%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL654+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n008.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 03:00:26 PM UTC 2026
% Result : Theorem 0.10s 0.44s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL654+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 5 00:39:24 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.44 % SZS status Theorem
% 0.10/0.44 % SZS output start Proof
% 0.10/0.44 tff(r1_type, type, (
% 0.10/0.44 r1: ( $i * $i ) > $o)).
% 0.10/0.44 tff(tptp_fun_Y_3_type, type, (
% 0.10/0.44 tptp_fun_Y_3: $i > $i)).
% 0.10/0.44 tff(tptp_fun_Y_6_type, type, (
% 0.10/0.44 tptp_fun_Y_6: $i)).
% 0.10/0.44 tff(p1_type, type, (
% 0.10/0.44 p1: $i > $o)).
% 0.10/0.44 tff(tptp_fun_Y_2_type, type, (
% 0.10/0.44 tptp_fun_Y_2: $i > $i)).
% 0.10/0.44 tff(tptp_fun_X_7_type, type, (
% 0.10/0.44 tptp_fun_X_7: $i)).
% 0.10/0.44 tff(tptp_fun_X_4_type, type, (
% 0.10/0.44 tptp_fun_X_4: $i > $i)).
% 0.10/0.44 tff(tptp_fun_Y_8_type, type, (
% 0.10/0.44 tptp_fun_Y_8: $i)).
% 0.10/0.44 tff(tptp_fun_X_0_type, type, (
% 0.10/0.44 tptp_fun_X_0: $i)).
% 0.10/0.44 tff(tptp_fun_X_5_type, type, (
% 0.10/0.44 tptp_fun_X_5: $i > $i)).
% 0.10/0.44 tff(tptp_fun_Y_1_type, type, (
% 0.10/0.44 tptp_fun_Y_1: $i > $i)).
% 0.10/0.44 tff(1,assumption,(~r1(Y!6, Y!6)), introduced(assumption)).
% 0.10/0.44 tff(2,plain,
% 0.10/0.44 (^[X: $i] : refl(r1(X, X) <=> r1(X, X))),
% 0.10/0.44 inference(bind,[status(th)],[])).
% 0.10/0.44 tff(3,plain,
% 0.10/0.44 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 0.10/0.44 inference(quant_intro,[status(thm)],[2])).
% 0.10/0.44 tff(4,plain,
% 0.10/0.44 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 0.10/0.44 inference(rewrite,[status(thm)],[])).
% 0.10/0.44 tff(5,axiom,(![X: $i] : r1(X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reflexivity')).
% 0.10/0.44 tff(6,plain,
% 0.10/0.44 (![X: $i] : r1(X, X)),
% 0.10/0.44 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.10/0.44 tff(7,plain,(
% 0.10/0.44 ![X: $i] : r1(X, X)),
% 0.10/0.44 inference(skolemize,[status(sab)],[6])).
% 0.10/0.44 tff(8,plain,
% 0.10/0.44 (![X: $i] : r1(X, X)),
% 0.10/0.44 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.10/0.44 tff(9,plain,
% 0.10/0.44 ((~![X: $i] : r1(X, X)) | r1(Y!6, Y!6)),
% 0.10/0.44 inference(quant_inst,[status(thm)],[])).
% 0.10/0.44 tff(10,plain,
% 0.10/0.44 ($false),
% 0.10/0.44 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.10/0.44 tff(11,plain,(r1(Y!6, Y!6)), inference(lemma,lemma(discharge,[]))).
% 0.10/0.44 tff(12,assumption,(~((~r1(X!7, tptp_fun_Y_2(X!7))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X!7), X)))))), introduced(assumption)).
% 0.10/0.44 tff(13,plain,
% 0.10/0.44 (((~r1(X!7, tptp_fun_Y_2(X!7))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X!7), X))))) | r1(X!7, tptp_fun_Y_2(X!7))),
% 0.10/0.44 inference(tautology,[status(thm)],[])).
% 0.10/0.44 tff(14,plain,
% 0.10/0.44 (r1(X!7, tptp_fun_Y_2(X!7))),
% 0.10/0.44 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.10/0.44 tff(15,assumption,(![Y: $i] : (p1(Y) | (~r1(X!7, Y)))), introduced(assumption)).
% 0.10/0.44 tff(16,plain,
% 0.10/0.44 ((![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] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_5(Y))) & (r1(X!0, Y!6) & ![X: $i] : (p1(X) | (~r1(Y!6, X))) & r1(Y!6, X!7) & (~(p1(Y!8) | (~r1(X!7, Y!8)))))) <=> (![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] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_5(Y))) & r1(X!0, Y!6) & ![X: $i] : (p1(X) | (~r1(Y!6, X))) & r1(Y!6, X!7) & (~(p1(Y!8) | (~r1(X!7, Y!8)))))),
% 0.10/0.44 inference(rewrite,[status(thm)],[])).
% 0.10/0.44 tff(17,plain,
% 0.10/0.44 ((r1(X!0, Y!6) & ![X: $i] : (p1(X) | (~r1(Y!6, X))) & (r1(Y!6, X!7) & (~(p1(Y!8) | (~r1(X!7, Y!8)))))) <=> (r1(X!0, Y!6) & ![X: $i] : (p1(X) | (~r1(Y!6, X))) & r1(Y!6, X!7) & (~(p1(Y!8) | (~r1(X!7, Y!8)))))),
% 0.10/0.44 inference(rewrite,[status(thm)],[])).
% 0.10/0.44 tff(18,plain,
% 0.10/0.44 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))))),
% 0.10/0.44 inference(bind,[status(th)],[])).
% 0.10/0.44 tff(19,plain,
% 0.10/0.44 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))))),
% 0.10/0.44 inference(quant_intro,[status(thm)],[18])).
% 0.10/0.44 tff(20,plain,
% 0.10/0.44 (^[Y: $i] : trans(monotonicity(rewrite((![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))) <=> (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))))))),
% 0.10/0.44 inference(bind,[status(th)],[])).
% 0.10/0.44 tff(21,plain,
% 0.10/0.44 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))))),
% 0.10/0.44 inference(quant_intro,[status(thm)],[20])).
% 0.10/0.44 tff(22,plain,
% 0.10/0.44 (^[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)))))))))),
% 0.10/0.44 inference(bind,[status(th)],[])).
% 0.10/0.44 tff(23,plain,
% 0.10/0.44 (![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)))))))),
% 0.10/0.44 inference(quant_intro,[status(thm)],[22])).
% 0.10/0.44 tff(24,plain,
% 0.10/0.45 ((![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)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_5(Y))) & (r1(X!0, Y!6) & ![X: $i] : (p1(X) | (~r1(Y!6, X))) & (r1(Y!6, X!7) & (~(p1(Y!8) | (~r1(X!7, Y!8))))))) <=> (![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] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_5(Y))) & (r1(X!0, Y!6) & ![X: $i] : (p1(X) | (~r1(Y!6, X))) & r1(Y!6, X!7) & (~(p1(Y!8) | (~r1(X!7, Y!8))))))),
% 0.10/0.45 inference(monotonicity,[status(thm)],[23, 21, 19, 17])).
% 0.10/0.45 tff(25,plain,
% 0.10/0.45 ((![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)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_5(Y))) & (r1(X!0, Y!6) & ![X: $i] : (p1(X) | (~r1(Y!6, X))) & (r1(Y!6, X!7) & (~(p1(Y!8) | (~r1(X!7, Y!8))))))) <=> (![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] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_5(Y))) & r1(X!0, Y!6) & ![X: $i] : (p1(X) | (~r1(Y!6, X))) & r1(Y!6, X!7) & (~(p1(Y!8) | (~r1(X!7, Y!8)))))),
% 0.10/0.45 inference(transitivity,[status(thm)],[24, 16])).
% 0.10/0.45 tff(26,plain,
% 0.10/0.45 (?[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] : ((~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] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, 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))))))) <=> ?[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] : ((~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] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, 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)))))))),
% 0.10/0.45 inference(rewrite,[status(thm)],[])).
% 0.10/0.45 tff(27,plain,
% 0.10/0.45 ((~(~?[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] : ((~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] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, 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))))))))) <=> ?[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] : ((~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] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, 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)))))))),
% 0.10/0.45 inference(rewrite,[status(thm)],[])).
% 0.10/0.45 tff(28,plain,
% 0.10/0.45 ((~?[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)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, 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)) | $false))))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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] : ((~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] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, 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))))))))),
% 0.10/0.45 inference(rewrite,[status(thm)],[])).
% 0.10/0.45 tff(29,plain,
% 0.10/0.45 ((~(~?[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)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, 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)) | $false))))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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] : ((~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] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, 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)))))))))),
% 0.10/0.45 inference(monotonicity,[status(thm)],[28])).
% 0.10/0.45 tff(30,plain,
% 0.10/0.45 ((~(~?[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)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, 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)) | $false))))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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] : ((~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] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, 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)))))))),
% 0.10/0.45 inference(transitivity,[status(thm)],[29, 27])).
% 0.10/0.45 tff(31,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)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, 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)) | $false))))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','main')).
% 0.10/0.45 tff(32,plain,
% 0.10/0.45 (?[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] : ((~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] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, 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)))))))),
% 0.10/0.45 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.10/0.45 tff(33,plain,
% 0.10/0.45 (?[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] : ((~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] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, 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)))))))),
% 0.10/0.46 inference(modus_ponens,[status(thm)],[32, 26])).
% 0.10/0.46 tff(34,plain,
% 0.10/0.46 (![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] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_5(Y))) & r1(X!0, Y!6) & ![X: $i] : (p1(X) | (~r1(Y!6, X))) & r1(Y!6, X!7) & (~(p1(Y!8) | (~r1(X!7, Y!8))))),
% 0.10/0.46 inference(modus_ponens,[status(thm)],[33, 25])).
% 0.10/0.46 tff(35,plain,
% 0.10/0.46 (~(p1(Y!8) | (~r1(X!7, Y!8)))),
% 0.10/0.46 inference(and_elim,[status(thm)],[34])).
% 0.10/0.46 tff(36,plain,
% 0.10/0.46 (r1(X!7, Y!8)),
% 0.10/0.46 inference(or_elim,[status(thm)],[35])).
% 0.10/0.46 tff(37,plain,
% 0.10/0.46 (~p1(Y!8)),
% 0.10/0.46 inference(or_elim,[status(thm)],[35])).
% 0.10/0.46 tff(38,plain,
% 0.10/0.46 (((~![Y: $i] : (p1(Y) | (~r1(X!7, Y)))) | (p1(Y!8) | (~r1(X!7, Y!8)))) <=> ((~![Y: $i] : (p1(Y) | (~r1(X!7, Y)))) | p1(Y!8) | (~r1(X!7, Y!8)))),
% 0.10/0.46 inference(rewrite,[status(thm)],[])).
% 0.10/0.46 tff(39,plain,
% 0.10/0.46 ((~![Y: $i] : (p1(Y) | (~r1(X!7, Y)))) | (p1(Y!8) | (~r1(X!7, Y!8)))),
% 0.10/0.46 inference(quant_inst,[status(thm)],[])).
% 0.10/0.46 tff(40,plain,
% 0.10/0.46 ((~![Y: $i] : (p1(Y) | (~r1(X!7, Y)))) | p1(Y!8) | (~r1(X!7, Y!8))),
% 0.10/0.46 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.10/0.46 tff(41,plain,
% 0.10/0.46 ($false),
% 0.10/0.46 inference(unit_resolution,[status(thm)],[40, 37, 36, 15])).
% 0.10/0.46 tff(42,plain,(~![Y: $i] : (p1(Y) | (~r1(X!7, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.10/0.46 tff(43,plain,
% 0.10/0.46 (r1(X!0, Y!6)),
% 0.10/0.46 inference(and_elim,[status(thm)],[34])).
% 0.10/0.46 tff(44,plain,
% 0.10/0.46 (^[Y: $i] : refl(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))))),
% 0.10/0.46 inference(bind,[status(th)],[])).
% 0.10/0.46 tff(45,plain,
% 0.10/0.46 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))))),
% 0.10/0.46 inference(quant_intro,[status(thm)],[44])).
% 0.10/0.46 tff(46,plain,
% 0.10/0.46 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))))),
% 0.10/0.46 inference(bind,[status(th)],[])).
% 0.10/0.46 tff(47,plain,
% 0.10/0.46 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))))),
% 0.10/0.46 inference(quant_intro,[status(thm)],[46])).
% 0.10/0.46 tff(48,plain,
% 0.10/0.46 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))))),
% 0.10/0.46 inference(transitivity,[status(thm)],[47, 45])).
% 0.10/0.46 tff(49,plain,
% 0.10/0.46 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))))),
% 0.10/0.46 inference(and_elim,[status(thm)],[34])).
% 0.10/0.46 tff(50,plain,
% 0.10/0.46 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))))),
% 0.10/0.46 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.10/0.46 tff(51,plain,
% 0.10/0.46 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))))) | ((~r1(X!0, Y!6)) | ![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))))) | (~r1(X!0, Y!6)) | ![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))))),
% 0.10/0.46 inference(rewrite,[status(thm)],[])).
% 0.10/0.46 tff(52,plain,
% 0.10/0.46 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))))) | ((~r1(X!0, Y!6)) | ![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))))),
% 0.10/0.46 inference(quant_inst,[status(thm)],[])).
% 0.10/0.46 tff(53,plain,
% 0.10/0.46 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))))) | (~r1(X!0, Y!6)) | ![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))),
% 0.10/0.46 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.10/0.46 tff(54,plain,
% 0.10/0.46 (![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))),
% 0.10/0.46 inference(unit_resolution,[status(thm)],[53, 50, 43])).
% 0.10/0.46 tff(55,plain,
% 0.10/0.46 (r1(Y!6, X!7)),
% 0.10/0.46 inference(and_elim,[status(thm)],[34])).
% 0.10/0.46 tff(56,plain,
% 0.10/0.46 (((~![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) | ((~r1(Y!6, X!7)) | ![Y: $i] : ((~r1(X!7, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X!7, Y))))) <=> ((~![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) | (~r1(Y!6, X!7)) | ![Y: $i] : ((~r1(X!7, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X!7, Y))))),
% 0.10/0.46 inference(rewrite,[status(thm)],[])).
% 0.10/0.46 tff(57,plain,
% 0.10/0.46 (((~r1(Y!6, X!7)) | ![Y: $i] : (p1(Y) | (~r1(X!7, Y))) | ![Y: $i] : ((~r1(X!7, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))) <=> ((~r1(Y!6, X!7)) | ![Y: $i] : ((~r1(X!7, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X!7, Y))))),
% 0.10/0.46 inference(rewrite,[status(thm)],[])).
% 0.10/0.46 tff(58,plain,
% 0.10/0.46 (((~![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) | ((~r1(Y!6, X!7)) | ![Y: $i] : (p1(Y) | (~r1(X!7, Y))) | ![Y: $i] : ((~r1(X!7, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) <=> ((~![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) | ((~r1(Y!6, X!7)) | ![Y: $i] : ((~r1(X!7, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X!7, Y)))))),
% 0.10/0.46 inference(monotonicity,[status(thm)],[57])).
% 0.10/0.46 tff(59,plain,
% 0.10/0.46 (((~![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) | ((~r1(Y!6, X!7)) | ![Y: $i] : (p1(Y) | (~r1(X!7, Y))) | ![Y: $i] : ((~r1(X!7, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) <=> ((~![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) | (~r1(Y!6, X!7)) | ![Y: $i] : ((~r1(X!7, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X!7, Y))))),
% 0.10/0.46 inference(transitivity,[status(thm)],[58, 56])).
% 0.10/0.46 tff(60,plain,
% 0.10/0.46 ((~![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) | ((~r1(Y!6, X!7)) | ![Y: $i] : (p1(Y) | (~r1(X!7, Y))) | ![Y: $i] : ((~r1(X!7, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))),
% 0.10/0.46 inference(quant_inst,[status(thm)],[])).
% 0.10/0.46 tff(61,plain,
% 0.10/0.46 ((~![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) | (~r1(Y!6, X!7)) | ![Y: $i] : ((~r1(X!7, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X!7, Y)))),
% 0.10/0.46 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.10/0.46 tff(62,plain,
% 0.10/0.46 (![Y: $i] : ((~r1(X!7, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X!7, Y)))),
% 0.10/0.46 inference(unit_resolution,[status(thm)],[61, 55, 54])).
% 0.10/0.46 tff(63,plain,
% 0.10/0.46 (![Y: $i] : ((~r1(X!7, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))),
% 0.10/0.46 inference(unit_resolution,[status(thm)],[62, 42])).
% 0.10/0.46 tff(64,plain,
% 0.10/0.46 (((~![Y: $i] : ((~r1(X!7, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))) | ((~r1(X!7, tptp_fun_Y_2(X!7))) | (~(p1(tptp_fun_X_4(tptp_fun_Y_2(X!7))) | (~r1(tptp_fun_Y_2(X!7), tptp_fun_X_4(tptp_fun_Y_2(X!7)))))))) <=> ((~![Y: $i] : ((~r1(X!7, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))) | (~r1(X!7, tptp_fun_Y_2(X!7))) | (~(p1(tptp_fun_X_4(tptp_fun_Y_2(X!7))) | (~r1(tptp_fun_Y_2(X!7), tptp_fun_X_4(tptp_fun_Y_2(X!7)))))))),
% 0.10/0.46 inference(rewrite,[status(thm)],[])).
% 0.10/0.46 tff(65,plain,
% 0.10/0.46 ((~![Y: $i] : ((~r1(X!7, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))) | ((~r1(X!7, tptp_fun_Y_2(X!7))) | (~(p1(tptp_fun_X_4(tptp_fun_Y_2(X!7))) | (~r1(tptp_fun_Y_2(X!7), tptp_fun_X_4(tptp_fun_Y_2(X!7)))))))),
% 0.10/0.46 inference(quant_inst,[status(thm)],[])).
% 0.10/0.46 tff(66,plain,
% 0.10/0.46 ((~![Y: $i] : ((~r1(X!7, Y)) | (~(p1(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))) | (~r1(X!7, tptp_fun_Y_2(X!7))) | (~(p1(tptp_fun_X_4(tptp_fun_Y_2(X!7))) | (~r1(tptp_fun_Y_2(X!7), tptp_fun_X_4(tptp_fun_Y_2(X!7))))))),
% 0.10/0.46 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.10/0.46 tff(67,plain,
% 0.10/0.46 (~(p1(tptp_fun_X_4(tptp_fun_Y_2(X!7))) | (~r1(tptp_fun_Y_2(X!7), tptp_fun_X_4(tptp_fun_Y_2(X!7)))))),
% 0.10/0.46 inference(unit_resolution,[status(thm)],[66, 63, 14])).
% 0.10/0.46 tff(68,plain,
% 0.10/0.46 ((p1(tptp_fun_X_4(tptp_fun_Y_2(X!7))) | (~r1(tptp_fun_Y_2(X!7), tptp_fun_X_4(tptp_fun_Y_2(X!7))))) | r1(tptp_fun_Y_2(X!7), tptp_fun_X_4(tptp_fun_Y_2(X!7)))),
% 0.10/0.46 inference(tautology,[status(thm)],[])).
% 0.10/0.46 tff(69,plain,
% 0.10/0.46 (r1(tptp_fun_Y_2(X!7), tptp_fun_X_4(tptp_fun_Y_2(X!7)))),
% 0.10/0.46 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.10/0.46 tff(70,plain,
% 0.10/0.46 ((p1(tptp_fun_X_4(tptp_fun_Y_2(X!7))) | (~r1(tptp_fun_Y_2(X!7), tptp_fun_X_4(tptp_fun_Y_2(X!7))))) | (~p1(tptp_fun_X_4(tptp_fun_Y_2(X!7))))),
% 0.10/0.46 inference(tautology,[status(thm)],[])).
% 0.10/0.46 tff(71,plain,
% 0.10/0.46 (~p1(tptp_fun_X_4(tptp_fun_Y_2(X!7)))),
% 0.10/0.46 inference(unit_resolution,[status(thm)],[70, 67])).
% 0.10/0.46 tff(72,plain,
% 0.10/0.46 (((~r1(X!7, tptp_fun_Y_2(X!7))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X!7), X))))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X!7), X)))),
% 0.10/0.46 inference(tautology,[status(thm)],[])).
% 0.10/0.46 tff(73,plain,
% 0.10/0.46 (![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X!7), X)))),
% 0.10/0.46 inference(unit_resolution,[status(thm)],[72, 12])).
% 0.10/0.46 tff(74,plain,
% 0.10/0.46 (((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X!7), X)))) | (p1(tptp_fun_X_4(tptp_fun_Y_2(X!7))) | (~r1(tptp_fun_Y_2(X!7), tptp_fun_X_4(tptp_fun_Y_2(X!7)))))) <=> ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X!7), X)))) | p1(tptp_fun_X_4(tptp_fun_Y_2(X!7))) | (~r1(tptp_fun_Y_2(X!7), tptp_fun_X_4(tptp_fun_Y_2(X!7)))))),
% 0.10/0.46 inference(rewrite,[status(thm)],[])).
% 0.10/0.46 tff(75,plain,
% 0.10/0.46 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X!7), X)))) | (p1(tptp_fun_X_4(tptp_fun_Y_2(X!7))) | (~r1(tptp_fun_Y_2(X!7), tptp_fun_X_4(tptp_fun_Y_2(X!7)))))),
% 0.10/0.46 inference(quant_inst,[status(thm)],[])).
% 0.10/0.46 tff(76,plain,
% 0.10/0.46 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X!7), X)))) | p1(tptp_fun_X_4(tptp_fun_Y_2(X!7))) | (~r1(tptp_fun_Y_2(X!7), tptp_fun_X_4(tptp_fun_Y_2(X!7))))),
% 0.10/0.46 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.10/0.46 tff(77,plain,
% 0.10/0.46 ($false),
% 0.10/0.46 inference(unit_resolution,[status(thm)],[76, 73, 71, 69])).
% 0.10/0.46 tff(78,plain,((~r1(X!7, tptp_fun_Y_2(X!7))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X!7), X))))), inference(lemma,lemma(discharge,[]))).
% 0.10/0.46 tff(79,assumption,(![X: $i] : ((~r1(Y!6, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))))), introduced(assumption)).
% 0.10/0.46 tff(80,plain,
% 0.10/0.46 (((~![X: $i] : ((~r1(Y!6, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))))) | ((~r1(Y!6, X!7)) | (~((~r1(X!7, tptp_fun_Y_2(X!7))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X!7), X)))))))) <=> ((~![X: $i] : ((~r1(Y!6, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))))) | (~r1(Y!6, X!7)) | (~((~r1(X!7, tptp_fun_Y_2(X!7))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X!7), X)))))))),
% 0.10/0.46 inference(rewrite,[status(thm)],[])).
% 0.10/0.46 tff(81,plain,
% 0.10/0.46 ((~![X: $i] : ((~r1(Y!6, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))))) | ((~r1(Y!6, X!7)) | (~((~r1(X!7, tptp_fun_Y_2(X!7))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X!7), X)))))))),
% 0.10/0.46 inference(quant_inst,[status(thm)],[])).
% 0.10/0.46 tff(82,plain,
% 0.10/0.46 ((~![X: $i] : ((~r1(Y!6, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))))) | (~r1(Y!6, X!7)) | (~((~r1(X!7, tptp_fun_Y_2(X!7))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X!7), X))))))),
% 0.10/0.46 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.10/0.46 tff(83,plain,
% 0.10/0.46 ($false),
% 0.10/0.46 inference(unit_resolution,[status(thm)],[82, 55, 79, 78])).
% 0.10/0.46 tff(84,plain,(~![X: $i] : ((~r1(Y!6, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))))), inference(lemma,lemma(discharge,[]))).
% 0.10/0.46 tff(85,plain,
% 0.10/0.46 (^[Y: $i] : refl(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))))))),
% 0.10/0.46 inference(bind,[status(th)],[])).
% 0.10/0.46 tff(86,plain,
% 0.10/0.46 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))))),
% 0.10/0.46 inference(quant_intro,[status(thm)],[85])).
% 0.10/0.46 tff(87,plain,
% 0.10/0.46 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))))))),
% 0.10/0.46 inference(bind,[status(th)],[])).
% 0.10/0.46 tff(88,plain,
% 0.10/0.46 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))))),
% 0.10/0.47 inference(quant_intro,[status(thm)],[87])).
% 0.10/0.47 tff(89,plain,
% 0.10/0.47 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))))),
% 0.10/0.47 inference(transitivity,[status(thm)],[88, 86])).
% 0.10/0.47 tff(90,plain,
% 0.10/0.47 (^[Y: $i] : trans(monotonicity(quant_intro(proof_bind(^[X: $i] : rewrite(((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) <=> ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))))), (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) <=> ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))))), (((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))))), rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))))), (((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))))))),
% 0.10/0.47 inference(bind,[status(th)],[])).
% 0.10/0.47 tff(91,plain,
% 0.10/0.47 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))))),
% 0.10/0.47 inference(quant_intro,[status(thm)],[90])).
% 0.10/0.47 tff(92,plain,
% 0.10/0.47 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_2(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))))),
% 0.10/0.47 inference(and_elim,[status(thm)],[34])).
% 0.10/0.47 tff(93,plain,
% 0.10/0.47 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))))),
% 0.10/0.47 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.10/0.47 tff(94,plain,
% 0.10/0.47 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))))),
% 0.10/0.47 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.10/0.47 tff(95,plain,
% 0.10/0.47 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))))) | ((~r1(X!0, Y!6)) | ![X: $i] : ((~r1(Y!6, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y!6, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))))) | (~r1(X!0, Y!6)) | ![X: $i] : ((~r1(Y!6, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y!6, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))))),
% 0.10/0.47 inference(rewrite,[status(thm)],[])).
% 0.10/0.47 tff(96,plain,
% 0.10/0.47 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))))) | ((~r1(X!0, Y!6)) | ![X: $i] : ((~r1(Y!6, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y!6, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))))),
% 0.10/0.47 inference(quant_inst,[status(thm)],[])).
% 0.10/0.47 tff(97,plain,
% 0.10/0.47 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X))))))))) | (~r1(X!0, Y!6)) | ![X: $i] : ((~r1(Y!6, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y!6, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))))),
% 0.10/0.47 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.10/0.47 tff(98,plain,
% 0.10/0.47 (![X: $i] : ((~r1(Y!6, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))) | ![X: $i] : ((~r1(Y!6, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_2(X), X)))))))),
% 0.10/0.47 inference(unit_resolution,[status(thm)],[97, 94, 43])).
% 0.10/0.47 tff(99,plain,
% 0.10/0.47 (![X: $i] : ((~r1(Y!6, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))),
% 0.10/0.47 inference(unit_resolution,[status(thm)],[98, 84])).
% 0.10/0.47 tff(100,plain,
% 0.10/0.47 (((~![X: $i] : ((~r1(Y!6, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))) | ((~r1(Y!6, Y!6)) | (~(p1(tptp_fun_Y_3(Y!6)) | (~r1(Y!6, tptp_fun_Y_3(Y!6))))))) <=> ((~![X: $i] : ((~r1(Y!6, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))) | (~r1(Y!6, Y!6)) | (~(p1(tptp_fun_Y_3(Y!6)) | (~r1(Y!6, tptp_fun_Y_3(Y!6))))))),
% 0.10/0.47 inference(rewrite,[status(thm)],[])).
% 0.10/0.47 tff(101,plain,
% 0.10/0.47 ((~![X: $i] : ((~r1(Y!6, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))) | ((~r1(Y!6, Y!6)) | (~(p1(tptp_fun_Y_3(Y!6)) | (~r1(Y!6, tptp_fun_Y_3(Y!6))))))),
% 0.10/0.47 inference(quant_inst,[status(thm)],[])).
% 0.10/0.47 tff(102,plain,
% 0.10/0.47 ((~![X: $i] : ((~r1(Y!6, X)) | (~(p1(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))) | (~r1(Y!6, Y!6)) | (~(p1(tptp_fun_Y_3(Y!6)) | (~r1(Y!6, tptp_fun_Y_3(Y!6)))))),
% 0.10/0.47 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.10/0.47 tff(103,plain,
% 0.10/0.47 (~(p1(tptp_fun_Y_3(Y!6)) | (~r1(Y!6, tptp_fun_Y_3(Y!6))))),
% 0.10/0.47 inference(unit_resolution,[status(thm)],[102, 99, 11])).
% 0.10/0.47 tff(104,plain,
% 0.10/0.47 ((p1(tptp_fun_Y_3(Y!6)) | (~r1(Y!6, tptp_fun_Y_3(Y!6)))) | r1(Y!6, tptp_fun_Y_3(Y!6))),
% 0.10/0.47 inference(tautology,[status(thm)],[])).
% 0.10/0.47 tff(105,plain,
% 0.10/0.47 (r1(Y!6, tptp_fun_Y_3(Y!6))),
% 0.10/0.47 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.10/0.47 tff(106,plain,
% 0.10/0.47 ((p1(tptp_fun_Y_3(Y!6)) | (~r1(Y!6, tptp_fun_Y_3(Y!6)))) | (~p1(tptp_fun_Y_3(Y!6)))),
% 0.10/0.47 inference(tautology,[status(thm)],[])).
% 0.10/0.47 tff(107,plain,
% 0.10/0.47 (~p1(tptp_fun_Y_3(Y!6))),
% 0.10/0.47 inference(unit_resolution,[status(thm)],[106, 103])).
% 0.10/0.47 tff(108,plain,
% 0.10/0.47 (^[X: $i] : refl((p1(X) | (~r1(Y!6, X))) <=> (p1(X) | (~r1(Y!6, X))))),
% 0.10/0.47 inference(bind,[status(th)],[])).
% 0.10/0.47 tff(109,plain,
% 0.10/0.47 (![X: $i] : (p1(X) | (~r1(Y!6, X))) <=> ![X: $i] : (p1(X) | (~r1(Y!6, X)))),
% 0.10/0.47 inference(quant_intro,[status(thm)],[108])).
% 0.10/0.47 tff(110,plain,
% 0.10/0.47 (![X: $i] : (p1(X) | (~r1(Y!6, X)))),
% 0.10/0.47 inference(and_elim,[status(thm)],[34])).
% 0.10/0.47 tff(111,plain,
% 0.10/0.47 (![X: $i] : (p1(X) | (~r1(Y!6, X)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.21/0.47 tff(112,plain,
% 0.21/0.47 (((~![X: $i] : (p1(X) | (~r1(Y!6, X)))) | (p1(tptp_fun_Y_3(Y!6)) | (~r1(Y!6, tptp_fun_Y_3(Y!6))))) <=> ((~![X: $i] : (p1(X) | (~r1(Y!6, X)))) | p1(tptp_fun_Y_3(Y!6)) | (~r1(Y!6, tptp_fun_Y_3(Y!6))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(113,plain,
% 0.21/0.47 ((~![X: $i] : (p1(X) | (~r1(Y!6, X)))) | (p1(tptp_fun_Y_3(Y!6)) | (~r1(Y!6, tptp_fun_Y_3(Y!6))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(114,plain,
% 0.21/0.47 ((~![X: $i] : (p1(X) | (~r1(Y!6, X)))) | p1(tptp_fun_Y_3(Y!6)) | (~r1(Y!6, tptp_fun_Y_3(Y!6)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.21/0.47 tff(115,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[114, 111, 107, 105])).
% 0.21/0.47 % SZS output end Proof
% 0.21/0.47 % E exiting
%------------------------------------------------------------------------------