%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE001+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:12:49 AM UTC 2025
% Result : Theorem 0.21s 0.38s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : KLE001+1 : TPTP v9.0.0. Released v4.0.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Jun 19 18:50:08 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.21/0.38 % SZS status Theorem
% 0.21/0.38 % SZS output start Proof
% 0.21/0.38 tff(addition_type, type, (
% 0.21/0.38 addition: ( $i * $i ) > $i)).
% 0.21/0.38 tff(tptp_fun_X2_0_type, type, (
% 0.21/0.38 tptp_fun_X2_0: $i)).
% 0.21/0.38 tff(tptp_fun_X0_2_type, type, (
% 0.21/0.38 tptp_fun_X0_2: $i)).
% 0.21/0.38 tff(leq_type, type, (
% 0.21/0.38 leq: ( $i * $i ) > $o)).
% 0.21/0.38 tff(tptp_fun_X1_1_type, type, (
% 0.21/0.38 tptp_fun_X1_1: $i)).
% 0.21/0.38 tff(1,plain,
% 0.21/0.38 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(2,plain,
% 0.21/0.38 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.38 tff(3,plain,
% 0.21/0.38 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(4,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 0.21/0.38 tff(5,plain,
% 0.21/0.38 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.38 tff(6,plain,(
% 0.21/0.38 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.21/0.38 inference(skolemize,[status(sab)],[5])).
% 0.21/0.38 tff(7,plain,
% 0.21/0.38 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.38 tff(8,plain,
% 0.21/0.38 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X0!2, X2!0) = addition(X2!0, X0!2))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(9,plain,
% 0.21/0.38 (addition(X0!2, X2!0) = addition(X2!0, X0!2)),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.38 tff(10,plain,
% 0.21/0.38 (addition(X2!0, X0!2) = addition(X0!2, X2!0)),
% 0.21/0.38 inference(symmetry,[status(thm)],[9])).
% 0.21/0.38 tff(11,plain,
% 0.21/0.38 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(12,plain,
% 0.21/0.38 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.21/0.38 inference(quant_intro,[status(thm)],[11])).
% 0.21/0.38 tff(13,plain,
% 0.21/0.38 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(14,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_idempotence')).
% 0.21/0.38 tff(15,plain,
% 0.21/0.38 (![A: $i] : (addition(A, A) = A)),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.21/0.38 tff(16,plain,(
% 0.21/0.38 ![A: $i] : (addition(A, A) = A)),
% 0.21/0.38 inference(skolemize,[status(sab)],[15])).
% 0.21/0.38 tff(17,plain,
% 0.21/0.38 (![A: $i] : (addition(A, A) = A)),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.21/0.38 tff(18,plain,
% 0.21/0.38 ((~![A: $i] : (addition(A, A) = A)) | (addition(addition(X2!0, X0!2), addition(X2!0, X0!2)) = addition(X2!0, X0!2))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(19,plain,
% 0.21/0.38 (addition(addition(X2!0, X0!2), addition(X2!0, X0!2)) = addition(X2!0, X0!2)),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.21/0.38 tff(20,plain,
% 0.21/0.38 (addition(addition(X0!2, X2!0), addition(X0!2, X2!0)) = addition(addition(X2!0, X0!2), addition(X2!0, X0!2))),
% 0.21/0.38 inference(monotonicity,[status(thm)],[9, 9])).
% 0.21/0.38 tff(21,plain,
% 0.21/0.38 (addition(addition(X0!2, X2!0), addition(X0!2, X2!0)) = addition(X0!2, X2!0)),
% 0.21/0.38 inference(transitivity,[status(thm)],[20, 19, 10])).
% 0.21/0.38 tff(22,plain,
% 0.21/0.38 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(23,plain,
% 0.21/0.38 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[22])).
% 0.21/0.38 tff(24,plain,
% 0.21/0.38 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(25,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','order')).
% 0.21/0.38 tff(26,plain,
% 0.21/0.38 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.21/0.38 tff(27,plain,(
% 0.21/0.38 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.21/0.39 inference(skolemize,[status(sab)],[26])).
% 0.21/0.39 tff(28,plain,
% 0.21/0.39 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.21/0.39 tff(29,plain,
% 0.21/0.39 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(X0!2, X2!0), addition(X0!2, X2!0)) <=> (addition(addition(X0!2, X2!0), addition(X0!2, X2!0)) = addition(X0!2, X2!0)))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(30,plain,
% 0.21/0.39 (leq(addition(X0!2, X2!0), addition(X0!2, X2!0)) <=> (addition(addition(X0!2, X2!0), addition(X0!2, X2!0)) = addition(X0!2, X2!0))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.21/0.39 tff(31,plain,
% 0.21/0.39 ((~![X0: $i, X1: $i, X2: $i] : ((~leq(X0, X1)) | leq(addition(X0, X2), addition(X0, X2)))) <=> (~![X0: $i, X1: $i, X2: $i] : ((~leq(X0, X1)) | leq(addition(X0, X2), addition(X0, X2))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(32,plain,
% 0.21/0.39 ((~![X0: $i, X1: $i, X2: $i] : (leq(X0, X1) => leq(addition(X0, X2), addition(X0, X2)))) <=> (~![X0: $i, X1: $i, X2: $i] : ((~leq(X0, X1)) | leq(addition(X0, X2), addition(X0, X2))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(33,axiom,(~![X0: $i, X1: $i, X2: $i] : (leq(X0, X1) => leq(addition(X0, X2), addition(X0, X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 0.21/0.39 tff(34,plain,
% 0.21/0.39 (~![X0: $i, X1: $i, X2: $i] : ((~leq(X0, X1)) | leq(addition(X0, X2), addition(X0, X2)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.21/0.39 tff(35,plain,
% 0.21/0.39 (~![X0: $i, X1: $i, X2: $i] : ((~leq(X0, X1)) | leq(addition(X0, X2), addition(X0, X2)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[34, 31])).
% 0.21/0.39 tff(36,plain,
% 0.21/0.39 (~![X0: $i, X1: $i, X2: $i] : ((~leq(X0, X1)) | leq(addition(X0, X2), addition(X0, X2)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.21/0.39 tff(37,plain,
% 0.21/0.39 (~![X0: $i, X1: $i, X2: $i] : ((~leq(X0, X1)) | leq(addition(X0, X2), addition(X0, X2)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[36, 31])).
% 0.21/0.39 tff(38,plain,(
% 0.21/0.39 ~((~leq(X0!2, X1!1)) | leq(addition(X0!2, X2!0), addition(X0!2, X2!0)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[37])).
% 0.21/0.39 tff(39,plain,
% 0.21/0.39 (~leq(addition(X0!2, X2!0), addition(X0!2, X2!0))),
% 0.21/0.39 inference(or_elim,[status(thm)],[38])).
% 0.21/0.39 tff(40,plain,
% 0.21/0.39 ((~(leq(addition(X0!2, X2!0), addition(X0!2, X2!0)) <=> (addition(addition(X0!2, X2!0), addition(X0!2, X2!0)) = addition(X0!2, X2!0)))) | leq(addition(X0!2, X2!0), addition(X0!2, X2!0)) | (~(addition(addition(X0!2, X2!0), addition(X0!2, X2!0)) = addition(X0!2, X2!0)))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(41,plain,
% 0.21/0.39 ((~(leq(addition(X0!2, X2!0), addition(X0!2, X2!0)) <=> (addition(addition(X0!2, X2!0), addition(X0!2, X2!0)) = addition(X0!2, X2!0)))) | (~(addition(addition(X0!2, X2!0), addition(X0!2, X2!0)) = addition(X0!2, X2!0)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.21/0.39 tff(42,plain,
% 0.21/0.39 (~(addition(addition(X0!2, X2!0), addition(X0!2, X2!0)) = addition(X0!2, X2!0))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[41, 30])).
% 0.21/0.39 tff(43,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[42, 21])).
% 0.21/0.39 % SZS output end Proof
% 0.21/0.39 % E exiting
%------------------------------------------------------------------------------