%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE093+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 Jun 21 05:13:01 AM UTC 2025
% Result : Theorem 0.21s 0.44s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE093+1 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 18:59:20 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.44 % SZS status Theorem
% 0.21/0.44 % SZS output start Proof
% 0.21/0.44 tff(one_type, type, (
% 0.21/0.44 one: $i)).
% 0.21/0.44 tff(domain_type, type, (
% 0.21/0.44 domain: $i > $i)).
% 0.21/0.44 tff(star_type, type, (
% 0.21/0.44 star: $i > $i)).
% 0.21/0.44 tff(tptp_fun_X0_0_type, type, (
% 0.21/0.44 tptp_fun_X0_0: $i)).
% 0.21/0.44 tff(addition_type, type, (
% 0.21/0.44 addition: ( $i * $i ) > $i)).
% 0.21/0.44 tff(multiplication_type, type, (
% 0.21/0.44 multiplication: ( $i * $i ) > $i)).
% 0.21/0.44 tff(leq_type, type, (
% 0.21/0.44 leq: ( $i * $i ) > $o)).
% 0.21/0.44 tff(1,plain,
% 0.21/0.44 (^[X0: $i] : refl((addition(domain(X0), one) = one) <=> (addition(domain(X0), one) = one))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(2,plain,
% 0.21/0.44 (![X0: $i] : (addition(domain(X0), one) = one) <=> ![X0: $i] : (addition(domain(X0), one) = one)),
% 0.21/0.44 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.44 tff(3,plain,
% 0.21/0.44 (![X0: $i] : (addition(domain(X0), one) = one) <=> ![X0: $i] : (addition(domain(X0), one) = one)),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(4,axiom,(![X0: $i] : (addition(domain(X0), one) = one)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax','domain3')).
% 0.21/0.44 tff(5,plain,
% 0.21/0.44 (![X0: $i] : (addition(domain(X0), one) = one)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.44 tff(6,plain,(
% 0.21/0.44 ![X0: $i] : (addition(domain(X0), one) = one)),
% 0.21/0.44 inference(skolemize,[status(sab)],[5])).
% 0.21/0.44 tff(7,plain,
% 0.21/0.44 (![X0: $i] : (addition(domain(X0), one) = one)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.44 tff(8,plain,
% 0.21/0.44 ((~![X0: $i] : (addition(domain(X0), one) = one)) | (addition(domain(star(X0!0)), one) = one)),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(9,plain,
% 0.21/0.44 (addition(domain(star(X0!0)), one) = one),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.44 tff(10,plain,
% 0.21/0.44 (addition(domain(star(X0!0)), addition(domain(star(X0!0)), one)) = addition(domain(star(X0!0)), one)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[9])).
% 0.21/0.44 tff(11,plain,
% 0.21/0.44 (^[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)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(12,plain,
% 0.21/0.44 (![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))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[11])).
% 0.21/0.44 tff(13,plain,
% 0.21/0.44 (![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))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(14,axiom,(![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','additive_associativity')).
% 0.21/0.44 tff(15,plain,
% 0.21/0.44 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.21/0.44 tff(16,plain,(
% 0.21/0.44 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.21/0.44 inference(skolemize,[status(sab)],[15])).
% 0.21/0.44 tff(17,plain,
% 0.21/0.44 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.21/0.44 tff(18,plain,
% 0.21/0.44 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(domain(star(X0!0)), addition(domain(star(X0!0)), one)) = addition(addition(domain(star(X0!0)), domain(star(X0!0))), one))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(19,plain,
% 0.21/0.44 (addition(domain(star(X0!0)), addition(domain(star(X0!0)), one)) = addition(addition(domain(star(X0!0)), domain(star(X0!0))), one)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.21/0.44 tff(20,plain,
% 0.21/0.44 (addition(addition(domain(star(X0!0)), domain(star(X0!0))), one) = addition(domain(star(X0!0)), addition(domain(star(X0!0)), one))),
% 0.21/0.44 inference(symmetry,[status(thm)],[19])).
% 0.21/0.44 tff(21,plain,
% 0.21/0.44 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(22,plain,
% 0.21/0.44 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[21])).
% 0.21/0.44 tff(23,plain,
% 0.21/0.44 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(24,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','additive_commutativity')).
% 0.21/0.44 tff(25,plain,
% 0.21/0.44 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.21/0.44 tff(26,plain,(
% 0.21/0.44 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.21/0.44 inference(skolemize,[status(sab)],[25])).
% 0.21/0.44 tff(27,plain,
% 0.21/0.44 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.21/0.44 tff(28,plain,
% 0.21/0.44 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(domain(star(X0!0)), domain(star(X0!0))), one) = addition(one, addition(domain(star(X0!0)), domain(star(X0!0)))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(29,plain,
% 0.21/0.44 (addition(addition(domain(star(X0!0)), domain(star(X0!0))), one) = addition(one, addition(domain(star(X0!0)), domain(star(X0!0))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.21/0.44 tff(30,plain,
% 0.21/0.44 (addition(one, addition(domain(star(X0!0)), domain(star(X0!0)))) = addition(addition(domain(star(X0!0)), domain(star(X0!0))), one)),
% 0.21/0.44 inference(symmetry,[status(thm)],[29])).
% 0.21/0.44 tff(31,plain,
% 0.21/0.44 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(32,plain,
% 0.21/0.44 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.21/0.44 inference(quant_intro,[status(thm)],[31])).
% 0.21/0.44 tff(33,plain,
% 0.21/0.44 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(34,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','additive_idempotence')).
% 0.21/0.44 tff(35,plain,
% 0.21/0.44 (![A: $i] : (addition(A, A) = A)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.21/0.44 tff(36,plain,(
% 0.21/0.44 ![A: $i] : (addition(A, A) = A)),
% 0.21/0.44 inference(skolemize,[status(sab)],[35])).
% 0.21/0.44 tff(37,plain,
% 0.21/0.44 (![A: $i] : (addition(A, A) = A)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.21/0.44 tff(38,plain,
% 0.21/0.44 ((~![A: $i] : (addition(A, A) = A)) | (addition(domain(star(X0!0)), domain(star(X0!0))) = domain(star(X0!0)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(39,plain,
% 0.21/0.44 (addition(domain(star(X0!0)), domain(star(X0!0))) = domain(star(X0!0))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.21/0.44 tff(40,plain,
% 0.21/0.44 (domain(star(X0!0)) = addition(domain(star(X0!0)), domain(star(X0!0)))),
% 0.21/0.44 inference(symmetry,[status(thm)],[39])).
% 0.21/0.44 tff(41,plain,
% 0.21/0.44 ((~![X0: $i] : (addition(domain(X0), one) = one)) | (addition(domain(one), one) = one)),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(42,plain,
% 0.21/0.44 (addition(domain(one), one) = one),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[41, 7])).
% 0.21/0.44 tff(43,plain,
% 0.21/0.44 (one = addition(domain(star(X0!0)), one)),
% 0.21/0.44 inference(symmetry,[status(thm)],[9])).
% 0.21/0.44 tff(44,plain,
% 0.21/0.44 (domain(one) = domain(addition(domain(star(X0!0)), one))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[43])).
% 0.21/0.44 tff(45,plain,
% 0.21/0.44 (domain(addition(domain(star(X0!0)), one)) = domain(one)),
% 0.21/0.44 inference(symmetry,[status(thm)],[44])).
% 0.21/0.44 tff(46,plain,
% 0.21/0.44 (^[X0: $i, X1: $i] : refl((domain(addition(X0, X1)) = addition(domain(X0), domain(X1))) <=> (domain(addition(X0, X1)) = addition(domain(X0), domain(X1))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(47,plain,
% 0.21/0.44 (![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1))) <=> ![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[46])).
% 0.21/0.44 tff(48,plain,
% 0.21/0.44 (![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1))) <=> ![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(49,axiom,(![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax','domain5')).
% 0.21/0.45 tff(50,plain,
% 0.21/0.45 (![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.21/0.45 tff(51,plain,(
% 0.21/0.45 ![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[50])).
% 0.21/0.45 tff(52,plain,
% 0.21/0.45 (![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.21/0.45 tff(53,plain,
% 0.21/0.45 ((~![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))) | (domain(addition(domain(star(X0!0)), one)) = addition(domain(domain(star(X0!0))), domain(one)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(54,plain,
% 0.21/0.45 (domain(addition(domain(star(X0!0)), one)) = addition(domain(domain(star(X0!0))), domain(one))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.21/0.45 tff(55,plain,
% 0.21/0.45 (addition(domain(domain(star(X0!0))), domain(one)) = domain(addition(domain(star(X0!0)), one))),
% 0.21/0.45 inference(symmetry,[status(thm)],[54])).
% 0.21/0.45 tff(56,plain,
% 0.21/0.45 (addition(domain(domain(star(X0!0))), domain(one)) = domain(one)),
% 0.21/0.45 inference(transitivity,[status(thm)],[55, 45])).
% 0.21/0.45 tff(57,plain,
% 0.21/0.45 (addition(addition(domain(domain(star(X0!0))), domain(one)), one) = addition(domain(one), one)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[56])).
% 0.21/0.45 tff(58,plain,
% 0.21/0.45 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(domain(domain(star(X0!0))), domain(one)), one) = addition(one, addition(domain(domain(star(X0!0))), domain(one))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(59,plain,
% 0.21/0.45 (addition(addition(domain(domain(star(X0!0))), domain(one)), one) = addition(one, addition(domain(domain(star(X0!0))), domain(one)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[58, 27])).
% 0.21/0.45 tff(60,plain,
% 0.21/0.45 (addition(one, addition(domain(domain(star(X0!0))), domain(one))) = addition(addition(domain(domain(star(X0!0))), domain(one)), one)),
% 0.21/0.45 inference(symmetry,[status(thm)],[59])).
% 0.21/0.45 tff(61,plain,
% 0.21/0.45 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(62,plain,
% 0.21/0.45 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.21/0.45 inference(quant_intro,[status(thm)],[61])).
% 0.21/0.45 tff(63,plain,
% 0.21/0.45 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(64,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','multiplicative_right_identity')).
% 0.21/0.45 tff(65,plain,
% 0.21/0.45 (![A: $i] : (multiplication(A, one) = A)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.21/0.45 tff(66,plain,(
% 0.21/0.45 ![A: $i] : (multiplication(A, one) = A)),
% 0.21/0.45 inference(skolemize,[status(sab)],[65])).
% 0.21/0.45 tff(67,plain,
% 0.21/0.45 (![A: $i] : (multiplication(A, one) = A)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.21/0.45 tff(68,plain,
% 0.21/0.45 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(addition(domain(domain(star(X0!0))), domain(one)), one) = addition(domain(domain(star(X0!0))), domain(one)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(69,plain,
% 0.21/0.45 (multiplication(addition(domain(domain(star(X0!0))), domain(one)), one) = addition(domain(domain(star(X0!0))), domain(one))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.21/0.45 tff(70,plain,
% 0.21/0.45 (multiplication(addition(domain(domain(star(X0!0))), domain(one)), one) = multiplication(domain(one), one)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[56])).
% 0.21/0.45 tff(71,plain,
% 0.21/0.45 (multiplication(domain(one), one) = multiplication(addition(domain(domain(star(X0!0))), domain(one)), one)),
% 0.21/0.45 inference(symmetry,[status(thm)],[70])).
% 0.21/0.45 tff(72,plain,
% 0.21/0.45 (multiplication(domain(one), one) = addition(domain(domain(star(X0!0))), domain(one))),
% 0.21/0.45 inference(transitivity,[status(thm)],[71, 69])).
% 0.21/0.45 tff(73,plain,
% 0.21/0.45 (addition(one, multiplication(domain(one), one)) = addition(one, addition(domain(domain(star(X0!0))), domain(one)))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[72])).
% 0.21/0.45 tff(74,plain,
% 0.21/0.45 ((~![X0: $i] : (addition(domain(X0), one) = one)) | (addition(domain(multiplication(star(X0!0), X0!0)), one) = one)),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(75,plain,
% 0.21/0.45 (addition(domain(multiplication(star(X0!0), X0!0)), one) = one),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[74, 7])).
% 0.21/0.45 tff(76,plain,
% 0.21/0.45 (addition(addition(domain(multiplication(star(X0!0), X0!0)), one), multiplication(domain(one), one)) = addition(one, multiplication(domain(one), one))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[75])).
% 0.21/0.45 tff(77,plain,
% 0.21/0.45 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(domain(multiplication(star(X0!0), X0!0)), addition(one, multiplication(domain(one), one))) = addition(addition(domain(multiplication(star(X0!0), X0!0)), one), multiplication(domain(one), one)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(78,plain,
% 0.21/0.45 (addition(domain(multiplication(star(X0!0), X0!0)), addition(one, multiplication(domain(one), one))) = addition(addition(domain(multiplication(star(X0!0), X0!0)), one), multiplication(domain(one), one))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[77, 17])).
% 0.21/0.45 tff(79,plain,
% 0.21/0.45 (^[X0: $i] : refl((addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(80,plain,
% 0.21/0.45 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[79])).
% 0.21/0.45 tff(81,plain,
% 0.21/0.45 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(82,axiom,(![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax','domain1')).
% 0.21/0.45 tff(83,plain,
% 0.21/0.45 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.21/0.45 tff(84,plain,(
% 0.21/0.45 ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.21/0.45 inference(skolemize,[status(sab)],[83])).
% 0.21/0.45 tff(85,plain,
% 0.21/0.45 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.21/0.45 tff(86,plain,
% 0.21/0.45 ((~![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))) | (addition(one, multiplication(domain(one), one)) = multiplication(domain(one), one))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(87,plain,
% 0.21/0.45 (addition(one, multiplication(domain(one), one)) = multiplication(domain(one), one)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.21/0.45 tff(88,plain,
% 0.21/0.45 (multiplication(domain(one), one) = addition(one, multiplication(domain(one), one))),
% 0.21/0.45 inference(symmetry,[status(thm)],[87])).
% 0.21/0.45 tff(89,plain,
% 0.21/0.45 (addition(domain(domain(star(X0!0))), domain(one)) = multiplication(addition(domain(domain(star(X0!0))), domain(one)), one)),
% 0.21/0.45 inference(symmetry,[status(thm)],[69])).
% 0.21/0.45 tff(90,plain,
% 0.21/0.45 (addition(domain(domain(star(X0!0))), domain(one)) = addition(one, multiplication(domain(one), one))),
% 0.21/0.45 inference(transitivity,[status(thm)],[89, 70, 88])).
% 0.21/0.45 tff(91,plain,
% 0.21/0.45 (addition(domain(multiplication(star(X0!0), X0!0)), addition(domain(domain(star(X0!0))), domain(one))) = addition(domain(multiplication(star(X0!0), X0!0)), addition(one, multiplication(domain(one), one)))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[90])).
% 0.21/0.45 tff(92,plain,
% 0.21/0.45 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(domain(domain(star(X0!0))), domain(one)), domain(multiplication(star(X0!0), X0!0))) = addition(domain(multiplication(star(X0!0), X0!0)), addition(domain(domain(star(X0!0))), domain(one))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(93,plain,
% 0.21/0.45 (addition(addition(domain(domain(star(X0!0))), domain(one)), domain(multiplication(star(X0!0), X0!0))) = addition(domain(multiplication(star(X0!0), X0!0)), addition(domain(domain(star(X0!0))), domain(one)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[92, 27])).
% 0.21/0.45 tff(94,plain,
% 0.21/0.45 (domain(one) = addition(domain(domain(star(X0!0))), domain(one))),
% 0.21/0.45 inference(transitivity,[status(thm)],[44, 54])).
% 0.21/0.45 tff(95,plain,
% 0.21/0.45 (addition(domain(one), domain(multiplication(star(X0!0), X0!0))) = addition(addition(domain(domain(star(X0!0))), domain(one)), domain(multiplication(star(X0!0), X0!0)))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[94])).
% 0.21/0.45 tff(96,plain,
% 0.21/0.45 ((~![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))) | (domain(addition(one, multiplication(star(X0!0), X0!0))) = addition(domain(one), domain(multiplication(star(X0!0), X0!0))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(97,plain,
% 0.21/0.45 (domain(addition(one, multiplication(star(X0!0), X0!0))) = addition(domain(one), domain(multiplication(star(X0!0), X0!0)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[96, 52])).
% 0.21/0.45 tff(98,plain,
% 0.21/0.45 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, multiplication(star(X0!0), X0!0)) = addition(multiplication(star(X0!0), X0!0), one))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(99,plain,
% 0.21/0.45 (addition(one, multiplication(star(X0!0), X0!0)) = addition(multiplication(star(X0!0), X0!0), one)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[98, 27])).
% 0.21/0.45 tff(100,plain,
% 0.21/0.45 (addition(multiplication(star(X0!0), X0!0), one) = addition(one, multiplication(star(X0!0), X0!0))),
% 0.21/0.45 inference(symmetry,[status(thm)],[99])).
% 0.21/0.45 tff(101,plain,
% 0.21/0.45 (domain(addition(multiplication(star(X0!0), X0!0), one)) = domain(addition(one, multiplication(star(X0!0), X0!0)))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[100])).
% 0.21/0.45 tff(102,plain,
% 0.21/0.45 (domain(addition(multiplication(star(X0!0), X0!0), one)) = one),
% 0.21/0.45 inference(transitivity,[status(thm)],[101, 97, 95, 93, 91, 78, 76, 73, 60, 57, 42])).
% 0.21/0.45 tff(103,plain,
% 0.21/0.45 (addition(domain(addition(multiplication(star(X0!0), X0!0), one)), domain(star(X0!0))) = addition(one, addition(domain(star(X0!0)), domain(star(X0!0))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[102, 40])).
% 0.21/0.45 tff(104,plain,
% 0.21/0.45 ((~![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))) | (domain(addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))) = addition(domain(addition(multiplication(star(X0!0), X0!0), one)), domain(star(X0!0))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(105,plain,
% 0.21/0.45 (domain(addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))) = addition(domain(addition(multiplication(star(X0!0), X0!0), one)), domain(star(X0!0)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[104, 52])).
% 0.21/0.45 tff(106,plain,
% 0.21/0.45 (addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)) = addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[100])).
% 0.21/0.45 tff(107,plain,
% 0.21/0.45 (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))),
% 0.21/0.45 inference(symmetry,[status(thm)],[106])).
% 0.21/0.45 tff(108,plain,
% 0.21/0.45 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(109,plain,
% 0.21/0.45 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[108])).
% 0.21/0.45 tff(110,plain,
% 0.21/0.45 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(111,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','order')).
% 0.21/0.45 tff(112,plain,
% 0.21/0.45 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.21/0.45 tff(113,plain,(
% 0.21/0.45 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.21/0.45 inference(skolemize,[status(sab)],[112])).
% 0.21/0.45 tff(114,plain,
% 0.21/0.45 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.21/0.45 tff(115,plain,
% 0.21/0.45 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) <=> (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = star(X0!0)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(116,plain,
% 0.21/0.45 (leq(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) <=> (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = star(X0!0))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.21/0.45 tff(117,plain,
% 0.21/0.45 (^[A: $i] : refl(leq(addition(one, multiplication(star(A), A)), star(A)) <=> leq(addition(one, multiplication(star(A), A)), star(A)))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(118,plain,
% 0.21/0.45 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[117])).
% 0.21/0.45 tff(119,plain,
% 0.21/0.45 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(120,axiom,(![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','star_unfold_left')).
% 0.21/0.45 tff(121,plain,
% 0.21/0.45 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.21/0.45 tff(122,plain,(
% 0.21/0.45 ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 0.21/0.45 inference(skolemize,[status(sab)],[121])).
% 0.21/0.45 tff(123,plain,
% 0.21/0.45 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.21/0.45 tff(124,plain,
% 0.21/0.45 ((~![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))) | leq(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(125,plain,
% 0.21/0.45 (leq(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.21/0.45 tff(126,plain,
% 0.21/0.45 ((~(leq(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) <=> (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = star(X0!0)))) | (~leq(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))) | (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = star(X0!0))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(127,plain,
% 0.21/0.45 ((~(leq(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) <=> (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = star(X0!0)))) | (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = star(X0!0))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.21/0.45 tff(128,plain,
% 0.21/0.45 (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = star(X0!0)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[127, 116])).
% 0.21/0.45 tff(129,plain,
% 0.21/0.45 (star(X0!0) = addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 0.21/0.45 inference(symmetry,[status(thm)],[128])).
% 0.21/0.45 tff(130,plain,
% 0.21/0.45 (star(X0!0) = addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))),
% 0.21/0.45 inference(transitivity,[status(thm)],[129, 107])).
% 0.21/0.45 tff(131,plain,
% 0.21/0.45 (domain(star(X0!0)) = domain(addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[130])).
% 0.21/0.45 tff(132,plain,
% 0.21/0.45 (domain(star(X0!0)) = one),
% 0.21/0.45 inference(transitivity,[status(thm)],[131, 105, 103, 30, 20, 10, 9])).
% 0.21/0.45 tff(133,plain,
% 0.21/0.45 ((~![X0: $i] : (domain(star(X0)) = one)) <=> (~![X0: $i] : (domain(star(X0)) = one))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(134,axiom,(~![X0: $i] : (domain(star(X0)) = one)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.21/0.46 tff(135,plain,
% 0.21/0.46 (~![X0: $i] : (domain(star(X0)) = one)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.21/0.46 tff(136,plain,
% 0.21/0.46 (~![X0: $i] : (domain(star(X0)) = one)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[135, 133])).
% 0.21/0.46 tff(137,plain,
% 0.21/0.46 (~![X0: $i] : (domain(star(X0)) = one)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[136, 133])).
% 0.21/0.46 tff(138,plain,
% 0.21/0.46 (~![X0: $i] : (domain(star(X0)) = one)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.21/0.46 tff(139,plain,(
% 0.21/0.46 ~(domain(star(X0!0)) = one)),
% 0.21/0.46 inference(skolemize,[status(sab)],[138])).
% 0.21/0.46 tff(140,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[139, 132])).
% 0.21/0.46 % SZS output end Proof
% 0.21/0.46 % E exiting
%------------------------------------------------------------------------------