%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE029+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 0.11s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : KLE029+1 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 18:54:24 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.37 % SZS status Theorem
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(tptp_fun_X2_2_type, type, (
% 0.11/0.37 tptp_fun_X2_2: $i)).
% 0.11/0.37 tff(addition_type, type, (
% 0.11/0.37 addition: ( $i * $i ) > $i)).
% 0.11/0.37 tff(tptp_fun_X3_1_type, type, (
% 0.11/0.37 tptp_fun_X3_1: ( $i * $i * $i ) > $i)).
% 0.11/0.37 tff(tptp_fun_X1_3_type, type, (
% 0.11/0.37 tptp_fun_X1_3: $i)).
% 0.11/0.37 tff(tptp_fun_X0_4_type, type, (
% 0.11/0.37 tptp_fun_X0_4: $i)).
% 0.11/0.37 tff(leq_type, type, (
% 0.11/0.37 leq: ( $i * $i ) > $o)).
% 0.11/0.37 tff(ismeet_type, type, (
% 0.11/0.37 ismeet: ( $i * $i * $i ) > $o)).
% 0.11/0.37 tff(tptp_fun_X3_0_type, type, (
% 0.11/0.37 tptp_fun_X3_0: ( $i * $i * $i ) > $i)).
% 0.11/0.37 tff(ismeetu_type, type, (
% 0.11/0.37 ismeetu: ( $i * $i * $i ) > $o)).
% 0.11/0.37 tff(1,plain,
% 0.11/0.37 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(4,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','order')).
% 0.11/0.37 tff(5,plain,
% 0.11/0.37 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.11/0.37 tff(6,plain,(
% 0.11/0.37 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.11/0.37 inference(skolemize,[status(sab)],[5])).
% 0.11/0.37 tff(7,plain,
% 0.11/0.37 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.11/0.37 tff(8,plain,
% 0.11/0.37 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(X0!4, X2!2) <=> (addition(X0!4, X2!2) = X2!2))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(9,plain,
% 0.11/0.37 (leq(X0!4, X2!2) <=> (addition(X0!4, X2!2) = X2!2)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.11/0.37 tff(10,assumption,(~ismeet(X0!4, X1!3, X2!2)), introduced(assumption)).
% 0.11/0.37 tff(11,plain,
% 0.11/0.37 ((~(ismeet(X0!4, X1!3, X2!2) <=> ismeetu(X0!4, X1!3, X2!2))) <=> (~(ismeet(X0!4, X1!3, X2!2) <=> ismeetu(X0!4, X1!3, X2!2)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(12,plain,
% 0.11/0.37 ((~![X0: $i, X1: $i, X2: $i] : (ismeet(X0, X1, X2) <=> ismeetu(X0, X1, X2))) <=> (~![X0: $i, X1: $i, X2: $i] : (ismeet(X0, X1, X2) <=> ismeetu(X0, X1, X2)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(13,axiom,(~![X0: $i, X1: $i, X2: $i] : (ismeet(X0, X1, X2) <=> ismeetu(X0, X1, X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 (~![X0: $i, X1: $i, X2: $i] : (ismeet(X0, X1, X2) <=> ismeetu(X0, X1, X2))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.11/0.37 tff(15,plain,
% 0.11/0.37 (~![X0: $i, X1: $i, X2: $i] : (ismeet(X0, X1, X2) <=> ismeetu(X0, X1, X2))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[14, 12])).
% 0.11/0.37 tff(16,plain,
% 0.11/0.37 (~![X0: $i, X1: $i, X2: $i] : (ismeet(X0, X1, X2) <=> ismeetu(X0, X1, X2))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 (~![X0: $i, X1: $i, X2: $i] : (ismeet(X0, X1, X2) <=> ismeetu(X0, X1, X2))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.11/0.37 tff(18,plain,(
% 0.11/0.37 ~(ismeet(X0!4, X1!3, X2!2) <=> ismeetu(X0!4, X1!3, X2!2))),
% 0.11/0.37 inference(skolemize,[status(sab)],[17])).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 (~(ismeet(X0!4, X1!3, X2!2) <=> ismeetu(X0!4, X1!3, X2!2))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 ((ismeet(X0!4, X1!3, X2!2) <=> ismeetu(X0!4, X1!3, X2!2)) | ismeet(X0!4, X1!3, X2!2) | ismeetu(X0!4, X1!3, X2!2)),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(21,plain,
% 0.11/0.37 (ismeet(X0!4, X1!3, X2!2) | ismeetu(X0!4, X1!3, X2!2)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 (ismeetu(X0!4, X1!3, X2!2)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[21, 10])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 (^[X0: $i, X1: $i, X2: $i] : rewrite((~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : (~(((~leq(X3, X1)) | (~leq(X3, X0))) <=> leq(X3, X2))))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))))) <=> (~((~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))) | (~((~ismeetu(X2, X0, X1)) | ![X3: $i] : (~(((~leq(X3, X1)) | (~leq(X3, X0))) <=> leq(X3, X2))))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(24,plain,
% 0.11/0.37 (![X0: $i, X1: $i, X2: $i] : (~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : (~(((~leq(X3, X1)) | (~leq(X3, X0))) <=> leq(X3, X2))))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))))) <=> ![X0: $i, X1: $i, X2: $i] : (~((~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))) | (~((~ismeetu(X2, X0, X1)) | ![X3: $i] : (~(((~leq(X3, X1)) | (~leq(X3, X0))) <=> leq(X3, X2)))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[23])).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 (^[X0: $i, X1: $i, X2: $i] : refl((~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : (~(((~leq(X3, X1)) | (~leq(X3, X0))) <=> leq(X3, X2))))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))))) <=> (~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : (~(((~leq(X3, X1)) | (~leq(X3, X0))) <=> leq(X3, X2))))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(26,plain,
% 0.11/0.37 (![X0: $i, X1: $i, X2: $i] : (~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : (~(((~leq(X3, X1)) | (~leq(X3, X0))) <=> leq(X3, X2))))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))))) <=> ![X0: $i, X1: $i, X2: $i] : (~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : (~(((~leq(X3, X1)) | (~leq(X3, X0))) <=> leq(X3, X2))))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[25])).
% 0.11/0.37 tff(27,plain,
% 0.11/0.37 (^[X0: $i, X1: $i, X2: $i] : rewrite((~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : (~(((~leq(X3, X1)) | (~leq(X3, X0))) <=> leq(X3, X2))))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))))) <=> (~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : (~(((~leq(X3, X1)) | (~leq(X3, X0))) <=> leq(X3, X2))))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 (![X0: $i, X1: $i, X2: $i] : (~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : (~(((~leq(X3, X1)) | (~leq(X3, X0))) <=> leq(X3, X2))))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))))) <=> ![X0: $i, X1: $i, X2: $i] : (~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : (~(((~leq(X3, X1)) | (~leq(X3, X0))) <=> leq(X3, X2))))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[27])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 (![X0: $i, X1: $i, X2: $i] : (~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : (~(((~leq(X3, X1)) | (~leq(X3, X0))) <=> leq(X3, X2))))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))))) <=> ![X0: $i, X1: $i, X2: $i] : (~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : (~(((~leq(X3, X1)) | (~leq(X3, X0))) <=> leq(X3, X2))))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))))))),
% 0.11/0.37 inference(transitivity,[status(thm)],[28, 26])).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 (^[X0: $i, X1: $i, X2: $i] : trans(monotonicity(rewrite(((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((leq(X3, X0) & leq(X3, X1)) <=> leq(X3, X2))) <=> ((~ismeetu(X2, X0, X1)) | ![X3: $i] : (~(((~leq(X3, X1)) | (~leq(X3, X0))) <=> leq(X3, X2))))), trans(monotonicity(trans(monotonicity(trans(trans(monotonicity(rewrite((leq(tptp_fun_X3_1(X2, X1, X0), X0) & leq(tptp_fun_X3_1(X2, X1, X0), X1)) <=> (~((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))))), (((leq(tptp_fun_X3_1(X2, X1, X0), X0) & leq(tptp_fun_X3_1(X2, X1, X0), X1)) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)) <=> ((~((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1)))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))), rewrite(((~((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1)))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)) <=> (~(((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))), (((leq(tptp_fun_X3_1(X2, X1, X0), X0) & leq(tptp_fun_X3_1(X2, X1, X0), X1)) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)) <=> (~(((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))))), rewrite((~(((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))) <=> (~(((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))), (((leq(tptp_fun_X3_1(X2, X1, X0), X0) & leq(tptp_fun_X3_1(X2, X1, X0), X1)) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)) <=> (~(((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))))), ((~((leq(tptp_fun_X3_1(X2, X1, X0), X0) & leq(tptp_fun_X3_1(X2, X1, X0), X1)) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))) <=> (~(~(((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))))), rewrite((~(~(((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))) <=> (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))), ((~((leq(tptp_fun_X3_1(X2, X1, X0), X0) & leq(tptp_fun_X3_1(X2, X1, X0), X1)) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))) <=> (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))), ((ismeetu(X2, X0, X1) | (~((leq(tptp_fun_X3_1(X2, X1, X0), X0) & leq(tptp_fun_X3_1(X2, X1, X0), X1)) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))) <=> (ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))))), rewrite((ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))) <=> (ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))), ((ismeetu(X2, X0, X1) | (~((leq(tptp_fun_X3_1(X2, X1, X0), X0) & leq(tptp_fun_X3_1(X2, X1, X0), X1)) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))) <=> (ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))))), ((((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((leq(X3, X0) & leq(X3, X1)) <=> leq(X3, X2))) & (ismeetu(X2, X0, X1) | (~((leq(tptp_fun_X3_1(X2, X1, X0), X0) & leq(tptp_fun_X3_1(X2, X1, X0), X1)) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))))) <=> (((~ismeetu(X2, X0, X1)) | ![X3: $i] : (~(((~leq(X3, X1)) | (~leq(X3, X0))) <=> leq(X3, X2)))) & (ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))))), rewrite((((~ismeetu(X2, X0, X1)) | ![X3: $i] : (~(((~leq(X3, X1)) | (~leq(X3, X0))) <=> leq(X3, X2)))) & (ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))) <=> (~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : (~(((~leq(X3, X1)) | (~leq(X3, X0))) <=> leq(X3, X2))))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))))))), ((((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((leq(X3, X0) & leq(X3, X1)) <=> leq(X3, X2))) & (ismeetu(X2, X0, X1) | (~((leq(tptp_fun_X3_1(X2, X1, X0), X0) & leq(tptp_fun_X3_1(X2, X1, X0), X1)) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))))) <=> (~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : (~(((~leq(X3, X1)) | (~leq(X3, X0))) <=> leq(X3, X2))))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(31,plain,
% 0.11/0.37 (![X0: $i, X1: $i, X2: $i] : (((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((leq(X3, X0) & leq(X3, X1)) <=> leq(X3, X2))) & (ismeetu(X2, X0, X1) | (~((leq(tptp_fun_X3_1(X2, X1, X0), X0) & leq(tptp_fun_X3_1(X2, X1, X0), X1)) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))))) <=> ![X0: $i, X1: $i, X2: $i] : (~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : (~(((~leq(X3, X1)) | (~leq(X3, X0))) <=> leq(X3, X2))))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[30])).
% 0.11/0.37 tff(32,plain,
% 0.11/0.37 (![X0: $i, X1: $i, X2: $i] : (ismeetu(X2, X0, X1) <=> ![X3: $i] : ((leq(X3, X0) & leq(X3, X1)) <=> leq(X3, X2))) <=> ![X0: $i, X1: $i, X2: $i] : (ismeetu(X2, X0, X1) <=> ![X3: $i] : ((leq(X3, X0) & leq(X3, X1)) <=> leq(X3, X2)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(33,axiom,(![X0: $i, X1: $i, X2: $i] : (ismeetu(X2, X0, X1) <=> ![X3: $i] : ((leq(X3, X0) & leq(X3, X1)) <=> leq(X3, X2)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+3.ax','ismeetu')).
% 0.11/0.37 tff(34,plain,
% 0.11/0.37 (![X0: $i, X1: $i, X2: $i] : (ismeetu(X2, X0, X1) <=> ![X3: $i] : ((leq(X3, X0) & leq(X3, X1)) <=> leq(X3, X2)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.11/0.37 tff(35,plain,(
% 0.11/0.37 ![X0: $i, X1: $i, X2: $i] : (((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((leq(X3, X0) & leq(X3, X1)) <=> leq(X3, X2))) & (ismeetu(X2, X0, X1) | (~((leq(tptp_fun_X3_1(X2, X1, X0), X0) & leq(tptp_fun_X3_1(X2, X1, X0), X1)) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))))),
% 0.11/0.37 inference(skolemize,[status(sab)],[34])).
% 0.11/0.37 tff(36,plain,
% 0.11/0.37 (![X0: $i, X1: $i, X2: $i] : (~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : (~(((~leq(X3, X1)) | (~leq(X3, X0))) <=> leq(X3, X2))))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.11/0.37 tff(37,plain,
% 0.11/0.37 (![X0: $i, X1: $i, X2: $i] : (~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : (~(((~leq(X3, X1)) | (~leq(X3, X0))) <=> leq(X3, X2))))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.11/0.37 tff(38,plain,
% 0.11/0.37 (![X0: $i, X1: $i, X2: $i] : (~((~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))) | (~((~ismeetu(X2, X0, X1)) | ![X3: $i] : (~(((~leq(X3, X1)) | (~leq(X3, X0))) <=> leq(X3, X2)))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[37, 24])).
% 0.11/0.37 tff(39,plain,
% 0.11/0.37 ((~![X0: $i, X1: $i, X2: $i] : (~((~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))) | (~((~ismeetu(X2, X0, X1)) | ![X3: $i] : (~(((~leq(X3, X1)) | (~leq(X3, X0))) <=> leq(X3, X2)))))))) | (~((~(ismeetu(X0!4, X1!3, X2!2) | (((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) <=> leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)))) | (~((~ismeetu(X0!4, X1!3, X2!2)) | ![X3: $i] : (~(((~leq(X3, X2!2)) | (~leq(X3, X1!3))) <=> leq(X3, X0!4)))))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(40,plain,
% 0.11/0.38 (~((~(ismeetu(X0!4, X1!3, X2!2) | (((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) <=> leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)))) | (~((~ismeetu(X0!4, X1!3, X2!2)) | ![X3: $i] : (~(((~leq(X3, X2!2)) | (~leq(X3, X1!3))) <=> leq(X3, X0!4))))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.11/0.38 tff(41,plain,
% 0.11/0.38 (((~(ismeetu(X0!4, X1!3, X2!2) | (((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) <=> leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)))) | (~((~ismeetu(X0!4, X1!3, X2!2)) | ![X3: $i] : (~(((~leq(X3, X2!2)) | (~leq(X3, X1!3))) <=> leq(X3, X0!4)))))) | ((~ismeetu(X0!4, X1!3, X2!2)) | ![X3: $i] : (~(((~leq(X3, X2!2)) | (~leq(X3, X1!3))) <=> leq(X3, X0!4))))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(42,plain,
% 0.11/0.38 ((~ismeetu(X0!4, X1!3, X2!2)) | ![X3: $i] : (~(((~leq(X3, X2!2)) | (~leq(X3, X1!3))) <=> leq(X3, X0!4)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.11/0.38 tff(43,plain,
% 0.11/0.38 ((~((~ismeetu(X0!4, X1!3, X2!2)) | ![X3: $i] : (~(((~leq(X3, X2!2)) | (~leq(X3, X1!3))) <=> leq(X3, X0!4))))) | (~ismeetu(X0!4, X1!3, X2!2)) | ![X3: $i] : (~(((~leq(X3, X2!2)) | (~leq(X3, X1!3))) <=> leq(X3, X0!4)))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(44,plain,
% 0.11/0.38 ((~ismeetu(X0!4, X1!3, X2!2)) | ![X3: $i] : (~(((~leq(X3, X2!2)) | (~leq(X3, X1!3))) <=> leq(X3, X0!4)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.11/0.38 tff(45,plain,
% 0.11/0.38 (![X3: $i] : (~(((~leq(X3, X2!2)) | (~leq(X3, X1!3))) <=> leq(X3, X0!4)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[44, 22])).
% 0.11/0.38 tff(46,plain,
% 0.11/0.38 ((~![X3: $i] : (~(((~leq(X3, X2!2)) | (~leq(X3, X1!3))) <=> leq(X3, X0!4)))) | (~(((~leq(X0!4, X2!2)) | (~leq(X0!4, X1!3))) <=> leq(X0!4, X0!4)))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(47,plain,
% 0.11/0.38 (~(((~leq(X0!4, X2!2)) | (~leq(X0!4, X1!3))) <=> leq(X0!4, X0!4))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.11/0.38 tff(48,plain,
% 0.11/0.38 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(X0!4, X0!4) <=> (addition(X0!4, X0!4) = X0!4))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(49,plain,
% 0.11/0.38 (leq(X0!4, X0!4) <=> (addition(X0!4, X0!4) = X0!4)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[48, 7])).
% 0.11/0.38 tff(50,assumption,(~(addition(X0!4, X0!4) = X0!4)), introduced(assumption)).
% 0.11/0.38 tff(51,plain,
% 0.11/0.38 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(52,plain,
% 0.11/0.38 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.11/0.38 inference(quant_intro,[status(thm)],[51])).
% 0.11/0.38 tff(53,plain,
% 0.11/0.38 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(54,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_idempotence')).
% 0.11/0.38 tff(55,plain,
% 0.11/0.38 (![A: $i] : (addition(A, A) = A)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.11/0.38 tff(56,plain,(
% 0.11/0.38 ![A: $i] : (addition(A, A) = A)),
% 0.11/0.38 inference(skolemize,[status(sab)],[55])).
% 0.11/0.38 tff(57,plain,
% 0.11/0.38 (![A: $i] : (addition(A, A) = A)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.11/0.38 tff(58,plain,
% 0.11/0.38 ((~![A: $i] : (addition(A, A) = A)) | (addition(X0!4, X0!4) = X0!4)),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(59,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[58, 57, 50])).
% 0.11/0.38 tff(60,plain,(addition(X0!4, X0!4) = X0!4), inference(lemma,lemma(discharge,[]))).
% 0.11/0.38 tff(61,plain,
% 0.11/0.38 ((~(leq(X0!4, X0!4) <=> (addition(X0!4, X0!4) = X0!4))) | leq(X0!4, X0!4) | (~(addition(X0!4, X0!4) = X0!4))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(62,plain,
% 0.11/0.38 ((~(leq(X0!4, X0!4) <=> (addition(X0!4, X0!4) = X0!4))) | leq(X0!4, X0!4)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.11/0.38 tff(63,plain,
% 0.11/0.38 (leq(X0!4, X0!4)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[62, 49])).
% 0.11/0.38 tff(64,plain,
% 0.11/0.38 ((((~leq(X0!4, X2!2)) | (~leq(X0!4, X1!3))) <=> leq(X0!4, X0!4)) | (~((~leq(X0!4, X2!2)) | (~leq(X0!4, X1!3)))) | (~leq(X0!4, X0!4))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(65,plain,
% 0.11/0.38 ((((~leq(X0!4, X2!2)) | (~leq(X0!4, X1!3))) <=> leq(X0!4, X0!4)) | (~((~leq(X0!4, X2!2)) | (~leq(X0!4, X1!3))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.11/0.38 tff(66,plain,
% 0.11/0.38 (~((~leq(X0!4, X2!2)) | (~leq(X0!4, X1!3)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[65, 47])).
% 0.11/0.38 tff(67,plain,
% 0.11/0.38 (((~leq(X0!4, X2!2)) | (~leq(X0!4, X1!3))) | leq(X0!4, X2!2)),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(68,plain,
% 0.11/0.38 (leq(X0!4, X2!2)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.11/0.38 tff(69,plain,
% 0.11/0.38 (((~leq(X0!4, X2!2)) | (~leq(X0!4, X1!3))) | leq(X0!4, X1!3)),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(70,plain,
% 0.11/0.38 (leq(X0!4, X1!3)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[69, 66])).
% 0.11/0.38 tff(71,plain,
% 0.11/0.38 (^[X0: $i, X1: $i, X2: $i] : rewrite((~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))))) <=> (~((~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))) | (~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(72,plain,
% 0.11/0.38 (![X0: $i, X1: $i, X2: $i] : (~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))))) <=> ![X0: $i, X1: $i, X2: $i] : (~((~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))) | (~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0))))))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[71])).
% 0.11/0.38 tff(73,plain,
% 0.11/0.38 (^[X0: $i, X1: $i, X2: $i] : refl((~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))))) <=> (~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(74,plain,
% 0.11/0.38 (![X0: $i, X1: $i, X2: $i] : (~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))))) <=> ![X0: $i, X1: $i, X2: $i] : (~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1))))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[73])).
% 0.11/0.38 tff(75,plain,
% 0.11/0.38 (^[X0: $i, X1: $i, X2: $i] : rewrite((~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))))) <=> (~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(76,plain,
% 0.11/0.38 (![X0: $i, X1: $i, X2: $i] : (~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))))) <=> ![X0: $i, X1: $i, X2: $i] : (~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1))))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[75])).
% 0.11/0.38 tff(77,plain,
% 0.11/0.38 (![X0: $i, X1: $i, X2: $i] : (~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))))) <=> ![X0: $i, X1: $i, X2: $i] : (~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1))))))))),
% 0.11/0.38 inference(transitivity,[status(thm)],[76, 74])).
% 0.11/0.38 tff(78,plain,
% 0.11/0.38 (^[X0: $i, X1: $i, X2: $i] : trans(monotonicity(rewrite(((~ismeet(X2, X0, X1)) | (leq(X2, X0) & leq(X2, X1) & ![X3: $i] : ((~(leq(X3, X0) & leq(X3, X1))) | leq(X3, X2)))) <=> ((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))), trans(monotonicity(rewrite((~((~(leq(tptp_fun_X3_0(X2, X1, X0), X0) & leq(tptp_fun_X3_0(X2, X1, X0), X1))) | leq(tptp_fun_X3_0(X2, X1, X0), X2))) <=> (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1))))), ((ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~((~(leq(tptp_fun_X3_0(X2, X1, X0), X0) & leq(tptp_fun_X3_0(X2, X1, X0), X1))) | leq(tptp_fun_X3_0(X2, X1, X0), X2)))) <=> (ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1))))))), rewrite((ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1))))) <=> (ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))), ((ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~((~(leq(tptp_fun_X3_0(X2, X1, X0), X0) & leq(tptp_fun_X3_0(X2, X1, X0), X1))) | leq(tptp_fun_X3_0(X2, X1, X0), X2)))) <=> (ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1))))))), ((((~ismeet(X2, X0, X1)) | (leq(X2, X0) & leq(X2, X1) & ![X3: $i] : ((~(leq(X3, X0) & leq(X3, X1))) | leq(X3, X2)))) & (ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~((~(leq(tptp_fun_X3_0(X2, X1, X0), X0) & leq(tptp_fun_X3_0(X2, X1, X0), X1))) | leq(tptp_fun_X3_0(X2, X1, X0), X2))))) <=> (((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0))))))) & (ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))))), rewrite((((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0))))))) & (ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))) <=> (~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1))))))))), ((((~ismeet(X2, X0, X1)) | (leq(X2, X0) & leq(X2, X1) & ![X3: $i] : ((~(leq(X3, X0) & leq(X3, X1))) | leq(X3, X2)))) & (ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~((~(leq(tptp_fun_X3_0(X2, X1, X0), X0) & leq(tptp_fun_X3_0(X2, X1, X0), X1))) | leq(tptp_fun_X3_0(X2, X1, X0), X2))))) <=> (~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1))))))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(79,plain,
% 0.11/0.38 (![X0: $i, X1: $i, X2: $i] : (((~ismeet(X2, X0, X1)) | (leq(X2, X0) & leq(X2, X1) & ![X3: $i] : ((~(leq(X3, X0) & leq(X3, X1))) | leq(X3, X2)))) & (ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~((~(leq(tptp_fun_X3_0(X2, X1, X0), X0) & leq(tptp_fun_X3_0(X2, X1, X0), X1))) | leq(tptp_fun_X3_0(X2, X1, X0), X2))))) <=> ![X0: $i, X1: $i, X2: $i] : (~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1))))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[78])).
% 0.11/0.38 tff(80,plain,
% 0.11/0.38 (^[X0: $i, X1: $i, X2: $i] : rewrite((((~ismeet(X2, X0, X1)) | (leq(X2, X0) & leq(X2, X1) & ![X3: $i] : ((~(leq(X3, X0) & leq(X3, X1))) | leq(X3, X2)))) & (ismeet(X2, X0, X1) | ((~leq(X2, X0)) | (~leq(X2, X1)) | (~((~(leq(tptp_fun_X3_0(X2, X1, X0), X0) & leq(tptp_fun_X3_0(X2, X1, X0), X1))) | leq(tptp_fun_X3_0(X2, X1, X0), X2)))))) <=> (((~ismeet(X2, X0, X1)) | (leq(X2, X0) & leq(X2, X1) & ![X3: $i] : ((~(leq(X3, X0) & leq(X3, X1))) | leq(X3, X2)))) & (ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~((~(leq(tptp_fun_X3_0(X2, X1, X0), X0) & leq(tptp_fun_X3_0(X2, X1, X0), X1))) | leq(tptp_fun_X3_0(X2, X1, X0), X2))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(81,plain,
% 0.11/0.38 (![X0: $i, X1: $i, X2: $i] : (((~ismeet(X2, X0, X1)) | (leq(X2, X0) & leq(X2, X1) & ![X3: $i] : ((~(leq(X3, X0) & leq(X3, X1))) | leq(X3, X2)))) & (ismeet(X2, X0, X1) | ((~leq(X2, X0)) | (~leq(X2, X1)) | (~((~(leq(tptp_fun_X3_0(X2, X1, X0), X0) & leq(tptp_fun_X3_0(X2, X1, X0), X1))) | leq(tptp_fun_X3_0(X2, X1, X0), X2)))))) <=> ![X0: $i, X1: $i, X2: $i] : (((~ismeet(X2, X0, X1)) | (leq(X2, X0) & leq(X2, X1) & ![X3: $i] : ((~(leq(X3, X0) & leq(X3, X1))) | leq(X3, X2)))) & (ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~((~(leq(tptp_fun_X3_0(X2, X1, X0), X0) & leq(tptp_fun_X3_0(X2, X1, X0), X1))) | leq(tptp_fun_X3_0(X2, X1, X0), X2)))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[80])).
% 0.11/0.38 tff(82,plain,
% 0.11/0.38 (![X0: $i, X1: $i, X2: $i] : (ismeet(X2, X0, X1) <=> (leq(X2, X0) & leq(X2, X1) & ![X3: $i] : ((~(leq(X3, X0) & leq(X3, X1))) | leq(X3, X2)))) <=> ![X0: $i, X1: $i, X2: $i] : (ismeet(X2, X0, X1) <=> (leq(X2, X0) & leq(X2, X1) & ![X3: $i] : ((~(leq(X3, X0) & leq(X3, X1))) | leq(X3, X2))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(83,plain,
% 0.11/0.38 (^[X0: $i, X1: $i, X2: $i] : rewrite((ismeet(X2, X0, X1) <=> ((leq(X2, X0) & leq(X2, X1)) & ![X3: $i] : ((leq(X3, X0) & leq(X3, X1)) => leq(X3, X2)))) <=> (ismeet(X2, X0, X1) <=> (leq(X2, X0) & leq(X2, X1) & ![X3: $i] : ((~(leq(X3, X0) & leq(X3, X1))) | leq(X3, X2)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(84,plain,
% 0.11/0.38 (![X0: $i, X1: $i, X2: $i] : (ismeet(X2, X0, X1) <=> ((leq(X2, X0) & leq(X2, X1)) & ![X3: $i] : ((leq(X3, X0) & leq(X3, X1)) => leq(X3, X2)))) <=> ![X0: $i, X1: $i, X2: $i] : (ismeet(X2, X0, X1) <=> (leq(X2, X0) & leq(X2, X1) & ![X3: $i] : ((~(leq(X3, X0) & leq(X3, X1))) | leq(X3, X2))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[83])).
% 0.11/0.38 tff(85,axiom,(![X0: $i, X1: $i, X2: $i] : (ismeet(X2, X0, X1) <=> ((leq(X2, X0) & leq(X2, X1)) & ![X3: $i] : ((leq(X3, X0) & leq(X3, X1)) => leq(X3, X2))))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+3.ax','ismeet')).
% 0.11/0.38 tff(86,plain,
% 0.11/0.38 (![X0: $i, X1: $i, X2: $i] : (ismeet(X2, X0, X1) <=> (leq(X2, X0) & leq(X2, X1) & ![X3: $i] : ((~(leq(X3, X0) & leq(X3, X1))) | leq(X3, X2))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.11/0.38 tff(87,plain,
% 0.11/0.38 (![X0: $i, X1: $i, X2: $i] : (ismeet(X2, X0, X1) <=> (leq(X2, X0) & leq(X2, X1) & ![X3: $i] : ((~(leq(X3, X0) & leq(X3, X1))) | leq(X3, X2))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.11/0.38 tff(88,plain,(
% 0.11/0.38 ![X0: $i, X1: $i, X2: $i] : (((~ismeet(X2, X0, X1)) | (leq(X2, X0) & leq(X2, X1) & ![X3: $i] : ((~(leq(X3, X0) & leq(X3, X1))) | leq(X3, X2)))) & (ismeet(X2, X0, X1) | ((~leq(X2, X0)) | (~leq(X2, X1)) | (~((~(leq(tptp_fun_X3_0(X2, X1, X0), X0) & leq(tptp_fun_X3_0(X2, X1, X0), X1))) | leq(tptp_fun_X3_0(X2, X1, X0), X2))))))),
% 0.11/0.38 inference(skolemize,[status(sab)],[87])).
% 0.11/0.38 tff(89,plain,
% 0.11/0.38 (![X0: $i, X1: $i, X2: $i] : (((~ismeet(X2, X0, X1)) | (leq(X2, X0) & leq(X2, X1) & ![X3: $i] : ((~(leq(X3, X0) & leq(X3, X1))) | leq(X3, X2)))) & (ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~((~(leq(tptp_fun_X3_0(X2, X1, X0), X0) & leq(tptp_fun_X3_0(X2, X1, X0), X1))) | leq(tptp_fun_X3_0(X2, X1, X0), X2)))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.11/0.38 tff(90,plain,
% 0.11/0.38 (![X0: $i, X1: $i, X2: $i] : (~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1))))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[89, 79])).
% 0.11/0.38 tff(91,plain,
% 0.11/0.38 (![X0: $i, X1: $i, X2: $i] : (~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1))))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[90, 77])).
% 0.11/0.38 tff(92,plain,
% 0.11/0.38 (![X0: $i, X1: $i, X2: $i] : (~((~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))) | (~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0))))))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[91, 72])).
% 0.11/0.38 tff(93,plain,
% 0.11/0.38 (((~![X0: $i, X1: $i, X2: $i] : (~((~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))) | (~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0))))))))))) | (~((~(ismeet(X0!4, X1!3, X2!2) | (~leq(X0!4, X2!2)) | (~leq(X0!4, X1!3)) | (~((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4))))) | (~((~ismeet(X0!4, X1!3, X2!2)) | (~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : (~((~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))) | (~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0))))))))))) | (~((~(ismeet(X0!4, X1!3, X2!2) | (~leq(X0!4, X2!2)) | (~leq(X0!4, X1!3)) | (~((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4))))) | (~((~ismeet(X0!4, X1!3, X2!2)) | (~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3)))))))))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(94,plain,
% 0.11/0.39 ((~((~(ismeet(X0!4, X1!3, X2!2) | (~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~(leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)))))) | (~((~ismeet(X0!4, X1!3, X2!2)) | (~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3)))))))))) <=> (~((~(ismeet(X0!4, X1!3, X2!2) | (~leq(X0!4, X2!2)) | (~leq(X0!4, X1!3)) | (~((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4))))) | (~((~ismeet(X0!4, X1!3, X2!2)) | (~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3))))))))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(95,plain,
% 0.11/0.39 (((~![X0: $i, X1: $i, X2: $i] : (~((~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))) | (~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0))))))))))) | (~((~(ismeet(X0!4, X1!3, X2!2) | (~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~(leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)))))) | (~((~ismeet(X0!4, X1!3, X2!2)) | (~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : (~((~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))) | (~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0))))))))))) | (~((~(ismeet(X0!4, X1!3, X2!2) | (~leq(X0!4, X2!2)) | (~leq(X0!4, X1!3)) | (~((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4))))) | (~((~ismeet(X0!4, X1!3, X2!2)) | (~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3)))))))))))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[94])).
% 0.11/0.39 tff(96,plain,
% 0.11/0.39 (((~![X0: $i, X1: $i, X2: $i] : (~((~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))) | (~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0))))))))))) | (~((~(ismeet(X0!4, X1!3, X2!2) | (~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~(leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)))))) | (~((~ismeet(X0!4, X1!3, X2!2)) | (~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : (~((~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))) | (~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0))))))))))) | (~((~(ismeet(X0!4, X1!3, X2!2) | (~leq(X0!4, X2!2)) | (~leq(X0!4, X1!3)) | (~((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4))))) | (~((~ismeet(X0!4, X1!3, X2!2)) | (~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3)))))))))))),
% 0.11/0.39 inference(transitivity,[status(thm)],[95, 93])).
% 0.11/0.39 tff(97,plain,
% 0.11/0.39 ((~![X0: $i, X1: $i, X2: $i] : (~((~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))) | (~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0))))))))))) | (~((~(ismeet(X0!4, X1!3, X2!2) | (~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~(leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)))))) | (~((~ismeet(X0!4, X1!3, X2!2)) | (~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3))))))))))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(98,plain,
% 0.11/0.39 ((~![X0: $i, X1: $i, X2: $i] : (~((~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))) | (~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0))))))))))) | (~((~(ismeet(X0!4, X1!3, X2!2) | (~leq(X0!4, X2!2)) | (~leq(X0!4, X1!3)) | (~((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4))))) | (~((~ismeet(X0!4, X1!3, X2!2)) | (~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3))))))))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.11/0.39 tff(99,plain,
% 0.11/0.39 (~((~(ismeet(X0!4, X1!3, X2!2) | (~leq(X0!4, X2!2)) | (~leq(X0!4, X1!3)) | (~((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4))))) | (~((~ismeet(X0!4, X1!3, X2!2)) | (~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3)))))))))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[98, 92])).
% 0.11/0.39 tff(100,plain,
% 0.11/0.39 (((~(ismeet(X0!4, X1!3, X2!2) | (~leq(X0!4, X2!2)) | (~leq(X0!4, X1!3)) | (~((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4))))) | (~((~ismeet(X0!4, X1!3, X2!2)) | (~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3))))))))) | (ismeet(X0!4, X1!3, X2!2) | (~leq(X0!4, X2!2)) | (~leq(X0!4, X1!3)) | (~((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4))))),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(101,plain,
% 0.11/0.39 (ismeet(X0!4, X1!3, X2!2) | (~leq(X0!4, X2!2)) | (~leq(X0!4, X1!3)) | (~((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4)))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.11/0.39 tff(102,plain,
% 0.11/0.39 ((~(ismeet(X0!4, X1!3, X2!2) | (~leq(X0!4, X2!2)) | (~leq(X0!4, X1!3)) | (~((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4))))) | ismeet(X0!4, X1!3, X2!2) | (~leq(X0!4, X2!2)) | (~leq(X0!4, X1!3)) | (~((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4)))),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(103,plain,
% 0.11/0.39 (ismeet(X0!4, X1!3, X2!2) | (~leq(X0!4, X2!2)) | (~leq(X0!4, X1!3)) | (~((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4)))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.11/0.40 tff(104,plain,
% 0.11/0.40 (~((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[103, 70, 10, 68])).
% 0.11/0.40 tff(105,plain,
% 0.11/0.40 (((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4)) | leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(106,plain,
% 0.11/0.40 (leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.11/0.40 tff(107,plain,
% 0.11/0.40 (((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4)) | leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(108,plain,
% 0.11/0.40 (leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[107, 104])).
% 0.11/0.40 tff(109,plain,
% 0.11/0.40 ((~((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)))) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3))),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(110,plain,
% 0.11/0.40 (~((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[109, 108, 106])).
% 0.11/0.40 tff(111,plain,
% 0.11/0.40 (((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4))),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(112,plain,
% 0.11/0.40 (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[111, 104])).
% 0.11/0.40 tff(113,plain,
% 0.11/0.40 ((((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3))) <=> leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4)) | ((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3))) | leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4)),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(114,plain,
% 0.11/0.40 (((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3))) <=> leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[113, 112, 110])).
% 0.11/0.40 tff(115,plain,
% 0.11/0.40 ((~![X3: $i] : (~(((~leq(X3, X2!2)) | (~leq(X3, X1!3))) <=> leq(X3, X0!4)))) | (~(((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3))) <=> leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4)))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(116,plain,
% 0.11/0.40 ($false),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[115, 45, 114])).
% 0.11/0.40 tff(117,plain,(ismeet(X0!4, X1!3, X2!2)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.40 tff(118,plain,
% 0.11/0.40 (((~(ismeet(X0!4, X1!3, X2!2) | (~leq(X0!4, X2!2)) | (~leq(X0!4, X1!3)) | (~((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4))))) | (~((~ismeet(X0!4, X1!3, X2!2)) | (~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3))))))))) | ((~ismeet(X0!4, X1!3, X2!2)) | (~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3)))))))),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(119,plain,
% 0.11/0.40 ((~ismeet(X0!4, X1!3, X2!2)) | (~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3))))))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[118, 99])).
% 0.11/0.40 tff(120,plain,
% 0.11/0.40 ((~((~ismeet(X0!4, X1!3, X2!2)) | (~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3)))))))) | (~ismeet(X0!4, X1!3, X2!2)) | (~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3))))))),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(121,plain,
% 0.11/0.40 ((~ismeet(X0!4, X1!3, X2!2)) | (~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3))))))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.11/0.40 tff(122,plain,
% 0.11/0.40 (~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3)))))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[121, 117])).
% 0.11/0.40 tff(123,plain,
% 0.11/0.40 (((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3))))) | leq(X0!4, X2!2)),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(124,plain,
% 0.11/0.40 (leq(X0!4, X2!2)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.11/0.40 tff(125,plain,
% 0.11/0.40 ((~(leq(X0!4, X2!2) <=> (addition(X0!4, X2!2) = X2!2))) | (~leq(X0!4, X2!2)) | (addition(X0!4, X2!2) = X2!2)),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(126,plain,
% 0.11/0.40 ((~(leq(X0!4, X2!2) <=> (addition(X0!4, X2!2) = X2!2))) | (addition(X0!4, X2!2) = X2!2)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.11/0.40 tff(127,plain,
% 0.11/0.40 (addition(X0!4, X2!2) = X2!2),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[126, 9])).
% 0.11/0.40 tff(128,assumption,(~((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2)))), introduced(assumption)).
% 0.11/0.40 tff(129,plain,
% 0.11/0.40 (((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) | leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2)),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(130,plain,
% 0.11/0.40 (leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.11/0.40 tff(131,plain,
% 0.11/0.40 ((ismeet(X0!4, X1!3, X2!2) <=> ismeetu(X0!4, X1!3, X2!2)) | (~ismeet(X0!4, X1!3, X2!2)) | (~ismeetu(X0!4, X1!3, X2!2))),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(132,plain,
% 0.11/0.40 ((~ismeet(X0!4, X1!3, X2!2)) | (~ismeetu(X0!4, X1!3, X2!2))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[131, 19])).
% 0.11/0.40 tff(133,plain,
% 0.11/0.40 (~ismeetu(X0!4, X1!3, X2!2)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[132, 117])).
% 0.11/0.40 tff(134,plain,
% 0.11/0.40 (((~(ismeetu(X0!4, X1!3, X2!2) | (((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) <=> leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)))) | (~((~ismeetu(X0!4, X1!3, X2!2)) | ![X3: $i] : (~(((~leq(X3, X2!2)) | (~leq(X3, X1!3))) <=> leq(X3, X0!4)))))) | (ismeetu(X0!4, X1!3, X2!2) | (((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) <=> leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)))),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(135,plain,
% 0.11/0.40 (ismeetu(X0!4, X1!3, X2!2) | (((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) <=> leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[134, 40])).
% 0.11/0.40 tff(136,plain,
% 0.11/0.40 ((~(ismeetu(X0!4, X1!3, X2!2) | (((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) <=> leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)))) | ismeetu(X0!4, X1!3, X2!2) | (((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) <=> leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4))),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(137,plain,
% 0.11/0.40 (ismeetu(X0!4, X1!3, X2!2) | (((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) <=> leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.11/0.40 tff(138,plain,
% 0.11/0.40 (((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) <=> leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[137, 133])).
% 0.11/0.40 tff(139,plain,
% 0.11/0.40 ((~(((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) <=> leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4))) | ((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4))),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(140,plain,
% 0.11/0.40 (((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.11/0.40 tff(141,plain,
% 0.11/0.40 (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[140, 128])).
% 0.11/0.40 tff(142,plain,
% 0.11/0.40 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(X0!4, X1!3) <=> (addition(X0!4, X1!3) = X1!3))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(143,plain,
% 0.11/0.40 (leq(X0!4, X1!3) <=> (addition(X0!4, X1!3) = X1!3)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[142, 7])).
% 0.11/0.40 tff(144,plain,
% 0.11/0.40 (((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3))))) | leq(X0!4, X1!3)),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(145,plain,
% 0.11/0.40 (leq(X0!4, X1!3)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[144, 122])).
% 0.11/0.40 tff(146,plain,
% 0.11/0.40 ((~(leq(X0!4, X1!3) <=> (addition(X0!4, X1!3) = X1!3))) | (~leq(X0!4, X1!3)) | (addition(X0!4, X1!3) = X1!3)),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(147,plain,
% 0.11/0.40 ((~(leq(X0!4, X1!3) <=> (addition(X0!4, X1!3) = X1!3))) | (addition(X0!4, X1!3) = X1!3)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.11/0.40 tff(148,plain,
% 0.11/0.40 (addition(X0!4, X1!3) = X1!3),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[147, 143])).
% 0.11/0.40 tff(149,plain,
% 0.11/0.40 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4) <=> (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4) = X0!4))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(150,plain,
% 0.11/0.40 (leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4) <=> (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4) = X0!4)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[149, 7])).
% 0.11/0.40 tff(151,assumption,(~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)), introduced(assumption)).
% 0.11/0.40 tff(152,plain,
% 0.11/0.40 (((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) | leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(153,plain,
% 0.11/0.40 ((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.11/0.40 tff(154,plain,
% 0.11/0.40 ((~(((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) <=> leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4))) | (~((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2)))) | leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(155,plain,
% 0.11/0.40 (leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[154, 153, 138])).
% 0.11/0.40 tff(156,plain,
% 0.11/0.40 ((~(leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4) <=> (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4) = X0!4))) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)) | (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4) = X0!4)),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(157,plain,
% 0.11/0.40 (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4) = X0!4),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[156, 155, 150])).
% 0.11/0.40 tff(158,plain,
% 0.11/0.40 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(159,plain,
% 0.11/0.40 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[158])).
% 0.11/0.40 tff(160,plain,
% 0.11/0.40 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(161,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 0.11/0.40 tff(162,plain,
% 0.11/0.40 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.19/0.41 tff(163,plain,(
% 0.19/0.41 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.19/0.41 inference(skolemize,[status(sab)],[162])).
% 0.19/0.41 tff(164,plain,
% 0.19/0.41 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[163, 159])).
% 0.19/0.41 tff(165,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4) = addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(166,plain,
% 0.19/0.41 (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4) = addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[165, 164])).
% 0.19/0.41 tff(167,plain,
% 0.19/0.41 (addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)) = addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)),
% 0.19/0.41 inference(symmetry,[status(thm)],[166])).
% 0.19/0.41 tff(168,plain,
% 0.19/0.41 (addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)) = X0!4),
% 0.19/0.41 inference(transitivity,[status(thm)],[167, 157])).
% 0.19/0.41 tff(169,plain,
% 0.19/0.41 (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3))) = addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[168])).
% 0.19/0.41 tff(170,plain,
% 0.19/0.41 (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3))) = X0!4),
% 0.19/0.41 inference(transitivity,[status(thm)],[169, 157])).
% 0.19/0.41 tff(171,plain,
% 0.19/0.41 (addition(addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3))), X1!3) = addition(X0!4, X1!3)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[170])).
% 0.19/0.41 tff(172,plain,
% 0.19/0.41 (^[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)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(173,plain,
% 0.19/0.41 (![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))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[172])).
% 0.19/0.41 tff(174,plain,
% 0.19/0.41 (![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))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(175,axiom,(![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_associativity')).
% 0.19/0.41 tff(176,plain,
% 0.19/0.41 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.19/0.41 tff(177,plain,(
% 0.19/0.41 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.19/0.41 inference(skolemize,[status(sab)],[176])).
% 0.19/0.41 tff(178,plain,
% 0.19/0.41 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[177, 173])).
% 0.19/0.41 tff(179,plain,
% 0.19/0.41 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), X1!3)) = addition(addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3))), X1!3))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(180,plain,
% 0.19/0.41 (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), X1!3)) = addition(addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3))), X1!3)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[179, 178])).
% 0.19/0.41 tff(181,plain,
% 0.19/0.41 (addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), X1!3) = addition(X0!4, X1!3)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[168])).
% 0.19/0.41 tff(182,plain,
% 0.19/0.41 (addition(X0!4, X1!3) = addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), X1!3)),
% 0.19/0.41 inference(symmetry,[status(thm)],[181])).
% 0.19/0.41 tff(183,plain,
% 0.19/0.41 (X1!3 = addition(X0!4, X1!3)),
% 0.19/0.41 inference(symmetry,[status(thm)],[148])).
% 0.19/0.41 tff(184,plain,
% 0.19/0.41 (X1!3 = addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), X1!3)),
% 0.19/0.41 inference(transitivity,[status(thm)],[183, 182])).
% 0.19/0.41 tff(185,plain,
% 0.19/0.41 (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3) = addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), X1!3))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[184])).
% 0.19/0.41 tff(186,plain,
% 0.19/0.41 (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3) = X1!3),
% 0.19/0.41 inference(transitivity,[status(thm)],[185, 180, 171, 148])).
% 0.19/0.41 tff(187,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3) <=> (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3) = X1!3))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(188,plain,
% 0.19/0.41 (leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3) <=> (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3) = X1!3)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[187, 7])).
% 0.19/0.41 tff(189,plain,
% 0.19/0.41 ((~(leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3) <=> (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3) = X1!3))) | leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3) | (~(addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3) = X1!3))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(190,plain,
% 0.19/0.41 ((~(leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3) <=> (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3) = X1!3))) | (~(addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3) = X1!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[189, 151])).
% 0.19/0.41 tff(191,plain,
% 0.19/0.41 (~(addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3) = X1!3)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[190, 188])).
% 0.19/0.41 tff(192,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[191, 186])).
% 0.19/0.41 tff(193,plain,(leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(194,plain,
% 0.19/0.41 (((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3))))) | ![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(195,plain,
% 0.19/0.41 (![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[194, 122])).
% 0.19/0.41 tff(196,plain,
% 0.19/0.41 (((~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3)))) | (leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)))) <=> ((~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3)))) | leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(197,plain,
% 0.19/0.41 ((~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3)))) | (leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(198,plain,
% 0.19/0.41 ((~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3)))) | leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.19/0.41 tff(199,plain,
% 0.19/0.41 (leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[198, 195])).
% 0.19/0.41 tff(200,plain,
% 0.19/0.41 (leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[199, 193])).
% 0.19/0.41 tff(201,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[200, 141, 130])).
% 0.19/0.41 tff(202,plain,((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(203,plain,
% 0.19/0.41 ((~((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2)))) | leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[154, 138])).
% 0.19/0.41 tff(204,plain,
% 0.19/0.41 (leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[203, 202])).
% 0.19/0.41 tff(205,plain,
% 0.19/0.41 ((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)) | (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4) = X0!4)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[156, 150])).
% 0.19/0.41 tff(206,plain,
% 0.19/0.41 (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4) = X0!4),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[205, 204])).
% 0.19/0.41 tff(207,plain,
% 0.19/0.41 ((~![A: $i] : (addition(A, A) = A)) | (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), tptp_fun_X3_1(X0!4, X2!2, X1!3)) = tptp_fun_X3_1(X0!4, X2!2, X1!3))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(208,plain,
% 0.19/0.41 (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), tptp_fun_X3_1(X0!4, X2!2, X1!3)) = tptp_fun_X3_1(X0!4, X2!2, X1!3)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[207, 57])).
% 0.19/0.41 tff(209,plain,
% 0.19/0.41 (addition(X0!4, addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), tptp_fun_X3_1(X0!4, X2!2, X1!3))) = addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[208])).
% 0.19/0.41 tff(210,plain,
% 0.19/0.41 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X0!4, addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), tptp_fun_X3_1(X0!4, X2!2, X1!3))) = addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), tptp_fun_X3_1(X0!4, X2!2, X1!3)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(211,plain,
% 0.19/0.41 (addition(X0!4, addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), tptp_fun_X3_1(X0!4, X2!2, X1!3))) = addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), tptp_fun_X3_1(X0!4, X2!2, X1!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[210, 178])).
% 0.19/0.41 tff(212,plain,
% 0.19/0.41 (addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), tptp_fun_X3_1(X0!4, X2!2, X1!3)) = addition(X0!4, addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), tptp_fun_X3_1(X0!4, X2!2, X1!3)))),
% 0.19/0.41 inference(symmetry,[status(thm)],[211])).
% 0.19/0.41 tff(213,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), tptp_fun_X3_1(X0!4, X2!2, X1!3)) = addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(214,plain,
% 0.19/0.41 (addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), tptp_fun_X3_1(X0!4, X2!2, X1!3)) = addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[213, 164])).
% 0.19/0.41 tff(215,plain,
% 0.19/0.41 (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3))) = addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), tptp_fun_X3_1(X0!4, X2!2, X1!3))),
% 0.19/0.41 inference(symmetry,[status(thm)],[214])).
% 0.19/0.41 tff(216,plain,
% 0.19/0.41 (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3))) = X0!4),
% 0.19/0.41 inference(transitivity,[status(thm)],[215, 212, 209, 167, 206])).
% 0.19/0.41 tff(217,plain,
% 0.19/0.41 (addition(addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3))), X2!2) = addition(X0!4, X2!2)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[216])).
% 0.19/0.41 tff(218,plain,
% 0.19/0.41 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), X2!2)) = addition(addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3))), X2!2))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(219,plain,
% 0.19/0.41 (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), X2!2)) = addition(addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3))), X2!2)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[218, 178])).
% 0.19/0.41 tff(220,plain,
% 0.19/0.41 (addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)) = X0!4),
% 0.19/0.41 inference(transitivity,[status(thm)],[167, 206])).
% 0.19/0.41 tff(221,plain,
% 0.19/0.41 (addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), X2!2) = addition(X0!4, X2!2)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[220])).
% 0.19/0.41 tff(222,plain,
% 0.19/0.41 (addition(X0!4, X2!2) = addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), X2!2)),
% 0.19/0.42 inference(symmetry,[status(thm)],[221])).
% 0.19/0.42 tff(223,plain,
% 0.19/0.42 (X2!2 = addition(X0!4, X2!2)),
% 0.19/0.42 inference(symmetry,[status(thm)],[127])).
% 0.19/0.42 tff(224,plain,
% 0.19/0.42 (X2!2 = addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), X2!2)),
% 0.19/0.42 inference(transitivity,[status(thm)],[223, 222])).
% 0.19/0.42 tff(225,plain,
% 0.19/0.42 (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2) = addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), X2!2))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[224])).
% 0.19/0.42 tff(226,plain,
% 0.19/0.42 (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2) = X2!2),
% 0.19/0.42 inference(transitivity,[status(thm)],[225, 219, 217, 127])).
% 0.19/0.42 tff(227,plain,
% 0.19/0.42 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2) <=> (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2) = X2!2))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(228,plain,
% 0.19/0.42 (leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2) <=> (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2) = X2!2)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[227, 7])).
% 0.19/0.42 tff(229,plain,
% 0.19/0.42 ((~((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2)))) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(230,plain,
% 0.19/0.42 ((~((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2)))) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[229, 193])).
% 0.19/0.42 tff(231,plain,
% 0.19/0.42 (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[230, 202])).
% 0.19/0.42 tff(232,plain,
% 0.19/0.42 ((~(leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2) <=> (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2) = X2!2))) | leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2) | (~(addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2) = X2!2))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(233,plain,
% 0.19/0.42 ((~(leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2) <=> (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2) = X2!2))) | (~(addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2) = X2!2))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[232, 231])).
% 0.19/0.42 tff(234,plain,
% 0.19/0.42 (~(addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2) = X2!2)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[233, 228])).
% 0.19/0.42 tff(235,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[234, 226])).
% 0.19/0.42 % SZS output end Proof
% 0.19/0.42 % E exiting
%------------------------------------------------------------------------------