TSTP Solution File: KLE139+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE139+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 17:24:17 EDT 2022
% Result : Theorem 0.23s 0.44s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : KLE139+1 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.36 % Computer : n002.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Sep 1 08:55:30 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.23/0.44 % SZS status Theorem
% 0.23/0.44 % SZS output start Proof
% 0.23/0.44 tff(addition_type, type, (
% 0.23/0.44 addition: ( $i * $i ) > $i)).
% 0.23/0.44 tff(one_type, type, (
% 0.23/0.44 one: $i)).
% 0.23/0.44 tff(multiplication_type, type, (
% 0.23/0.44 multiplication: ( $i * $i ) > $i)).
% 0.23/0.44 tff(tptp_fun_X0_0_type, type, (
% 0.23/0.44 tptp_fun_X0_0: $i)).
% 0.23/0.44 tff(strong_iteration_type, type, (
% 0.23/0.44 strong_iteration: $i > $i)).
% 0.23/0.44 tff(zero_type, type, (
% 0.23/0.44 zero: $i)).
% 0.23/0.44 tff(star_type, type, (
% 0.23/0.44 star: $i > $i)).
% 0.23/0.44 tff(1,plain,
% 0.23/0.44 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(2,plain,
% 0.23/0.44 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[1])).
% 0.23/0.44 tff(3,plain,
% 0.23/0.44 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(4,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','additive_commutativity')).
% 0.23/0.44 tff(5,plain,
% 0.23/0.44 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.23/0.44 tff(6,plain,(
% 0.23/0.44 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.23/0.44 inference(skolemize,[status(sab)],[5])).
% 0.23/0.44 tff(7,plain,
% 0.23/0.44 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.23/0.44 tff(8,plain,
% 0.23/0.44 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(strong_iteration(X0!0), X0!0), one) = addition(one, multiplication(strong_iteration(X0!0), X0!0)))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(9,plain,
% 0.23/0.44 (addition(multiplication(strong_iteration(X0!0), X0!0), one) = addition(one, multiplication(strong_iteration(X0!0), X0!0))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.23/0.44 tff(10,plain,
% 0.23/0.44 (addition(one, multiplication(strong_iteration(X0!0), X0!0)) = addition(multiplication(strong_iteration(X0!0), X0!0), one)),
% 0.23/0.44 inference(symmetry,[status(thm)],[9])).
% 0.23/0.44 tff(11,plain,
% 0.23/0.44 (^[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))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(12,plain,
% 0.23/0.44 (![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)))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[11])).
% 0.23/0.44 tff(13,plain,
% 0.23/0.44 (![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)))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 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')).
% 0.23/0.44 tff(15,plain,
% 0.23/0.44 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.23/0.44 tff(16,plain,(
% 0.23/0.44 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.23/0.44 inference(skolemize,[status(sab)],[15])).
% 0.23/0.44 tff(17,plain,
% 0.23/0.44 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.23/0.44 tff(18,plain,
% 0.23/0.44 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(star(X0!0), multiplication(strong_iteration(X0!0), zero)), X0!0) = addition(multiplication(star(X0!0), X0!0), multiplication(multiplication(strong_iteration(X0!0), zero), X0!0)))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(19,plain,
% 0.23/0.44 (multiplication(addition(star(X0!0), multiplication(strong_iteration(X0!0), zero)), X0!0) = addition(multiplication(star(X0!0), X0!0), multiplication(multiplication(strong_iteration(X0!0), zero), X0!0))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.23/0.44 tff(20,plain,
% 0.23/0.44 (^[A: $i] : refl((strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero))) <=> (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(21,plain,
% 0.23/0.44 (![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero))) <=> ![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[20])).
% 0.23/0.44 tff(22,plain,
% 0.23/0.44 (![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero))) <=> ![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(23,axiom,(![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','isolation')).
% 0.23/0.44 tff(24,plain,
% 0.23/0.44 (![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.23/0.44 tff(25,plain,(
% 0.23/0.44 ![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))),
% 0.23/0.44 inference(skolemize,[status(sab)],[24])).
% 0.23/0.44 tff(26,plain,
% 0.23/0.44 (![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.23/0.44 tff(27,plain,
% 0.23/0.44 ((~![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))) | (strong_iteration(X0!0) = addition(star(X0!0), multiplication(strong_iteration(X0!0), zero)))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(28,plain,
% 0.23/0.44 (strong_iteration(X0!0) = addition(star(X0!0), multiplication(strong_iteration(X0!0), zero))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.23/0.44 tff(29,plain,
% 0.23/0.44 (multiplication(strong_iteration(X0!0), X0!0) = multiplication(addition(star(X0!0), multiplication(strong_iteration(X0!0), zero)), X0!0)),
% 0.23/0.44 inference(monotonicity,[status(thm)],[28])).
% 0.23/0.44 tff(30,plain,
% 0.23/0.44 (multiplication(strong_iteration(X0!0), X0!0) = addition(multiplication(star(X0!0), X0!0), multiplication(multiplication(strong_iteration(X0!0), zero), X0!0))),
% 0.23/0.44 inference(transitivity,[status(thm)],[29, 19])).
% 0.23/0.44 tff(31,plain,
% 0.23/0.44 (addition(one, multiplication(strong_iteration(X0!0), X0!0)) = addition(one, addition(multiplication(star(X0!0), X0!0), multiplication(multiplication(strong_iteration(X0!0), zero), X0!0)))),
% 0.23/0.44 inference(monotonicity,[status(thm)],[30])).
% 0.23/0.44 tff(32,plain,
% 0.23/0.44 (addition(one, addition(multiplication(star(X0!0), X0!0), multiplication(multiplication(strong_iteration(X0!0), zero), X0!0))) = addition(one, multiplication(strong_iteration(X0!0), X0!0))),
% 0.23/0.44 inference(symmetry,[status(thm)],[31])).
% 0.23/0.44 tff(33,plain,
% 0.23/0.44 (^[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)))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(34,plain,
% 0.23/0.44 (![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))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[33])).
% 0.23/0.44 tff(35,plain,
% 0.23/0.44 (![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))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(36,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')).
% 0.23/0.44 tff(37,plain,
% 0.23/0.44 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.23/0.44 tff(38,plain,(
% 0.23/0.44 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.23/0.44 inference(skolemize,[status(sab)],[37])).
% 0.23/0.44 tff(39,plain,
% 0.23/0.44 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.23/0.44 tff(40,plain,
% 0.23/0.44 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(multiplication(star(X0!0), X0!0), multiplication(multiplication(strong_iteration(X0!0), zero), X0!0))) = addition(addition(one, multiplication(star(X0!0), X0!0)), multiplication(multiplication(strong_iteration(X0!0), zero), X0!0)))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(41,plain,
% 0.23/0.44 (addition(one, addition(multiplication(star(X0!0), X0!0), multiplication(multiplication(strong_iteration(X0!0), zero), X0!0))) = addition(addition(one, multiplication(star(X0!0), X0!0)), multiplication(multiplication(strong_iteration(X0!0), zero), X0!0))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.23/0.44 tff(42,plain,
% 0.23/0.44 (addition(addition(one, multiplication(star(X0!0), X0!0)), multiplication(multiplication(strong_iteration(X0!0), zero), X0!0)) = addition(one, addition(multiplication(star(X0!0), X0!0), multiplication(multiplication(strong_iteration(X0!0), zero), X0!0)))),
% 0.23/0.44 inference(symmetry,[status(thm)],[41])).
% 0.23/0.44 tff(43,plain,
% 0.23/0.44 (^[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))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(44,plain,
% 0.23/0.44 (![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)))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[43])).
% 0.23/0.44 tff(45,plain,
% 0.23/0.44 (![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)))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(46,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')).
% 0.23/0.44 tff(47,plain,
% 0.23/0.44 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.23/0.44 tff(48,plain,(
% 0.23/0.44 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.23/0.44 inference(skolemize,[status(sab)],[47])).
% 0.23/0.44 tff(49,plain,
% 0.23/0.44 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.23/0.44 tff(50,plain,
% 0.23/0.44 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!0, addition(multiplication(X0!0, strong_iteration(X0!0)), one)) = addition(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), multiplication(X0!0, one)))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(51,plain,
% 0.23/0.44 (multiplication(X0!0, addition(multiplication(X0!0, strong_iteration(X0!0)), one)) = addition(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), multiplication(X0!0, one))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.23/0.44 tff(52,plain,
% 0.23/0.44 (^[A: $i] : refl((strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(53,plain,
% 0.23/0.44 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[52])).
% 0.23/0.45 tff(54,plain,
% 0.23/0.45 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(55,axiom,(![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','infty_unfold1')).
% 0.23/0.45 tff(56,plain,
% 0.23/0.45 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.23/0.45 tff(57,plain,(
% 0.23/0.45 ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.23/0.45 inference(skolemize,[status(sab)],[56])).
% 0.23/0.45 tff(58,plain,
% 0.23/0.45 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.23/0.45 tff(59,plain,
% 0.23/0.45 ((~![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))) | (strong_iteration(X0!0) = addition(multiplication(X0!0, strong_iteration(X0!0)), one))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(60,plain,
% 0.23/0.45 (strong_iteration(X0!0) = addition(multiplication(X0!0, strong_iteration(X0!0)), one)),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.23/0.45 tff(61,plain,
% 0.23/0.45 (multiplication(X0!0, strong_iteration(X0!0)) = multiplication(X0!0, addition(multiplication(X0!0, strong_iteration(X0!0)), one))),
% 0.23/0.45 inference(monotonicity,[status(thm)],[60])).
% 0.23/0.45 tff(62,plain,
% 0.23/0.45 (multiplication(X0!0, strong_iteration(X0!0)) = addition(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), multiplication(X0!0, one))),
% 0.23/0.45 inference(transitivity,[status(thm)],[61, 51])).
% 0.23/0.45 tff(63,plain,
% 0.23/0.45 (multiplication(multiplication(X0!0, strong_iteration(X0!0)), zero) = multiplication(addition(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), multiplication(X0!0, one)), zero)),
% 0.23/0.45 inference(monotonicity,[status(thm)],[62])).
% 0.23/0.45 tff(64,plain,
% 0.23/0.45 (multiplication(addition(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), multiplication(X0!0, one)), zero) = multiplication(multiplication(X0!0, strong_iteration(X0!0)), zero)),
% 0.23/0.45 inference(symmetry,[status(thm)],[63])).
% 0.23/0.45 tff(65,plain,
% 0.23/0.45 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), multiplication(X0!0, one)), zero) = addition(multiplication(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), zero), multiplication(multiplication(X0!0, one), zero)))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(66,plain,
% 0.23/0.45 (multiplication(addition(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), multiplication(X0!0, one)), zero) = addition(multiplication(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), zero), multiplication(multiplication(X0!0, one), zero))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[65, 17])).
% 0.23/0.45 tff(67,plain,
% 0.23/0.45 (addition(multiplication(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), zero), multiplication(multiplication(X0!0, one), zero)) = multiplication(addition(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), multiplication(X0!0, one)), zero)),
% 0.23/0.45 inference(symmetry,[status(thm)],[66])).
% 0.23/0.45 tff(68,plain,
% 0.23/0.45 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(69,plain,
% 0.23/0.45 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.23/0.45 inference(quant_intro,[status(thm)],[68])).
% 0.23/0.45 tff(70,plain,
% 0.23/0.45 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(71,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','additive_identity')).
% 0.23/0.45 tff(72,plain,
% 0.23/0.45 (![A: $i] : (addition(A, zero) = A)),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.23/0.45 tff(73,plain,(
% 0.23/0.45 ![A: $i] : (addition(A, zero) = A)),
% 0.23/0.45 inference(skolemize,[status(sab)],[72])).
% 0.23/0.45 tff(74,plain,
% 0.23/0.45 (![A: $i] : (addition(A, zero) = A)),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.23/0.45 tff(75,plain,
% 0.23/0.45 ((~![A: $i] : (addition(A, zero) = A)) | (addition(addition(multiplication(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), zero), multiplication(multiplication(X0!0, one), zero)), zero) = addition(multiplication(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), zero), multiplication(multiplication(X0!0, one), zero)))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(76,plain,
% 0.23/0.45 (addition(addition(multiplication(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), zero), multiplication(multiplication(X0!0, one), zero)), zero) = addition(multiplication(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), zero), multiplication(multiplication(X0!0, one), zero))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.23/0.45 tff(77,plain,
% 0.23/0.45 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(78,plain,
% 0.23/0.45 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.23/0.45 inference(quant_intro,[status(thm)],[77])).
% 0.23/0.45 tff(79,plain,
% 0.23/0.45 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(80,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','multiplicative_left_identity')).
% 0.23/0.45 tff(81,plain,
% 0.23/0.45 (![A: $i] : (multiplication(one, A) = A)),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.23/0.45 tff(82,plain,(
% 0.23/0.45 ![A: $i] : (multiplication(one, A) = A)),
% 0.23/0.45 inference(skolemize,[status(sab)],[81])).
% 0.23/0.45 tff(83,plain,
% 0.23/0.45 (![A: $i] : (multiplication(one, A) = A)),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.23/0.45 tff(84,plain,
% 0.23/0.45 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, zero) = zero)),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(85,plain,
% 0.23/0.45 (multiplication(one, zero) = zero),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.23/0.45 tff(86,plain,
% 0.23/0.45 (addition(multiplication(addition(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), multiplication(X0!0, one)), zero), multiplication(one, zero)) = addition(addition(multiplication(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), zero), multiplication(multiplication(X0!0, one), zero)), zero)),
% 0.23/0.45 inference(monotonicity,[status(thm)],[66, 85])).
% 0.23/0.45 tff(87,plain,
% 0.23/0.45 (addition(multiplication(multiplication(X0!0, strong_iteration(X0!0)), zero), multiplication(one, zero)) = addition(multiplication(addition(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), multiplication(X0!0, one)), zero), multiplication(one, zero))),
% 0.23/0.45 inference(monotonicity,[status(thm)],[63])).
% 0.23/0.45 tff(88,plain,
% 0.23/0.45 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(multiplication(X0!0, strong_iteration(X0!0)), one), zero) = addition(multiplication(multiplication(X0!0, strong_iteration(X0!0)), zero), multiplication(one, zero)))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(89,plain,
% 0.23/0.45 (multiplication(addition(multiplication(X0!0, strong_iteration(X0!0)), one), zero) = addition(multiplication(multiplication(X0!0, strong_iteration(X0!0)), zero), multiplication(one, zero))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[88, 17])).
% 0.23/0.45 tff(90,plain,
% 0.23/0.45 (multiplication(strong_iteration(X0!0), zero) = multiplication(addition(multiplication(X0!0, strong_iteration(X0!0)), one), zero)),
% 0.23/0.45 inference(monotonicity,[status(thm)],[60])).
% 0.23/0.45 tff(91,plain,
% 0.23/0.45 (^[A: $i] : refl((multiplication(zero, A) = zero) <=> (multiplication(zero, A) = zero))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(92,plain,
% 0.23/0.45 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 0.23/0.45 inference(quant_intro,[status(thm)],[91])).
% 0.23/0.45 tff(93,plain,
% 0.23/0.45 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(94,axiom,(![A: $i] : (multiplication(zero, A) = zero)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','left_annihilation')).
% 0.23/0.45 tff(95,plain,
% 0.23/0.45 (![A: $i] : (multiplication(zero, A) = zero)),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.23/0.45 tff(96,plain,(
% 0.23/0.45 ![A: $i] : (multiplication(zero, A) = zero)),
% 0.23/0.45 inference(skolemize,[status(sab)],[95])).
% 0.23/0.45 tff(97,plain,
% 0.23/0.45 (![A: $i] : (multiplication(zero, A) = zero)),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.23/0.45 tff(98,plain,
% 0.23/0.45 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, X0!0) = zero)),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(99,plain,
% 0.23/0.45 (multiplication(zero, X0!0) = zero),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.23/0.45 tff(100,plain,
% 0.23/0.45 (addition(multiplication(X0!0, strong_iteration(X0!0)), one) = strong_iteration(X0!0)),
% 0.23/0.45 inference(symmetry,[status(thm)],[60])).
% 0.23/0.45 tff(101,plain,
% 0.23/0.45 (multiplication(addition(multiplication(X0!0, strong_iteration(X0!0)), one), multiplication(zero, X0!0)) = multiplication(strong_iteration(X0!0), zero)),
% 0.23/0.45 inference(monotonicity,[status(thm)],[100, 99])).
% 0.23/0.45 tff(102,plain,
% 0.23/0.45 (^[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)))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(103,plain,
% 0.23/0.45 (![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))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[102])).
% 0.23/0.45 tff(104,plain,
% 0.23/0.45 (![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))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(105,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')).
% 0.23/0.45 tff(106,plain,
% 0.23/0.45 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.23/0.45 tff(107,plain,(
% 0.23/0.45 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.23/0.45 inference(skolemize,[status(sab)],[106])).
% 0.23/0.45 tff(108,plain,
% 0.23/0.45 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.23/0.45 tff(109,plain,
% 0.23/0.45 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(addition(multiplication(X0!0, strong_iteration(X0!0)), one), multiplication(zero, X0!0)) = multiplication(multiplication(addition(multiplication(X0!0, strong_iteration(X0!0)), one), zero), X0!0))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(110,plain,
% 0.23/0.45 (multiplication(addition(multiplication(X0!0, strong_iteration(X0!0)), one), multiplication(zero, X0!0)) = multiplication(multiplication(addition(multiplication(X0!0, strong_iteration(X0!0)), one), zero), X0!0)),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.23/0.45 tff(111,plain,
% 0.23/0.45 (multiplication(multiplication(addition(multiplication(X0!0, strong_iteration(X0!0)), one), zero), X0!0) = multiplication(addition(multiplication(X0!0, strong_iteration(X0!0)), one), multiplication(zero, X0!0))),
% 0.23/0.45 inference(symmetry,[status(thm)],[110])).
% 0.23/0.45 tff(112,plain,
% 0.23/0.45 (multiplication(multiplication(strong_iteration(X0!0), zero), X0!0) = multiplication(multiplication(addition(multiplication(X0!0, strong_iteration(X0!0)), one), zero), X0!0)),
% 0.23/0.45 inference(monotonicity,[status(thm)],[90])).
% 0.23/0.45 tff(113,plain,
% 0.23/0.45 (multiplication(multiplication(strong_iteration(X0!0), zero), X0!0) = multiplication(multiplication(X0!0, strong_iteration(X0!0)), zero)),
% 0.23/0.45 inference(transitivity,[status(thm)],[112, 111, 101, 90, 89, 87, 86, 76, 67, 64])).
% 0.23/0.45 tff(114,plain,
% 0.23/0.45 (^[A: $i] : refl((addition(one, multiplication(star(A), A)) = star(A)) <=> (addition(one, multiplication(star(A), A)) = star(A)))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(115,plain,
% 0.23/0.45 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A)) <=> ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[114])).
% 0.23/0.45 tff(116,plain,
% 0.23/0.45 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A)) <=> ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(117,axiom,(![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','star_unfold2')).
% 0.23/0.45 tff(118,plain,
% 0.23/0.45 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.23/0.45 tff(119,plain,(
% 0.23/0.45 ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.23/0.45 inference(skolemize,[status(sab)],[118])).
% 0.23/0.45 tff(120,plain,
% 0.23/0.45 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.23/0.45 tff(121,plain,
% 0.23/0.45 ((~![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))) | (addition(one, multiplication(star(X0!0), X0!0)) = star(X0!0))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(122,plain,
% 0.23/0.45 (addition(one, multiplication(star(X0!0), X0!0)) = star(X0!0)),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.23/0.45 tff(123,plain,
% 0.23/0.45 (addition(addition(one, multiplication(star(X0!0), X0!0)), multiplication(multiplication(strong_iteration(X0!0), zero), X0!0)) = addition(star(X0!0), multiplication(multiplication(X0!0, strong_iteration(X0!0)), zero))),
% 0.23/0.45 inference(monotonicity,[status(thm)],[122, 113])).
% 0.23/0.45 tff(124,plain,
% 0.23/0.45 (addition(star(X0!0), multiplication(multiplication(X0!0, strong_iteration(X0!0)), zero)) = addition(addition(one, multiplication(star(X0!0), X0!0)), multiplication(multiplication(strong_iteration(X0!0), zero), X0!0))),
% 0.23/0.45 inference(symmetry,[status(thm)],[123])).
% 0.23/0.45 tff(125,plain,
% 0.23/0.45 (multiplication(X0!0, multiplication(strong_iteration(X0!0), zero)) = multiplication(X0!0, multiplication(addition(multiplication(X0!0, strong_iteration(X0!0)), one), zero))),
% 0.23/0.45 inference(monotonicity,[status(thm)],[90])).
% 0.23/0.45 tff(126,plain,
% 0.23/0.45 (multiplication(X0!0, multiplication(addition(multiplication(X0!0, strong_iteration(X0!0)), one), zero)) = multiplication(X0!0, multiplication(strong_iteration(X0!0), zero))),
% 0.23/0.45 inference(symmetry,[status(thm)],[125])).
% 0.23/0.45 tff(127,plain,
% 0.23/0.45 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X0!0, multiplication(addition(multiplication(X0!0, strong_iteration(X0!0)), one), zero)) = multiplication(multiplication(X0!0, addition(multiplication(X0!0, strong_iteration(X0!0)), one)), zero))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(128,plain,
% 0.23/0.45 (multiplication(X0!0, multiplication(addition(multiplication(X0!0, strong_iteration(X0!0)), one), zero)) = multiplication(multiplication(X0!0, addition(multiplication(X0!0, strong_iteration(X0!0)), one)), zero)),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[127, 108])).
% 0.23/0.45 tff(129,plain,
% 0.23/0.45 (multiplication(multiplication(X0!0, addition(multiplication(X0!0, strong_iteration(X0!0)), one)), zero) = multiplication(X0!0, multiplication(addition(multiplication(X0!0, strong_iteration(X0!0)), one), zero))),
% 0.23/0.45 inference(symmetry,[status(thm)],[128])).
% 0.23/0.45 tff(130,plain,
% 0.23/0.45 (multiplication(X0!0, addition(multiplication(X0!0, strong_iteration(X0!0)), one)) = multiplication(X0!0, strong_iteration(X0!0))),
% 0.23/0.45 inference(symmetry,[status(thm)],[61])).
% 0.23/0.46 tff(131,plain,
% 0.23/0.46 (multiplication(multiplication(X0!0, addition(multiplication(X0!0, strong_iteration(X0!0)), one)), zero) = multiplication(multiplication(X0!0, strong_iteration(X0!0)), zero)),
% 0.23/0.46 inference(monotonicity,[status(thm)],[130])).
% 0.23/0.46 tff(132,plain,
% 0.23/0.46 (multiplication(multiplication(X0!0, strong_iteration(X0!0)), zero) = multiplication(multiplication(X0!0, addition(multiplication(X0!0, strong_iteration(X0!0)), one)), zero)),
% 0.23/0.46 inference(symmetry,[status(thm)],[131])).
% 0.23/0.46 tff(133,plain,
% 0.23/0.46 (multiplication(multiplication(X0!0, strong_iteration(X0!0)), zero) = multiplication(X0!0, multiplication(strong_iteration(X0!0), zero))),
% 0.23/0.46 inference(transitivity,[status(thm)],[132, 129, 126])).
% 0.23/0.46 tff(134,plain,
% 0.23/0.46 (^[A: $i] : refl((addition(one, multiplication(A, star(A))) = star(A)) <=> (addition(one, multiplication(A, star(A))) = star(A)))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(135,plain,
% 0.23/0.46 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A)) <=> ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[134])).
% 0.23/0.46 tff(136,plain,
% 0.23/0.46 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A)) <=> ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(137,axiom,(![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','star_unfold1')).
% 0.23/0.46 tff(138,plain,
% 0.23/0.46 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.23/0.46 tff(139,plain,(
% 0.23/0.46 ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.23/0.46 inference(skolemize,[status(sab)],[138])).
% 0.23/0.46 tff(140,plain,
% 0.23/0.46 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.23/0.46 tff(141,plain,
% 0.23/0.46 ((~![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))) | (addition(one, multiplication(X0!0, star(X0!0))) = star(X0!0))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(142,plain,
% 0.23/0.46 (addition(one, multiplication(X0!0, star(X0!0))) = star(X0!0)),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.23/0.46 tff(143,plain,
% 0.23/0.46 (star(X0!0) = addition(one, multiplication(X0!0, star(X0!0)))),
% 0.23/0.46 inference(symmetry,[status(thm)],[142])).
% 0.23/0.46 tff(144,plain,
% 0.23/0.46 (addition(star(X0!0), multiplication(multiplication(X0!0, strong_iteration(X0!0)), zero)) = addition(addition(one, multiplication(X0!0, star(X0!0))), multiplication(X0!0, multiplication(strong_iteration(X0!0), zero)))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[143, 133])).
% 0.23/0.46 tff(145,plain,
% 0.23/0.46 (addition(addition(one, multiplication(X0!0, star(X0!0))), multiplication(X0!0, multiplication(strong_iteration(X0!0), zero))) = addition(star(X0!0), multiplication(multiplication(X0!0, strong_iteration(X0!0)), zero))),
% 0.23/0.46 inference(symmetry,[status(thm)],[144])).
% 0.23/0.46 tff(146,plain,
% 0.23/0.46 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(multiplication(X0!0, star(X0!0)), multiplication(X0!0, multiplication(strong_iteration(X0!0), zero)))) = addition(addition(one, multiplication(X0!0, star(X0!0))), multiplication(X0!0, multiplication(strong_iteration(X0!0), zero))))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(147,plain,
% 0.23/0.46 (addition(one, addition(multiplication(X0!0, star(X0!0)), multiplication(X0!0, multiplication(strong_iteration(X0!0), zero)))) = addition(addition(one, multiplication(X0!0, star(X0!0))), multiplication(X0!0, multiplication(strong_iteration(X0!0), zero)))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[146, 39])).
% 0.23/0.46 tff(148,plain,
% 0.23/0.46 (addition(star(X0!0), multiplication(strong_iteration(X0!0), zero)) = strong_iteration(X0!0)),
% 0.23/0.46 inference(symmetry,[status(thm)],[28])).
% 0.23/0.46 tff(149,plain,
% 0.23/0.46 (multiplication(X0!0, addition(star(X0!0), multiplication(strong_iteration(X0!0), zero))) = multiplication(X0!0, strong_iteration(X0!0))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[148])).
% 0.23/0.46 tff(150,plain,
% 0.23/0.46 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!0, addition(star(X0!0), multiplication(strong_iteration(X0!0), zero))) = addition(multiplication(X0!0, star(X0!0)), multiplication(X0!0, multiplication(strong_iteration(X0!0), zero))))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(151,plain,
% 0.23/0.46 (multiplication(X0!0, addition(star(X0!0), multiplication(strong_iteration(X0!0), zero))) = addition(multiplication(X0!0, star(X0!0)), multiplication(X0!0, multiplication(strong_iteration(X0!0), zero)))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[150, 49])).
% 0.23/0.46 tff(152,plain,
% 0.23/0.46 (addition(multiplication(X0!0, star(X0!0)), multiplication(X0!0, multiplication(strong_iteration(X0!0), zero))) = multiplication(X0!0, addition(star(X0!0), multiplication(strong_iteration(X0!0), zero)))),
% 0.23/0.46 inference(symmetry,[status(thm)],[151])).
% 0.23/0.46 tff(153,plain,
% 0.23/0.46 (addition(multiplication(X0!0, star(X0!0)), multiplication(X0!0, multiplication(strong_iteration(X0!0), zero))) = multiplication(X0!0, strong_iteration(X0!0))),
% 0.23/0.46 inference(transitivity,[status(thm)],[152, 149])).
% 0.23/0.46 tff(154,plain,
% 0.23/0.46 (addition(one, addition(multiplication(X0!0, star(X0!0)), multiplication(X0!0, multiplication(strong_iteration(X0!0), zero)))) = addition(one, multiplication(X0!0, strong_iteration(X0!0)))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[153])).
% 0.23/0.46 tff(155,plain,
% 0.23/0.46 (addition(one, multiplication(X0!0, strong_iteration(X0!0))) = addition(one, addition(multiplication(X0!0, star(X0!0)), multiplication(X0!0, multiplication(strong_iteration(X0!0), zero))))),
% 0.23/0.46 inference(symmetry,[status(thm)],[154])).
% 0.23/0.46 tff(156,plain,
% 0.23/0.46 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X0!0, strong_iteration(X0!0)), one) = addition(one, multiplication(X0!0, strong_iteration(X0!0))))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(157,plain,
% 0.23/0.46 (addition(multiplication(X0!0, strong_iteration(X0!0)), one) = addition(one, multiplication(X0!0, strong_iteration(X0!0)))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[156, 7])).
% 0.23/0.46 tff(158,plain,
% 0.23/0.46 (strong_iteration(X0!0) = addition(multiplication(strong_iteration(X0!0), X0!0), one)),
% 0.23/0.46 inference(transitivity,[status(thm)],[60, 157, 155, 147, 145, 124, 42, 32, 10])).
% 0.23/0.46 tff(159,plain,
% 0.23/0.46 ((~![X0: $i] : (strong_iteration(X0) = addition(multiplication(strong_iteration(X0), X0), one))) <=> (~![X0: $i] : (strong_iteration(X0) = addition(multiplication(strong_iteration(X0), X0), one)))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(160,axiom,(~![X0: $i] : (strong_iteration(X0) = addition(multiplication(strong_iteration(X0), X0), one))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 0.23/0.46 tff(161,plain,
% 0.23/0.46 (~![X0: $i] : (strong_iteration(X0) = addition(multiplication(strong_iteration(X0), X0), one))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.23/0.46 tff(162,plain,
% 0.23/0.46 (~![X0: $i] : (strong_iteration(X0) = addition(multiplication(strong_iteration(X0), X0), one))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[161, 159])).
% 0.23/0.46 tff(163,plain,
% 0.23/0.46 (~![X0: $i] : (strong_iteration(X0) = addition(multiplication(strong_iteration(X0), X0), one))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[162, 159])).
% 0.23/0.46 tff(164,plain,
% 0.23/0.46 (~![X0: $i] : (strong_iteration(X0) = addition(multiplication(strong_iteration(X0), X0), one))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[163, 159])).
% 0.23/0.46 tff(165,plain,
% 0.23/0.46 (~![X0: $i] : (strong_iteration(X0) = addition(multiplication(strong_iteration(X0), X0), one))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[164, 159])).
% 0.23/0.46 tff(166,plain,
% 0.23/0.46 (~![X0: $i] : (strong_iteration(X0) = addition(multiplication(strong_iteration(X0), X0), one))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[165, 159])).
% 0.23/0.46 tff(167,plain,
% 0.23/0.46 (~![X0: $i] : (strong_iteration(X0) = addition(multiplication(strong_iteration(X0), X0), one))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[166, 159])).
% 0.23/0.46 tff(168,plain,(
% 0.23/0.46 ~(strong_iteration(X0!0) = addition(multiplication(strong_iteration(X0!0), X0!0), one))),
% 0.23/0.46 inference(skolemize,[status(sab)],[167])).
% 0.23/0.46 tff(169,plain,
% 0.23/0.46 ($false),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[168, 158])).
% 0.23/0.46 % SZS output end Proof
%------------------------------------------------------------------------------