%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE037+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:12:54 AM UTC 2025
% Result : Theorem 0.56s 0.74s
% Output : Proof 0.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : KLE037+1 : TPTP v9.0.0. Released v4.0.0.
% 0.13/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n011.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Jun 19 18:55:56 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.56/0.74 % SZS status Theorem
% 0.56/0.74 % SZS output start Proof
% 0.56/0.74 tff(star_type, type, (
% 0.56/0.74 star: $i > $i)).
% 0.56/0.74 tff(tptp_fun_X0_0_type, type, (
% 0.56/0.74 tptp_fun_X0_0: $i)).
% 0.56/0.74 tff(addition_type, type, (
% 0.56/0.74 addition: ( $i * $i ) > $i)).
% 0.56/0.74 tff(one_type, type, (
% 0.56/0.74 one: $i)).
% 0.56/0.74 tff(multiplication_type, type, (
% 0.56/0.74 multiplication: ( $i * $i ) > $i)).
% 0.56/0.74 tff(leq_type, type, (
% 0.56/0.74 leq: ( $i * $i ) > $o)).
% 0.56/0.74 tff(1,plain,
% 0.56/0.74 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(2,plain,
% 0.56/0.74 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[1])).
% 0.56/0.74 tff(3,plain,
% 0.56/0.74 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(4,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','order')).
% 0.56/0.74 tff(5,plain,
% 0.56/0.74 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.56/0.74 tff(6,plain,(
% 0.56/0.74 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.56/0.74 inference(skolemize,[status(sab)],[5])).
% 0.56/0.74 tff(7,plain,
% 0.56/0.74 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.56/0.74 tff(8,plain,
% 0.56/0.74 ((~![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)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(9,plain,
% 0.56/0.74 (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))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.56/0.74 tff(10,plain,
% 0.56/0.74 (^[A: $i] : refl(leq(addition(one, multiplication(A, star(A))), star(A)) <=> leq(addition(one, multiplication(A, star(A))), star(A)))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(11,plain,
% 0.56/0.74 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[10])).
% 0.56/0.74 tff(12,plain,
% 0.56/0.74 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(13,axiom,(![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','star_unfold_right')).
% 0.56/0.74 tff(14,plain,
% 0.56/0.74 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.56/0.74 tff(15,plain,(
% 0.56/0.74 ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 0.56/0.74 inference(skolemize,[status(sab)],[14])).
% 0.56/0.74 tff(16,plain,
% 0.56/0.74 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.56/0.74 tff(17,plain,
% 0.56/0.74 ((~![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))) | leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(18,plain,
% 0.56/0.74 (leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.56/0.74 tff(19,plain,
% 0.56/0.74 ((~(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))),
% 0.56/0.74 inference(tautology,[status(thm)],[])).
% 0.56/0.74 tff(20,plain,
% 0.56/0.74 ((~(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))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.56/0.74 tff(21,plain,
% 0.56/0.74 (addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) = star(X0!0)),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[20, 9])).
% 0.56/0.74 tff(22,plain,
% 0.56/0.74 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(23,plain,
% 0.56/0.74 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[22])).
% 0.56/0.74 tff(24,plain,
% 0.56/0.74 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(25,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','additive_commutativity')).
% 0.56/0.74 tff(26,plain,
% 0.56/0.74 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.56/0.74 tff(27,plain,(
% 0.56/0.74 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.56/0.74 inference(skolemize,[status(sab)],[26])).
% 0.56/0.74 tff(28,plain,
% 0.56/0.74 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.56/0.74 tff(29,plain,
% 0.56/0.74 ((~![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))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(30,plain,
% 0.56/0.74 (addition(one, multiplication(X0!0, star(X0!0))) = addition(multiplication(X0!0, star(X0!0)), one)),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.56/0.74 tff(31,plain,
% 0.56/0.74 (addition(multiplication(X0!0, star(X0!0)), one) = addition(one, multiplication(X0!0, star(X0!0)))),
% 0.56/0.74 inference(symmetry,[status(thm)],[30])).
% 0.56/0.74 tff(32,plain,
% 0.56/0.74 (addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)) = addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[31])).
% 0.56/0.74 tff(33,plain,
% 0.56/0.74 (^[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)))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(34,plain,
% 0.56/0.74 (![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))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[33])).
% 0.56/0.74 tff(35,plain,
% 0.56/0.74 (![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))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(36,axiom,(![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','additive_associativity')).
% 0.56/0.74 tff(37,plain,
% 0.56/0.74 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.56/0.74 tff(38,plain,(
% 0.56/0.74 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.56/0.74 inference(skolemize,[status(sab)],[37])).
% 0.56/0.74 tff(39,plain,
% 0.56/0.74 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.56/0.74 tff(40,plain,
% 0.56/0.74 ((~![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)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(41,plain,
% 0.56/0.74 (addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0))) = addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.56/0.74 tff(42,plain,
% 0.56/0.74 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, star(X0!0)) = addition(star(X0!0), one))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(43,plain,
% 0.56/0.74 (addition(one, star(X0!0)) = addition(star(X0!0), one)),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[42, 28])).
% 0.56/0.74 tff(44,plain,
% 0.56/0.74 (addition(star(X0!0), one) = addition(one, star(X0!0))),
% 0.56/0.74 inference(symmetry,[status(thm)],[43])).
% 0.56/0.74 tff(45,plain,
% 0.56/0.74 (addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) = addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))),
% 0.56/0.74 inference(symmetry,[status(thm)],[32])).
% 0.56/0.74 tff(46,plain,
% 0.56/0.74 (star(X0!0) = addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))),
% 0.56/0.74 inference(symmetry,[status(thm)],[21])).
% 0.56/0.74 tff(47,plain,
% 0.56/0.74 (star(X0!0) = addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))),
% 0.56/0.74 inference(transitivity,[status(thm)],[46, 45])).
% 0.56/0.74 tff(48,plain,
% 0.56/0.74 (addition(star(X0!0), one) = addition(addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)), one)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[47])).
% 0.56/0.74 tff(49,plain,
% 0.56/0.74 (addition(addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)), one) = addition(star(X0!0), one)),
% 0.56/0.74 inference(symmetry,[status(thm)],[48])).
% 0.56/0.74 tff(50,plain,
% 0.56/0.74 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(X0!0, star(X0!0)), one), addition(star(X0!0), one)) = addition(addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)), one))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(51,plain,
% 0.56/0.74 (addition(addition(multiplication(X0!0, star(X0!0)), one), addition(star(X0!0), one)) = addition(addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)), one)),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[50, 39])).
% 0.56/0.74 tff(52,plain,
% 0.56/0.74 ((~![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))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(53,plain,
% 0.56/0.74 (addition(one, multiplication(star(X0!0), X0!0)) = addition(multiplication(star(X0!0), X0!0), one)),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[52, 28])).
% 0.56/0.74 tff(54,plain,
% 0.56/0.74 (addition(multiplication(star(X0!0), X0!0), one) = addition(one, multiplication(star(X0!0), X0!0))),
% 0.56/0.74 inference(symmetry,[status(thm)],[53])).
% 0.56/0.74 tff(55,plain,
% 0.56/0.74 (addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)) = addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[54])).
% 0.56/0.74 tff(56,plain,
% 0.56/0.74 (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))),
% 0.56/0.74 inference(symmetry,[status(thm)],[55])).
% 0.56/0.74 tff(57,plain,
% 0.56/0.74 ((~![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)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(58,plain,
% 0.56/0.74 (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))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[57, 7])).
% 0.56/0.74 tff(59,plain,
% 0.56/0.74 (^[A: $i] : refl(leq(addition(one, multiplication(star(A), A)), star(A)) <=> leq(addition(one, multiplication(star(A), A)), star(A)))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(60,plain,
% 0.56/0.74 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[59])).
% 0.56/0.74 tff(61,plain,
% 0.56/0.74 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(62,axiom,(![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','star_unfold_left')).
% 0.56/0.74 tff(63,plain,
% 0.56/0.74 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.56/0.74 tff(64,plain,(
% 0.56/0.74 ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 0.56/0.74 inference(skolemize,[status(sab)],[63])).
% 0.56/0.74 tff(65,plain,
% 0.56/0.74 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.56/0.74 tff(66,plain,
% 0.56/0.74 ((~![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))) | leq(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(67,plain,
% 0.56/0.74 (leq(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.56/0.74 tff(68,plain,
% 0.56/0.74 ((~(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))),
% 0.56/0.74 inference(tautology,[status(thm)],[])).
% 0.56/0.74 tff(69,plain,
% 0.56/0.74 ((~(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))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.56/0.74 tff(70,plain,
% 0.56/0.74 (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = star(X0!0)),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[69, 58])).
% 0.56/0.74 tff(71,plain,
% 0.56/0.74 (star(X0!0) = addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 0.56/0.74 inference(symmetry,[status(thm)],[70])).
% 0.56/0.74 tff(72,plain,
% 0.56/0.74 (star(X0!0) = addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))),
% 0.56/0.74 inference(transitivity,[status(thm)],[71, 56])).
% 0.56/0.74 tff(73,plain,
% 0.56/0.74 (multiplication(X0!0, star(X0!0)) = multiplication(X0!0, addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[72])).
% 0.56/0.74 tff(74,plain,
% 0.56/0.74 (multiplication(X0!0, addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))) = multiplication(X0!0, star(X0!0))),
% 0.56/0.74 inference(symmetry,[status(thm)],[73])).
% 0.56/0.74 tff(75,plain,
% 0.56/0.74 (^[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))))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(76,plain,
% 0.56/0.74 (![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)))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[75])).
% 0.56/0.74 tff(77,plain,
% 0.56/0.74 (![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)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(78,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','right_distributivity')).
% 0.56/0.74 tff(79,plain,
% 0.56/0.74 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.56/0.74 tff(80,plain,(
% 0.56/0.74 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.56/0.74 inference(skolemize,[status(sab)],[79])).
% 0.56/0.74 tff(81,plain,
% 0.56/0.74 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.56/0.74 tff(82,plain,
% 0.56/0.74 ((~![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))))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(83,plain,
% 0.56/0.74 (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)))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.56/0.74 tff(84,plain,
% 0.56/0.74 (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)))),
% 0.56/0.74 inference(symmetry,[status(thm)],[83])).
% 0.56/0.74 tff(85,plain,
% 0.56/0.74 (addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))) = multiplication(X0!0, star(X0!0))),
% 0.56/0.74 inference(transitivity,[status(thm)],[84, 74])).
% 0.56/0.74 tff(86,plain,
% 0.56/0.74 (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), one) = addition(multiplication(X0!0, star(X0!0)), one)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[85])).
% 0.56/0.74 tff(87,plain,
% 0.56/0.74 (addition(multiplication(X0!0, star(X0!0)), one) = addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), one)),
% 0.56/0.74 inference(symmetry,[status(thm)],[86])).
% 0.56/0.74 tff(88,plain,
% 0.56/0.74 (addition(addition(multiplication(X0!0, star(X0!0)), one), addition(star(X0!0), one)) = addition(addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), one), addition(star(X0!0), one))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[87])).
% 0.56/0.74 tff(89,plain,
% 0.56/0.74 (addition(addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), one), addition(star(X0!0), one)) = addition(addition(multiplication(X0!0, star(X0!0)), one), addition(star(X0!0), one))),
% 0.56/0.74 inference(symmetry,[status(thm)],[88])).
% 0.56/0.74 tff(90,plain,
% 0.56/0.74 ((~![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(one, addition(star(X0!0), one))) = addition(addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), one), addition(star(X0!0), one)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(91,plain,
% 0.56/0.74 (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(one, addition(star(X0!0), one))) = addition(addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), one), addition(star(X0!0), one))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[90, 39])).
% 0.56/0.74 tff(92,plain,
% 0.56/0.74 (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(one, addition(star(X0!0), one))) = addition(one, star(X0!0))),
% 0.56/0.74 inference(transitivity,[status(thm)],[91, 89, 51, 49, 44])).
% 0.56/0.74 tff(93,plain,
% 0.56/0.74 (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, addition(star(X0!0), one)))) = addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0)))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[85, 92])).
% 0.56/0.74 tff(94,plain,
% 0.56/0.74 ((~![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, addition(star(X0!0), one)))) = 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, addition(star(X0!0), one))))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(95,plain,
% 0.56/0.75 (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, addition(star(X0!0), one)))) = 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, addition(star(X0!0), one)))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[94, 39])).
% 0.56/0.75 tff(96,plain,
% 0.56/0.75 (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, addition(star(X0!0), one))) = 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, addition(star(X0!0), one))))),
% 0.56/0.75 inference(symmetry,[status(thm)],[95])).
% 0.56/0.75 tff(97,plain,
% 0.56/0.75 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 0.56/0.75 inference(bind,[status(th)],[])).
% 0.56/0.75 tff(98,plain,
% 0.56/0.75 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.56/0.75 inference(quant_intro,[status(thm)],[97])).
% 0.56/0.75 tff(99,plain,
% 0.56/0.75 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(100,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','additive_idempotence')).
% 0.56/0.75 tff(101,plain,
% 0.56/0.75 (![A: $i] : (addition(A, A) = A)),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.56/0.75 tff(102,plain,(
% 0.56/0.75 ![A: $i] : (addition(A, A) = A)),
% 0.56/0.75 inference(skolemize,[status(sab)],[101])).
% 0.56/0.75 tff(103,plain,
% 0.56/0.75 (![A: $i] : (addition(A, A) = A)),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.56/0.75 tff(104,plain,
% 0.56/0.75 ((~![A: $i] : (addition(A, A) = A)) | (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, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(105,plain,
% 0.56/0.75 (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, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.56/0.75 tff(106,plain,
% 0.56/0.75 (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(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))),
% 0.56/0.75 inference(symmetry,[status(thm)],[105])).
% 0.56/0.75 tff(107,plain,
% 0.56/0.75 (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(one, addition(star(X0!0), one))) = 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, addition(star(X0!0), one)))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[106])).
% 0.56/0.75 tff(108,plain,
% 0.56/0.75 (addition(addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), one), addition(star(X0!0), one)) = addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(one, addition(star(X0!0), one)))),
% 0.56/0.75 inference(symmetry,[status(thm)],[91])).
% 0.56/0.75 tff(109,plain,
% 0.56/0.75 (addition(addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)), one) = addition(addition(multiplication(X0!0, star(X0!0)), one), addition(star(X0!0), one))),
% 0.56/0.75 inference(symmetry,[status(thm)],[51])).
% 0.56/0.75 tff(110,plain,
% 0.56/0.75 (addition(one, star(X0!0)) = star(X0!0)),
% 0.56/0.75 inference(transitivity,[status(thm)],[43, 48, 109, 88, 108, 107, 96, 93, 41, 32, 21])).
% 0.56/0.75 tff(111,plain,
% 0.56/0.75 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(one, star(X0!0)) <=> (addition(one, star(X0!0)) = star(X0!0)))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(112,plain,
% 0.56/0.75 (leq(one, star(X0!0)) <=> (addition(one, star(X0!0)) = star(X0!0))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[111, 7])).
% 0.56/0.75 tff(113,plain,
% 0.56/0.75 ((~![X0: $i] : leq(one, star(X0))) <=> (~![X0: $i] : leq(one, star(X0)))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(114,axiom,(~![X0: $i] : leq(one, star(X0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 0.56/0.75 tff(115,plain,
% 0.56/0.75 (~![X0: $i] : leq(one, star(X0))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.56/0.75 tff(116,plain,
% 0.56/0.75 (~![X0: $i] : leq(one, star(X0))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[115, 113])).
% 0.56/0.75 tff(117,plain,
% 0.56/0.75 (~![X0: $i] : leq(one, star(X0))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[116, 113])).
% 0.56/0.75 tff(118,plain,
% 0.56/0.75 (~![X0: $i] : leq(one, star(X0))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.56/0.75 tff(119,plain,(
% 0.56/0.75 ~leq(one, star(X0!0))),
% 0.56/0.75 inference(skolemize,[status(sab)],[118])).
% 0.56/0.75 tff(120,plain,
% 0.56/0.75 ((~(leq(one, star(X0!0)) <=> (addition(one, star(X0!0)) = star(X0!0)))) | leq(one, star(X0!0)) | (~(addition(one, star(X0!0)) = star(X0!0)))),
% 0.56/0.75 inference(tautology,[status(thm)],[])).
% 0.56/0.75 tff(121,plain,
% 0.56/0.75 ((~(leq(one, star(X0!0)) <=> (addition(one, star(X0!0)) = star(X0!0)))) | (~(addition(one, star(X0!0)) = star(X0!0)))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.56/0.75 tff(122,plain,
% 0.56/0.75 (~(addition(one, star(X0!0)) = star(X0!0))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[121, 112])).
% 0.56/0.75 tff(123,plain,
% 0.56/0.75 ($false),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[122, 110])).
% 0.56/0.75 % SZS output end Proof
% 0.56/0.75 % E exiting
%------------------------------------------------------------------------------