%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL540+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% 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 : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 03:00:12 PM UTC 2026
% Result : Theorem 0.13s 0.41s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL540+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.09/0.35 % Computer : n013.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 4 16:03:06 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.41 % SZS status Theorem
% 0.13/0.41 % SZS output start Proof
% 0.13/0.41 tff(is_a_theorem_type, type, (
% 0.13/0.41 is_a_theorem: $i > $o)).
% 0.13/0.41 tff(implies_type, type, (
% 0.13/0.41 implies: ( $i * $i ) > $i)).
% 0.13/0.41 tff(and_type, type, (
% 0.13/0.41 and: ( $i * $i ) > $i)).
% 0.13/0.41 tff(tptp_fun_Y_61_type, type, (
% 0.13/0.41 tptp_fun_Y_61: $i)).
% 0.13/0.41 tff(tptp_fun_X_62_type, type, (
% 0.13/0.41 tptp_fun_X_62: $i)).
% 0.13/0.41 tff(and_3_type, type, (
% 0.13/0.41 and_3: $o)).
% 0.13/0.41 tff(tptp_fun_Y_20_type, type, (
% 0.13/0.41 tptp_fun_Y_20: $i)).
% 0.13/0.41 tff(tptp_fun_X_21_type, type, (
% 0.13/0.41 tptp_fun_X_21: $i)).
% 0.13/0.41 tff(adjunction_type, type, (
% 0.13/0.41 adjunction: $o)).
% 0.13/0.41 tff(modus_ponens_type, type, (
% 0.13/0.41 modus_ponens: $o)).
% 0.13/0.41 tff(tptp_fun_Y_3_type, type, (
% 0.13/0.41 tptp_fun_Y_3: $i)).
% 0.13/0.41 tff(tptp_fun_X_4_type, type, (
% 0.13/0.41 tptp_fun_X_4: $i)).
% 0.13/0.41 tff(1,plain,
% 0.13/0.41 (and_3 <=> and_3),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(2,axiom,(and_3), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax','hilbert_and_3')).
% 0.13/0.41 tff(3,plain,
% 0.13/0.41 (and_3),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.13/0.41 tff(4,plain,
% 0.13/0.41 (((~and_3) | ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))) <=> ((~and_3) | ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y)))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(5,plain,
% 0.13/0.41 (((~and_3) | ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))) <=> ((~and_3) | ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y)))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(6,plain,
% 0.13/0.41 ((((~and_3) | ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))) & (and_3 | (~is_a_theorem(implies(X!21, implies(Y!20, and(X!21, Y!20))))))) <=> (((~and_3) | ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))) & (and_3 | (~is_a_theorem(implies(X!21, implies(Y!20, and(X!21, Y!20)))))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[5])).
% 0.13/0.41 tff(7,plain,
% 0.13/0.41 ((and_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))) <=> (and_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y)))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(8,axiom,(and_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','and_3')).
% 0.13/0.41 tff(9,plain,
% 0.13/0.41 (and_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.13/0.41 tff(10,plain,
% 0.13/0.41 (and_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[9, 7])).
% 0.13/0.41 tff(11,plain,
% 0.13/0.41 (and_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[10, 7])).
% 0.13/0.41 tff(12,plain,
% 0.13/0.41 (and_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.13/0.41 tff(13,plain,(
% 0.13/0.41 ((~and_3) | ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))) & (and_3 | (~is_a_theorem(implies(X!21, implies(Y!20, and(X!21, Y!20))))))),
% 0.13/0.41 inference(skolemize,[status(sab)],[12])).
% 0.13/0.41 tff(14,plain,
% 0.13/0.41 (((~and_3) | ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))) & (and_3 | (~is_a_theorem(implies(X!21, implies(Y!20, and(X!21, Y!20))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.13/0.41 tff(15,plain,
% 0.13/0.41 ((~and_3) | ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))),
% 0.13/0.41 inference(and_elim,[status(thm)],[14])).
% 0.13/0.41 tff(16,plain,
% 0.13/0.41 ((~and_3) | ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[15, 4])).
% 0.13/0.41 tff(17,plain,
% 0.13/0.41 (![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[16, 3])).
% 0.13/0.41 tff(18,plain,
% 0.13/0.41 ((~![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))) | is_a_theorem(implies(X!62, implies(Y!61, and(X!62, Y!61))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(19,plain,
% 0.13/0.41 (is_a_theorem(implies(X!62, implies(Y!61, and(X!62, Y!61))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.13/0.41 tff(20,plain,
% 0.13/0.41 ((~adjunction) <=> (~adjunction)),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(21,axiom,(~adjunction), file('/export/starexec/sandbox/benchmark/theBenchmark.p','s1_0_adjunction')).
% 0.13/0.41 tff(22,plain,
% 0.13/0.41 (~adjunction),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.13/0.41 tff(23,plain,
% 0.13/0.41 ((adjunction | (~(is_a_theorem(and(X!62, Y!61)) | (~(is_a_theorem(X!62) & is_a_theorem(Y!61)))))) <=> (adjunction | (~(is_a_theorem(and(X!62, Y!61)) | (~is_a_theorem(X!62)) | (~is_a_theorem(Y!61)))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(24,plain,
% 0.13/0.41 (((~adjunction) | ![X: $i, Y: $i] : (is_a_theorem(and(X, Y)) | (~(is_a_theorem(X) & is_a_theorem(Y))))) <=> ((~adjunction) | ![X: $i, Y: $i] : (is_a_theorem(and(X, Y)) | (~(is_a_theorem(X) & is_a_theorem(Y)))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(25,plain,
% 0.13/0.41 ((((~adjunction) | ![X: $i, Y: $i] : (is_a_theorem(and(X, Y)) | (~(is_a_theorem(X) & is_a_theorem(Y))))) & (adjunction | (~(is_a_theorem(and(X!62, Y!61)) | (~(is_a_theorem(X!62) & is_a_theorem(Y!61))))))) <=> (((~adjunction) | ![X: $i, Y: $i] : (is_a_theorem(and(X, Y)) | (~(is_a_theorem(X) & is_a_theorem(Y))))) & (adjunction | (~(is_a_theorem(and(X!62, Y!61)) | (~(is_a_theorem(X!62) & is_a_theorem(Y!61)))))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[24])).
% 0.13/0.41 tff(26,plain,
% 0.13/0.41 ((adjunction <=> ![X: $i, Y: $i] : (is_a_theorem(and(X, Y)) | (~(is_a_theorem(X) & is_a_theorem(Y))))) <=> (adjunction <=> ![X: $i, Y: $i] : (is_a_theorem(and(X, Y)) | (~(is_a_theorem(X) & is_a_theorem(Y)))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(27,plain,
% 0.13/0.41 ((adjunction <=> ![X: $i, Y: $i] : ((is_a_theorem(X) & is_a_theorem(Y)) => is_a_theorem(and(X, Y)))) <=> (adjunction <=> ![X: $i, Y: $i] : (is_a_theorem(and(X, Y)) | (~(is_a_theorem(X) & is_a_theorem(Y)))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(28,axiom,(adjunction <=> ![X: $i, Y: $i] : ((is_a_theorem(X) & is_a_theorem(Y)) => is_a_theorem(and(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax','adjunction')).
% 0.13/0.41 tff(29,plain,
% 0.13/0.41 (adjunction <=> ![X: $i, Y: $i] : (is_a_theorem(and(X, Y)) | (~(is_a_theorem(X) & is_a_theorem(Y))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.13/0.41 tff(30,plain,
% 0.13/0.41 (adjunction <=> ![X: $i, Y: $i] : (is_a_theorem(and(X, Y)) | (~(is_a_theorem(X) & is_a_theorem(Y))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.13/0.41 tff(31,plain,
% 0.13/0.41 (adjunction <=> ![X: $i, Y: $i] : (is_a_theorem(and(X, Y)) | (~(is_a_theorem(X) & is_a_theorem(Y))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.13/0.41 tff(32,plain,
% 0.13/0.41 (adjunction <=> ![X: $i, Y: $i] : (is_a_theorem(and(X, Y)) | (~(is_a_theorem(X) & is_a_theorem(Y))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[31, 26])).
% 0.13/0.41 tff(33,plain,(
% 0.13/0.41 ((~adjunction) | ![X: $i, Y: $i] : (is_a_theorem(and(X, Y)) | (~(is_a_theorem(X) & is_a_theorem(Y))))) & (adjunction | (~(is_a_theorem(and(X!62, Y!61)) | (~(is_a_theorem(X!62) & is_a_theorem(Y!61))))))),
% 0.13/0.41 inference(skolemize,[status(sab)],[32])).
% 0.13/0.41 tff(34,plain,
% 0.13/0.41 (((~adjunction) | ![X: $i, Y: $i] : (is_a_theorem(and(X, Y)) | (~(is_a_theorem(X) & is_a_theorem(Y))))) & (adjunction | (~(is_a_theorem(and(X!62, Y!61)) | (~(is_a_theorem(X!62) & is_a_theorem(Y!61))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[33, 25])).
% 0.13/0.41 tff(35,plain,
% 0.13/0.41 (adjunction | (~(is_a_theorem(and(X!62, Y!61)) | (~(is_a_theorem(X!62) & is_a_theorem(Y!61)))))),
% 0.13/0.41 inference(and_elim,[status(thm)],[34])).
% 0.13/0.41 tff(36,plain,
% 0.13/0.41 (adjunction | (~(is_a_theorem(and(X!62, Y!61)) | (~is_a_theorem(X!62)) | (~is_a_theorem(Y!61))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[35, 23])).
% 0.13/0.41 tff(37,plain,
% 0.13/0.41 (~(is_a_theorem(and(X!62, Y!61)) | (~is_a_theorem(X!62)) | (~is_a_theorem(Y!61)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[36, 22])).
% 0.13/0.41 tff(38,plain,
% 0.13/0.41 ((is_a_theorem(and(X!62, Y!61)) | (~is_a_theorem(X!62)) | (~is_a_theorem(Y!61))) | is_a_theorem(X!62)),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(39,plain,
% 0.13/0.41 (is_a_theorem(X!62)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.13/0.41 tff(40,plain,
% 0.13/0.41 (modus_ponens <=> modus_ponens),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(41,axiom,(modus_ponens), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax','hilbert_modus_ponens')).
% 0.13/0.41 tff(42,plain,
% 0.13/0.41 (modus_ponens),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.13/0.41 tff(43,plain,
% 0.13/0.41 (((~modus_ponens) | ![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) <=> ((~modus_ponens) | ![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y)))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(44,plain,
% 0.13/0.41 (((~modus_ponens) | ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))) <=> ((~modus_ponens) | ![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y)))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(45,plain,
% 0.13/0.41 (((~modus_ponens) | ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))) <=> ((~modus_ponens) | ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(46,plain,
% 0.13/0.41 ((((~modus_ponens) | ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))) & (modus_ponens | (~(is_a_theorem(Y!3) | (~(is_a_theorem(X!4) & is_a_theorem(implies(X!4, Y!3)))))))) <=> (((~modus_ponens) | ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))) & (modus_ponens | (~(is_a_theorem(Y!3) | (~(is_a_theorem(X!4) & is_a_theorem(implies(X!4, Y!3))))))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[45])).
% 0.13/0.41 tff(47,plain,
% 0.13/0.41 ((modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))) <=> (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(48,plain,
% 0.13/0.41 ((modus_ponens <=> ![X: $i, Y: $i] : ((is_a_theorem(X) & is_a_theorem(implies(X, Y))) => is_a_theorem(Y))) <=> (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(49,axiom,(modus_ponens <=> ![X: $i, Y: $i] : ((is_a_theorem(X) & is_a_theorem(implies(X, Y))) => is_a_theorem(Y))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','modus_ponens')).
% 0.13/0.41 tff(50,plain,
% 0.13/0.41 (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.13/0.41 tff(51,plain,
% 0.13/0.41 (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[50, 47])).
% 0.13/0.41 tff(52,plain,
% 0.13/0.41 (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.13/0.41 tff(53,plain,
% 0.13/0.41 (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[52, 47])).
% 0.13/0.41 tff(54,plain,(
% 0.13/0.41 ((~modus_ponens) | ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))) & (modus_ponens | (~(is_a_theorem(Y!3) | (~(is_a_theorem(X!4) & is_a_theorem(implies(X!4, Y!3)))))))),
% 0.13/0.41 inference(skolemize,[status(sab)],[53])).
% 0.13/0.41 tff(55,plain,
% 0.13/0.41 (((~modus_ponens) | ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))) & (modus_ponens | (~(is_a_theorem(Y!3) | (~(is_a_theorem(X!4) & is_a_theorem(implies(X!4, Y!3)))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[54, 46])).
% 0.13/0.41 tff(56,plain,
% 0.13/0.41 ((~modus_ponens) | ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.13/0.41 inference(and_elim,[status(thm)],[55])).
% 0.13/0.41 tff(57,plain,
% 0.13/0.41 ((~modus_ponens) | ![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[56, 44])).
% 0.13/0.41 tff(58,plain,
% 0.13/0.41 ((~modus_ponens) | ![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[57, 43])).
% 0.13/0.41 tff(59,plain,
% 0.13/0.41 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[58, 42])).
% 0.13/0.41 tff(60,plain,
% 0.13/0.41 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | ((~is_a_theorem(X!62)) | is_a_theorem(implies(Y!61, and(X!62, Y!61))) | (~is_a_theorem(implies(X!62, implies(Y!61, and(X!62, Y!61))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(X!62)) | is_a_theorem(implies(Y!61, and(X!62, Y!61))) | (~is_a_theorem(implies(X!62, implies(Y!61, and(X!62, Y!61))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(61,plain,
% 0.13/0.41 ((is_a_theorem(implies(Y!61, and(X!62, Y!61))) | (~is_a_theorem(X!62)) | (~is_a_theorem(implies(X!62, implies(Y!61, and(X!62, Y!61)))))) <=> ((~is_a_theorem(X!62)) | is_a_theorem(implies(Y!61, and(X!62, Y!61))) | (~is_a_theorem(implies(X!62, implies(Y!61, and(X!62, Y!61))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(62,plain,
% 0.13/0.41 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(implies(Y!61, and(X!62, Y!61))) | (~is_a_theorem(X!62)) | (~is_a_theorem(implies(X!62, implies(Y!61, and(X!62, Y!61))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | ((~is_a_theorem(X!62)) | is_a_theorem(implies(Y!61, and(X!62, Y!61))) | (~is_a_theorem(implies(X!62, implies(Y!61, and(X!62, Y!61)))))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[61])).
% 0.13/0.41 tff(63,plain,
% 0.13/0.41 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(implies(Y!61, and(X!62, Y!61))) | (~is_a_theorem(X!62)) | (~is_a_theorem(implies(X!62, implies(Y!61, and(X!62, Y!61))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(X!62)) | is_a_theorem(implies(Y!61, and(X!62, Y!61))) | (~is_a_theorem(implies(X!62, implies(Y!61, and(X!62, Y!61))))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[62, 60])).
% 0.13/0.41 tff(64,plain,
% 0.13/0.41 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(implies(Y!61, and(X!62, Y!61))) | (~is_a_theorem(X!62)) | (~is_a_theorem(implies(X!62, implies(Y!61, and(X!62, Y!61))))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(65,plain,
% 0.13/0.41 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(X!62)) | is_a_theorem(implies(Y!61, and(X!62, Y!61))) | (~is_a_theorem(implies(X!62, implies(Y!61, and(X!62, Y!61)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.13/0.41 tff(66,plain,
% 0.13/0.41 (is_a_theorem(implies(Y!61, and(X!62, Y!61)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[65, 59, 39, 19])).
% 0.13/0.41 tff(67,plain,
% 0.13/0.41 ((is_a_theorem(and(X!62, Y!61)) | (~is_a_theorem(X!62)) | (~is_a_theorem(Y!61))) | is_a_theorem(Y!61)),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(68,plain,
% 0.13/0.41 (is_a_theorem(Y!61)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[67, 37])).
% 0.13/0.41 tff(69,plain,
% 0.13/0.41 ((is_a_theorem(and(X!62, Y!61)) | (~is_a_theorem(X!62)) | (~is_a_theorem(Y!61))) | (~is_a_theorem(and(X!62, Y!61)))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(70,plain,
% 0.13/0.41 (~is_a_theorem(and(X!62, Y!61))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[69, 37])).
% 0.13/0.41 tff(71,plain,
% 0.13/0.41 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(and(X!62, Y!61)) | (~is_a_theorem(Y!61)) | (~is_a_theorem(implies(Y!61, and(X!62, Y!61)))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(and(X!62, Y!61)) | (~is_a_theorem(Y!61)) | (~is_a_theorem(implies(Y!61, and(X!62, Y!61)))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(72,plain,
% 0.13/0.41 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(and(X!62, Y!61)) | (~is_a_theorem(Y!61)) | (~is_a_theorem(implies(Y!61, and(X!62, Y!61)))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(73,plain,
% 0.13/0.41 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(and(X!62, Y!61)) | (~is_a_theorem(Y!61)) | (~is_a_theorem(implies(Y!61, and(X!62, Y!61))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.13/0.41 tff(74,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[73, 59, 70, 68, 66])).
% 0.13/0.41 % SZS output end Proof
% 0.13/0.41 % E exiting
%------------------------------------------------------------------------------