%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE040+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:12:55 AM UTC 2025
% Result : Theorem 0.92s 1.09s
% Output : Proof 0.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE040+2 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n001.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 18:59:49 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.92/1.09 % SZS status Theorem
% 0.92/1.09 % SZS output start Proof
% 0.92/1.09 tff(star_type, type, (
% 0.92/1.09 star: $i > $i)).
% 0.92/1.09 tff(tptp_fun_X0_0_type, type, (
% 0.92/1.09 tptp_fun_X0_0: $i)).
% 0.92/1.09 tff(addition_type, type, (
% 0.92/1.09 addition: ( $i * $i ) > $i)).
% 0.92/1.09 tff(multiplication_type, type, (
% 0.92/1.09 multiplication: ( $i * $i ) > $i)).
% 0.92/1.09 tff(one_type, type, (
% 0.92/1.09 one: $i)).
% 0.92/1.09 tff(leq_type, type, (
% 0.92/1.09 leq: ( $i * $i ) > $o)).
% 0.92/1.09 tff(1,plain,
% 0.92/1.09 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 0.92/1.09 inference(bind,[status(th)],[])).
% 0.92/1.09 tff(2,plain,
% 0.92/1.09 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.92/1.09 inference(quant_intro,[status(thm)],[1])).
% 0.92/1.09 tff(3,plain,
% 0.92/1.09 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(4,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','order')).
% 0.92/1.09 tff(5,plain,
% 0.92/1.09 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.92/1.09 tff(6,plain,(
% 0.92/1.09 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.92/1.09 inference(skolemize,[status(sab)],[5])).
% 0.92/1.09 tff(7,plain,
% 0.92/1.09 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.92/1.09 tff(8,plain,
% 0.92/1.09 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) <=> (addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) = star(X0!0)))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(9,plain,
% 0.92/1.09 (leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) <=> (addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) = star(X0!0))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.92/1.09 tff(10,plain,
% 0.92/1.09 (^[A: $i] : refl(leq(addition(one, multiplication(A, star(A))), star(A)) <=> leq(addition(one, multiplication(A, star(A))), star(A)))),
% 0.92/1.09 inference(bind,[status(th)],[])).
% 0.92/1.09 tff(11,plain,
% 0.92/1.09 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 0.92/1.09 inference(quant_intro,[status(thm)],[10])).
% 0.92/1.09 tff(12,plain,
% 0.92/1.09 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(13,axiom,(![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','star_unfold_right')).
% 0.92/1.09 tff(14,plain,
% 0.92/1.09 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.92/1.09 tff(15,plain,(
% 0.92/1.09 ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 0.92/1.09 inference(skolemize,[status(sab)],[14])).
% 0.92/1.09 tff(16,plain,
% 0.92/1.09 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.92/1.09 tff(17,plain,
% 0.92/1.09 ((~![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))) | leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(18,plain,
% 0.92/1.09 (leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.92/1.09 tff(19,plain,
% 0.92/1.09 ((~(leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) <=> (addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) = star(X0!0)))) | (~leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))) | (addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) = star(X0!0))),
% 0.92/1.09 inference(tautology,[status(thm)],[])).
% 0.92/1.09 tff(20,plain,
% 0.92/1.09 ((~(leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) <=> (addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) = star(X0!0)))) | (addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) = star(X0!0))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.92/1.09 tff(21,plain,
% 0.92/1.09 (addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) = star(X0!0)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[20, 9])).
% 0.92/1.09 tff(22,plain,
% 0.92/1.09 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.92/1.09 inference(bind,[status(th)],[])).
% 0.92/1.09 tff(23,plain,
% 0.92/1.09 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.92/1.09 inference(quant_intro,[status(thm)],[22])).
% 0.92/1.09 tff(24,plain,
% 0.92/1.09 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(25,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','additive_commutativity')).
% 0.92/1.09 tff(26,plain,
% 0.92/1.09 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.92/1.09 tff(27,plain,(
% 0.92/1.09 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.92/1.09 inference(skolemize,[status(sab)],[26])).
% 0.92/1.09 tff(28,plain,
% 0.92/1.09 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.92/1.09 tff(29,plain,
% 0.92/1.09 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, multiplication(X0!0, star(X0!0))) = addition(multiplication(X0!0, star(X0!0)), one))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(30,plain,
% 0.92/1.09 (addition(one, multiplication(X0!0, star(X0!0))) = addition(multiplication(X0!0, star(X0!0)), one)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.92/1.09 tff(31,plain,
% 0.92/1.09 (addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) = addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[30])).
% 0.92/1.09 tff(32,plain,
% 0.92/1.09 (addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)) = addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))),
% 0.92/1.09 inference(symmetry,[status(thm)],[31])).
% 0.92/1.09 tff(33,plain,
% 0.92/1.09 (^[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)))),
% 0.92/1.09 inference(bind,[status(th)],[])).
% 0.92/1.09 tff(34,plain,
% 0.92/1.09 (![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))),
% 0.92/1.09 inference(quant_intro,[status(thm)],[33])).
% 0.92/1.09 tff(35,plain,
% 0.92/1.09 (![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))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(36,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')).
% 0.92/1.09 tff(37,plain,
% 0.92/1.09 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.92/1.09 tff(38,plain,(
% 0.92/1.09 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.92/1.09 inference(skolemize,[status(sab)],[37])).
% 0.92/1.09 tff(39,plain,
% 0.92/1.09 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.92/1.09 tff(40,plain,
% 0.92/1.09 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0))) = addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(41,plain,
% 0.92/1.09 (addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0))) = addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.92/1.09 tff(42,plain,
% 0.92/1.09 ((~![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))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(43,plain,
% 0.92/1.09 (addition(one, multiplication(star(X0!0), X0!0)) = addition(multiplication(star(X0!0), X0!0), one)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[42, 28])).
% 0.92/1.09 tff(44,plain,
% 0.92/1.09 (addition(multiplication(star(X0!0), X0!0), one) = addition(one, multiplication(star(X0!0), X0!0))),
% 0.92/1.09 inference(symmetry,[status(thm)],[43])).
% 0.92/1.09 tff(45,plain,
% 0.92/1.09 (addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)) = addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[44])).
% 0.92/1.09 tff(46,plain,
% 0.92/1.09 (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))),
% 0.92/1.09 inference(symmetry,[status(thm)],[45])).
% 0.92/1.09 tff(47,plain,
% 0.92/1.09 ((~![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)))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(48,plain,
% 0.92/1.09 (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))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[47, 7])).
% 0.92/1.09 tff(49,plain,
% 0.92/1.09 (^[A: $i] : refl(leq(addition(one, multiplication(star(A), A)), star(A)) <=> leq(addition(one, multiplication(star(A), A)), star(A)))),
% 0.92/1.09 inference(bind,[status(th)],[])).
% 0.92/1.09 tff(50,plain,
% 0.92/1.09 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 0.92/1.09 inference(quant_intro,[status(thm)],[49])).
% 0.92/1.09 tff(51,plain,
% 0.92/1.09 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(52,axiom,(![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','star_unfold_left')).
% 0.92/1.09 tff(53,plain,
% 0.92/1.09 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.92/1.09 tff(54,plain,(
% 0.92/1.09 ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 0.92/1.09 inference(skolemize,[status(sab)],[53])).
% 0.92/1.09 tff(55,plain,
% 0.92/1.09 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.92/1.09 tff(56,plain,
% 0.92/1.09 ((~![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))) | leq(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(57,plain,
% 0.92/1.09 (leq(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.92/1.09 tff(58,plain,
% 0.92/1.09 ((~(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))),
% 0.92/1.09 inference(tautology,[status(thm)],[])).
% 0.92/1.09 tff(59,plain,
% 0.92/1.09 ((~(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))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.92/1.09 tff(60,plain,
% 0.92/1.09 (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = star(X0!0)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[59, 48])).
% 0.92/1.09 tff(61,plain,
% 0.92/1.09 (star(X0!0) = addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 0.92/1.09 inference(symmetry,[status(thm)],[60])).
% 0.92/1.09 tff(62,plain,
% 0.92/1.09 (star(X0!0) = addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))),
% 0.92/1.09 inference(transitivity,[status(thm)],[61, 46])).
% 0.92/1.09 tff(63,plain,
% 0.92/1.09 (multiplication(X0!0, star(X0!0)) = multiplication(X0!0, addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[62])).
% 0.92/1.09 tff(64,plain,
% 0.92/1.09 (multiplication(X0!0, addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))) = multiplication(X0!0, star(X0!0))),
% 0.92/1.09 inference(symmetry,[status(thm)],[63])).
% 0.92/1.09 tff(65,plain,
% 0.92/1.09 (^[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))))),
% 0.92/1.09 inference(bind,[status(th)],[])).
% 0.92/1.09 tff(66,plain,
% 0.92/1.09 (![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)))),
% 0.92/1.09 inference(quant_intro,[status(thm)],[65])).
% 0.92/1.09 tff(67,plain,
% 0.92/1.09 (![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)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(68,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','right_distributivity')).
% 0.92/1.09 tff(69,plain,
% 0.92/1.09 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.92/1.09 tff(70,plain,(
% 0.92/1.09 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.92/1.09 inference(skolemize,[status(sab)],[69])).
% 0.92/1.09 tff(71,plain,
% 0.92/1.09 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.92/1.09 tff(72,plain,
% 0.92/1.09 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!0, addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))) = addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(73,plain,
% 0.92/1.09 (multiplication(X0!0, addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))) = addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.92/1.09 tff(74,plain,
% 0.92/1.09 (addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))) = multiplication(X0!0, addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)))),
% 0.92/1.09 inference(symmetry,[status(thm)],[73])).
% 0.92/1.09 tff(75,plain,
% 0.92/1.09 (addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))) = multiplication(X0!0, star(X0!0))),
% 0.92/1.09 inference(transitivity,[status(thm)],[74, 64])).
% 0.92/1.09 tff(76,plain,
% 0.92/1.09 (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))) = addition(multiplication(X0!0, star(X0!0)), multiplication(X0!0, star(X0!0)))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[75, 75])).
% 0.92/1.09 tff(77,plain,
% 0.92/1.09 (addition(multiplication(X0!0, star(X0!0)), multiplication(X0!0, star(X0!0))) = addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))),
% 0.92/1.09 inference(symmetry,[status(thm)],[76])).
% 0.92/1.09 tff(78,plain,
% 0.92/1.09 ((~![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), star(X0!0))) = addition(multiplication(X0!0, star(X0!0)), multiplication(X0!0, star(X0!0))))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(79,plain,
% 0.92/1.09 (multiplication(X0!0, addition(star(X0!0), star(X0!0))) = addition(multiplication(X0!0, star(X0!0)), multiplication(X0!0, star(X0!0)))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[78, 71])).
% 0.92/1.09 tff(80,plain,
% 0.92/1.09 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 0.92/1.09 inference(bind,[status(th)],[])).
% 0.92/1.09 tff(81,plain,
% 0.92/1.09 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.92/1.09 inference(quant_intro,[status(thm)],[80])).
% 0.92/1.09 tff(82,plain,
% 0.92/1.09 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(83,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','additive_idempotence')).
% 0.92/1.09 tff(84,plain,
% 0.92/1.09 (![A: $i] : (addition(A, A) = A)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.92/1.09 tff(85,plain,(
% 0.92/1.09 ![A: $i] : (addition(A, A) = A)),
% 0.92/1.09 inference(skolemize,[status(sab)],[84])).
% 0.92/1.09 tff(86,plain,
% 0.92/1.09 (![A: $i] : (addition(A, A) = A)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.92/1.09 tff(87,plain,
% 0.92/1.09 ((~![A: $i] : (addition(A, A) = A)) | (addition(star(X0!0), star(X0!0)) = star(X0!0))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(88,plain,
% 0.92/1.09 (addition(star(X0!0), star(X0!0)) = star(X0!0)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.92/1.09 tff(89,plain,
% 0.92/1.09 (multiplication(X0!0, addition(star(X0!0), star(X0!0))) = multiplication(X0!0, star(X0!0))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[88])).
% 0.92/1.09 tff(90,plain,
% 0.92/1.09 (multiplication(X0!0, star(X0!0)) = multiplication(X0!0, addition(star(X0!0), star(X0!0)))),
% 0.92/1.09 inference(symmetry,[status(thm)],[89])).
% 0.92/1.09 tff(91,plain,
% 0.92/1.09 (multiplication(X0!0, star(X0!0)) = addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))),
% 0.92/1.09 inference(transitivity,[status(thm)],[90, 79, 77])).
% 0.92/1.09 tff(92,plain,
% 0.92/1.09 (addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0))) = addition(addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), addition(one, star(X0!0)))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[91])).
% 0.92/1.09 tff(93,plain,
% 0.92/1.09 (addition(addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), addition(one, star(X0!0))) = addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0)))),
% 0.92/1.09 inference(symmetry,[status(thm)],[92])).
% 0.92/1.09 tff(94,plain,
% 0.92/1.09 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0)))) = addition(addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), addition(one, star(X0!0))))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(95,plain,
% 0.92/1.09 (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0)))) = addition(addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), addition(one, star(X0!0)))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[94, 39])).
% 0.92/1.09 tff(96,plain,
% 0.92/1.09 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0))) = addition(addition(one, star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(97,plain,
% 0.92/1.09 (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0))) = addition(addition(one, star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[96, 28])).
% 0.92/1.09 tff(98,plain,
% 0.92/1.09 (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0)))) = addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(addition(one, star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[97])).
% 0.92/1.09 tff(99,plain,
% 0.92/1.09 (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(addition(one, star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))) = addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0))))),
% 0.92/1.09 inference(symmetry,[status(thm)],[98])).
% 0.92/1.09 tff(100,plain,
% 0.92/1.09 (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0))) = addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0)))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[75])).
% 0.92/1.09 tff(101,plain,
% 0.92/1.09 (addition(addition(one, star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))) = addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0)))),
% 0.92/1.09 inference(symmetry,[status(thm)],[97])).
% 0.92/1.09 tff(102,plain,
% 0.92/1.09 (addition(addition(one, star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))) = star(X0!0)),
% 0.92/1.09 inference(transitivity,[status(thm)],[101, 100, 41, 32, 21])).
% 0.92/1.09 tff(103,plain,
% 0.92/1.09 (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(addition(one, star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))) = addition(multiplication(X0!0, star(X0!0)), star(X0!0))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[75, 102])).
% 0.92/1.09 tff(104,plain,
% 0.92/1.09 (addition(multiplication(X0!0, star(X0!0)), star(X0!0)) = addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(addition(one, star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))))),
% 0.92/1.09 inference(symmetry,[status(thm)],[103])).
% 0.92/1.09 tff(105,plain,
% 0.92/1.09 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), addition(one, star(X0!0))) = addition(addition(one, star(X0!0)), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(106,plain,
% 0.92/1.09 (addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), addition(one, star(X0!0))) = addition(addition(one, star(X0!0)), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[105, 28])).
% 0.92/1.09 tff(107,plain,
% 0.92/1.09 (multiplication(star(X0!0), X0!0) = multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)), X0!0)),
% 0.92/1.09 inference(monotonicity,[status(thm)],[62])).
% 0.92/1.09 tff(108,plain,
% 0.92/1.09 (multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)), X0!0) = multiplication(star(X0!0), X0!0)),
% 0.92/1.09 inference(symmetry,[status(thm)],[107])).
% 0.92/1.09 tff(109,plain,
% 0.92/1.09 (^[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))))),
% 0.92/1.09 inference(bind,[status(th)],[])).
% 0.92/1.09 tff(110,plain,
% 0.92/1.09 (![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)))),
% 0.92/1.09 inference(quant_intro,[status(thm)],[109])).
% 0.92/1.09 tff(111,plain,
% 0.92/1.09 (![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)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(112,axiom,(![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','left_distributivity')).
% 0.92/1.09 tff(113,plain,
% 0.92/1.09 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.92/1.09 tff(114,plain,(
% 0.92/1.09 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.92/1.09 inference(skolemize,[status(sab)],[113])).
% 0.92/1.09 tff(115,plain,
% 0.92/1.09 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.92/1.09 tff(116,plain,
% 0.92/1.09 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)), X0!0) = addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(117,plain,
% 0.92/1.09 (multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)), X0!0) = addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.92/1.09 tff(118,plain,
% 0.92/1.09 (addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)) = multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)), X0!0)),
% 0.92/1.09 inference(symmetry,[status(thm)],[117])).
% 0.92/1.09 tff(119,plain,
% 0.92/1.09 (addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)) = multiplication(star(X0!0), X0!0)),
% 0.92/1.09 inference(transitivity,[status(thm)],[118, 108])).
% 0.92/1.09 tff(120,plain,
% 0.92/1.09 (addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), addition(one, star(X0!0))) = addition(multiplication(star(X0!0), X0!0), addition(one, star(X0!0)))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[119])).
% 0.92/1.10 tff(121,plain,
% 0.92/1.10 (addition(multiplication(star(X0!0), X0!0), addition(one, star(X0!0))) = addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), addition(one, star(X0!0)))),
% 0.92/1.10 inference(symmetry,[status(thm)],[120])).
% 0.92/1.10 tff(122,plain,
% 0.92/1.10 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(star(X0!0), X0!0), addition(one, star(X0!0))) = addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(123,plain,
% 0.92/1.10 (addition(multiplication(star(X0!0), X0!0), addition(one, star(X0!0))) = addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[122, 39])).
% 0.92/1.10 tff(124,plain,
% 0.92/1.10 (addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)) = addition(multiplication(star(X0!0), X0!0), addition(one, star(X0!0)))),
% 0.92/1.10 inference(symmetry,[status(thm)],[123])).
% 0.92/1.10 tff(125,plain,
% 0.92/1.10 (star(X0!0) = addition(addition(one, star(X0!0)), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)))),
% 0.92/1.10 inference(transitivity,[status(thm)],[61, 46, 124, 121, 106])).
% 0.92/1.10 tff(126,plain,
% 0.92/1.10 (multiplication(X0!0, star(X0!0)) = addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))),
% 0.92/1.10 inference(transitivity,[status(thm)],[63, 73])).
% 0.92/1.10 tff(127,plain,
% 0.92/1.10 (addition(multiplication(X0!0, star(X0!0)), star(X0!0)) = addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(addition(one, star(X0!0)), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[126, 125])).
% 0.92/1.10 tff(128,plain,
% 0.92/1.10 (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(addition(one, star(X0!0)), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)))) = addition(multiplication(X0!0, star(X0!0)), star(X0!0))),
% 0.92/1.10 inference(symmetry,[status(thm)],[127])).
% 0.92/1.10 tff(129,plain,
% 0.92/1.10 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(addition(one, star(X0!0)), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)))) = addition(addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0))), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(130,plain,
% 0.92/1.10 (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(addition(one, star(X0!0)), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)))) = addition(addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0))), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[129, 39])).
% 0.92/1.10 tff(131,plain,
% 0.92/1.10 (addition(addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0))), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))) = addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(addition(one, star(X0!0)), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))))),
% 0.92/1.10 inference(symmetry,[status(thm)],[130])).
% 0.92/1.10 tff(132,plain,
% 0.92/1.10 (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0))) = star(X0!0)),
% 0.92/1.10 inference(transitivity,[status(thm)],[100, 41, 32, 21])).
% 0.92/1.10 tff(133,plain,
% 0.92/1.10 (addition(addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0))), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))) = addition(star(X0!0), multiplication(star(X0!0), X0!0))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[132, 119])).
% 0.92/1.10 tff(134,plain,
% 0.92/1.10 (addition(star(X0!0), multiplication(star(X0!0), X0!0)) = addition(addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0))), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)))),
% 0.92/1.10 inference(symmetry,[status(thm)],[133])).
% 0.92/1.10 tff(135,plain,
% 0.92/1.10 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(star(X0!0), X0!0), star(X0!0)) = addition(star(X0!0), multiplication(star(X0!0), X0!0)))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(136,plain,
% 0.92/1.10 (addition(multiplication(star(X0!0), X0!0), star(X0!0)) = addition(star(X0!0), multiplication(star(X0!0), X0!0))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[135, 28])).
% 0.92/1.10 tff(137,plain,
% 0.92/1.10 (star(X0!0) = addition(star(X0!0), star(X0!0))),
% 0.92/1.10 inference(symmetry,[status(thm)],[88])).
% 0.92/1.10 tff(138,plain,
% 0.92/1.10 (addition(multiplication(star(X0!0), X0!0), star(X0!0)) = addition(multiplication(star(X0!0), X0!0), addition(star(X0!0), star(X0!0)))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[137])).
% 0.92/1.10 tff(139,plain,
% 0.92/1.10 (addition(multiplication(star(X0!0), X0!0), addition(star(X0!0), star(X0!0))) = addition(multiplication(star(X0!0), X0!0), star(X0!0))),
% 0.92/1.10 inference(symmetry,[status(thm)],[138])).
% 0.92/1.10 tff(140,plain,
% 0.92/1.10 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(star(X0!0), X0!0), addition(star(X0!0), star(X0!0))) = addition(addition(multiplication(star(X0!0), X0!0), star(X0!0)), star(X0!0)))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(141,plain,
% 0.92/1.10 (addition(multiplication(star(X0!0), X0!0), addition(star(X0!0), star(X0!0))) = addition(addition(multiplication(star(X0!0), X0!0), star(X0!0)), star(X0!0))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[140, 39])).
% 0.92/1.10 tff(142,plain,
% 0.92/1.10 (addition(addition(multiplication(star(X0!0), X0!0), star(X0!0)), star(X0!0)) = addition(multiplication(star(X0!0), X0!0), addition(star(X0!0), star(X0!0)))),
% 0.92/1.10 inference(symmetry,[status(thm)],[141])).
% 0.92/1.10 tff(143,plain,
% 0.92/1.10 (addition(addition(multiplication(star(X0!0), X0!0), star(X0!0)), star(X0!0)) = star(X0!0)),
% 0.92/1.10 inference(transitivity,[status(thm)],[142, 139, 136, 134, 131, 128, 104, 99, 95, 93, 41, 32, 21])).
% 0.92/1.10 tff(144,plain,
% 0.92/1.10 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(multiplication(star(X0!0), X0!0), star(X0!0)), star(X0!0)) <=> (addition(addition(multiplication(star(X0!0), X0!0), star(X0!0)), star(X0!0)) = star(X0!0)))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(145,plain,
% 0.92/1.10 (leq(addition(multiplication(star(X0!0), X0!0), star(X0!0)), star(X0!0)) <=> (addition(addition(multiplication(star(X0!0), X0!0), star(X0!0)), star(X0!0)) = star(X0!0))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[144, 7])).
% 0.92/1.10 tff(146,plain,
% 0.92/1.10 ((~![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), star(X0!0))) = addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(147,plain,
% 0.92/1.10 (addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0))) = addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[146, 39])).
% 0.92/1.10 tff(148,plain,
% 0.92/1.10 (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0)))),
% 0.92/1.10 inference(symmetry,[status(thm)],[147])).
% 0.92/1.10 tff(149,plain,
% 0.92/1.10 (star(X0!0) = addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0)))),
% 0.92/1.10 inference(transitivity,[status(thm)],[61, 148])).
% 0.92/1.10 tff(150,plain,
% 0.92/1.10 (addition(one, star(X0!0)) = addition(one, addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0))))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[149])).
% 0.92/1.10 tff(151,plain,
% 0.92/1.10 (addition(one, addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0)))) = addition(one, star(X0!0))),
% 0.92/1.10 inference(symmetry,[status(thm)],[150])).
% 0.92/1.10 tff(152,plain,
% 0.92/1.10 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0)))) = addition(addition(one, one), addition(multiplication(star(X0!0), X0!0), star(X0!0))))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(153,plain,
% 0.92/1.10 (addition(one, addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0)))) = addition(addition(one, one), addition(multiplication(star(X0!0), X0!0), star(X0!0)))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[152, 39])).
% 0.92/1.10 tff(154,plain,
% 0.92/1.10 (addition(addition(one, one), addition(multiplication(star(X0!0), X0!0), star(X0!0))) = addition(one, addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0))))),
% 0.92/1.10 inference(symmetry,[status(thm)],[153])).
% 0.92/1.10 tff(155,plain,
% 0.92/1.10 ((~![A: $i] : (addition(A, A) = A)) | (addition(one, one) = one)),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(156,plain,
% 0.92/1.10 (addition(one, one) = one),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[155, 86])).
% 0.92/1.10 tff(157,plain,
% 0.92/1.10 (addition(addition(one, one), addition(multiplication(star(X0!0), X0!0), star(X0!0))) = addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0)))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[156])).
% 0.92/1.10 tff(158,plain,
% 0.92/1.10 (addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0))) = addition(addition(one, one), addition(multiplication(star(X0!0), X0!0), star(X0!0)))),
% 0.92/1.10 inference(symmetry,[status(thm)],[157])).
% 0.92/1.10 tff(159,plain,
% 0.92/1.10 (star(X0!0) = addition(one, star(X0!0))),
% 0.92/1.10 inference(transitivity,[status(thm)],[61, 148, 158, 154, 151])).
% 0.92/1.10 tff(160,plain,
% 0.92/1.10 (multiplication(star(X0!0), star(X0!0)) = multiplication(star(X0!0), addition(one, star(X0!0)))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[159])).
% 0.92/1.10 tff(161,plain,
% 0.92/1.10 (multiplication(star(X0!0), addition(one, star(X0!0))) = multiplication(star(X0!0), star(X0!0))),
% 0.92/1.10 inference(symmetry,[status(thm)],[160])).
% 0.92/1.10 tff(162,plain,
% 0.92/1.10 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, star(X0!0)) = addition(star(X0!0), one))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(163,plain,
% 0.92/1.10 (addition(one, star(X0!0)) = addition(star(X0!0), one)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[162, 28])).
% 0.92/1.10 tff(164,plain,
% 0.92/1.10 (multiplication(star(X0!0), addition(one, star(X0!0))) = multiplication(star(X0!0), addition(star(X0!0), one))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[163])).
% 0.92/1.10 tff(165,plain,
% 0.92/1.10 (multiplication(star(X0!0), addition(star(X0!0), one)) = multiplication(star(X0!0), addition(one, star(X0!0)))),
% 0.92/1.10 inference(symmetry,[status(thm)],[164])).
% 0.92/1.10 tff(166,plain,
% 0.92/1.10 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(star(X0!0), addition(star(X0!0), one)) = addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), one)))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(167,plain,
% 0.92/1.10 (multiplication(star(X0!0), addition(star(X0!0), one)) = addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), one))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[166, 71])).
% 0.92/1.10 tff(168,plain,
% 0.92/1.10 (addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), one)) = multiplication(star(X0!0), addition(star(X0!0), one))),
% 0.92/1.10 inference(symmetry,[status(thm)],[167])).
% 0.92/1.10 tff(169,plain,
% 0.92/1.10 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(star(X0!0), addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))) = addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), X0!0), one)), multiplication(star(X0!0), star(X0!0))))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(170,plain,
% 0.92/1.10 (multiplication(star(X0!0), addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))) = addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), X0!0), one)), multiplication(star(X0!0), star(X0!0)))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[169, 71])).
% 0.92/1.10 tff(171,plain,
% 0.92/1.10 (addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)) = star(X0!0)),
% 0.92/1.10 inference(transitivity,[status(thm)],[45, 60])).
% 0.92/1.10 tff(172,plain,
% 0.92/1.10 (multiplication(star(X0!0), addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))) = multiplication(star(X0!0), star(X0!0))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[171])).
% 0.92/1.10 tff(173,plain,
% 0.92/1.10 (multiplication(star(X0!0), star(X0!0)) = multiplication(star(X0!0), addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)))),
% 0.92/1.10 inference(symmetry,[status(thm)],[172])).
% 0.92/1.10 tff(174,plain,
% 0.92/1.10 (multiplication(star(X0!0), star(X0!0)) = addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), X0!0), one)), multiplication(star(X0!0), star(X0!0)))),
% 0.92/1.10 inference(transitivity,[status(thm)],[173, 170])).
% 0.92/1.10 tff(175,plain,
% 0.92/1.10 (addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), one)) = addition(addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), X0!0), one)), multiplication(star(X0!0), star(X0!0))), multiplication(star(X0!0), one))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[174])).
% 0.92/1.10 tff(176,plain,
% 0.92/1.10 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), X0!0), one)), multiplication(star(X0!0), star(X0!0))), multiplication(star(X0!0), one)) = addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), one))),
% 0.92/1.10 inference(symmetry,[status(thm)],[175])).
% 0.92/1.10 tff(177,plain,
% 0.92/1.10 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(178,plain,
% 0.92/1.10 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.92/1.10 inference(quant_intro,[status(thm)],[177])).
% 0.92/1.10 tff(179,plain,
% 0.92/1.10 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(180,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','multiplicative_right_identity')).
% 0.92/1.10 tff(181,plain,
% 0.92/1.10 (![A: $i] : (multiplication(A, one) = A)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.92/1.10 tff(182,plain,(
% 0.92/1.10 ![A: $i] : (multiplication(A, one) = A)),
% 0.92/1.10 inference(skolemize,[status(sab)],[181])).
% 0.92/1.10 tff(183,plain,
% 0.92/1.10 (![A: $i] : (multiplication(A, one) = A)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[182, 178])).
% 0.92/1.10 tff(184,plain,
% 0.92/1.10 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(star(X0!0), one) = star(X0!0))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(185,plain,
% 0.92/1.10 (multiplication(star(X0!0), one) = star(X0!0)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.92/1.10 tff(186,plain,
% 0.92/1.10 (addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), X0!0), one)), multiplication(star(X0!0), star(X0!0))) = multiplication(star(X0!0), addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)))),
% 0.92/1.10 inference(symmetry,[status(thm)],[170])).
% 0.92/1.10 tff(187,plain,
% 0.92/1.10 (addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), X0!0), one)), multiplication(star(X0!0), star(X0!0))) = multiplication(star(X0!0), star(X0!0))),
% 0.92/1.10 inference(transitivity,[status(thm)],[186, 172])).
% 0.92/1.10 tff(188,plain,
% 0.92/1.10 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), X0!0), one)), multiplication(star(X0!0), star(X0!0))), multiplication(star(X0!0), one)) = addition(multiplication(star(X0!0), star(X0!0)), star(X0!0))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[187, 185])).
% 0.92/1.10 tff(189,plain,
% 0.92/1.10 (addition(multiplication(star(X0!0), star(X0!0)), star(X0!0)) = addition(addition(multiplication(star(X0!0), addition(multiplication(star(X0!0), X0!0), one)), multiplication(star(X0!0), star(X0!0))), multiplication(star(X0!0), one))),
% 0.92/1.10 inference(symmetry,[status(thm)],[188])).
% 0.92/1.10 tff(190,plain,
% 0.92/1.10 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(star(X0!0), multiplication(star(X0!0), star(X0!0))) = addition(multiplication(star(X0!0), star(X0!0)), star(X0!0)))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(191,plain,
% 0.92/1.10 (addition(star(X0!0), multiplication(star(X0!0), star(X0!0))) = addition(multiplication(star(X0!0), star(X0!0)), star(X0!0))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[190, 28])).
% 0.92/1.10 tff(192,plain,
% 0.92/1.10 (addition(star(X0!0), multiplication(star(X0!0), star(X0!0))) = multiplication(star(X0!0), star(X0!0))),
% 0.92/1.10 inference(transitivity,[status(thm)],[191, 189, 176, 168, 165, 161])).
% 0.92/1.10 tff(193,plain,
% 0.92/1.10 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(star(X0!0), multiplication(star(X0!0), star(X0!0))) <=> (addition(star(X0!0), multiplication(star(X0!0), star(X0!0))) = multiplication(star(X0!0), star(X0!0))))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(194,plain,
% 0.92/1.10 (leq(star(X0!0), multiplication(star(X0!0), star(X0!0))) <=> (addition(star(X0!0), multiplication(star(X0!0), star(X0!0))) = multiplication(star(X0!0), star(X0!0)))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[193, 7])).
% 0.92/1.10 tff(195,assumption,(~leq(star(X0!0), multiplication(star(X0!0), star(X0!0)))), introduced(assumption)).
% 0.92/1.10 tff(196,plain,
% 0.92/1.10 ((~(leq(star(X0!0), multiplication(star(X0!0), star(X0!0))) <=> (addition(star(X0!0), multiplication(star(X0!0), star(X0!0))) = multiplication(star(X0!0), star(X0!0))))) | leq(star(X0!0), multiplication(star(X0!0), star(X0!0))) | (~(addition(star(X0!0), multiplication(star(X0!0), star(X0!0))) = multiplication(star(X0!0), star(X0!0))))),
% 0.92/1.10 inference(tautology,[status(thm)],[])).
% 0.92/1.10 tff(197,plain,
% 0.92/1.10 ((~(leq(star(X0!0), multiplication(star(X0!0), star(X0!0))) <=> (addition(star(X0!0), multiplication(star(X0!0), star(X0!0))) = multiplication(star(X0!0), star(X0!0))))) | (~(addition(star(X0!0), multiplication(star(X0!0), star(X0!0))) = multiplication(star(X0!0), star(X0!0))))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[196, 195])).
% 0.92/1.10 tff(198,plain,
% 0.92/1.10 (~(addition(star(X0!0), multiplication(star(X0!0), star(X0!0))) = multiplication(star(X0!0), star(X0!0)))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[197, 194])).
% 0.92/1.10 tff(199,plain,
% 0.92/1.10 ($false),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[198, 192])).
% 0.92/1.10 tff(200,plain,(leq(star(X0!0), multiplication(star(X0!0), star(X0!0)))), inference(lemma,lemma(discharge,[]))).
% 0.92/1.10 tff(201,plain,
% 0.92/1.10 ((~(~((~leq(multiplication(star(X0!0), star(X0!0)), star(X0!0))) | (~leq(star(X0!0), multiplication(star(X0!0), star(X0!0))))))) <=> ((~leq(multiplication(star(X0!0), star(X0!0)), star(X0!0))) | (~leq(star(X0!0), multiplication(star(X0!0), star(X0!0)))))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(202,plain,
% 0.92/1.10 ((leq(multiplication(star(X0!0), star(X0!0)), star(X0!0)) & leq(star(X0!0), multiplication(star(X0!0), star(X0!0)))) <=> (~((~leq(multiplication(star(X0!0), star(X0!0)), star(X0!0))) | (~leq(star(X0!0), multiplication(star(X0!0), star(X0!0))))))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(203,plain,
% 0.92/1.10 ((~(leq(multiplication(star(X0!0), star(X0!0)), star(X0!0)) & leq(star(X0!0), multiplication(star(X0!0), star(X0!0))))) <=> (~(~((~leq(multiplication(star(X0!0), star(X0!0)), star(X0!0))) | (~leq(star(X0!0), multiplication(star(X0!0), star(X0!0)))))))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[202])).
% 0.92/1.10 tff(204,plain,
% 0.92/1.10 ((~(leq(multiplication(star(X0!0), star(X0!0)), star(X0!0)) & leq(star(X0!0), multiplication(star(X0!0), star(X0!0))))) <=> ((~leq(multiplication(star(X0!0), star(X0!0)), star(X0!0))) | (~leq(star(X0!0), multiplication(star(X0!0), star(X0!0)))))),
% 0.92/1.10 inference(transitivity,[status(thm)],[203, 201])).
% 0.92/1.10 tff(205,plain,
% 0.92/1.10 ((~![X0: $i] : (leq(multiplication(star(X0), star(X0)), star(X0)) & leq(star(X0), multiplication(star(X0), star(X0))))) <=> (~![X0: $i] : (leq(multiplication(star(X0), star(X0)), star(X0)) & leq(star(X0), multiplication(star(X0), star(X0)))))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(206,axiom,(~![X0: $i] : (leq(multiplication(star(X0), star(X0)), star(X0)) & leq(star(X0), multiplication(star(X0), star(X0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.92/1.10 tff(207,plain,
% 0.92/1.10 (~![X0: $i] : (leq(multiplication(star(X0), star(X0)), star(X0)) & leq(star(X0), multiplication(star(X0), star(X0))))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.92/1.10 tff(208,plain,
% 0.92/1.10 (~![X0: $i] : (leq(multiplication(star(X0), star(X0)), star(X0)) & leq(star(X0), multiplication(star(X0), star(X0))))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[207, 205])).
% 0.92/1.10 tff(209,plain,
% 0.92/1.10 (~![X0: $i] : (leq(multiplication(star(X0), star(X0)), star(X0)) & leq(star(X0), multiplication(star(X0), star(X0))))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[208, 205])).
% 0.92/1.10 tff(210,plain,
% 0.92/1.10 (~![X0: $i] : (leq(multiplication(star(X0), star(X0)), star(X0)) & leq(star(X0), multiplication(star(X0), star(X0))))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[209, 205])).
% 0.92/1.10 tff(211,plain,(
% 0.92/1.10 ~(leq(multiplication(star(X0!0), star(X0!0)), star(X0!0)) & leq(star(X0!0), multiplication(star(X0!0), star(X0!0))))),
% 0.92/1.10 inference(skolemize,[status(sab)],[210])).
% 0.92/1.10 tff(212,plain,
% 0.92/1.10 ((~leq(multiplication(star(X0!0), star(X0!0)), star(X0!0))) | (~leq(star(X0!0), multiplication(star(X0!0), star(X0!0))))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[211, 204])).
% 0.92/1.10 tff(213,plain,
% 0.92/1.10 (~leq(multiplication(star(X0!0), star(X0!0)), star(X0!0))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[212, 200])).
% 0.92/1.10 tff(214,plain,
% 0.92/1.10 (^[A: $i, B: $i, C: $i] : refl(((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A)) <=> ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A)))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(215,plain,
% 0.92/1.10 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[214])).
% 0.92/1.10 tff(216,plain,
% 0.92/1.10 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(217,plain,
% 0.92/1.10 (^[A: $i, B: $i, C: $i] : rewrite((leq(addition(multiplication(A, B), C), A) => leq(multiplication(C, star(B)), A)) <=> ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A)))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(218,plain,
% 0.92/1.10 (![A: $i, B: $i, C: $i] : (leq(addition(multiplication(A, B), C), A) => leq(multiplication(C, star(B)), A)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[217])).
% 0.92/1.10 tff(219,axiom,(![A: $i, B: $i, C: $i] : (leq(addition(multiplication(A, B), C), A) => leq(multiplication(C, star(B)), A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','star_induction_right')).
% 0.92/1.10 tff(220,plain,
% 0.92/1.10 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.92/1.10 tff(221,plain,
% 0.92/1.10 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[220, 216])).
% 0.92/1.10 tff(222,plain,(
% 0.92/1.10 ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 0.92/1.10 inference(skolemize,[status(sab)],[221])).
% 0.92/1.10 tff(223,plain,
% 0.92/1.10 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[222, 215])).
% 0.92/1.10 tff(224,plain,
% 0.92/1.10 (((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))) | ((~leq(addition(multiplication(star(X0!0), X0!0), star(X0!0)), star(X0!0))) | leq(multiplication(star(X0!0), star(X0!0)), star(X0!0)))) <=> ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))) | (~leq(addition(multiplication(star(X0!0), X0!0), star(X0!0)), star(X0!0))) | leq(multiplication(star(X0!0), star(X0!0)), star(X0!0)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(225,plain,
% 0.92/1.10 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))) | ((~leq(addition(multiplication(star(X0!0), X0!0), star(X0!0)), star(X0!0))) | leq(multiplication(star(X0!0), star(X0!0)), star(X0!0)))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(226,plain,
% 0.92/1.10 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))) | (~leq(addition(multiplication(star(X0!0), X0!0), star(X0!0)), star(X0!0))) | leq(multiplication(star(X0!0), star(X0!0)), star(X0!0))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.92/1.10 tff(227,plain,
% 0.92/1.10 (~leq(addition(multiplication(star(X0!0), X0!0), star(X0!0)), star(X0!0))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[226, 223, 213])).
% 0.92/1.10 tff(228,plain,
% 0.92/1.10 ((~(leq(addition(multiplication(star(X0!0), X0!0), star(X0!0)), star(X0!0)) <=> (addition(addition(multiplication(star(X0!0), X0!0), star(X0!0)), star(X0!0)) = star(X0!0)))) | leq(addition(multiplication(star(X0!0), X0!0), star(X0!0)), star(X0!0)) | (~(addition(addition(multiplication(star(X0!0), X0!0), star(X0!0)), star(X0!0)) = star(X0!0)))),
% 0.92/1.10 inference(tautology,[status(thm)],[])).
% 0.92/1.10 tff(229,plain,
% 0.92/1.10 ((~(leq(addition(multiplication(star(X0!0), X0!0), star(X0!0)), star(X0!0)) <=> (addition(addition(multiplication(star(X0!0), X0!0), star(X0!0)), star(X0!0)) = star(X0!0)))) | (~(addition(addition(multiplication(star(X0!0), X0!0), star(X0!0)), star(X0!0)) = star(X0!0)))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[228, 227])).
% 0.92/1.10 tff(230,plain,
% 0.92/1.10 (~(addition(addition(multiplication(star(X0!0), X0!0), star(X0!0)), star(X0!0)) = star(X0!0))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[229, 145])).
% 0.92/1.10 tff(231,plain,
% 0.92/1.10 ($false),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[230, 143])).
% 0.92/1.10 % SZS output end Proof
% 0.92/1.11 % E exiting
%------------------------------------------------------------------------------