(multiplication(star(X2!0), X0!2), X1!1)), multiplication(one, X0!2)) = addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2)),
% 0.19/0.45 inference(transitivity,[status(thm)],[173, 169, 166])).
% 0.19/0.45 tff(175,plain,
% 0.19/0.45 (addition(addition(addition(X0!2, multiplication(multiplication(star(X2!0), X0!2), X1!1)), multiplication(one, X0!2)), multiplication(multiplication(X2!0, star(X2!0)), X0!2)) = addition(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(multiplication(X2!0, star(X2!0)), X0!2))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[174])).
% 0.19/0.45 tff(176,plain,
% 0.19/0.45 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(X0!2, multiplication(multiplication(star(X2!0), X0!2), X1!1)), addition(multiplication(one, X0!2), multiplication(multiplication(X2!0, star(X2!0)), X0!2))) = addition(addition(addition(X0!2, multiplication(multiplication(star(X2!0), X0!2), X1!1)), multiplication(one, X0!2)), multiplication(multiplication(X2!0, star(X2!0)), X0!2)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(177,plain,
% 0.19/0.45 (addition(addition(X0!2, multiplication(multiplication(star(X2!0), X0!2), X1!1)), addition(multiplication(one, X0!2), multiplication(multiplication(X2!0, star(X2!0)), X0!2))) = addition(addition(addition(X0!2, multiplication(multiplication(star(X2!0), X0!2), X1!1)), multiplication(one, X0!2)), multiplication(multiplication(X2!0, star(X2!0)), X0!2))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[176, 138])).
% 0.19/0.45 tff(178,plain,
% 0.19/0.45 (multiplication(star(X2!0), X0!2) = addition(multiplication(one, X0!2), multiplication(multiplication(X2!0, star(X2!0)), X0!2))),
% 0.19/0.45 inference(transitivity,[status(thm)],[143, 19])).
% 0.19/0.45 tff(179,plain,
% 0.19/0.45 (addition(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2)) = addition(addition(X0!2, multiplication(multiplication(star(X2!0), X0!2), X1!1)), addition(multiplication(one, X0!2), multiplication(multiplication(X2!0, star(X2!0)), X0!2)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[171, 178])).
% 0.19/0.45 tff(180,plain,
% 0.19/0.45 (addition(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2)) = multiplication(star(X2!0), X0!2)),
% 0.19/0.45 inference(transitivity,[status(thm)],[179, 177, 175, 156, 153, 150, 140, 131, 30, 20, 10])).
% 0.19/0.45 tff(181,plain,
% 0.19/0.45 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2)) <=> (addition(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2)) = multiplication(star(X2!0), X0!2)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(182,plain,
% 0.19/0.45 (leq(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2)) <=> (addition(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2)) = multiplication(star(X2!0), X0!2))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[181, 101])).
% 0.19/0.45 tff(183,plain,
% 0.19/0.45 (~leq(multiplication(X0!2, star(X1!1)), multiplication(star(X2!0), X0!2))),
% 0.19/0.45 inference(or_elim,[status(thm)],[114])).
% 0.19/0.45 tff(184,plain,
% 0.19/0.45 (^[A: $i, B: $i, C: $i] : refl(((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C)) <=> ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C)))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(185,plain,
% 0.19/0.45 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[184])).
% 0.19/0.45 tff(186,plain,
% 0.19/0.45 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(187,plain,
% 0.19/0.45 (^[A: $i, B: $i, C: $i] : rewrite((leq(addition(multiplication(C, A), B), C) => leq(multiplication(B, star(A)), C)) <=> ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C)))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(188,plain,
% 0.19/0.45 (![A: $i, B: $i, C: $i] : (leq(addition(multiplication(C, A), B), C) => leq(multiplication(B, star(A)), C)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[187])).
% 0.19/0.45 tff(189,axiom,(![A: $i, B: $i, C: $i] : (leq(addition(multiplication(C, A), B), C) => leq(multiplication(B, star(A)), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','star_induction2')).
% 0.19/0.45 tff(190,plain,
% 0.19/0.45 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.19/0.45 tff(191,plain,
% 0.19/0.45 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[190, 186])).
% 0.19/0.45 tff(192,plain,(
% 0.19/0.45 ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))),
% 0.19/0.45 inference(skolemize,[status(sab)],[191])).
% 0.19/0.45 tff(193,plain,
% 0.19/0.45 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[192, 185])).
% 0.19/0.45 tff(194,plain,
% 0.19/0.45 (((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))) | ((~leq(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2))) | leq(multiplication(X0!2, star(X1!1)), multiplication(star(X2!0), X0!2)))) <=> ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))) | (~leq(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2))) | leq(multiplication(X0!2, star(X1!1)), multiplication(star(X2!0), X0!2)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(195,plain,
% 0.19/0.45 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))) | ((~leq(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2))) | leq(multiplication(X0!2, star(X1!1)), multiplication(star(X2!0), X0!2)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(196,plain,
% 0.19/0.45 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))) | (~leq(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2))) | leq(multiplication(X0!2, star(X1!1)), multiplication(star(X2!0), X0!2))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.19/0.45 tff(197,plain,
% 0.19/0.45 (~leq(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[196, 193, 183])).
% 0.19/0.45 tff(198,plain,
% 0.19/0.45 ((~(leq(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2)) <=> (addition(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2)) = multiplication(star(X2!0), X0!2)))) | leq(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2)) | (~(addition(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2)) = multiplication(star(X2!0), X0!2)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(199,plain,
% 0.19/0.45 ((~(leq(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2)) <=> (addition(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2)) = multiplication(star(X2!0), X0!2)))) | (~(addition(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2)) = multiplication(star(X2!0), X0!2)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.19/0.45 tff(200,plain,
% 0.19/0.45 (~(addition(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2)) = multiplication(star(X2!0), X0!2))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[199, 182])).
% 0.19/0.46 tff(201,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[200, 180])).
% 0.19/0.46 % SZS output end Proof
%------------------------------------------------------------------------------