TSTP Solution File: KLE148+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE148+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 17:24:20 EDT 2022
% Result : Theorem 2.06s 1.54s
% Output : Proof 2.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE148+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n027.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 09:04:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 2.06/1.54 % SZS status Theorem
% 2.06/1.54 % SZS output start Proof
% 2.06/1.54 tff(tptp_fun_X0_1_type, type, (
% 2.06/1.54 tptp_fun_X0_1: $i)).
% 2.06/1.54 tff(addition_type, type, (
% 2.06/1.54 addition: ( $i * $i ) > $i)).
% 2.06/1.54 tff(multiplication_type, type, (
% 2.06/1.54 multiplication: ( $i * $i ) > $i)).
% 2.06/1.54 tff(strong_iteration_type, type, (
% 2.06/1.54 strong_iteration: $i > $i)).
% 2.06/1.54 tff(tptp_fun_X1_0_type, type, (
% 2.06/1.54 tptp_fun_X1_0: $i)).
% 2.06/1.54 tff(zero_type, type, (
% 2.06/1.54 zero: $i)).
% 2.06/1.54 tff(one_type, type, (
% 2.06/1.54 one: $i)).
% 2.06/1.54 tff(leq_type, type, (
% 2.06/1.54 leq: ( $i * $i ) > $o)).
% 2.06/1.54 tff(1,plain,
% 2.06/1.54 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 2.06/1.54 inference(bind,[status(th)],[])).
% 2.06/1.54 tff(2,plain,
% 2.06/1.54 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 2.06/1.54 inference(quant_intro,[status(thm)],[1])).
% 2.06/1.54 tff(3,plain,
% 2.06/1.54 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 2.06/1.54 inference(rewrite,[status(thm)],[])).
% 2.06/1.54 tff(4,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','additive_identity')).
% 2.06/1.54 tff(5,plain,
% 2.06/1.54 (![A: $i] : (addition(A, zero) = A)),
% 2.06/1.54 inference(modus_ponens,[status(thm)],[4, 3])).
% 2.06/1.54 tff(6,plain,(
% 2.06/1.54 ![A: $i] : (addition(A, zero) = A)),
% 2.06/1.54 inference(skolemize,[status(sab)],[5])).
% 2.06/1.54 tff(7,plain,
% 2.06/1.54 (![A: $i] : (addition(A, zero) = A)),
% 2.06/1.54 inference(modus_ponens,[status(thm)],[6, 2])).
% 2.06/1.54 tff(8,plain,
% 2.06/1.54 ((~![A: $i] : (addition(A, zero) = A)) | (addition(X0!1, zero) = X0!1)),
% 2.06/1.54 inference(quant_inst,[status(thm)],[])).
% 2.06/1.54 tff(9,plain,
% 2.06/1.54 (addition(X0!1, zero) = X0!1),
% 2.06/1.54 inference(unit_resolution,[status(thm)],[8, 7])).
% 2.06/1.54 tff(10,plain,
% 2.06/1.54 (^[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))))),
% 2.06/1.54 inference(bind,[status(th)],[])).
% 2.06/1.54 tff(11,plain,
% 2.06/1.54 (![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)))),
% 2.06/1.54 inference(quant_intro,[status(thm)],[10])).
% 2.06/1.54 tff(12,plain,
% 2.06/1.54 (![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)))),
% 2.06/1.54 inference(rewrite,[status(thm)],[])).
% 2.06/1.54 tff(13,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')).
% 2.06/1.54 tff(14,plain,
% 2.06/1.54 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 2.06/1.54 inference(modus_ponens,[status(thm)],[13, 12])).
% 2.06/1.54 tff(15,plain,(
% 2.06/1.54 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 2.06/1.54 inference(skolemize,[status(sab)],[14])).
% 2.06/1.54 tff(16,plain,
% 2.06/1.54 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 2.06/1.54 inference(modus_ponens,[status(thm)],[15, 11])).
% 2.06/1.54 tff(17,plain,
% 2.06/1.54 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X1!0, addition(multiplication(X1!0, strong_iteration(X1!0)), one)) = addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one)))),
% 2.06/1.54 inference(quant_inst,[status(thm)],[])).
% 2.06/1.54 tff(18,plain,
% 2.06/1.54 (multiplication(X1!0, addition(multiplication(X1!0, strong_iteration(X1!0)), one)) = addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one))),
% 2.06/1.54 inference(unit_resolution,[status(thm)],[17, 16])).
% 2.06/1.54 tff(19,plain,
% 2.06/1.54 (^[A: $i] : refl((strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)))),
% 2.06/1.54 inference(bind,[status(th)],[])).
% 2.06/1.54 tff(20,plain,
% 2.06/1.54 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 2.06/1.54 inference(quant_intro,[status(thm)],[19])).
% 2.06/1.54 tff(21,plain,
% 2.06/1.54 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 2.06/1.54 inference(rewrite,[status(thm)],[])).
% 2.06/1.54 tff(22,axiom,(![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','infty_unfold1')).
% 2.06/1.54 tff(23,plain,
% 2.06/1.54 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 2.06/1.54 inference(modus_ponens,[status(thm)],[22, 21])).
% 2.06/1.54 tff(24,plain,(
% 2.06/1.54 ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 2.06/1.54 inference(skolemize,[status(sab)],[23])).
% 2.06/1.54 tff(25,plain,
% 2.06/1.54 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 2.06/1.54 inference(modus_ponens,[status(thm)],[24, 20])).
% 2.06/1.54 tff(26,plain,
% 2.06/1.54 ((~![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))) | (strong_iteration(X1!0) = addition(multiplication(X1!0, strong_iteration(X1!0)), one))),
% 2.06/1.54 inference(quant_inst,[status(thm)],[])).
% 2.06/1.54 tff(27,plain,
% 2.06/1.54 (strong_iteration(X1!0) = addition(multiplication(X1!0, strong_iteration(X1!0)), one)),
% 2.06/1.54 inference(unit_resolution,[status(thm)],[26, 25])).
% 2.06/1.54 tff(28,plain,
% 2.06/1.54 (multiplication(X1!0, strong_iteration(X1!0)) = multiplication(X1!0, addition(multiplication(X1!0, strong_iteration(X1!0)), one))),
% 2.06/1.54 inference(monotonicity,[status(thm)],[27])).
% 2.06/1.54 tff(29,plain,
% 2.06/1.54 (multiplication(X1!0, strong_iteration(X1!0)) = addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one))),
% 2.06/1.54 inference(transitivity,[status(thm)],[28, 18])).
% 2.06/1.54 tff(30,plain,
% 2.06/1.54 (multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0))) = multiplication(X0!1, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one)))),
% 2.06/1.54 inference(monotonicity,[status(thm)],[29])).
% 2.06/1.54 tff(31,plain,
% 2.06/1.54 (multiplication(X1!0, addition(multiplication(X1!0, strong_iteration(X1!0)), one)) = multiplication(X1!0, strong_iteration(X1!0))),
% 2.06/1.54 inference(symmetry,[status(thm)],[28])).
% 2.06/1.54 tff(32,plain,
% 2.06/1.54 (multiplication(X0!1, multiplication(X1!0, addition(multiplication(X1!0, strong_iteration(X1!0)), one))) = multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0)))),
% 2.06/1.54 inference(monotonicity,[status(thm)],[31])).
% 2.06/1.54 tff(33,plain,
% 2.06/1.54 (^[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)))),
% 2.06/1.54 inference(bind,[status(th)],[])).
% 2.06/1.54 tff(34,plain,
% 2.06/1.54 (![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))),
% 2.06/1.54 inference(quant_intro,[status(thm)],[33])).
% 2.06/1.54 tff(35,plain,
% 2.06/1.54 (![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))),
% 2.06/1.54 inference(rewrite,[status(thm)],[])).
% 2.06/1.54 tff(36,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')).
% 2.06/1.54 tff(37,plain,
% 2.06/1.54 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 2.06/1.54 inference(modus_ponens,[status(thm)],[36, 35])).
% 2.06/1.54 tff(38,plain,(
% 2.06/1.54 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 2.06/1.54 inference(skolemize,[status(sab)],[37])).
% 2.06/1.54 tff(39,plain,
% 2.06/1.54 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 2.06/1.54 inference(modus_ponens,[status(thm)],[38, 34])).
% 2.06/1.54 tff(40,plain,
% 2.06/1.54 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X0!1, multiplication(X1!0, addition(multiplication(X1!0, strong_iteration(X1!0)), one))) = multiplication(multiplication(X0!1, X1!0), addition(multiplication(X1!0, strong_iteration(X1!0)), one)))),
% 2.06/1.54 inference(quant_inst,[status(thm)],[])).
% 2.06/1.54 tff(41,plain,
% 2.06/1.54 (multiplication(X0!1, multiplication(X1!0, addition(multiplication(X1!0, strong_iteration(X1!0)), one))) = multiplication(multiplication(X0!1, X1!0), addition(multiplication(X1!0, strong_iteration(X1!0)), one))),
% 2.06/1.54 inference(unit_resolution,[status(thm)],[40, 39])).
% 2.06/1.54 tff(42,plain,
% 2.06/1.54 (multiplication(multiplication(X0!1, X1!0), addition(multiplication(X1!0, strong_iteration(X1!0)), one)) = multiplication(X0!1, multiplication(X1!0, addition(multiplication(X1!0, strong_iteration(X1!0)), one)))),
% 2.06/1.54 inference(symmetry,[status(thm)],[41])).
% 2.06/1.54 tff(43,plain,
% 2.06/1.54 (multiplication(X0!1, strong_iteration(X1!0)) = multiplication(X0!1, addition(multiplication(X1!0, strong_iteration(X1!0)), one))),
% 2.06/1.54 inference(monotonicity,[status(thm)],[27])).
% 2.06/1.54 tff(44,plain,
% 2.06/1.54 (multiplication(X0!1, addition(multiplication(X1!0, strong_iteration(X1!0)), one)) = multiplication(X0!1, strong_iteration(X1!0))),
% 2.06/1.54 inference(symmetry,[status(thm)],[43])).
% 2.06/1.54 tff(45,plain,
% 2.06/1.54 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!1, addition(multiplication(X1!0, strong_iteration(X1!0)), one)) = addition(multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X0!1, one)))),
% 2.06/1.54 inference(quant_inst,[status(thm)],[])).
% 2.06/1.54 tff(46,plain,
% 2.06/1.54 (multiplication(X0!1, addition(multiplication(X1!0, strong_iteration(X1!0)), one)) = addition(multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X0!1, one))),
% 2.06/1.54 inference(unit_resolution,[status(thm)],[45, 16])).
% 2.06/1.54 tff(47,plain,
% 2.06/1.54 (addition(multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X0!1, one)) = multiplication(X0!1, addition(multiplication(X1!0, strong_iteration(X1!0)), one))),
% 2.06/1.54 inference(symmetry,[status(thm)],[46])).
% 2.06/1.54 tff(48,plain,
% 2.06/1.54 (multiplication(X0!1, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one))) = multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0)))),
% 2.06/1.54 inference(symmetry,[status(thm)],[30])).
% 2.06/1.54 tff(49,plain,
% 2.06/1.54 (addition(multiplication(X0!1, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one))), multiplication(X0!1, one)) = addition(multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X0!1, one))),
% 2.06/1.54 inference(monotonicity,[status(thm)],[48])).
% 2.06/1.54 tff(50,plain,
% 2.06/1.54 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 2.06/1.54 inference(bind,[status(th)],[])).
% 2.06/1.54 tff(51,plain,
% 2.06/1.54 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 2.06/1.54 inference(quant_intro,[status(thm)],[50])).
% 2.06/1.54 tff(52,plain,
% 2.06/1.54 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 2.06/1.54 inference(rewrite,[status(thm)],[])).
% 2.06/1.54 tff(53,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','multiplicative_right_identity')).
% 2.06/1.54 tff(54,plain,
% 2.06/1.54 (![A: $i] : (multiplication(A, one) = A)),
% 2.06/1.54 inference(modus_ponens,[status(thm)],[53, 52])).
% 2.06/1.54 tff(55,plain,(
% 2.06/1.54 ![A: $i] : (multiplication(A, one) = A)),
% 2.06/1.54 inference(skolemize,[status(sab)],[54])).
% 2.06/1.54 tff(56,plain,
% 2.06/1.54 (![A: $i] : (multiplication(A, one) = A)),
% 2.06/1.54 inference(modus_ponens,[status(thm)],[55, 51])).
% 2.06/1.54 tff(57,plain,
% 2.06/1.54 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(X0!1, one) = X0!1)),
% 2.06/1.54 inference(quant_inst,[status(thm)],[])).
% 2.07/1.54 tff(58,plain,
% 2.07/1.54 (multiplication(X0!1, one) = X0!1),
% 2.07/1.54 inference(unit_resolution,[status(thm)],[57, 56])).
% 2.07/1.54 tff(59,plain,
% 2.07/1.54 (X0!1 = multiplication(X0!1, one)),
% 2.07/1.54 inference(symmetry,[status(thm)],[58])).
% 2.07/1.54 tff(60,plain,
% 2.07/1.54 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 2.07/1.54 inference(bind,[status(th)],[])).
% 2.07/1.54 tff(61,plain,
% 2.07/1.54 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 2.07/1.54 inference(quant_intro,[status(thm)],[60])).
% 2.07/1.54 tff(62,plain,
% 2.07/1.54 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 2.07/1.54 inference(rewrite,[status(thm)],[])).
% 2.07/1.54 tff(63,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','idempotence')).
% 2.07/1.54 tff(64,plain,
% 2.07/1.54 (![A: $i] : (addition(A, A) = A)),
% 2.07/1.54 inference(modus_ponens,[status(thm)],[63, 62])).
% 2.07/1.54 tff(65,plain,(
% 2.07/1.54 ![A: $i] : (addition(A, A) = A)),
% 2.07/1.54 inference(skolemize,[status(sab)],[64])).
% 2.07/1.54 tff(66,plain,
% 2.07/1.54 (![A: $i] : (addition(A, A) = A)),
% 2.07/1.54 inference(modus_ponens,[status(thm)],[65, 61])).
% 2.07/1.54 tff(67,plain,
% 2.07/1.54 ((~![A: $i] : (addition(A, A) = A)) | (addition(X0!1, X0!1) = X0!1)),
% 2.07/1.54 inference(quant_inst,[status(thm)],[])).
% 2.07/1.54 tff(68,plain,
% 2.07/1.54 (addition(X0!1, X0!1) = X0!1),
% 2.07/1.54 inference(unit_resolution,[status(thm)],[67, 66])).
% 2.07/1.54 tff(69,plain,
% 2.07/1.54 (addition(multiplication(X0!1, one), X0!1) = addition(X0!1, X0!1)),
% 2.07/1.54 inference(monotonicity,[status(thm)],[58])).
% 2.07/1.54 tff(70,plain,
% 2.07/1.54 (addition(multiplication(X0!1, one), X0!1) = multiplication(X0!1, one)),
% 2.07/1.54 inference(transitivity,[status(thm)],[69, 68, 59])).
% 2.07/1.54 tff(71,plain,
% 2.07/1.54 (addition(multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0))), addition(multiplication(X0!1, one), X0!1)) = addition(multiplication(X0!1, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one))), multiplication(X0!1, one))),
% 2.07/1.54 inference(monotonicity,[status(thm)],[30, 70])).
% 2.07/1.54 tff(72,plain,
% 2.07/1.54 (^[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)))),
% 2.07/1.54 inference(bind,[status(th)],[])).
% 2.07/1.54 tff(73,plain,
% 2.07/1.54 (![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))),
% 2.07/1.54 inference(quant_intro,[status(thm)],[72])).
% 2.07/1.54 tff(74,plain,
% 2.07/1.54 (![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))),
% 2.07/1.54 inference(rewrite,[status(thm)],[])).
% 2.07/1.54 tff(75,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')).
% 2.07/1.54 tff(76,plain,
% 2.07/1.54 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 2.07/1.54 inference(modus_ponens,[status(thm)],[75, 74])).
% 2.07/1.54 tff(77,plain,(
% 2.07/1.54 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 2.07/1.54 inference(skolemize,[status(sab)],[76])).
% 2.07/1.54 tff(78,plain,
% 2.07/1.54 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 2.07/1.54 inference(modus_ponens,[status(thm)],[77, 73])).
% 2.07/1.54 tff(79,plain,
% 2.07/1.54 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0))), addition(multiplication(X0!1, one), X0!1)) = addition(addition(multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X0!1, one)), X0!1))),
% 2.07/1.54 inference(quant_inst,[status(thm)],[])).
% 2.07/1.54 tff(80,plain,
% 2.07/1.54 (addition(multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0))), addition(multiplication(X0!1, one), X0!1)) = addition(addition(multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X0!1, one)), X0!1)),
% 2.07/1.54 inference(unit_resolution,[status(thm)],[79, 78])).
% 2.07/1.54 tff(81,plain,
% 2.07/1.54 (addition(addition(multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X0!1, one)), X0!1) = addition(multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0))), addition(multiplication(X0!1, one), X0!1))),
% 2.07/1.54 inference(symmetry,[status(thm)],[80])).
% 2.07/1.54 tff(82,plain,
% 2.07/1.54 (multiplication(X0!1, strong_iteration(X1!0)) = addition(multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X0!1, one))),
% 2.07/1.54 inference(transitivity,[status(thm)],[43, 46])).
% 2.07/1.54 tff(83,plain,
% 2.07/1.54 (addition(multiplication(X0!1, strong_iteration(X1!0)), X0!1) = addition(addition(multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X0!1, one)), X0!1)),
% 2.07/1.54 inference(monotonicity,[status(thm)],[82])).
% 2.07/1.54 tff(84,plain,
% 2.07/1.54 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 2.07/1.54 inference(bind,[status(th)],[])).
% 2.07/1.54 tff(85,plain,
% 2.07/1.54 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 2.07/1.54 inference(quant_intro,[status(thm)],[84])).
% 2.07/1.54 tff(86,plain,
% 2.07/1.54 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 2.07/1.54 inference(rewrite,[status(thm)],[])).
% 2.07/1.54 tff(87,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','additive_commutativity')).
% 2.07/1.54 tff(88,plain,
% 2.07/1.54 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 2.07/1.54 inference(modus_ponens,[status(thm)],[87, 86])).
% 2.07/1.54 tff(89,plain,(
% 2.07/1.54 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 2.07/1.54 inference(skolemize,[status(sab)],[88])).
% 2.07/1.54 tff(90,plain,
% 2.07/1.54 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 2.07/1.54 inference(modus_ponens,[status(thm)],[89, 85])).
% 2.07/1.54 tff(91,plain,
% 2.07/1.54 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X0!1, multiplication(X0!1, strong_iteration(X1!0))) = addition(multiplication(X0!1, strong_iteration(X1!0)), X0!1))),
% 2.07/1.54 inference(quant_inst,[status(thm)],[])).
% 2.07/1.54 tff(92,plain,
% 2.07/1.54 (addition(X0!1, multiplication(X0!1, strong_iteration(X1!0))) = addition(multiplication(X0!1, strong_iteration(X1!0)), X0!1)),
% 2.07/1.54 inference(unit_resolution,[status(thm)],[91, 90])).
% 2.07/1.54 tff(93,plain,
% 2.07/1.54 (addition(X0!1, multiplication(X0!1, strong_iteration(X1!0))) = multiplication(X0!1, strong_iteration(X1!0))),
% 2.07/1.54 inference(transitivity,[status(thm)],[92, 83, 81, 71, 49, 47, 44])).
% 2.07/1.54 tff(94,plain,
% 2.07/1.54 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 2.07/1.54 inference(bind,[status(th)],[])).
% 2.07/1.54 tff(95,plain,
% 2.07/1.54 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 2.07/1.54 inference(quant_intro,[status(thm)],[94])).
% 2.07/1.54 tff(96,plain,
% 2.07/1.54 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 2.07/1.54 inference(rewrite,[status(thm)],[])).
% 2.07/1.54 tff(97,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','order')).
% 2.07/1.54 tff(98,plain,
% 2.07/1.54 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 2.07/1.54 inference(modus_ponens,[status(thm)],[97, 96])).
% 2.07/1.54 tff(99,plain,(
% 2.07/1.54 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 2.07/1.54 inference(skolemize,[status(sab)],[98])).
% 2.07/1.54 tff(100,plain,
% 2.07/1.54 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 2.07/1.54 inference(modus_ponens,[status(thm)],[99, 95])).
% 2.07/1.54 tff(101,plain,
% 2.07/1.54 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(X0!1, multiplication(X0!1, strong_iteration(X1!0))) <=> (addition(X0!1, multiplication(X0!1, strong_iteration(X1!0))) = multiplication(X0!1, strong_iteration(X1!0))))),
% 2.07/1.54 inference(quant_inst,[status(thm)],[])).
% 2.07/1.54 tff(102,plain,
% 2.07/1.54 (leq(X0!1, multiplication(X0!1, strong_iteration(X1!0))) <=> (addition(X0!1, multiplication(X0!1, strong_iteration(X1!0))) = multiplication(X0!1, strong_iteration(X1!0)))),
% 2.07/1.54 inference(unit_resolution,[status(thm)],[101, 100])).
% 2.07/1.54 tff(103,assumption,(~leq(X0!1, multiplication(X0!1, strong_iteration(X1!0)))), introduced(assumption)).
% 2.07/1.54 tff(104,plain,
% 2.07/1.54 ((~(leq(X0!1, multiplication(X0!1, strong_iteration(X1!0))) <=> (addition(X0!1, multiplication(X0!1, strong_iteration(X1!0))) = multiplication(X0!1, strong_iteration(X1!0))))) | leq(X0!1, multiplication(X0!1, strong_iteration(X1!0))) | (~(addition(X0!1, multiplication(X0!1, strong_iteration(X1!0))) = multiplication(X0!1, strong_iteration(X1!0))))),
% 2.07/1.54 inference(tautology,[status(thm)],[])).
% 2.07/1.54 tff(105,plain,
% 2.07/1.54 ((~(leq(X0!1, multiplication(X0!1, strong_iteration(X1!0))) <=> (addition(X0!1, multiplication(X0!1, strong_iteration(X1!0))) = multiplication(X0!1, strong_iteration(X1!0))))) | (~(addition(X0!1, multiplication(X0!1, strong_iteration(X1!0))) = multiplication(X0!1, strong_iteration(X1!0))))),
% 2.07/1.54 inference(unit_resolution,[status(thm)],[104, 103])).
% 2.07/1.54 tff(106,plain,
% 2.07/1.54 (~(addition(X0!1, multiplication(X0!1, strong_iteration(X1!0))) = multiplication(X0!1, strong_iteration(X1!0)))),
% 2.07/1.54 inference(unit_resolution,[status(thm)],[105, 102])).
% 2.07/1.54 tff(107,plain,
% 2.07/1.54 ($false),
% 2.07/1.54 inference(unit_resolution,[status(thm)],[106, 93])).
% 2.07/1.54 tff(108,plain,(leq(X0!1, multiplication(X0!1, strong_iteration(X1!0)))), inference(lemma,lemma(discharge,[]))).
% 2.07/1.54 tff(109,plain,
% 2.07/1.54 ((~(~((~((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1))) | (~leq(X0!1, multiplication(X0!1, strong_iteration(X1!0))))))) <=> ((~((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1))) | (~leq(X0!1, multiplication(X0!1, strong_iteration(X1!0)))))),
% 2.07/1.54 inference(rewrite,[status(thm)],[])).
% 2.07/1.54 tff(110,plain,
% 2.07/1.54 ((((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1)) & leq(X0!1, multiplication(X0!1, strong_iteration(X1!0)))) <=> (~((~((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1))) | (~leq(X0!1, multiplication(X0!1, strong_iteration(X1!0))))))),
% 2.07/1.54 inference(rewrite,[status(thm)],[])).
% 2.07/1.54 tff(111,plain,
% 2.07/1.54 ((~(((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1)) & leq(X0!1, multiplication(X0!1, strong_iteration(X1!0))))) <=> (~(~((~((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1))) | (~leq(X0!1, multiplication(X0!1, strong_iteration(X1!0)))))))),
% 2.07/1.54 inference(monotonicity,[status(thm)],[110])).
% 2.07/1.54 tff(112,plain,
% 2.07/1.54 ((~(((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1)) & leq(X0!1, multiplication(X0!1, strong_iteration(X1!0))))) <=> ((~((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1))) | (~leq(X0!1, multiplication(X0!1, strong_iteration(X1!0)))))),
% 2.07/1.54 inference(transitivity,[status(thm)],[111, 109])).
% 2.07/1.54 tff(113,plain,
% 2.07/1.54 ((~![X0: $i, X1: $i] : (((~(multiplication(X0, X1) = zero)) | leq(multiplication(X0, strong_iteration(X1)), X0)) & leq(X0, multiplication(X0, strong_iteration(X1))))) <=> (~![X0: $i, X1: $i] : (((~(multiplication(X0, X1) = zero)) | leq(multiplication(X0, strong_iteration(X1)), X0)) & leq(X0, multiplication(X0, strong_iteration(X1)))))),
% 2.07/1.54 inference(rewrite,[status(thm)],[])).
% 2.07/1.54 tff(114,plain,
% 2.07/1.54 ((~![X0: $i, X1: $i] : (((multiplication(X0, X1) = zero) => leq(multiplication(X0, strong_iteration(X1)), X0)) & leq(X0, multiplication(X0, strong_iteration(X1))))) <=> (~![X0: $i, X1: $i] : (((~(multiplication(X0, X1) = zero)) | leq(multiplication(X0, strong_iteration(X1)), X0)) & leq(X0, multiplication(X0, strong_iteration(X1)))))),
% 2.07/1.54 inference(rewrite,[status(thm)],[])).
% 2.07/1.54 tff(115,axiom,(~![X0: $i, X1: $i] : (((multiplication(X0, X1) = zero) => leq(multiplication(X0, strong_iteration(X1)), X0)) & leq(X0, multiplication(X0, strong_iteration(X1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 2.07/1.54 tff(116,plain,
% 2.07/1.54 (~![X0: $i, X1: $i] : (((~(multiplication(X0, X1) = zero)) | leq(multiplication(X0, strong_iteration(X1)), X0)) & leq(X0, multiplication(X0, strong_iteration(X1))))),
% 2.07/1.54 inference(modus_ponens,[status(thm)],[115, 114])).
% 2.07/1.54 tff(117,plain,
% 2.07/1.54 (~![X0: $i, X1: $i] : (((~(multiplication(X0, X1) = zero)) | leq(multiplication(X0, strong_iteration(X1)), X0)) & leq(X0, multiplication(X0, strong_iteration(X1))))),
% 2.07/1.54 inference(modus_ponens,[status(thm)],[116, 113])).
% 2.07/1.54 tff(118,plain,
% 2.07/1.54 (~![X0: $i, X1: $i] : (((~(multiplication(X0, X1) = zero)) | leq(multiplication(X0, strong_iteration(X1)), X0)) & leq(X0, multiplication(X0, strong_iteration(X1))))),
% 2.07/1.54 inference(modus_ponens,[status(thm)],[117, 113])).
% 2.07/1.54 tff(119,plain,
% 2.07/1.54 (~![X0: $i, X1: $i] : (((~(multiplication(X0, X1) = zero)) | leq(multiplication(X0, strong_iteration(X1)), X0)) & leq(X0, multiplication(X0, strong_iteration(X1))))),
% 2.07/1.54 inference(modus_ponens,[status(thm)],[118, 113])).
% 2.07/1.54 tff(120,plain,
% 2.07/1.54 (~![X0: $i, X1: $i] : (((~(multiplication(X0, X1) = zero)) | leq(multiplication(X0, strong_iteration(X1)), X0)) & leq(X0, multiplication(X0, strong_iteration(X1))))),
% 2.07/1.54 inference(modus_ponens,[status(thm)],[119, 113])).
% 2.07/1.54 tff(121,plain,
% 2.07/1.54 (~![X0: $i, X1: $i] : (((~(multiplication(X0, X1) = zero)) | leq(multiplication(X0, strong_iteration(X1)), X0)) & leq(X0, multiplication(X0, strong_iteration(X1))))),
% 2.07/1.54 inference(modus_ponens,[status(thm)],[120, 113])).
% 2.07/1.54 tff(122,plain,
% 2.07/1.54 (~![X0: $i, X1: $i] : (((~(multiplication(X0, X1) = zero)) | leq(multiplication(X0, strong_iteration(X1)), X0)) & leq(X0, multiplication(X0, strong_iteration(X1))))),
% 2.07/1.54 inference(modus_ponens,[status(thm)],[121, 113])).
% 2.07/1.54 tff(123,plain,(
% 2.07/1.54 ~(((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1)) & leq(X0!1, multiplication(X0!1, strong_iteration(X1!0))))),
% 2.07/1.54 inference(skolemize,[status(sab)],[122])).
% 2.07/1.54 tff(124,plain,
% 2.07/1.54 ((~((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1))) | (~leq(X0!1, multiplication(X0!1, strong_iteration(X1!0))))),
% 2.07/1.54 inference(modus_ponens,[status(thm)],[123, 112])).
% 2.07/1.54 tff(125,plain,
% 2.07/1.54 (~((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1))),
% 2.07/1.54 inference(unit_resolution,[status(thm)],[124, 108])).
% 2.07/1.54 tff(126,plain,
% 2.07/1.54 (((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1)) | (multiplication(X0!1, X1!0) = zero)),
% 2.07/1.54 inference(tautology,[status(thm)],[])).
% 2.07/1.54 tff(127,plain,
% 2.07/1.54 (multiplication(X0!1, X1!0) = zero),
% 2.07/1.54 inference(unit_resolution,[status(thm)],[126, 125])).
% 2.07/1.54 tff(128,plain,
% 2.07/1.54 (zero = multiplication(X0!1, X1!0)),
% 2.07/1.54 inference(symmetry,[status(thm)],[127])).
% 2.07/1.54 tff(129,plain,
% 2.07/1.54 (multiplication(zero, addition(multiplication(X1!0, strong_iteration(X1!0)), one)) = multiplication(multiplication(X0!1, X1!0), addition(multiplication(X1!0, strong_iteration(X1!0)), one))),
% 2.07/1.54 inference(monotonicity,[status(thm)],[128])).
% 2.07/1.54 tff(130,plain,
% 2.07/1.54 (^[A: $i] : refl((multiplication(zero, A) = zero) <=> (multiplication(zero, A) = zero))),
% 2.07/1.54 inference(bind,[status(th)],[])).
% 2.07/1.54 tff(131,plain,
% 2.07/1.54 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 2.07/1.54 inference(quant_intro,[status(thm)],[130])).
% 2.07/1.54 tff(132,plain,
% 2.07/1.54 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 2.07/1.54 inference(rewrite,[status(thm)],[])).
% 2.07/1.54 tff(133,axiom,(![A: $i] : (multiplication(zero, A) = zero)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','left_annihilation')).
% 2.07/1.54 tff(134,plain,
% 2.07/1.54 (![A: $i] : (multiplication(zero, A) = zero)),
% 2.07/1.54 inference(modus_ponens,[status(thm)],[133, 132])).
% 2.07/1.54 tff(135,plain,(
% 2.07/1.54 ![A: $i] : (multiplication(zero, A) = zero)),
% 2.07/1.54 inference(skolemize,[status(sab)],[134])).
% 2.07/1.54 tff(136,plain,
% 2.07/1.54 (![A: $i] : (multiplication(zero, A) = zero)),
% 2.07/1.54 inference(modus_ponens,[status(thm)],[135, 131])).
% 2.07/1.54 tff(137,plain,
% 2.07/1.54 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, addition(multiplication(X1!0, strong_iteration(X1!0)), one)) = zero)),
% 2.07/1.54 inference(quant_inst,[status(thm)],[])).
% 2.07/1.54 tff(138,plain,
% 2.07/1.54 (multiplication(zero, addition(multiplication(X1!0, strong_iteration(X1!0)), one)) = zero),
% 2.07/1.54 inference(unit_resolution,[status(thm)],[137, 136])).
% 2.07/1.54 tff(139,plain,
% 2.07/1.54 (zero = multiplication(zero, addition(multiplication(X1!0, strong_iteration(X1!0)), one))),
% 2.07/1.54 inference(symmetry,[status(thm)],[138])).
% 2.07/1.54 tff(140,plain,
% 2.07/1.54 (zero = multiplication(X0!1, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one)))),
% 2.07/1.54 inference(transitivity,[status(thm)],[139, 129, 42, 32, 30])).
% 2.07/1.54 tff(141,plain,
% 2.07/1.54 (addition(X0!1, zero) = addition(multiplication(X0!1, one), multiplication(X0!1, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one))))),
% 2.07/1.54 inference(monotonicity,[status(thm)],[59, 140])).
% 2.07/1.54 tff(142,plain,
% 2.07/1.54 (addition(multiplication(X0!1, one), multiplication(X0!1, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one)))) = addition(X0!1, zero)),
% 2.07/1.54 inference(symmetry,[status(thm)],[141])).
% 2.07/1.54 tff(143,plain,
% 2.07/1.54 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!1, addition(one, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one)))) = addition(multiplication(X0!1, one), multiplication(X0!1, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one)))))),
% 2.07/1.54 inference(quant_inst,[status(thm)],[])).
% 2.07/1.54 tff(144,plain,
% 2.07/1.54 (multiplication(X0!1, addition(one, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one)))) = addition(multiplication(X0!1, one), multiplication(X0!1, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one))))),
% 2.07/1.54 inference(unit_resolution,[status(thm)],[143, 16])).
% 2.07/1.54 tff(145,plain,
% 2.07/1.54 (addition(multiplication(X1!0, strong_iteration(X1!0)), one) = strong_iteration(X1!0)),
% 2.07/1.54 inference(symmetry,[status(thm)],[27])).
% 2.07/1.54 tff(146,plain,
% 2.07/1.54 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X1!0, strong_iteration(X1!0)), one) = addition(one, multiplication(X1!0, strong_iteration(X1!0))))),
% 2.07/1.54 inference(quant_inst,[status(thm)],[])).
% 2.07/1.54 tff(147,plain,
% 2.07/1.54 (addition(multiplication(X1!0, strong_iteration(X1!0)), one) = addition(one, multiplication(X1!0, strong_iteration(X1!0)))),
% 2.07/1.54 inference(unit_resolution,[status(thm)],[146, 90])).
% 2.07/1.54 tff(148,plain,
% 2.07/1.54 (addition(one, multiplication(X1!0, strong_iteration(X1!0))) = addition(multiplication(X1!0, strong_iteration(X1!0)), one)),
% 2.07/1.54 inference(symmetry,[status(thm)],[147])).
% 2.07/1.54 tff(149,plain,
% 2.07/1.54 (addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one)) = multiplication(X1!0, addition(multiplication(X1!0, strong_iteration(X1!0)), one))),
% 2.07/1.54 inference(symmetry,[status(thm)],[18])).
% 2.07/1.54 tff(150,plain,
% 2.07/1.54 (addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one)) = multiplication(X1!0, strong_iteration(X1!0))),
% 2.07/1.54 inference(transitivity,[status(thm)],[149, 31])).
% 2.07/1.54 tff(151,plain,
% 2.07/1.54 (addition(one, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one))) = addition(one, multiplication(X1!0, strong_iteration(X1!0)))),
% 2.07/1.54 inference(monotonicity,[status(thm)],[150])).
% 2.07/1.54 tff(152,plain,
% 2.07/1.54 (addition(one, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one))) = strong_iteration(X1!0)),
% 2.07/1.54 inference(transitivity,[status(thm)],[151, 148, 145])).
% 2.07/1.54 tff(153,plain,
% 2.07/1.54 (multiplication(X0!1, addition(one, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one)))) = multiplication(X0!1, strong_iteration(X1!0))),
% 2.07/1.54 inference(monotonicity,[status(thm)],[152])).
% 2.07/1.54 tff(154,plain,
% 2.07/1.54 (multiplication(X0!1, strong_iteration(X1!0)) = multiplication(X0!1, addition(one, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one))))),
% 2.07/1.54 inference(symmetry,[status(thm)],[153])).
% 2.07/1.54 tff(155,plain,
% 2.07/1.54 ((~(leq(X0!1, multiplication(X0!1, strong_iteration(X1!0))) <=> (addition(X0!1, multiplication(X0!1, strong_iteration(X1!0))) = multiplication(X0!1, strong_iteration(X1!0))))) | (~leq(X0!1, multiplication(X0!1, strong_iteration(X1!0)))) | (addition(X0!1, multiplication(X0!1, strong_iteration(X1!0))) = multiplication(X0!1, strong_iteration(X1!0)))),
% 2.07/1.55 inference(tautology,[status(thm)],[])).
% 2.07/1.55 tff(156,plain,
% 2.07/1.55 ((~(leq(X0!1, multiplication(X0!1, strong_iteration(X1!0))) <=> (addition(X0!1, multiplication(X0!1, strong_iteration(X1!0))) = multiplication(X0!1, strong_iteration(X1!0))))) | (addition(X0!1, multiplication(X0!1, strong_iteration(X1!0))) = multiplication(X0!1, strong_iteration(X1!0)))),
% 2.07/1.55 inference(unit_resolution,[status(thm)],[155, 108])).
% 2.07/1.55 tff(157,plain,
% 2.07/1.55 (addition(X0!1, multiplication(X0!1, strong_iteration(X1!0))) = multiplication(X0!1, strong_iteration(X1!0))),
% 2.07/1.55 inference(unit_resolution,[status(thm)],[156, 102])).
% 2.07/1.55 tff(158,plain,
% 2.07/1.55 (addition(multiplication(X0!1, strong_iteration(X1!0)), X0!1) = addition(X0!1, multiplication(X0!1, strong_iteration(X1!0)))),
% 2.07/1.55 inference(symmetry,[status(thm)],[92])).
% 2.07/1.55 tff(159,plain,
% 2.07/1.55 (addition(multiplication(X0!1, strong_iteration(X1!0)), X0!1) = X0!1),
% 2.07/1.55 inference(transitivity,[status(thm)],[158, 157, 154, 144, 142, 9])).
% 2.07/1.55 tff(160,plain,
% 2.07/1.55 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1) <=> (addition(multiplication(X0!1, strong_iteration(X1!0)), X0!1) = X0!1))),
% 2.07/1.55 inference(quant_inst,[status(thm)],[])).
% 2.07/1.55 tff(161,plain,
% 2.07/1.55 (leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1) <=> (addition(multiplication(X0!1, strong_iteration(X1!0)), X0!1) = X0!1)),
% 2.07/1.55 inference(unit_resolution,[status(thm)],[160, 100])).
% 2.07/1.55 tff(162,plain,
% 2.07/1.55 (((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1)) | (~leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1))),
% 2.07/1.55 inference(tautology,[status(thm)],[])).
% 2.07/1.55 tff(163,plain,
% 2.07/1.55 (~leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1)),
% 2.07/1.55 inference(unit_resolution,[status(thm)],[162, 125])).
% 2.07/1.55 tff(164,plain,
% 2.07/1.55 ((~(leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1) <=> (addition(multiplication(X0!1, strong_iteration(X1!0)), X0!1) = X0!1))) | leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1) | (~(addition(multiplication(X0!1, strong_iteration(X1!0)), X0!1) = X0!1))),
% 2.07/1.55 inference(tautology,[status(thm)],[])).
% 2.07/1.55 tff(165,plain,
% 2.07/1.55 ((~(leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1) <=> (addition(multiplication(X0!1, strong_iteration(X1!0)), X0!1) = X0!1))) | (~(addition(multiplication(X0!1, strong_iteration(X1!0)), X0!1) = X0!1))),
% 2.07/1.55 inference(unit_resolution,[status(thm)],[164, 163])).
% 2.07/1.55 tff(166,plain,
% 2.07/1.55 (~(addition(multiplication(X0!1, strong_iteration(X1!0)), X0!1) = X0!1)),
% 2.07/1.55 inference(unit_resolution,[status(thm)],[165, 161])).
% 2.07/1.55 tff(167,plain,
% 2.07/1.55 ($false),
% 2.07/1.55 inference(unit_resolution,[status(thm)],[166, 159])).
% 2.07/1.55 % SZS output end Proof
%------------------------------------------------------------------------------