%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL682+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% 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 : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 03:00:38 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 : LCL682+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.07/0.35 % Computer : n014.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Fri Sep 4 16:06:59 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.13/0.41 % SZS status Theorem
% 0.13/0.41 % SZS output start Proof
% 0.13/0.41 tff(r1_type, type, (
% 0.13/0.41 r1: ( $i * $i ) > $o)).
% 0.13/0.41 tff(tptp_fun_Y_5_type, type, (
% 0.13/0.41 tptp_fun_Y_5: $i)).
% 0.13/0.41 tff(p12_type, type, (
% 0.13/0.41 p12: $i > $o)).
% 0.13/0.41 tff(p16_type, type, (
% 0.13/0.41 p16: $i > $o)).
% 0.13/0.41 tff(p14_type, type, (
% 0.13/0.41 p14: $i > $o)).
% 0.13/0.41 tff(tptp_fun_X_0_type, type, (
% 0.13/0.41 tptp_fun_X_0: $i)).
% 0.13/0.41 tff(tptp_fun_X_8_type, type, (
% 0.13/0.41 tptp_fun_X_8: $i)).
% 0.13/0.41 tff(tptp_fun_Y_7_type, type, (
% 0.13/0.41 tptp_fun_Y_7: $i)).
% 0.13/0.41 tff(p11_type, type, (
% 0.13/0.41 p11: $i > $o)).
% 0.13/0.41 tff(tptp_fun_X_6_type, type, (
% 0.13/0.41 tptp_fun_X_6: $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(tptp_fun_Y_3_type, type, (
% 0.13/0.41 tptp_fun_Y_3: $i)).
% 0.13/0.41 tff(p13_type, type, (
% 0.13/0.41 p13: $i > $o)).
% 0.13/0.41 tff(tptp_fun_X_2_type, type, (
% 0.13/0.41 tptp_fun_X_2: $i)).
% 0.13/0.41 tff(tptp_fun_Y_1_type, type, (
% 0.13/0.41 tptp_fun_Y_1: $i)).
% 0.13/0.41 tff(p15_type, type, (
% 0.13/0.41 p15: $i > $o)).
% 0.13/0.41 tff(1,plain,
% 0.13/0.41 ((![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p16(X) | (~r1(Y, X))) & ![X: $i] : (p12(X) | (~r1(Y, X))) & ![X: $i] : (p14(X) | (~r1(Y, X))))) & (r1(X!0, Y!1) & (~(p15(X!2) | (~r1(Y!1, X!2))))) & (r1(X!0, Y!3) & (~(p13(X!4) | (~r1(Y!3, X!4))))) & (r1(X!0, Y!5) & (~(p12(X!6) | (~r1(Y!5, X!6))))) & (r1(X!0, Y!7) & (~(p11(X!8) | (~r1(Y!7, X!8)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p16(X) | (~r1(Y, X))) & ![X: $i] : (p12(X) | (~r1(Y, X))) & ![X: $i] : (p14(X) | (~r1(Y, X))))) & r1(X!0, Y!1) & (~(p15(X!2) | (~r1(Y!1, X!2)))) & r1(X!0, Y!3) & (~(p13(X!4) | (~r1(Y!3, X!4)))) & r1(X!0, Y!5) & (~(p12(X!6) | (~r1(Y!5, X!6)))) & r1(X!0, Y!7) & (~(p11(X!8) | (~r1(Y!7, X!8)))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(2,plain,
% 0.13/0.41 (?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p15(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p13(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p12(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p11(X) | (~r1(Y, X)))))) <=> ?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p15(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p13(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p12(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p11(X) | (~r1(Y, X))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(3,plain,
% 0.13/0.41 ((~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p15(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p13(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p12(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p11(X) | (~r1(Y, X)))))))) <=> ?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p15(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p13(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p12(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p11(X) | (~r1(Y, X))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(4,plain,
% 0.13/0.41 ((~?[X: $i] : (~(((((~![Y: $i] : ((~r1(X, Y)) | (~((((~![X: $i] : ((~r1(Y, X)) | p16(X))) | (~![X: $i] : ((~r1(Y, X)) | p12(X)))) | (~![X: $i] : ((~r1(Y, X)) | p14(X)))) | (~![X: $i] : ((~r1(Y, X)) | p12(X))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p15(X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p13(X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p12(X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p11(X)))))) <=> (~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p15(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p13(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p12(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p11(X) | (~r1(Y, X)))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(5,plain,
% 0.13/0.41 ((~(~?[X: $i] : (~(((((~![Y: $i] : ((~r1(X, Y)) | (~((((~![X: $i] : ((~r1(Y, X)) | p16(X))) | (~![X: $i] : ((~r1(Y, X)) | p12(X)))) | (~![X: $i] : ((~r1(Y, X)) | p14(X)))) | (~![X: $i] : ((~r1(Y, X)) | p12(X))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p15(X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p13(X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p12(X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p11(X))))))) <=> (~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p15(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p13(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p12(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p11(X) | (~r1(Y, X))))))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[4])).
% 0.13/0.41 tff(6,plain,
% 0.13/0.41 ((~(~?[X: $i] : (~(((((~![Y: $i] : ((~r1(X, Y)) | (~((((~![X: $i] : ((~r1(Y, X)) | p16(X))) | (~![X: $i] : ((~r1(Y, X)) | p12(X)))) | (~![X: $i] : ((~r1(Y, X)) | p14(X)))) | (~![X: $i] : ((~r1(Y, X)) | p12(X))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p15(X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p13(X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p12(X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p11(X))))))) <=> ?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p15(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p13(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p12(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p11(X) | (~r1(Y, X))))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[5, 3])).
% 0.13/0.41 tff(7,axiom,(~(~?[X: $i] : (~(((((~![Y: $i] : ((~r1(X, Y)) | (~((((~![X: $i] : ((~r1(Y, X)) | p16(X))) | (~![X: $i] : ((~r1(Y, X)) | p12(X)))) | (~![X: $i] : ((~r1(Y, X)) | p14(X)))) | (~![X: $i] : ((~r1(Y, X)) | p12(X))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p15(X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p13(X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p12(X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p11(X))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','main')).
% 0.13/0.41 tff(8,plain,
% 0.13/0.41 (?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p15(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p13(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p12(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p11(X) | (~r1(Y, X))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.13/0.41 tff(9,plain,
% 0.13/0.41 (?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p15(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p13(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p12(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p11(X) | (~r1(Y, X))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.13/0.41 tff(10,plain,
% 0.13/0.41 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p16(X) | (~r1(Y, X))) & ![X: $i] : (p12(X) | (~r1(Y, X))) & ![X: $i] : (p14(X) | (~r1(Y, X))))) & r1(X!0, Y!1) & (~(p15(X!2) | (~r1(Y!1, X!2)))) & r1(X!0, Y!3) & (~(p13(X!4) | (~r1(Y!3, X!4)))) & r1(X!0, Y!5) & (~(p12(X!6) | (~r1(Y!5, X!6)))) & r1(X!0, Y!7) & (~(p11(X!8) | (~r1(Y!7, X!8))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.13/0.41 tff(11,plain,
% 0.13/0.41 (r1(X!0, Y!5)),
% 0.13/0.41 inference(and_elim,[status(thm)],[10])).
% 0.13/0.41 tff(12,plain,
% 0.13/0.41 (^[Y: $i] : refl(((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X))))))) <=> ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(13,plain,
% 0.13/0.41 (![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[12])).
% 0.13/0.41 tff(14,plain,
% 0.13/0.41 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X))))))) <=> ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(15,plain,
% 0.13/0.41 (![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[14])).
% 0.13/0.41 tff(16,plain,
% 0.13/0.41 (![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[15, 13])).
% 0.13/0.41 tff(17,plain,
% 0.13/0.41 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (![X: $i] : (p16(X) | (~r1(Y, X))) & ![X: $i] : (p12(X) | (~r1(Y, X))) & ![X: $i] : (p14(X) | (~r1(Y, X))))) <=> ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(18,plain,
% 0.13/0.41 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p16(X) | (~r1(Y, X))) & ![X: $i] : (p12(X) | (~r1(Y, X))) & ![X: $i] : (p14(X) | (~r1(Y, X))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[17])).
% 0.13/0.41 tff(19,plain,
% 0.13/0.41 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p16(X) | (~r1(Y, X))) & ![X: $i] : (p12(X) | (~r1(Y, X))) & ![X: $i] : (p14(X) | (~r1(Y, X)))))),
% 0.13/0.41 inference(and_elim,[status(thm)],[10])).
% 0.13/0.41 tff(20,plain,
% 0.13/0.41 (![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.13/0.41 tff(21,plain,
% 0.13/0.41 (![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.13/0.41 tff(22,plain,
% 0.13/0.41 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))) | ((~r1(X!0, Y!5)) | (~((~![X: $i] : (p14(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p12(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p16(X) | (~r1(Y!5, X)))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))) | (~r1(X!0, Y!5)) | (~((~![X: $i] : (p14(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p12(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p16(X) | (~r1(Y!5, X)))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(23,plain,
% 0.13/0.41 (((~r1(X!0, Y!5)) | (~((~![X: $i] : (p16(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p12(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p14(X) | (~r1(Y!5, X))))))) <=> ((~r1(X!0, Y!5)) | (~((~![X: $i] : (p14(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p12(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p16(X) | (~r1(Y!5, X)))))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(24,plain,
% 0.13/0.42 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))) | ((~r1(X!0, Y!5)) | (~((~![X: $i] : (p16(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p12(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p14(X) | (~r1(Y!5, X)))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))) | ((~r1(X!0, Y!5)) | (~((~![X: $i] : (p14(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p12(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p16(X) | (~r1(Y!5, X))))))))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[23])).
% 0.13/0.42 tff(25,plain,
% 0.13/0.42 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))) | ((~r1(X!0, Y!5)) | (~((~![X: $i] : (p16(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p12(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p14(X) | (~r1(Y!5, X)))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))) | (~r1(X!0, Y!5)) | (~((~![X: $i] : (p14(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p12(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p16(X) | (~r1(Y!5, X)))))))),
% 0.13/0.42 inference(transitivity,[status(thm)],[24, 22])).
% 0.13/0.42 tff(26,plain,
% 0.13/0.42 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))) | ((~r1(X!0, Y!5)) | (~((~![X: $i] : (p16(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p12(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p14(X) | (~r1(Y!5, X)))))))),
% 0.13/0.42 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(27,plain,
% 0.13/0.42 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))) | (~r1(X!0, Y!5)) | (~((~![X: $i] : (p14(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p12(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p16(X) | (~r1(Y!5, X))))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.13/0.42 tff(28,plain,
% 0.13/0.42 (~((~![X: $i] : (p14(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p12(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p16(X) | (~r1(Y!5, X)))))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[27, 21, 11])).
% 0.13/0.42 tff(29,plain,
% 0.13/0.42 (((~![X: $i] : (p14(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p12(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p16(X) | (~r1(Y!5, X))))) | ![X: $i] : (p12(X) | (~r1(Y!5, X)))),
% 0.13/0.42 inference(tautology,[status(thm)],[])).
% 0.13/0.42 tff(30,plain,
% 0.13/0.42 (![X: $i] : (p12(X) | (~r1(Y!5, X)))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.13/0.42 tff(31,plain,
% 0.13/0.42 (~(p12(X!6) | (~r1(Y!5, X!6)))),
% 0.13/0.42 inference(and_elim,[status(thm)],[10])).
% 0.13/0.42 tff(32,plain,
% 0.13/0.42 (r1(Y!5, X!6)),
% 0.13/0.42 inference(or_elim,[status(thm)],[31])).
% 0.13/0.42 tff(33,plain,
% 0.13/0.42 (~p12(X!6)),
% 0.13/0.42 inference(or_elim,[status(thm)],[31])).
% 0.13/0.42 tff(34,plain,
% 0.13/0.42 (((~![X: $i] : (p12(X) | (~r1(Y!5, X)))) | (p12(X!6) | (~r1(Y!5, X!6)))) <=> ((~![X: $i] : (p12(X) | (~r1(Y!5, X)))) | p12(X!6) | (~r1(Y!5, X!6)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(35,plain,
% 0.13/0.42 ((~![X: $i] : (p12(X) | (~r1(Y!5, X)))) | (p12(X!6) | (~r1(Y!5, X!6)))),
% 0.13/0.42 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(36,plain,
% 0.13/0.42 ((~![X: $i] : (p12(X) | (~r1(Y!5, X)))) | p12(X!6) | (~r1(Y!5, X!6))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.13/0.42 tff(37,plain,
% 0.13/0.42 ($false),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[36, 33, 32, 30])).
% 0.13/0.42 % SZS output end Proof
% 0.13/0.42 % E exiting
%------------------------------------------------------------------------------