%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL638+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n016.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 03:00:18 PM UTC 2026
% Result : Theorem 0.14s 0.41s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL638+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 : n016.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 19:42:47 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.14/0.41 % SZS status Theorem
% 0.14/0.41 % SZS output start Proof
% 0.14/0.41 tff(r1_type, type, (
% 0.14/0.41 r1: ( $i * $i ) > $o)).
% 0.14/0.41 tff(tptp_fun_X_6_type, type, (
% 0.14/0.41 tptp_fun_X_6: $i > $i)).
% 0.14/0.41 tff(tptp_fun_Y_7_type, type, (
% 0.14/0.41 tptp_fun_Y_7: $i)).
% 0.14/0.41 tff(p1_type, type, (
% 0.14/0.41 p1: $i > $o)).
% 0.14/0.41 tff(tptp_fun_X_5_type, type, (
% 0.14/0.41 tptp_fun_X_5: $i > $i)).
% 0.14/0.41 tff(tptp_fun_X_0_type, type, (
% 0.14/0.41 tptp_fun_X_0: $i)).
% 0.14/0.41 tff(tptp_fun_X_4_type, type, (
% 0.14/0.41 tptp_fun_X_4: $i > $i)).
% 0.14/0.41 tff(tptp_fun_X_3_type, type, (
% 0.14/0.41 tptp_fun_X_3: $i > $i)).
% 0.14/0.41 tff(tptp_fun_Y_2_type, type, (
% 0.14/0.41 tptp_fun_Y_2: $i > $i)).
% 0.14/0.41 tff(tptp_fun_Y_1_type, type, (
% 0.14/0.41 tptp_fun_Y_1: $i > $i)).
% 0.14/0.41 tff(1,assumption,(~(p1(tptp_fun_X_5(Y!7)) | (~r1(Y!7, tptp_fun_X_5(Y!7))))), introduced(assumption)).
% 0.14/0.41 tff(2,plain,
% 0.14/0.41 ((p1(tptp_fun_X_5(Y!7)) | (~r1(Y!7, tptp_fun_X_5(Y!7)))) | r1(Y!7, tptp_fun_X_5(Y!7))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(3,plain,
% 0.14/0.41 (r1(Y!7, tptp_fun_X_5(Y!7))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.14/0.41 tff(4,plain,
% 0.14/0.41 ((p1(tptp_fun_X_5(Y!7)) | (~r1(Y!7, tptp_fun_X_5(Y!7)))) | (~p1(tptp_fun_X_5(Y!7)))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(5,plain,
% 0.14/0.41 (~p1(tptp_fun_X_5(Y!7))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.14/0.41 tff(6,plain,
% 0.14/0.41 (^[X: $i] : refl((p1(X) | (~r1(Y!7, X))) <=> (p1(X) | (~r1(Y!7, X))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(7,plain,
% 0.14/0.41 (![X: $i] : (p1(X) | (~r1(Y!7, X))) <=> ![X: $i] : (p1(X) | (~r1(Y!7, X)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[6])).
% 0.14/0.41 tff(8,plain,
% 0.14/0.41 ((![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) & ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y))) & ((~p1(Y!7)) & r1(X!0, Y!7) & ![X: $i] : (p1(X) | (~r1(Y!7, X))))) <=> (![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) & ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y))) & (~p1(Y!7)) & r1(X!0, Y!7) & ![X: $i] : (p1(X) | (~r1(Y!7, X))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(9,plain,
% 0.14/0.41 (((~p1(Y!7)) & r1(X!0, Y!7) & ![X: $i] : (p1(X) | (~r1(Y!7, X)))) <=> ((~p1(Y!7)) & r1(X!0, Y!7) & ![X: $i] : (p1(X) | (~r1(Y!7, X))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(10,plain,
% 0.14/0.41 (^[Y: $i] : trans(monotonicity(rewrite((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(11,plain,
% 0.14/0.42 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[10])).
% 0.14/0.42 tff(12,plain,
% 0.14/0.42 (^[Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))) <=> (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))), ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))))), rewrite((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))), ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(13,plain,
% 0.14/0.42 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[12])).
% 0.14/0.42 tff(14,plain,
% 0.14/0.42 (^[Y: $i] : trans(monotonicity(rewrite((![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X)))))) | (~p1(Y))) <=> ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X)))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X)))))) | (~p1(Y)))) <=> ((~r1(X!0, Y)) | ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X)))))))))), rewrite(((~r1(X!0, Y)) | ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X)))))))) <=> ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X)))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X)))))) | (~p1(Y)))) <=> ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X)))))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(15,plain,
% 0.14/0.42 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X)))))) | (~p1(Y)))) <=> ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X)))))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[14])).
% 0.14/0.42 tff(16,plain,
% 0.14/0.42 (^[Y: $i] : trans(monotonicity(rewrite((![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | p1(Y)) <=> (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | p1(Y))) <=> ((~r1(X!0, Y)) | (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))), rewrite(((~r1(X!0, Y)) | (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) <=> (p1(Y) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | p1(Y))) <=> (p1(Y) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(17,plain,
% 0.14/0.42 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | p1(Y))) <=> ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[16])).
% 0.14/0.42 tff(18,plain,
% 0.14/0.42 ((![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | p1(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X)))))) | (~p1(Y)))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y))) & ((~p1(Y!7)) & r1(X!0, Y!7) & ![X: $i] : (p1(X) | (~r1(Y!7, X))))) <=> (![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) & ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y))) & ((~p1(Y!7)) & r1(X!0, Y!7) & ![X: $i] : (p1(X) | (~r1(Y!7, X)))))),
% 0.14/0.42 inference(monotonicity,[status(thm)],[17, 15, 13, 11, 9])).
% 0.14/0.42 tff(19,plain,
% 0.14/0.42 ((![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | p1(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X)))))) | (~p1(Y)))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y))) & ((~p1(Y!7)) & r1(X!0, Y!7) & ![X: $i] : (p1(X) | (~r1(Y!7, X))))) <=> (![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) & ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y))) & (~p1(Y!7)) & r1(X!0, Y!7) & ![X: $i] : (p1(X) | (~r1(Y!7, X))))),
% 0.14/0.42 inference(transitivity,[status(thm)],[18, 8])).
% 0.14/0.42 tff(20,plain,
% 0.14/0.42 (?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))) <=> ?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(21,plain,
% 0.14/0.42 ((~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))))) <=> ?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(22,plain,
% 0.14/0.42 ((~?[X: $i] : (~((((((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~p1(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) <=> (~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(23,plain,
% 0.14/0.42 ((~(~?[X: $i] : (~((((((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~p1(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) <=> (~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))))),
% 0.14/0.42 inference(monotonicity,[status(thm)],[22])).
% 0.14/0.42 tff(24,plain,
% 0.14/0.42 ((~(~?[X: $i] : (~((((((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~p1(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) <=> ?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))),
% 0.14/0.43 inference(transitivity,[status(thm)],[23, 21])).
% 0.14/0.43 tff(25,axiom,(~(~?[X: $i] : (~((((((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~p1(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','main')).
% 0.14/0.43 tff(26,plain,
% 0.14/0.43 (?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.14/0.43 tff(27,plain,
% 0.14/0.43 (?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[26, 20])).
% 0.14/0.43 tff(28,plain,
% 0.14/0.43 (![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) & ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_2(X))) | (~r1(X, tptp_fun_Y_2(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y))) & (~p1(Y!7)) & r1(X!0, Y!7) & ![X: $i] : (p1(X) | (~r1(Y!7, X)))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[27, 19])).
% 0.14/0.43 tff(29,plain,
% 0.14/0.43 (![X: $i] : (p1(X) | (~r1(Y!7, X)))),
% 0.14/0.43 inference(and_elim,[status(thm)],[28])).
% 0.14/0.43 tff(30,plain,
% 0.14/0.43 (![X: $i] : (p1(X) | (~r1(Y!7, X)))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[29, 7])).
% 0.14/0.43 tff(31,plain,
% 0.14/0.43 (((~![X: $i] : (p1(X) | (~r1(Y!7, X)))) | (p1(tptp_fun_X_5(Y!7)) | (~r1(Y!7, tptp_fun_X_5(Y!7))))) <=> ((~![X: $i] : (p1(X) | (~r1(Y!7, X)))) | p1(tptp_fun_X_5(Y!7)) | (~r1(Y!7, tptp_fun_X_5(Y!7))))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(32,plain,
% 0.14/0.43 ((~![X: $i] : (p1(X) | (~r1(Y!7, X)))) | (p1(tptp_fun_X_5(Y!7)) | (~r1(Y!7, tptp_fun_X_5(Y!7))))),
% 0.14/0.43 inference(quant_inst,[status(thm)],[])).
% 0.14/0.43 tff(33,plain,
% 0.14/0.43 ((~![X: $i] : (p1(X) | (~r1(Y!7, X)))) | p1(tptp_fun_X_5(Y!7)) | (~r1(Y!7, tptp_fun_X_5(Y!7)))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.14/0.43 tff(34,plain,
% 0.14/0.43 ($false),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[33, 30, 5, 3])).
% 0.14/0.43 tff(35,plain,(p1(tptp_fun_X_5(Y!7)) | (~r1(Y!7, tptp_fun_X_5(Y!7)))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.43 tff(36,plain,
% 0.14/0.43 (r1(X!0, Y!7)),
% 0.14/0.43 inference(and_elim,[status(thm)],[28])).
% 0.14/0.43 tff(37,plain,
% 0.14/0.43 (^[Y: $i] : rewrite((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))) <=> ((~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))),
% 0.14/0.43 inference(bind,[status(th)],[])).
% 0.14/0.43 tff(38,plain,
% 0.14/0.43 (![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.14/0.43 inference(quant_intro,[status(thm)],[37])).
% 0.14/0.43 tff(39,plain,
% 0.14/0.43 (^[Y: $i] : refl((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))),
% 0.14/0.43 inference(bind,[status(th)],[])).
% 0.14/0.43 tff(40,plain,
% 0.14/0.43 (![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))),
% 0.14/0.43 inference(quant_intro,[status(thm)],[39])).
% 0.14/0.43 tff(41,plain,
% 0.14/0.43 (^[Y: $i] : rewrite((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))),
% 0.14/0.43 inference(bind,[status(th)],[])).
% 0.14/0.43 tff(42,plain,
% 0.14/0.43 (![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))),
% 0.14/0.43 inference(quant_intro,[status(thm)],[41])).
% 0.14/0.43 tff(43,plain,
% 0.14/0.43 (![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))),
% 0.14/0.43 inference(transitivity,[status(thm)],[42, 40])).
% 0.14/0.43 tff(44,plain,
% 0.14/0.43 (![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))),
% 0.14/0.43 inference(and_elim,[status(thm)],[28])).
% 0.14/0.43 tff(45,plain,
% 0.14/0.43 (![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.14/0.43 tff(46,plain,
% 0.14/0.43 (![Y: $i] : ((~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.14/0.43 tff(47,plain,
% 0.14/0.43 (((~![Y: $i] : ((~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | ((~r1(X!0, Y!7)) | (~(p1(tptp_fun_X_5(Y!7)) | (~r1(Y!7, tptp_fun_X_5(Y!7))))) | ![X: $i] : ((~r1(Y!7, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(X!0, Y!7)) | (~(p1(tptp_fun_X_5(Y!7)) | (~r1(Y!7, tptp_fun_X_5(Y!7))))) | ![X: $i] : ((~r1(Y!7, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(48,plain,
% 0.14/0.43 ((~![Y: $i] : ((~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | ((~r1(X!0, Y!7)) | (~(p1(tptp_fun_X_5(Y!7)) | (~r1(Y!7, tptp_fun_X_5(Y!7))))) | ![X: $i] : ((~r1(Y!7, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.14/0.43 inference(quant_inst,[status(thm)],[])).
% 0.14/0.43 tff(49,plain,
% 0.14/0.43 ((~![Y: $i] : ((~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(X!0, Y!7)) | (~(p1(tptp_fun_X_5(Y!7)) | (~r1(Y!7, tptp_fun_X_5(Y!7))))) | ![X: $i] : ((~r1(Y!7, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.14/0.43 tff(50,plain,
% 0.14/0.43 ((~(p1(tptp_fun_X_5(Y!7)) | (~r1(Y!7, tptp_fun_X_5(Y!7))))) | ![X: $i] : ((~r1(Y!7, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[49, 46, 36])).
% 0.14/0.43 tff(51,plain,
% 0.14/0.43 (![X: $i] : ((~r1(Y!7, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[50, 35])).
% 0.14/0.43 tff(52,plain,
% 0.14/0.43 (^[Y: $i] : refl(((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y))) <=> ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y))))),
% 0.14/0.43 inference(bind,[status(th)],[])).
% 0.14/0.43 tff(53,plain,
% 0.14/0.43 (![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y))) <=> ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y)))),
% 0.14/0.43 inference(quant_intro,[status(thm)],[52])).
% 0.14/0.43 tff(54,plain,
% 0.14/0.43 (![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y)))),
% 0.14/0.43 inference(and_elim,[status(thm)],[28])).
% 0.14/0.43 tff(55,plain,
% 0.14/0.43 (![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y)))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.14/0.43 tff(56,plain,
% 0.14/0.43 (((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y)))) | ((~r1(X!0, Y!7)) | r1(Y!7, tptp_fun_X_6(Y!7)))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y)))) | (~r1(X!0, Y!7)) | r1(Y!7, tptp_fun_X_6(Y!7)))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(57,plain,
% 0.14/0.43 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y)))) | ((~r1(X!0, Y!7)) | r1(Y!7, tptp_fun_X_6(Y!7)))),
% 0.14/0.43 inference(quant_inst,[status(thm)],[])).
% 0.14/0.43 tff(58,plain,
% 0.14/0.43 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_6(Y)))) | (~r1(X!0, Y!7)) | r1(Y!7, tptp_fun_X_6(Y!7))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.14/0.43 tff(59,plain,
% 0.14/0.43 (r1(Y!7, tptp_fun_X_6(Y!7))),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[58, 55, 36])).
% 0.14/0.43 tff(60,plain,
% 0.14/0.43 (((~![X: $i] : ((~r1(Y!7, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ((~r1(Y!7, tptp_fun_X_6(Y!7))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_6(Y!7), Y))))) <=> ((~![X: $i] : ((~r1(Y!7, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~r1(Y!7, tptp_fun_X_6(Y!7))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_6(Y!7), Y))))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(61,plain,
% 0.14/0.43 ((~![X: $i] : ((~r1(Y!7, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ((~r1(Y!7, tptp_fun_X_6(Y!7))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_6(Y!7), Y))))),
% 0.14/0.43 inference(quant_inst,[status(thm)],[])).
% 0.14/0.43 tff(62,plain,
% 0.14/0.43 ((~![X: $i] : ((~r1(Y!7, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~r1(Y!7, tptp_fun_X_6(Y!7))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_6(Y!7), Y)))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.14/0.43 tff(63,plain,
% 0.14/0.43 (![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_6(Y!7), Y)))),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[62, 59, 51])).
% 0.14/0.43 tff(64,plain,
% 0.14/0.43 (~p1(Y!7)),
% 0.14/0.43 inference(and_elim,[status(thm)],[28])).
% 0.14/0.43 tff(65,plain,
% 0.14/0.43 (^[Y: $i] : refl((p1(Y) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) <=> (p1(Y) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))),
% 0.14/0.43 inference(bind,[status(th)],[])).
% 0.14/0.43 tff(66,plain,
% 0.14/0.43 (![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) <=> ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))),
% 0.14/0.43 inference(quant_intro,[status(thm)],[65])).
% 0.14/0.43 tff(67,plain,
% 0.14/0.43 (^[Y: $i] : rewrite((p1(Y) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) <=> (p1(Y) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))),
% 0.14/0.43 inference(bind,[status(th)],[])).
% 0.14/0.43 tff(68,plain,
% 0.14/0.43 (![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) <=> ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))),
% 0.14/0.43 inference(quant_intro,[status(thm)],[67])).
% 0.14/0.43 tff(69,plain,
% 0.14/0.43 (![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) <=> ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))),
% 0.14/0.43 inference(transitivity,[status(thm)],[68, 66])).
% 0.14/0.43 tff(70,plain,
% 0.14/0.43 (![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))),
% 0.14/0.43 inference(and_elim,[status(thm)],[28])).
% 0.14/0.43 tff(71,plain,
% 0.14/0.43 (![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.14/0.43 tff(72,plain,
% 0.14/0.43 (((~![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (p1(Y!7) | (~r1(X!0, Y!7)) | ![X: $i] : ((~r1(Y!7, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | p1(Y!7) | (~r1(X!0, Y!7)) | ![X: $i] : ((~r1(Y!7, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(73,plain,
% 0.14/0.43 ((~![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (p1(Y!7) | (~r1(X!0, Y!7)) | ![X: $i] : ((~r1(Y!7, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))),
% 0.14/0.43 inference(quant_inst,[status(thm)],[])).
% 0.14/0.43 tff(74,plain,
% 0.14/0.43 ((~![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | p1(Y!7) | (~r1(X!0, Y!7)) | ![X: $i] : ((~r1(Y!7, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.14/0.43 tff(75,plain,
% 0.14/0.43 (![X: $i] : ((~r1(Y!7, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[74, 71, 64, 36])).
% 0.14/0.43 tff(76,plain,
% 0.14/0.43 (((~![X: $i] : ((~r1(Y!7, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) | ((~r1(Y!7, tptp_fun_X_6(Y!7))) | (~(p1(tptp_fun_Y_1(tptp_fun_X_6(Y!7))) | (~r1(tptp_fun_X_6(Y!7), tptp_fun_Y_1(tptp_fun_X_6(Y!7)))))))) <=> ((~![X: $i] : ((~r1(Y!7, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) | (~r1(Y!7, tptp_fun_X_6(Y!7))) | (~(p1(tptp_fun_Y_1(tptp_fun_X_6(Y!7))) | (~r1(tptp_fun_X_6(Y!7), tptp_fun_Y_1(tptp_fun_X_6(Y!7)))))))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(77,plain,
% 0.14/0.43 ((~![X: $i] : ((~r1(Y!7, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) | ((~r1(Y!7, tptp_fun_X_6(Y!7))) | (~(p1(tptp_fun_Y_1(tptp_fun_X_6(Y!7))) | (~r1(tptp_fun_X_6(Y!7), tptp_fun_Y_1(tptp_fun_X_6(Y!7)))))))),
% 0.14/0.43 inference(quant_inst,[status(thm)],[])).
% 0.14/0.43 tff(78,plain,
% 0.14/0.43 ((~![X: $i] : ((~r1(Y!7, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) | (~r1(Y!7, tptp_fun_X_6(Y!7))) | (~(p1(tptp_fun_Y_1(tptp_fun_X_6(Y!7))) | (~r1(tptp_fun_X_6(Y!7), tptp_fun_Y_1(tptp_fun_X_6(Y!7))))))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.14/0.44 tff(79,plain,
% 0.14/0.44 (~(p1(tptp_fun_Y_1(tptp_fun_X_6(Y!7))) | (~r1(tptp_fun_X_6(Y!7), tptp_fun_Y_1(tptp_fun_X_6(Y!7)))))),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[78, 75, 59])).
% 0.14/0.44 tff(80,plain,
% 0.14/0.44 ((p1(tptp_fun_Y_1(tptp_fun_X_6(Y!7))) | (~r1(tptp_fun_X_6(Y!7), tptp_fun_Y_1(tptp_fun_X_6(Y!7))))) | r1(tptp_fun_X_6(Y!7), tptp_fun_Y_1(tptp_fun_X_6(Y!7)))),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.44 tff(81,plain,
% 0.14/0.44 (r1(tptp_fun_X_6(Y!7), tptp_fun_Y_1(tptp_fun_X_6(Y!7)))),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.14/0.44 tff(82,plain,
% 0.14/0.44 ((p1(tptp_fun_Y_1(tptp_fun_X_6(Y!7))) | (~r1(tptp_fun_X_6(Y!7), tptp_fun_Y_1(tptp_fun_X_6(Y!7))))) | (~p1(tptp_fun_Y_1(tptp_fun_X_6(Y!7))))),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.44 tff(83,plain,
% 0.14/0.44 (~p1(tptp_fun_Y_1(tptp_fun_X_6(Y!7)))),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[82, 79])).
% 0.14/0.44 tff(84,plain,
% 0.14/0.44 (((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_6(Y!7), Y)))) | (p1(tptp_fun_Y_1(tptp_fun_X_6(Y!7))) | (~r1(tptp_fun_X_6(Y!7), tptp_fun_Y_1(tptp_fun_X_6(Y!7)))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_6(Y!7), Y)))) | p1(tptp_fun_Y_1(tptp_fun_X_6(Y!7))) | (~r1(tptp_fun_X_6(Y!7), tptp_fun_Y_1(tptp_fun_X_6(Y!7)))))),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.44 tff(85,plain,
% 0.14/0.44 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_6(Y!7), Y)))) | (p1(tptp_fun_Y_1(tptp_fun_X_6(Y!7))) | (~r1(tptp_fun_X_6(Y!7), tptp_fun_Y_1(tptp_fun_X_6(Y!7)))))),
% 0.14/0.44 inference(quant_inst,[status(thm)],[])).
% 0.14/0.44 tff(86,plain,
% 0.14/0.44 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_6(Y!7), Y)))) | p1(tptp_fun_Y_1(tptp_fun_X_6(Y!7))) | (~r1(tptp_fun_X_6(Y!7), tptp_fun_Y_1(tptp_fun_X_6(Y!7))))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.14/0.44 tff(87,plain,
% 0.14/0.44 ($false),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[86, 83, 81, 63])).
% 0.14/0.44 % SZS output end Proof
% 0.14/0.44 % E exiting
%------------------------------------------------------------------------------