TSTP Solution File: LCL672+1.001 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL672+1.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 04:57:42 EDT 2022
% Result : Theorem 5.29s 3.56s
% Output : Proof 5.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL672+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 23:50:04 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.18/0.34 Usage: tptp [options] [-file:]file
% 0.18/0.34 -h, -? prints this message.
% 0.18/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.18/0.34 -m, -model generate model.
% 0.18/0.34 -p, -proof generate proof.
% 0.18/0.34 -c, -core generate unsat core of named formulas.
% 0.18/0.34 -st, -statistics display statistics.
% 0.18/0.34 -t:timeout set timeout (in second).
% 0.18/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.18/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.18/0.34 -<param>:<value> configuration parameter and value.
% 0.18/0.34 -o:<output-file> file to place output in.
% 5.29/3.56 % SZS status Theorem
% 5.29/3.56 % SZS output start Proof
% 5.29/3.56 tff(p1_type, type, (
% 5.29/3.56 p1: $i > $o)).
% 5.29/3.56 tff(tptp_fun_Y_6_type, type, (
% 5.29/3.56 tptp_fun_Y_6: $i > $i)).
% 5.29/3.56 tff(tptp_fun_X_7_type, type, (
% 5.29/3.56 tptp_fun_X_7: $i > $i)).
% 5.29/3.56 tff(tptp_fun_X_10_type, type, (
% 5.29/3.56 tptp_fun_X_10: $i)).
% 5.29/3.56 tff(r1_type, type, (
% 5.29/3.56 r1: ( $i * $i ) > $o)).
% 5.29/3.56 tff(tptp_fun_X_4_type, type, (
% 5.29/3.56 tptp_fun_X_4: $i > $i)).
% 5.29/3.56 tff(tptp_fun_Y_3_type, type, (
% 5.29/3.56 tptp_fun_Y_3: $i > $i)).
% 5.29/3.56 tff(tptp_fun_Y_8_type, type, (
% 5.29/3.56 tptp_fun_Y_8: $i)).
% 5.29/3.56 tff(tptp_fun_X_9_type, type, (
% 5.29/3.56 tptp_fun_X_9: $i)).
% 5.29/3.56 tff(tptp_fun_X_0_type, type, (
% 5.29/3.56 tptp_fun_X_0: $i)).
% 5.29/3.56 tff(p2_type, type, (
% 5.29/3.56 p2: $i > $o)).
% 5.29/3.56 tff(tptp_fun_Y_5_type, type, (
% 5.29/3.56 tptp_fun_Y_5: $i > $i)).
% 5.29/3.56 tff(tptp_fun_Y_2_type, type, (
% 5.29/3.56 tptp_fun_Y_2: $i)).
% 5.29/3.56 tff(tptp_fun_Y_1_type, type, (
% 5.29/3.56 tptp_fun_Y_1: $i)).
% 5.29/3.56 tff(1,assumption,(~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | p1(tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))), introduced(assumption)).
% 5.29/3.56 tff(2,plain,
% 5.29/3.56 (((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | p1(tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~p1(tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))),
% 5.29/3.56 inference(tautology,[status(thm)],[])).
% 5.29/3.56 tff(3,plain,
% 5.29/3.56 (~p1(tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 5.29/3.56 inference(unit_resolution,[status(thm)],[2, 1])).
% 5.29/3.56 tff(4,plain,
% 5.29/3.56 (((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | p1(tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 5.29/3.56 inference(tautology,[status(thm)],[])).
% 5.29/3.56 tff(5,plain,
% 5.29/3.56 (r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 5.29/3.56 inference(unit_resolution,[status(thm)],[4, 1])).
% 5.29/3.56 tff(6,assumption,(~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))), introduced(assumption)).
% 5.29/3.56 tff(7,plain,
% 5.29/3.56 (((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | (~p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))),
% 5.29/3.56 inference(tautology,[status(thm)],[])).
% 5.29/3.56 tff(8,plain,
% 5.29/3.56 (~p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))),
% 5.29/3.56 inference(unit_resolution,[status(thm)],[7, 6])).
% 5.29/3.56 tff(9,plain,
% 5.29/3.56 (^[Y: $i] : refl((p1(Y) | (~r1(X!10, Y))) <=> (p1(Y) | (~r1(X!10, Y))))),
% 5.29/3.56 inference(bind,[status(th)],[])).
% 5.29/3.56 tff(10,plain,
% 5.29/3.56 (![Y: $i] : (p1(Y) | (~r1(X!10, Y))) <=> ![Y: $i] : (p1(Y) | (~r1(X!10, Y)))),
% 5.29/3.56 inference(quant_intro,[status(thm)],[9])).
% 5.29/3.56 tff(11,plain,
% 5.29/3.56 (((~((~r1(X!0, Y!1)) | p1(Y!1))) & (~(p2(Y!2) | (~r1(X!0, Y!2)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) & (r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & r1(Y!8, X!10) & ![Y: $i] : (p1(Y) | (~r1(X!10, Y))))) <=> ((~((~r1(X!0, Y!1)) | p1(Y!1))) & (~(p2(Y!2) | (~r1(X!0, Y!2)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) & r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & r1(Y!8, X!10) & ![Y: $i] : (p1(Y) | (~r1(X!10, Y))))),
% 5.29/3.56 inference(rewrite,[status(thm)],[])).
% 5.29/3.56 tff(12,plain,
% 5.29/3.56 ((r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (r1(Y!8, X!10) & ![Y: $i] : (p1(Y) | (~r1(X!10, Y))))) <=> (r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & r1(Y!8, X!10) & ![Y: $i] : (p1(Y) | (~r1(X!10, Y))))),
% 5.29/3.56 inference(rewrite,[status(thm)],[])).
% 5.29/3.56 tff(13,plain,
% 5.29/3.56 (((~(~r1(Y!8, X!10))) & ![Y: $i] : ((~r1(X!10, Y)) | p1(Y))) <=> (r1(Y!8, X!10) & ![Y: $i] : (p1(Y) | (~r1(X!10, Y))))),
% 5.29/3.56 inference(rewrite,[status(thm)],[])).
% 5.29/3.56 tff(14,plain,
% 5.29/3.56 ((~((~r1(Y!8, X!9)) | p1(X!9))) <=> (~((~r1(Y!8, X!9)) | p1(X!9)))),
% 5.29/3.56 inference(rewrite,[status(thm)],[])).
% 5.29/3.56 tff(15,plain,
% 5.29/3.56 ((~(~r1(X!0, Y!8))) <=> r1(X!0, Y!8)),
% 5.29/3.56 inference(rewrite,[status(thm)],[])).
% 5.29/3.56 tff(16,plain,
% 5.29/3.56 (((~(~r1(X!0, Y!8))) & (~((~r1(Y!8, X!9)) | p1(X!9))) & ((~(~r1(Y!8, X!10))) & ![Y: $i] : ((~r1(X!10, Y)) | p1(Y)))) <=> (r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (r1(Y!8, X!10) & ![Y: $i] : (p1(Y) | (~r1(X!10, Y)))))),
% 5.29/3.56 inference(monotonicity,[status(thm)],[15, 14, 13])).
% 5.29/3.56 tff(17,plain,
% 5.29/3.56 (((~(~r1(X!0, Y!8))) & (~((~r1(Y!8, X!9)) | p1(X!9))) & ((~(~r1(Y!8, X!10))) & ![Y: $i] : ((~r1(X!10, Y)) | p1(Y)))) <=> (r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & r1(Y!8, X!10) & ![Y: $i] : (p1(Y) | (~r1(X!10, Y))))),
% 5.29/3.56 inference(transitivity,[status(thm)],[16, 12])).
% 5.29/3.56 tff(18,plain,
% 5.29/3.56 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))))),
% 5.29/3.56 inference(rewrite,[status(thm)],[])).
% 5.29/3.56 tff(19,plain,
% 5.29/3.56 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | p1(Y)) <=> (p1(Y) | (~r1(X!0, Y))))),
% 5.29/3.56 inference(bind,[status(th)],[])).
% 5.29/3.56 tff(20,plain,
% 5.29/3.56 (![Y: $i] : ((~r1(X!0, Y)) | p1(Y)) <=> ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))),
% 5.29/3.56 inference(quant_intro,[status(thm)],[19])).
% 5.29/3.56 tff(21,plain,
% 5.29/3.56 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) <=> ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))))),
% 5.29/3.56 inference(bind,[status(th)],[])).
% 5.29/3.56 tff(22,plain,
% 5.29/3.56 (![Y: $i] : ((~r1(X!0, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))),
% 5.29/3.56 inference(quant_intro,[status(thm)],[21])).
% 5.29/3.56 tff(23,plain,
% 5.29/3.56 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 5.29/3.56 inference(monotonicity,[status(thm)],[22, 20])).
% 5.29/3.56 tff(24,plain,
% 5.29/3.56 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))))),
% 5.29/3.56 inference(transitivity,[status(thm)],[23, 18])).
% 5.29/3.56 tff(25,plain,
% 5.29/3.56 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))),
% 5.29/3.57 inference(rewrite,[status(thm)],[])).
% 5.29/3.57 tff(26,plain,
% 5.29/3.57 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : rewrite(((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) <=> ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))), (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) <=> ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))), ((![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))) <=> (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))), rewrite((![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))) <=> (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))), ((![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))) <=> (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))),
% 5.29/3.57 inference(bind,[status(th)],[])).
% 5.29/3.57 tff(27,plain,
% 5.29/3.57 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))),
% 5.29/3.57 inference(quant_intro,[status(thm)],[26])).
% 5.29/3.57 tff(28,plain,
% 5.29/3.57 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 5.29/3.57 inference(monotonicity,[status(thm)],[27, 20])).
% 5.29/3.57 tff(29,plain,
% 5.29/3.57 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))),
% 5.29/3.57 inference(transitivity,[status(thm)],[28, 25])).
% 5.29/3.57 tff(30,plain,
% 5.29/3.57 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))),
% 5.29/3.57 inference(rewrite,[status(thm)],[])).
% 5.29/3.57 tff(31,plain,
% 5.29/3.57 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) <=> ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))),
% 5.29/3.57 inference(bind,[status(th)],[])).
% 5.29/3.57 tff(32,plain,
% 5.29/3.57 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))),
% 5.29/3.57 inference(quant_intro,[status(thm)],[31])).
% 5.29/3.57 tff(33,plain,
% 5.29/3.57 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 5.29/3.57 inference(monotonicity,[status(thm)],[32, 20])).
% 5.29/3.57 tff(34,plain,
% 5.29/3.57 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))),
% 5.29/3.57 inference(transitivity,[status(thm)],[33, 30])).
% 5.29/3.57 tff(35,plain,
% 5.29/3.57 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 5.29/3.57 inference(rewrite,[status(thm)],[])).
% 5.29/3.57 tff(36,plain,
% 5.29/3.57 (^[Y: $i] : trans(monotonicity(rewrite((![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y))) <=> ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) <=> ((~r1(X!0, Y)) | ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))), rewrite(((~r1(X!0, Y)) | ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))) <=> ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) <=> ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))),
% 5.29/3.57 inference(bind,[status(th)],[])).
% 5.29/3.57 tff(37,plain,
% 5.29/3.57 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) <=> ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))),
% 5.29/3.57 inference(quant_intro,[status(thm)],[36])).
% 5.29/3.57 tff(38,plain,
% 5.29/3.57 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 5.29/3.57 inference(monotonicity,[status(thm)],[37, 20])).
% 5.29/3.57 tff(39,plain,
% 5.29/3.57 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 5.29/3.57 inference(transitivity,[status(thm)],[38, 35])).
% 5.29/3.57 tff(40,plain,
% 5.29/3.57 ((~((~r1(X!0, Y!1)) | p1(Y!1))) <=> (~((~r1(X!0, Y!1)) | p1(Y!1)))),
% 5.29/3.57 inference(rewrite,[status(thm)],[])).
% 5.29/3.57 tff(41,plain,
% 5.29/3.57 (((~((~r1(X!0, Y!1)) | p1(Y!1))) & (~(p2(Y!2) | (~r1(X!0, Y!2)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & ((~(~r1(X!0, Y!8))) & (~((~r1(Y!8, X!9)) | p1(X!9))) & ((~(~r1(Y!8, X!10))) & ![Y: $i] : ((~r1(X!10, Y)) | p1(Y))))) <=> ((~((~r1(X!0, Y!1)) | p1(Y!1))) & (~(p2(Y!2) | (~r1(X!0, Y!2)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) & (r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & r1(Y!8, X!10) & ![Y: $i] : (p1(Y) | (~r1(X!10, Y)))))),
% 5.29/3.58 inference(monotonicity,[status(thm)],[40, 39, 34, 29, 24, 17])).
% 5.29/3.58 tff(42,plain,
% 5.29/3.58 (((~((~r1(X!0, Y!1)) | p1(Y!1))) & (~(p2(Y!2) | (~r1(X!0, Y!2)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & ((~(~r1(X!0, Y!8))) & (~((~r1(Y!8, X!9)) | p1(X!9))) & ((~(~r1(Y!8, X!10))) & ![Y: $i] : ((~r1(X!10, Y)) | p1(Y))))) <=> ((~((~r1(X!0, Y!1)) | p1(Y!1))) & (~(p2(Y!2) | (~r1(X!0, Y!2)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) & r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & r1(Y!8, X!10) & ![Y: $i] : (p1(Y) | (~r1(X!10, Y))))),
% 5.29/3.58 inference(transitivity,[status(thm)],[41, 11])).
% 5.29/3.58 tff(43,plain,
% 5.29/3.58 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ((~![Y: $i] : (p2(Y) | (~r1(X, 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)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, 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)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, 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)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ((~![Y: $i] : (p2(Y) | (~r1(X, 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)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, 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)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, 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)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))),
% 5.37/3.58 inference(rewrite,[status(thm)],[])).
% 5.37/3.58 tff(44,plain,
% 5.37/3.58 ((~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ((~![Y: $i] : (p2(Y) | (~r1(X, 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)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, 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)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, 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)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ((~![Y: $i] : (p2(Y) | (~r1(X, 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)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, 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)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, 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)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))),
% 5.37/3.58 inference(rewrite,[status(thm)],[])).
% 5.37/3.58 tff(45,plain,
% 5.37/3.58 ((~?[X: $i] : (~(((((((((~![Y: $i] : ((~r1(X, Y)) | p2(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)) | p1(Y)))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(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)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(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)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p2(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)) | p1(Y))))) <=> (~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ((~![Y: $i] : (p2(Y) | (~r1(X, 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)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, 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)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, 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)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))),
% 5.37/3.58 inference(rewrite,[status(thm)],[])).
% 5.37/3.58 tff(46,plain,
% 5.37/3.58 ((~(~?[X: $i] : (~(((((((((~![Y: $i] : ((~r1(X, Y)) | p2(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)) | p1(Y)))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(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)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(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)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p2(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)) | p1(Y)))))) <=> (~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ((~![Y: $i] : (p2(Y) | (~r1(X, 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)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, 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)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, 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)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))),
% 5.37/3.58 inference(monotonicity,[status(thm)],[45])).
% 5.37/3.58 tff(47,plain,
% 5.37/3.58 ((~(~?[X: $i] : (~(((((((((~![Y: $i] : ((~r1(X, Y)) | p2(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)) | p1(Y)))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(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)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(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)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p2(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)) | p1(Y)))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ((~![Y: $i] : (p2(Y) | (~r1(X, 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)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, 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)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, 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)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))),
% 5.37/3.59 inference(transitivity,[status(thm)],[46, 44])).
% 5.37/3.59 tff(48,axiom,(~(~?[X: $i] : (~(((((((((~![Y: $i] : ((~r1(X, Y)) | p2(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)) | p1(Y)))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(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)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(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)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p2(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)) | p1(Y)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','main')).
% 5.37/3.59 tff(49,plain,
% 5.37/3.59 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ((~![Y: $i] : (p2(Y) | (~r1(X, 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)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, 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)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, 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)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))),
% 5.37/3.59 inference(modus_ponens,[status(thm)],[48, 47])).
% 5.37/3.59 tff(50,plain,
% 5.37/3.59 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ((~![Y: $i] : (p2(Y) | (~r1(X, 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)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, 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)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, 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)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))),
% 5.37/3.59 inference(modus_ponens,[status(thm)],[49, 43])).
% 5.37/3.59 tff(51,plain,
% 5.37/3.59 ((~((~r1(X!0, Y!1)) | p1(Y!1))) & (~(p2(Y!2) | (~r1(X!0, Y!2)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) & r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & r1(Y!8, X!10) & ![Y: $i] : (p1(Y) | (~r1(X!10, Y)))),
% 5.37/3.59 inference(modus_ponens,[status(thm)],[50, 42])).
% 5.37/3.59 tff(52,plain,
% 5.37/3.59 (![Y: $i] : (p1(Y) | (~r1(X!10, Y)))),
% 5.37/3.59 inference(and_elim,[status(thm)],[51])).
% 5.37/3.59 tff(53,plain,
% 5.37/3.59 (![Y: $i] : (p1(Y) | (~r1(X!10, Y)))),
% 5.37/3.59 inference(modus_ponens,[status(thm)],[52, 10])).
% 5.37/3.59 tff(54,plain,
% 5.37/3.59 (((~![Y: $i] : (p1(Y) | (~r1(X!10, Y)))) | (p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(X!10, tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(X!10, Y)))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(X!10, tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))))),
% 5.37/3.59 inference(rewrite,[status(thm)],[])).
% 5.37/3.59 tff(55,plain,
% 5.37/3.59 ((~![Y: $i] : (p1(Y) | (~r1(X!10, Y)))) | (p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(X!10, tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))))),
% 5.37/3.59 inference(quant_inst,[status(thm)],[])).
% 5.37/3.59 tff(56,plain,
% 5.37/3.59 ((~![Y: $i] : (p1(Y) | (~r1(X!10, Y)))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(X!10, tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))),
% 5.37/3.59 inference(modus_ponens,[status(thm)],[55, 54])).
% 5.37/3.59 tff(57,plain,
% 5.37/3.59 (~r1(X!10, tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))),
% 5.37/3.59 inference(unit_resolution,[status(thm)],[56, 53, 8])).
% 5.37/3.59 tff(58,plain,
% 5.37/3.59 (((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))),
% 5.37/3.59 inference(tautology,[status(thm)],[])).
% 5.37/3.59 tff(59,plain,
% 5.37/3.59 (r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))),
% 5.37/3.59 inference(unit_resolution,[status(thm)],[58, 6])).
% 5.37/3.59 tff(60,plain,
% 5.37/3.59 (r1(Y!8, X!10)),
% 5.37/3.59 inference(and_elim,[status(thm)],[51])).
% 5.37/3.59 tff(61,plain,
% 5.37/3.59 (r1(X!0, Y!8)),
% 5.37/3.59 inference(and_elim,[status(thm)],[51])).
% 5.37/3.59 tff(62,plain,
% 5.37/3.59 (![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 5.37/3.59 inference(rewrite,[status(thm)],[])).
% 5.37/3.59 tff(63,plain,
% 5.37/3.59 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((r1(X, Y) & r1(Y, Z)) <=> (~((~r1(Y, Z)) | (~r1(X, Y))))), ((~(r1(X, Y) & r1(Y, Z))) <=> (~(~((~r1(Y, Z)) | (~r1(X, Y))))))), rewrite((~(~((~r1(Y, Z)) | (~r1(X, Y))))) <=> ((~r1(Y, Z)) | (~r1(X, Y)))), ((~(r1(X, Y) & r1(Y, Z))) <=> ((~r1(Y, Z)) | (~r1(X, Y))))), (((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)) <=> (((~r1(Y, Z)) | (~r1(X, Y))) | r1(X, Z)))), rewrite((((~r1(Y, Z)) | (~r1(X, Y))) | r1(X, Z)) <=> (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))), (((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)) <=> (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))))),
% 5.37/3.59 inference(bind,[status(th)],[])).
% 5.37/3.59 tff(64,plain,
% 5.37/3.59 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 5.37/3.59 inference(quant_intro,[status(thm)],[63])).
% 5.37/3.59 tff(65,plain,
% 5.37/3.59 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 5.37/3.59 inference(rewrite,[status(thm)],[])).
% 5.37/3.59 tff(66,plain,
% 5.37/3.59 (^[X: $i, Y: $i, Z: $i] : rewrite(((r1(X, Y) & r1(Y, Z)) => r1(X, Z)) <=> ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)))),
% 5.37/3.59 inference(bind,[status(th)],[])).
% 5.37/3.59 tff(67,plain,
% 5.37/3.59 (![X: $i, Y: $i, Z: $i] : ((r1(X, Y) & r1(Y, Z)) => r1(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 5.37/3.59 inference(quant_intro,[status(thm)],[66])).
% 5.37/3.59 tff(68,axiom,(![X: $i, Y: $i, Z: $i] : ((r1(X, Y) & r1(Y, Z)) => r1(X, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','transitivity')).
% 5.37/3.59 tff(69,plain,
% 5.37/3.59 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 5.37/3.59 inference(modus_ponens,[status(thm)],[68, 67])).
% 5.37/3.59 tff(70,plain,
% 5.37/3.59 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 5.37/3.59 inference(modus_ponens,[status(thm)],[69, 65])).
% 5.37/3.59 tff(71,plain,(
% 5.37/3.59 ![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 5.37/3.59 inference(skolemize,[status(sab)],[70])).
% 5.37/3.59 tff(72,plain,
% 5.37/3.59 (![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 5.37/3.59 inference(modus_ponens,[status(thm)],[71, 64])).
% 5.37/3.59 tff(73,plain,
% 5.37/3.59 (![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 5.37/3.59 inference(modus_ponens,[status(thm)],[72, 62])).
% 5.37/3.59 tff(74,plain,
% 5.37/3.59 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, Y!8)) | (~r1(Y!8, X!10)) | r1(X!0, X!10))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!8)) | (~r1(Y!8, X!10)) | r1(X!0, X!10))),
% 5.37/3.59 inference(rewrite,[status(thm)],[])).
% 5.37/3.59 tff(75,plain,
% 5.37/3.59 ((r1(X!0, X!10) | (~r1(Y!8, X!10)) | (~r1(X!0, Y!8))) <=> ((~r1(X!0, Y!8)) | (~r1(Y!8, X!10)) | r1(X!0, X!10))),
% 5.37/3.59 inference(rewrite,[status(thm)],[])).
% 5.37/3.59 tff(76,plain,
% 5.37/3.59 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!10) | (~r1(Y!8, X!10)) | (~r1(X!0, Y!8)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, Y!8)) | (~r1(Y!8, X!10)) | r1(X!0, X!10)))),
% 5.37/3.59 inference(monotonicity,[status(thm)],[75])).
% 5.37/3.59 tff(77,plain,
% 5.37/3.59 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!10) | (~r1(Y!8, X!10)) | (~r1(X!0, Y!8)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!8)) | (~r1(Y!8, X!10)) | r1(X!0, X!10))),
% 5.37/3.59 inference(transitivity,[status(thm)],[76, 74])).
% 5.37/3.59 tff(78,plain,
% 5.37/3.59 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!10) | (~r1(Y!8, X!10)) | (~r1(X!0, Y!8)))),
% 5.37/3.59 inference(quant_inst,[status(thm)],[])).
% 5.37/3.59 tff(79,plain,
% 5.37/3.59 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!8)) | (~r1(Y!8, X!10)) | r1(X!0, X!10)),
% 5.37/3.59 inference(modus_ponens,[status(thm)],[78, 77])).
% 5.37/3.59 tff(80,plain,
% 5.37/3.59 (r1(X!0, X!10)),
% 5.37/3.59 inference(unit_resolution,[status(thm)],[79, 73, 61, 60])).
% 5.37/3.59 tff(81,assumption,(![Y: $i] : (p2(Y) | (~r1(X!0, Y)))), introduced(assumption)).
% 5.37/3.59 tff(82,plain,
% 5.37/3.59 (~(p2(Y!2) | (~r1(X!0, Y!2)))),
% 5.37/3.59 inference(and_elim,[status(thm)],[51])).
% 5.37/3.59 tff(83,plain,
% 5.37/3.59 (r1(X!0, Y!2)),
% 5.37/3.59 inference(or_elim,[status(thm)],[82])).
% 5.37/3.59 tff(84,plain,
% 5.37/3.59 (~p2(Y!2)),
% 5.37/3.59 inference(or_elim,[status(thm)],[82])).
% 5.37/3.59 tff(85,plain,
% 5.37/3.59 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)))) | (p2(Y!2) | (~r1(X!0, Y!2)))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)))) | p2(Y!2) | (~r1(X!0, Y!2)))),
% 5.37/3.59 inference(rewrite,[status(thm)],[])).
% 5.37/3.59 tff(86,plain,
% 5.37/3.59 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)))) | (p2(Y!2) | (~r1(X!0, Y!2)))),
% 5.37/3.59 inference(quant_inst,[status(thm)],[])).
% 5.37/3.59 tff(87,plain,
% 5.37/3.59 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)))) | p2(Y!2) | (~r1(X!0, Y!2))),
% 5.37/3.59 inference(modus_ponens,[status(thm)],[86, 85])).
% 5.37/3.59 tff(88,plain,
% 5.37/3.59 ($false),
% 5.37/3.59 inference(unit_resolution,[status(thm)],[87, 84, 83, 81])).
% 5.37/3.59 tff(89,plain,(~![Y: $i] : (p2(Y) | (~r1(X!0, Y)))), inference(lemma,lemma(discharge,[]))).
% 5.37/3.59 tff(90,assumption,(![Y: $i] : (p1(Y) | (~r1(X!0, Y)))), introduced(assumption)).
% 5.37/3.59 tff(91,plain,
% 5.37/3.59 (~((~r1(X!0, Y!1)) | p1(Y!1))),
% 5.37/3.59 inference(and_elim,[status(thm)],[51])).
% 5.37/3.59 tff(92,plain,
% 5.37/3.59 (~p1(Y!1)),
% 5.37/3.59 inference(or_elim,[status(thm)],[91])).
% 5.37/3.59 tff(93,plain,
% 5.37/3.59 (r1(X!0, Y!1)),
% 5.37/3.59 inference(or_elim,[status(thm)],[91])).
% 5.37/3.59 tff(94,plain,
% 5.37/3.59 (((~![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) | (p1(Y!1) | (~r1(X!0, Y!1)))) <=> ((~![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) | p1(Y!1) | (~r1(X!0, Y!1)))),
% 5.37/3.59 inference(rewrite,[status(thm)],[])).
% 5.37/3.59 tff(95,plain,
% 5.37/3.59 ((~![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) | (p1(Y!1) | (~r1(X!0, Y!1)))),
% 5.37/3.59 inference(quant_inst,[status(thm)],[])).
% 5.37/3.59 tff(96,plain,
% 5.37/3.59 ((~![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) | p1(Y!1) | (~r1(X!0, Y!1))),
% 5.37/3.59 inference(modus_ponens,[status(thm)],[95, 94])).
% 5.37/3.59 tff(97,plain,
% 5.37/3.59 ($false),
% 5.37/3.59 inference(unit_resolution,[status(thm)],[96, 93, 92, 90])).
% 5.37/3.59 tff(98,plain,(~![Y: $i] : (p1(Y) | (~r1(X!0, Y)))), inference(lemma,lemma(discharge,[]))).
% 5.37/3.59 tff(99,plain,
% 5.37/3.59 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))))),
% 5.37/3.59 inference(rewrite,[status(thm)],[])).
% 5.37/3.59 tff(100,plain,
% 5.37/3.59 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))),
% 5.37/3.59 inference(and_elim,[status(thm)],[51])).
% 5.37/3.59 tff(101,plain,
% 5.37/3.59 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))),
% 5.37/3.59 inference(modus_ponens,[status(thm)],[100, 99])).
% 5.37/3.59 tff(102,plain,
% 5.37/3.59 (![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))),
% 5.37/3.59 inference(unit_resolution,[status(thm)],[101, 98, 89])).
% 5.37/3.59 tff(103,plain,
% 5.37/3.59 (((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ((~r1(X!0, X!10)) | r1(X!10, tptp_fun_X_7(X!10)))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | (~r1(X!0, X!10)) | r1(X!10, tptp_fun_X_7(X!10)))),
% 5.37/3.59 inference(rewrite,[status(thm)],[])).
% 5.37/3.59 tff(104,plain,
% 5.37/3.59 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ((~r1(X!0, X!10)) | r1(X!10, tptp_fun_X_7(X!10)))),
% 5.37/3.59 inference(quant_inst,[status(thm)],[])).
% 5.37/3.59 tff(105,plain,
% 5.37/3.59 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | (~r1(X!0, X!10)) | r1(X!10, tptp_fun_X_7(X!10))),
% 5.37/3.59 inference(modus_ponens,[status(thm)],[104, 103])).
% 5.37/3.59 tff(106,plain,
% 5.37/3.59 (r1(X!10, tptp_fun_X_7(X!10))),
% 5.37/3.59 inference(unit_resolution,[status(thm)],[105, 102, 80])).
% 5.37/3.59 tff(107,plain,
% 5.37/3.59 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | r1(X!0, tptp_fun_X_7(X!10)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | r1(X!0, tptp_fun_X_7(X!10)))),
% 5.37/3.60 inference(rewrite,[status(thm)],[])).
% 5.37/3.60 tff(108,plain,
% 5.37/3.60 ((r1(X!0, tptp_fun_X_7(X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | (~r1(X!0, X!10))) <=> ((~r1(X!0, X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | r1(X!0, tptp_fun_X_7(X!10)))),
% 5.37/3.60 inference(rewrite,[status(thm)],[])).
% 5.37/3.60 tff(109,plain,
% 5.37/3.60 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_7(X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | (~r1(X!0, X!10)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | r1(X!0, tptp_fun_X_7(X!10))))),
% 5.37/3.60 inference(monotonicity,[status(thm)],[108])).
% 5.37/3.60 tff(110,plain,
% 5.37/3.60 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_7(X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | (~r1(X!0, X!10)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | r1(X!0, tptp_fun_X_7(X!10)))),
% 5.37/3.60 inference(transitivity,[status(thm)],[109, 107])).
% 5.37/3.60 tff(111,plain,
% 5.37/3.60 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_7(X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | (~r1(X!0, X!10)))),
% 5.37/3.60 inference(quant_inst,[status(thm)],[])).
% 5.37/3.60 tff(112,plain,
% 5.37/3.60 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | r1(X!0, tptp_fun_X_7(X!10))),
% 5.37/3.60 inference(modus_ponens,[status(thm)],[111, 110])).
% 5.37/3.60 tff(113,plain,
% 5.37/3.60 (r1(X!0, tptp_fun_X_7(X!10))),
% 5.37/3.60 inference(unit_resolution,[status(thm)],[112, 73, 80, 106])).
% 5.37/3.60 tff(114,plain,
% 5.37/3.60 (((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ((~r1(X!0, tptp_fun_X_7(X!10))) | r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | (~r1(X!0, tptp_fun_X_7(X!10))) | r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 5.37/3.60 inference(rewrite,[status(thm)],[])).
% 5.37/3.60 tff(115,plain,
% 5.37/3.60 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ((~r1(X!0, tptp_fun_X_7(X!10))) | r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 5.37/3.60 inference(quant_inst,[status(thm)],[])).
% 5.37/3.60 tff(116,plain,
% 5.37/3.60 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | (~r1(X!0, tptp_fun_X_7(X!10))) | r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))),
% 5.37/3.60 inference(modus_ponens,[status(thm)],[115, 114])).
% 5.37/3.60 tff(117,plain,
% 5.37/3.60 (r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))),
% 5.37/3.60 inference(unit_resolution,[status(thm)],[116, 102, 113])).
% 5.37/3.60 tff(118,plain,
% 5.37/3.60 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 5.37/3.60 inference(rewrite,[status(thm)],[])).
% 5.37/3.60 tff(119,plain,
% 5.37/3.60 ((r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(X!0, tptp_fun_X_7(X!10)))) <=> ((~r1(X!0, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 5.37/3.60 inference(rewrite,[status(thm)],[])).
% 5.37/3.60 tff(120,plain,
% 5.37/3.60 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(X!0, tptp_fun_X_7(X!10))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 5.37/3.60 inference(monotonicity,[status(thm)],[119])).
% 5.37/3.60 tff(121,plain,
% 5.37/3.60 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(X!0, tptp_fun_X_7(X!10))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 5.37/3.60 inference(transitivity,[status(thm)],[120, 118])).
% 5.37/3.60 tff(122,plain,
% 5.37/3.60 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(X!0, tptp_fun_X_7(X!10))))),
% 5.37/3.60 inference(quant_inst,[status(thm)],[])).
% 5.37/3.60 tff(123,plain,
% 5.37/3.60 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))),
% 5.37/3.60 inference(modus_ponens,[status(thm)],[122, 121])).
% 5.37/3.60 tff(124,plain,
% 5.37/3.60 (r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))),
% 5.37/3.60 inference(unit_resolution,[status(thm)],[123, 73, 113, 117])).
% 5.37/3.60 tff(125,plain,
% 5.37/3.60 (((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 5.37/3.60 inference(rewrite,[status(thm)],[])).
% 5.37/3.60 tff(126,plain,
% 5.37/3.60 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 5.37/3.60 inference(quant_inst,[status(thm)],[])).
% 5.37/3.60 tff(127,plain,
% 5.37/3.60 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 5.37/3.60 inference(modus_ponens,[status(thm)],[126, 125])).
% 5.37/3.60 tff(128,plain,
% 5.37/3.60 (r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 5.37/3.60 inference(unit_resolution,[status(thm)],[127, 102, 124])).
% 5.37/3.60 tff(129,plain,
% 5.37/3.60 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!10, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!10, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 5.37/3.60 inference(rewrite,[status(thm)],[])).
% 5.37/3.60 tff(130,plain,
% 5.37/3.60 ((r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(X!10, tptp_fun_X_7(X!10)))) <=> ((~r1(X!10, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 5.37/3.60 inference(rewrite,[status(thm)],[])).
% 5.37/3.60 tff(131,plain,
% 5.37/3.60 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(X!10, tptp_fun_X_7(X!10))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!10, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 5.37/3.60 inference(monotonicity,[status(thm)],[130])).
% 5.37/3.60 tff(132,plain,
% 5.37/3.60 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(X!10, tptp_fun_X_7(X!10))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!10, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 5.37/3.60 inference(transitivity,[status(thm)],[131, 129])).
% 5.37/3.60 tff(133,plain,
% 5.37/3.60 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(X!10, tptp_fun_X_7(X!10))))),
% 5.37/3.60 inference(quant_inst,[status(thm)],[])).
% 5.37/3.60 tff(134,plain,
% 5.37/3.60 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!10, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10)))),
% 5.37/3.60 inference(modus_ponens,[status(thm)],[133, 132])).
% 5.37/3.60 tff(135,plain,
% 5.37/3.60 (r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10)))),
% 5.37/3.60 inference(unit_resolution,[status(thm)],[134, 73, 106, 117])).
% 5.37/3.60 tff(136,plain,
% 5.37/3.60 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 5.37/3.60 inference(rewrite,[status(thm)],[])).
% 5.37/3.60 tff(137,plain,
% 5.37/3.60 ((r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10))))) <=> ((~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 5.37/3.60 inference(rewrite,[status(thm)],[])).
% 5.37/3.60 tff(138,plain,
% 5.37/3.60 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))),
% 5.37/3.60 inference(monotonicity,[status(thm)],[137])).
% 5.37/3.60 tff(139,plain,
% 5.37/3.60 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 5.37/3.60 inference(transitivity,[status(thm)],[138, 136])).
% 5.37/3.60 tff(140,plain,
% 5.37/3.60 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 5.37/3.60 inference(quant_inst,[status(thm)],[])).
% 5.37/3.60 tff(141,plain,
% 5.37/3.60 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 5.37/3.60 inference(modus_ponens,[status(thm)],[140, 139])).
% 5.37/3.60 tff(142,plain,
% 5.37/3.60 (r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 5.37/3.60 inference(unit_resolution,[status(thm)],[141, 73, 135, 128])).
% 5.37/3.60 tff(143,plain,
% 5.37/3.60 (((~![Y: $i] : (p1(Y) | (~r1(X!10, Y)))) | (p1(tptp_fun_X_7(tptp_fun_X_7(X!10))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10)))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(X!10, Y)))) | p1(tptp_fun_X_7(tptp_fun_X_7(X!10))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 5.37/3.61 inference(rewrite,[status(thm)],[])).
% 5.37/3.61 tff(144,plain,
% 5.37/3.61 ((~![Y: $i] : (p1(Y) | (~r1(X!10, Y)))) | (p1(tptp_fun_X_7(tptp_fun_X_7(X!10))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 5.37/3.61 inference(quant_inst,[status(thm)],[])).
% 5.37/3.61 tff(145,plain,
% 5.37/3.61 ((~![Y: $i] : (p1(Y) | (~r1(X!10, Y)))) | p1(tptp_fun_X_7(tptp_fun_X_7(X!10))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 5.37/3.61 inference(modus_ponens,[status(thm)],[144, 143])).
% 5.37/3.61 tff(146,plain,
% 5.37/3.61 (p1(tptp_fun_X_7(tptp_fun_X_7(X!10)))),
% 5.37/3.61 inference(unit_resolution,[status(thm)],[145, 53, 135])).
% 5.37/3.61 tff(147,plain,
% 5.37/3.61 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))),
% 5.37/3.61 inference(rewrite,[status(thm)],[])).
% 5.37/3.61 tff(148,plain,
% 5.37/3.61 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 5.37/3.61 inference(rewrite,[status(thm)],[])).
% 5.37/3.61 tff(149,plain,
% 5.37/3.61 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))),
% 5.37/3.61 inference(and_elim,[status(thm)],[51])).
% 5.37/3.61 tff(150,plain,
% 5.37/3.61 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))),
% 5.37/3.61 inference(modus_ponens,[status(thm)],[149, 148])).
% 5.37/3.61 tff(151,plain,
% 5.37/3.61 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))),
% 5.37/3.61 inference(modus_ponens,[status(thm)],[150, 147])).
% 5.37/3.61 tff(152,plain,
% 5.37/3.61 (![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))),
% 5.37/3.61 inference(unit_resolution,[status(thm)],[151, 98, 89])).
% 5.37/3.61 tff(153,plain,
% 5.37/3.61 (((~![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))) | ((~p1(tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | ![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))) <=> ((~![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))) | (~p1(tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | ![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))),
% 5.37/3.61 inference(rewrite,[status(thm)],[])).
% 5.37/3.61 tff(154,plain,
% 5.37/3.61 ((~![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))) | ((~p1(tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | ![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))),
% 5.37/3.61 inference(quant_inst,[status(thm)],[])).
% 5.37/3.61 tff(155,plain,
% 5.37/3.61 ((~![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))) | (~p1(tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | ![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))),
% 5.37/3.61 inference(modus_ponens,[status(thm)],[154, 153])).
% 5.37/3.61 tff(156,plain,
% 5.37/3.61 (![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))),
% 5.37/3.61 inference(unit_resolution,[status(thm)],[155, 152, 124, 146])).
% 5.37/3.61 tff(157,plain,
% 5.37/3.61 (((~![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~((~p1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~((~p1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))))),
% 5.37/3.61 inference(rewrite,[status(thm)],[])).
% 5.37/3.61 tff(158,plain,
% 5.37/3.61 (((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~p1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))))) <=> ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~((~p1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))))),
% 5.37/3.61 inference(rewrite,[status(thm)],[])).
% 5.37/3.61 tff(159,plain,
% 5.37/3.61 (((~![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~p1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~((~p1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))))))),
% 5.37/3.61 inference(monotonicity,[status(thm)],[158])).
% 5.37/3.61 tff(160,plain,
% 5.37/3.61 (((~![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~p1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~((~p1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))))),
% 5.37/3.61 inference(transitivity,[status(thm)],[159, 157])).
% 5.37/3.61 tff(161,plain,
% 5.37/3.61 ((~![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~p1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))))),
% 5.37/3.61 inference(quant_inst,[status(thm)],[])).
% 5.37/3.61 tff(162,plain,
% 5.37/3.61 ((~![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~((~p1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))))),
% 5.37/3.61 inference(modus_ponens,[status(thm)],[161, 160])).
% 5.37/3.61 tff(163,plain,
% 5.37/3.61 (~((~p1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))),
% 5.37/3.61 inference(unit_resolution,[status(thm)],[162, 128, 156])).
% 5.37/3.61 tff(164,plain,
% 5.37/3.61 (((~p1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 5.37/3.61 inference(tautology,[status(thm)],[])).
% 5.37/3.61 tff(165,plain,
% 5.37/3.61 (r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 5.37/3.61 inference(unit_resolution,[status(thm)],[164, 163])).
% 5.37/3.61 tff(166,plain,
% 5.37/3.61 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))),
% 5.37/3.61 inference(rewrite,[status(thm)],[])).
% 5.37/3.61 tff(167,plain,
% 5.37/3.61 ((r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) <=> ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))),
% 5.37/3.61 inference(rewrite,[status(thm)],[])).
% 5.37/3.61 tff(168,plain,
% 5.37/3.61 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))),
% 5.37/3.61 inference(monotonicity,[status(thm)],[167])).
% 5.37/3.61 tff(169,plain,
% 5.37/3.61 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))),
% 5.37/3.61 inference(transitivity,[status(thm)],[168, 166])).
% 5.37/3.61 tff(170,plain,
% 5.37/3.61 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))),
% 5.37/3.61 inference(quant_inst,[status(thm)],[])).
% 5.37/3.61 tff(171,plain,
% 5.37/3.61 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 5.37/3.61 inference(modus_ponens,[status(thm)],[170, 169])).
% 5.37/3.61 tff(172,plain,
% 5.37/3.61 (r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 5.37/3.61 inference(unit_resolution,[status(thm)],[171, 73, 165, 142])).
% 5.37/3.61 tff(173,plain,
% 5.37/3.61 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | r1(X!10, tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | r1(X!10, tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))),
% 5.37/3.61 inference(rewrite,[status(thm)],[])).
% 5.37/3.61 tff(174,plain,
% 5.37/3.61 ((r1(X!10, tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | (~r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) <=> ((~r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | r1(X!10, tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))),
% 5.37/3.61 inference(rewrite,[status(thm)],[])).
% 5.37/3.61 tff(175,plain,
% 5.37/3.61 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!10, tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | (~r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | r1(X!10, tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))))),
% 5.37/3.61 inference(monotonicity,[status(thm)],[174])).
% 5.37/3.61 tff(176,plain,
% 5.37/3.61 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!10, tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | (~r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | r1(X!10, tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))),
% 5.37/3.61 inference(transitivity,[status(thm)],[175, 173])).
% 5.37/3.61 tff(177,plain,
% 5.37/3.61 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!10, tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | (~r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))),
% 5.37/3.61 inference(quant_inst,[status(thm)],[])).
% 5.37/3.61 tff(178,plain,
% 5.37/3.61 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | r1(X!10, tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))),
% 5.37/3.61 inference(modus_ponens,[status(thm)],[177, 176])).
% 5.37/3.61 tff(179,plain,
% 5.37/3.61 ($false),
% 5.37/3.61 inference(unit_resolution,[status(thm)],[178, 73, 172, 59, 57])).
% 5.37/3.61 tff(180,plain,((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))), inference(lemma,lemma(discharge,[]))).
% 5.37/3.61 tff(181,assumption,(![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))), introduced(assumption)).
% 5.37/3.61 tff(182,plain,
% 5.37/3.61 (((~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))) | ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))))) <=> ((~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))))),
% 5.37/3.61 inference(rewrite,[status(thm)],[])).
% 5.37/3.61 tff(183,plain,
% 5.37/3.61 (((~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) <=> ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))))),
% 5.37/3.61 inference(rewrite,[status(thm)],[])).
% 5.37/3.61 tff(184,plain,
% 5.37/3.61 ((~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))) <=> (~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))))),
% 5.37/3.61 inference(rewrite,[status(thm)],[])).
% 5.37/3.61 tff(185,plain,
% 5.37/3.61 (((~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) <=> ((~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))),
% 5.37/3.62 inference(monotonicity,[status(thm)],[184])).
% 5.37/3.62 tff(186,plain,
% 5.37/3.62 (((~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) <=> ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))))),
% 5.37/3.62 inference(transitivity,[status(thm)],[185, 183])).
% 5.37/3.62 tff(187,plain,
% 5.37/3.62 (((~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))) | ((~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))) <=> ((~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))) | ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))))))),
% 5.37/3.62 inference(monotonicity,[status(thm)],[186])).
% 5.37/3.62 tff(188,plain,
% 5.37/3.62 (((~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))) | ((~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))) <=> ((~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))))),
% 5.37/3.62 inference(transitivity,[status(thm)],[187, 182])).
% 5.37/3.62 tff(189,plain,
% 5.37/3.62 ((~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))) | ((~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))),
% 5.37/3.62 inference(quant_inst,[status(thm)],[])).
% 5.37/3.62 tff(190,plain,
% 5.37/3.62 ((~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))))),
% 5.37/3.62 inference(modus_ponens,[status(thm)],[189, 188])).
% 5.37/3.62 tff(191,plain,
% 5.37/3.62 ($false),
% 5.37/3.62 inference(unit_resolution,[status(thm)],[190, 165, 181, 180])).
% 5.37/3.62 tff(192,plain,(~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))), inference(lemma,lemma(discharge,[]))).
% 5.37/3.62 tff(193,plain,
% 5.37/3.62 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))),
% 5.37/3.62 inference(rewrite,[status(thm)],[])).
% 5.37/3.62 tff(194,plain,
% 5.37/3.62 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))),
% 5.37/3.62 inference(bind,[status(th)],[])).
% 5.37/3.62 tff(195,plain,
% 5.37/3.62 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))),
% 5.37/3.62 inference(quant_intro,[status(thm)],[194])).
% 5.37/3.62 tff(196,plain,
% 5.37/3.62 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))),
% 5.37/3.62 inference(monotonicity,[status(thm)],[195])).
% 5.37/3.62 tff(197,plain,
% 5.37/3.62 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))),
% 5.37/3.62 inference(transitivity,[status(thm)],[196, 193])).
% 5.37/3.62 tff(198,plain,
% 5.37/3.62 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))),
% 5.37/3.62 inference(rewrite,[status(thm)],[])).
% 5.37/3.62 tff(199,plain,
% 5.37/3.62 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))),
% 5.37/3.62 inference(and_elim,[status(thm)],[51])).
% 5.37/3.62 tff(200,plain,
% 5.37/3.62 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))),
% 5.37/3.62 inference(modus_ponens,[status(thm)],[199, 198])).
% 5.37/3.62 tff(201,plain,
% 5.37/3.62 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))),
% 5.37/3.62 inference(modus_ponens,[status(thm)],[200, 197])).
% 5.37/3.62 tff(202,plain,
% 5.37/3.62 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))),
% 5.37/3.62 inference(unit_resolution,[status(thm)],[201, 98, 89])).
% 5.37/3.62 tff(203,plain,
% 5.37/3.62 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X))))),
% 5.37/3.62 inference(rewrite,[status(thm)],[])).
% 5.37/3.62 tff(204,plain,
% 5.37/3.62 (((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | ![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) <=> ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X))))),
% 5.37/3.62 inference(rewrite,[status(thm)],[])).
% 5.37/3.62 tff(205,plain,
% 5.37/3.62 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | ![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)))))),
% 5.37/3.62 inference(monotonicity,[status(thm)],[204])).
% 5.37/3.62 tff(206,plain,
% 5.37/3.62 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | ![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X))))),
% 5.37/3.62 inference(transitivity,[status(thm)],[205, 203])).
% 5.37/3.62 tff(207,plain,
% 5.37/3.62 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | ![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))),
% 5.37/3.62 inference(quant_inst,[status(thm)],[])).
% 5.37/3.62 tff(208,plain,
% 5.37/3.62 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)))),
% 5.37/3.62 inference(modus_ponens,[status(thm)],[207, 206])).
% 5.37/3.62 tff(209,plain,
% 5.37/3.62 (![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)))),
% 5.37/3.62 inference(unit_resolution,[status(thm)],[208, 202, 124])).
% 5.37/3.62 tff(210,plain,
% 5.37/3.62 (((~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)))) | ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))))) <=> ((~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))))),
% 5.37/3.62 inference(rewrite,[status(thm)],[])).
% 5.37/3.62 tff(211,plain,
% 5.37/3.62 ((![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) <=> ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))))),
% 5.37/3.62 inference(rewrite,[status(thm)],[])).
% 5.37/3.62 tff(212,plain,
% 5.37/3.62 (^[Y: $i] : trans(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) <=> (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))), (((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) <=> ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))), rewrite(((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) <=> ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))), (((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) <=> ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))))),
% 5.37/3.62 inference(bind,[status(th)],[])).
% 5.37/3.62 tff(213,plain,
% 5.37/3.62 (![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) <=> ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))),
% 5.37/3.62 inference(quant_intro,[status(thm)],[212])).
% 5.37/3.62 tff(214,plain,
% 5.37/3.62 (^[Y: $i] : rewrite(((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | p1(Y)) <=> (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))))),
% 5.37/3.62 inference(bind,[status(th)],[])).
% 5.37/3.62 tff(215,plain,
% 5.37/3.62 (![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | p1(Y)) <=> ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))),
% 5.37/3.62 inference(quant_intro,[status(thm)],[214])).
% 5.37/3.62 tff(216,plain,
% 5.37/3.62 ((![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | p1(Y)) | ![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) <=> (![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))),
% 5.37/3.62 inference(monotonicity,[status(thm)],[215, 213])).
% 5.37/3.62 tff(217,plain,
% 5.37/3.62 ((![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | p1(Y)) | ![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) <=> ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))))),
% 5.37/3.62 inference(transitivity,[status(thm)],[216, 211])).
% 5.37/3.62 tff(218,plain,
% 5.37/3.62 (((~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)))) | (![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | p1(Y)) | ![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) <=> ((~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)))) | ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))))),
% 5.37/3.62 inference(monotonicity,[status(thm)],[217])).
% 5.37/3.62 tff(219,plain,
% 5.37/3.62 (((~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)))) | (![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | p1(Y)) | ![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) <=> ((~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))))),
% 5.37/3.62 inference(transitivity,[status(thm)],[218, 210])).
% 5.37/3.62 tff(220,plain,
% 5.37/3.62 ((~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)))) | (![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | p1(Y)) | ![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))),
% 5.37/3.62 inference(quant_inst,[status(thm)],[])).
% 5.37/3.63 tff(221,plain,
% 5.37/3.63 ((~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))),
% 5.37/3.63 inference(modus_ponens,[status(thm)],[220, 219])).
% 5.37/3.63 tff(222,plain,
% 5.37/3.63 (![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))),
% 5.37/3.63 inference(unit_resolution,[status(thm)],[221, 128, 209])).
% 5.37/3.63 tff(223,plain,
% 5.37/3.63 (![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))),
% 5.37/3.63 inference(unit_resolution,[status(thm)],[222, 192])).
% 5.37/3.63 tff(224,plain,
% 5.37/3.63 (((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))) | (p1(tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))) | p1(tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))),
% 5.37/3.63 inference(rewrite,[status(thm)],[])).
% 5.37/3.63 tff(225,plain,
% 5.37/3.63 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))) | (p1(tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))),
% 5.37/3.63 inference(quant_inst,[status(thm)],[])).
% 5.37/3.63 tff(226,plain,
% 5.37/3.63 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))) | p1(tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))),
% 5.37/3.63 inference(modus_ponens,[status(thm)],[225, 224])).
% 5.37/3.63 tff(227,plain,
% 5.37/3.63 ($false),
% 5.37/3.63 inference(unit_resolution,[status(thm)],[226, 223, 5, 3])).
% 5.37/3.63 tff(228,plain,((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | p1(tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))), inference(lemma,lemma(discharge,[]))).
% 5.37/3.63 tff(229,plain,
% 5.37/3.63 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!8, X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | r1(Y!8, tptp_fun_X_7(X!10)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | r1(Y!8, tptp_fun_X_7(X!10)))),
% 5.37/3.63 inference(rewrite,[status(thm)],[])).
% 5.37/3.63 tff(230,plain,
% 5.37/3.63 ((r1(Y!8, tptp_fun_X_7(X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | (~r1(Y!8, X!10))) <=> ((~r1(Y!8, X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | r1(Y!8, tptp_fun_X_7(X!10)))),
% 5.37/3.63 inference(rewrite,[status(thm)],[])).
% 5.37/3.63 tff(231,plain,
% 5.37/3.63 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | (~r1(Y!8, X!10)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!8, X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | r1(Y!8, tptp_fun_X_7(X!10))))),
% 5.37/3.63 inference(monotonicity,[status(thm)],[230])).
% 5.37/3.63 tff(232,plain,
% 5.37/3.63 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | (~r1(Y!8, X!10)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | r1(Y!8, tptp_fun_X_7(X!10)))),
% 5.37/3.63 inference(transitivity,[status(thm)],[231, 229])).
% 5.37/3.63 tff(233,plain,
% 5.37/3.63 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | (~r1(Y!8, X!10)))),
% 5.37/3.63 inference(quant_inst,[status(thm)],[])).
% 5.37/3.63 tff(234,plain,
% 5.37/3.63 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | r1(Y!8, tptp_fun_X_7(X!10))),
% 5.37/3.63 inference(modus_ponens,[status(thm)],[233, 232])).
% 5.37/3.63 tff(235,plain,
% 5.37/3.63 (r1(Y!8, tptp_fun_X_7(X!10))),
% 5.37/3.63 inference(unit_resolution,[status(thm)],[234, 73, 60, 106])).
% 5.37/3.63 tff(236,plain,
% 5.37/3.63 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!8, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 5.37/3.63 inference(rewrite,[status(thm)],[])).
% 5.37/3.63 tff(237,plain,
% 5.37/3.63 ((r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(Y!8, tptp_fun_X_7(X!10)))) <=> ((~r1(Y!8, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 5.37/3.63 inference(rewrite,[status(thm)],[])).
% 5.37/3.63 tff(238,plain,
% 5.37/3.63 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(Y!8, tptp_fun_X_7(X!10))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!8, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 5.37/3.63 inference(monotonicity,[status(thm)],[237])).
% 5.37/3.63 tff(239,plain,
% 5.37/3.63 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(Y!8, tptp_fun_X_7(X!10))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 5.37/3.63 inference(transitivity,[status(thm)],[238, 236])).
% 5.37/3.63 tff(240,plain,
% 5.37/3.63 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(Y!8, tptp_fun_X_7(X!10))))),
% 5.37/3.63 inference(quant_inst,[status(thm)],[])).
% 5.37/3.63 tff(241,plain,
% 5.37/3.63 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10)))),
% 5.37/3.63 inference(modus_ponens,[status(thm)],[240, 239])).
% 5.37/3.63 tff(242,plain,
% 5.37/3.63 (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10)))),
% 5.37/3.63 inference(unit_resolution,[status(thm)],[241, 73, 235, 117])).
% 5.37/3.63 tff(243,plain,
% 5.37/3.63 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 5.37/3.63 inference(rewrite,[status(thm)],[])).
% 5.37/3.63 tff(244,plain,
% 5.37/3.63 ((r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10))))) <=> ((~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 5.37/3.63 inference(rewrite,[status(thm)],[])).
% 5.37/3.63 tff(245,plain,
% 5.37/3.63 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))),
% 5.37/3.63 inference(monotonicity,[status(thm)],[244])).
% 5.37/3.63 tff(246,plain,
% 5.37/3.63 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 5.37/3.63 inference(transitivity,[status(thm)],[245, 243])).
% 5.37/3.63 tff(247,plain,
% 5.37/3.63 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 5.37/3.63 inference(quant_inst,[status(thm)],[])).
% 5.37/3.63 tff(248,plain,
% 5.37/3.63 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 5.37/3.63 inference(modus_ponens,[status(thm)],[247, 246])).
% 5.37/3.63 tff(249,plain,
% 5.37/3.63 (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 5.37/3.63 inference(unit_resolution,[status(thm)],[248, 73, 242, 128])).
% 5.37/3.63 tff(250,assumption,(~r1(X!9, X!9)), introduced(assumption)).
% 5.37/3.63 tff(251,plain,
% 5.37/3.63 (^[X: $i] : refl(r1(X, X) <=> r1(X, X))),
% 5.37/3.63 inference(bind,[status(th)],[])).
% 5.37/3.63 tff(252,plain,
% 5.37/3.63 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 5.37/3.63 inference(quant_intro,[status(thm)],[251])).
% 5.37/3.63 tff(253,plain,
% 5.37/3.63 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 5.37/3.63 inference(rewrite,[status(thm)],[])).
% 5.37/3.63 tff(254,axiom,(![X: $i] : r1(X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reflexivity')).
% 5.37/3.63 tff(255,plain,
% 5.37/3.63 (![X: $i] : r1(X, X)),
% 5.37/3.63 inference(modus_ponens,[status(thm)],[254, 253])).
% 5.37/3.63 tff(256,plain,(
% 5.37/3.63 ![X: $i] : r1(X, X)),
% 5.37/3.63 inference(skolemize,[status(sab)],[255])).
% 5.37/3.63 tff(257,plain,
% 5.37/3.63 (![X: $i] : r1(X, X)),
% 5.37/3.63 inference(modus_ponens,[status(thm)],[256, 252])).
% 5.37/3.63 tff(258,plain,
% 5.37/3.63 ((~![X: $i] : r1(X, X)) | r1(X!9, X!9)),
% 5.37/3.63 inference(quant_inst,[status(thm)],[])).
% 5.37/3.63 tff(259,plain,
% 5.37/3.63 ($false),
% 5.37/3.63 inference(unit_resolution,[status(thm)],[258, 257, 250])).
% 5.37/3.63 tff(260,plain,(r1(X!9, X!9)), inference(lemma,lemma(discharge,[]))).
% 5.37/3.63 tff(261,assumption,(![Y: $i] : (p1(Y) | (~r1(X!9, Y)))), introduced(assumption)).
% 5.37/3.63 tff(262,plain,
% 5.37/3.63 (~((~r1(Y!8, X!9)) | p1(X!9))),
% 5.37/3.63 inference(and_elim,[status(thm)],[51])).
% 5.37/3.63 tff(263,plain,
% 5.37/3.63 (~p1(X!9)),
% 5.37/3.63 inference(or_elim,[status(thm)],[262])).
% 5.37/3.63 tff(264,plain,
% 5.37/3.63 (((~![Y: $i] : (p1(Y) | (~r1(X!9, Y)))) | (p1(X!9) | (~r1(X!9, X!9)))) <=> ((~![Y: $i] : (p1(Y) | (~r1(X!9, Y)))) | p1(X!9) | (~r1(X!9, X!9)))),
% 5.37/3.63 inference(rewrite,[status(thm)],[])).
% 5.37/3.63 tff(265,plain,
% 5.37/3.63 ((~![Y: $i] : (p1(Y) | (~r1(X!9, Y)))) | (p1(X!9) | (~r1(X!9, X!9)))),
% 5.37/3.63 inference(quant_inst,[status(thm)],[])).
% 5.37/3.63 tff(266,plain,
% 5.37/3.63 ((~![Y: $i] : (p1(Y) | (~r1(X!9, Y)))) | p1(X!9) | (~r1(X!9, X!9))),
% 5.37/3.63 inference(modus_ponens,[status(thm)],[265, 264])).
% 5.37/3.63 tff(267,plain,
% 5.37/3.63 ($false),
% 5.37/3.63 inference(unit_resolution,[status(thm)],[266, 263, 261, 260])).
% 5.37/3.63 tff(268,plain,(~![Y: $i] : (p1(Y) | (~r1(X!9, Y)))), inference(lemma,lemma(discharge,[]))).
% 5.37/3.63 tff(269,plain,
% 5.37/3.63 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | ((~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | (~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))),
% 5.37/3.64 inference(rewrite,[status(thm)],[])).
% 5.37/3.64 tff(270,plain,
% 5.37/3.64 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | ((~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))),
% 5.37/3.64 inference(quant_inst,[status(thm)],[])).
% 5.37/3.64 tff(271,plain,
% 5.37/3.64 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | (~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))),
% 5.37/3.64 inference(modus_ponens,[status(thm)],[270, 269])).
% 5.37/3.64 tff(272,plain,
% 5.37/3.64 (![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))),
% 5.37/3.64 inference(unit_resolution,[status(thm)],[271, 202, 61])).
% 5.37/3.64 tff(273,plain,
% 5.37/3.64 (r1(Y!8, X!9)),
% 5.37/3.64 inference(or_elim,[status(thm)],[262])).
% 5.37/3.64 tff(274,plain,
% 5.37/3.64 (((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!9, Y))))) <=> ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | (~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!9, Y))))),
% 5.37/3.64 inference(rewrite,[status(thm)],[])).
% 5.37/3.64 tff(275,plain,
% 5.37/3.64 (((~r1(Y!8, X!9)) | ![Y: $i] : (p1(Y) | (~r1(X!9, Y))) | ![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))) <=> ((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!9, Y))))),
% 5.37/3.64 inference(rewrite,[status(thm)],[])).
% 5.37/3.64 tff(276,plain,
% 5.37/3.64 (^[Y: $i] : rewrite(((~r1(X!9, Y)) | p1(Y)) <=> (p1(Y) | (~r1(X!9, Y))))),
% 5.37/3.64 inference(bind,[status(th)],[])).
% 5.37/3.64 tff(277,plain,
% 5.37/3.64 (![Y: $i] : ((~r1(X!9, Y)) | p1(Y)) <=> ![Y: $i] : (p1(Y) | (~r1(X!9, Y)))),
% 5.37/3.64 inference(quant_intro,[status(thm)],[276])).
% 5.37/3.64 tff(278,plain,
% 5.37/3.64 (((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))) <=> ((~r1(Y!8, X!9)) | ![Y: $i] : (p1(Y) | (~r1(X!9, Y))) | ![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))),
% 5.37/3.64 inference(monotonicity,[status(thm)],[277])).
% 5.37/3.64 tff(279,plain,
% 5.37/3.64 (((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))) <=> ((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!9, Y))))),
% 5.37/3.64 inference(transitivity,[status(thm)],[278, 275])).
% 5.37/3.64 tff(280,plain,
% 5.37/3.64 (((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) <=> ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!9, Y)))))),
% 5.37/3.64 inference(monotonicity,[status(thm)],[279])).
% 5.37/3.64 tff(281,plain,
% 5.37/3.64 (((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) <=> ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | (~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!9, Y))))),
% 5.37/3.64 inference(transitivity,[status(thm)],[280, 274])).
% 5.37/3.64 tff(282,plain,
% 5.37/3.64 ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))),
% 5.37/3.64 inference(quant_inst,[status(thm)],[])).
% 5.37/3.64 tff(283,plain,
% 5.37/3.64 ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | (~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!9, Y)))),
% 5.37/3.64 inference(modus_ponens,[status(thm)],[282, 281])).
% 5.37/3.64 tff(284,plain,
% 5.37/3.64 (![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!9, Y)))),
% 5.37/3.64 inference(unit_resolution,[status(thm)],[283, 273, 272])).
% 5.37/3.64 tff(285,plain,
% 5.37/3.64 (![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))),
% 5.37/3.64 inference(unit_resolution,[status(thm)],[284, 268])).
% 5.37/3.64 tff(286,assumption,((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))), introduced(assumption)).
% 5.37/3.64 tff(287,plain,
% 5.37/3.64 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, Y!8)) | (~r1(Y!8, X!9)) | r1(X!0, X!9))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!8)) | (~r1(Y!8, X!9)) | r1(X!0, X!9))),
% 5.37/3.64 inference(rewrite,[status(thm)],[])).
% 5.37/3.64 tff(288,plain,
% 5.37/3.64 ((r1(X!0, X!9) | (~r1(Y!8, X!9)) | (~r1(X!0, Y!8))) <=> ((~r1(X!0, Y!8)) | (~r1(Y!8, X!9)) | r1(X!0, X!9))),
% 5.37/3.64 inference(rewrite,[status(thm)],[])).
% 5.37/3.64 tff(289,plain,
% 5.37/3.64 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!9) | (~r1(Y!8, X!9)) | (~r1(X!0, Y!8)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, Y!8)) | (~r1(Y!8, X!9)) | r1(X!0, X!9)))),
% 5.37/3.64 inference(monotonicity,[status(thm)],[288])).
% 5.37/3.64 tff(290,plain,
% 5.37/3.64 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!9) | (~r1(Y!8, X!9)) | (~r1(X!0, Y!8)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!8)) | (~r1(Y!8, X!9)) | r1(X!0, X!9))),
% 5.37/3.64 inference(transitivity,[status(thm)],[289, 287])).
% 5.37/3.64 tff(291,plain,
% 5.37/3.64 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!9) | (~r1(Y!8, X!9)) | (~r1(X!0, Y!8)))),
% 5.37/3.64 inference(quant_inst,[status(thm)],[])).
% 5.37/3.64 tff(292,plain,
% 5.37/3.64 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!8)) | (~r1(Y!8, X!9)) | r1(X!0, X!9)),
% 5.37/3.64 inference(modus_ponens,[status(thm)],[291, 290])).
% 5.37/3.64 tff(293,plain,
% 5.37/3.64 (r1(X!0, X!9)),
% 5.37/3.64 inference(unit_resolution,[status(thm)],[292, 73, 61, 273])).
% 5.37/3.64 tff(294,plain,
% 5.37/3.64 (((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ((~r1(X!0, X!9)) | r1(X!9, tptp_fun_X_7(X!9)))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | (~r1(X!0, X!9)) | r1(X!9, tptp_fun_X_7(X!9)))),
% 5.37/3.64 inference(rewrite,[status(thm)],[])).
% 5.37/3.64 tff(295,plain,
% 5.37/3.64 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ((~r1(X!0, X!9)) | r1(X!9, tptp_fun_X_7(X!9)))),
% 5.37/3.64 inference(quant_inst,[status(thm)],[])).
% 5.37/3.64 tff(296,plain,
% 5.37/3.64 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | (~r1(X!0, X!9)) | r1(X!9, tptp_fun_X_7(X!9))),
% 5.37/3.64 inference(modus_ponens,[status(thm)],[295, 294])).
% 5.37/3.64 tff(297,plain,
% 5.37/3.64 (r1(X!9, tptp_fun_X_7(X!9))),
% 5.37/3.64 inference(unit_resolution,[status(thm)],[296, 102, 293])).
% 5.37/3.64 tff(298,plain,
% 5.37/3.64 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | r1(X!0, tptp_fun_X_7(X!9)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | r1(X!0, tptp_fun_X_7(X!9)))),
% 5.37/3.64 inference(rewrite,[status(thm)],[])).
% 5.37/3.64 tff(299,plain,
% 5.37/3.64 ((r1(X!0, tptp_fun_X_7(X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | (~r1(X!0, X!9))) <=> ((~r1(X!0, X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | r1(X!0, tptp_fun_X_7(X!9)))),
% 5.37/3.64 inference(rewrite,[status(thm)],[])).
% 5.37/3.64 tff(300,plain,
% 5.37/3.64 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_7(X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | (~r1(X!0, X!9)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | r1(X!0, tptp_fun_X_7(X!9))))),
% 5.37/3.64 inference(monotonicity,[status(thm)],[299])).
% 5.37/3.64 tff(301,plain,
% 5.37/3.64 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_7(X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | (~r1(X!0, X!9)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | r1(X!0, tptp_fun_X_7(X!9)))),
% 5.37/3.64 inference(transitivity,[status(thm)],[300, 298])).
% 5.37/3.64 tff(302,plain,
% 5.37/3.64 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_7(X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | (~r1(X!0, X!9)))),
% 5.37/3.64 inference(quant_inst,[status(thm)],[])).
% 5.37/3.64 tff(303,plain,
% 5.37/3.64 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | r1(X!0, tptp_fun_X_7(X!9))),
% 5.37/3.64 inference(modus_ponens,[status(thm)],[302, 301])).
% 5.37/3.64 tff(304,plain,
% 5.37/3.64 (r1(X!0, tptp_fun_X_7(X!9))),
% 5.37/3.64 inference(unit_resolution,[status(thm)],[303, 73, 293, 297])).
% 5.37/3.64 tff(305,plain,
% 5.37/3.64 (((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ((~r1(X!0, tptp_fun_X_7(X!9))) | r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | (~r1(X!0, tptp_fun_X_7(X!9))) | r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 5.37/3.64 inference(rewrite,[status(thm)],[])).
% 5.37/3.64 tff(306,plain,
% 5.37/3.64 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ((~r1(X!0, tptp_fun_X_7(X!9))) | r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 5.37/3.64 inference(quant_inst,[status(thm)],[])).
% 5.37/3.64 tff(307,plain,
% 5.37/3.64 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | (~r1(X!0, tptp_fun_X_7(X!9))) | r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))),
% 5.37/3.64 inference(modus_ponens,[status(thm)],[306, 305])).
% 5.37/3.64 tff(308,plain,
% 5.37/3.64 (r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))),
% 5.37/3.64 inference(unit_resolution,[status(thm)],[307, 102, 304])).
% 5.37/3.64 tff(309,plain,
% 5.37/3.64 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 5.37/3.64 inference(rewrite,[status(thm)],[])).
% 5.37/3.64 tff(310,plain,
% 5.37/3.64 ((r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(X!0, tptp_fun_X_7(X!9)))) <=> ((~r1(X!0, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 5.37/3.65 inference(rewrite,[status(thm)],[])).
% 5.37/3.65 tff(311,plain,
% 5.37/3.65 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(X!0, tptp_fun_X_7(X!9))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 5.37/3.65 inference(monotonicity,[status(thm)],[310])).
% 5.37/3.65 tff(312,plain,
% 5.37/3.65 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(X!0, tptp_fun_X_7(X!9))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 5.37/3.65 inference(transitivity,[status(thm)],[311, 309])).
% 5.37/3.65 tff(313,plain,
% 5.37/3.65 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(X!0, tptp_fun_X_7(X!9))))),
% 5.37/3.65 inference(quant_inst,[status(thm)],[])).
% 5.37/3.65 tff(314,plain,
% 5.37/3.65 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9)))),
% 5.37/3.65 inference(modus_ponens,[status(thm)],[313, 312])).
% 5.37/3.65 tff(315,plain,
% 5.37/3.65 (r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9)))),
% 5.37/3.65 inference(unit_resolution,[status(thm)],[314, 73, 304, 308])).
% 5.37/3.65 tff(316,plain,
% 5.37/3.65 (((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 5.37/3.65 inference(rewrite,[status(thm)],[])).
% 5.37/3.65 tff(317,plain,
% 5.37/3.65 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 5.37/3.65 inference(quant_inst,[status(thm)],[])).
% 5.37/3.65 tff(318,plain,
% 5.37/3.65 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 5.37/3.65 inference(modus_ponens,[status(thm)],[317, 316])).
% 5.37/3.65 tff(319,plain,
% 5.37/3.65 (r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 5.37/3.65 inference(unit_resolution,[status(thm)],[318, 102, 315])).
% 5.37/3.65 tff(320,plain,
% 5.37/3.65 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 5.37/3.65 inference(rewrite,[status(thm)],[])).
% 5.37/3.65 tff(321,plain,
% 5.37/3.65 ((r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9))))) <=> ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 5.37/3.65 inference(rewrite,[status(thm)],[])).
% 5.37/3.65 tff(322,plain,
% 5.37/3.65 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 5.37/3.65 inference(monotonicity,[status(thm)],[321])).
% 5.37/3.65 tff(323,plain,
% 5.37/3.65 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 5.37/3.65 inference(transitivity,[status(thm)],[322, 320])).
% 5.37/3.65 tff(324,plain,
% 5.37/3.65 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 5.37/3.65 inference(quant_inst,[status(thm)],[])).
% 5.37/3.65 tff(325,plain,
% 5.37/3.65 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 5.37/3.65 inference(modus_ponens,[status(thm)],[324, 323])).
% 5.37/3.65 tff(326,plain,
% 5.37/3.65 (r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 5.37/3.65 inference(unit_resolution,[status(thm)],[325, 73, 315, 319])).
% 5.37/3.65 tff(327,plain,
% 5.37/3.65 (((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 5.37/3.65 inference(rewrite,[status(thm)],[])).
% 5.37/3.65 tff(328,plain,
% 5.37/3.65 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 5.37/3.65 inference(quant_inst,[status(thm)],[])).
% 5.37/3.65 tff(329,plain,
% 5.37/3.65 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 5.37/3.65 inference(modus_ponens,[status(thm)],[328, 327])).
% 5.37/3.65 tff(330,plain,
% 5.37/3.65 (r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 5.37/3.65 inference(unit_resolution,[status(thm)],[329, 102, 326])).
% 5.37/3.65 tff(331,plain,
% 5.37/3.65 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!9, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!9, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 5.37/3.65 inference(rewrite,[status(thm)],[])).
% 5.37/3.65 tff(332,plain,
% 5.37/3.65 ((r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(X!9, tptp_fun_X_7(X!9)))) <=> ((~r1(X!9, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 5.37/3.65 inference(rewrite,[status(thm)],[])).
% 5.37/3.65 tff(333,plain,
% 5.37/3.65 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(X!9, tptp_fun_X_7(X!9))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!9, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 5.37/3.65 inference(monotonicity,[status(thm)],[332])).
% 5.37/3.65 tff(334,plain,
% 5.37/3.65 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(X!9, tptp_fun_X_7(X!9))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!9, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 5.37/3.65 inference(transitivity,[status(thm)],[333, 331])).
% 5.37/3.65 tff(335,plain,
% 5.37/3.65 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(X!9, tptp_fun_X_7(X!9))))),
% 5.37/3.65 inference(quant_inst,[status(thm)],[])).
% 5.37/3.65 tff(336,plain,
% 5.37/3.65 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!9, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9)))),
% 5.37/3.65 inference(modus_ponens,[status(thm)],[335, 334])).
% 5.37/3.65 tff(337,plain,
% 5.37/3.65 (r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9)))),
% 5.37/3.65 inference(unit_resolution,[status(thm)],[336, 73, 297, 308])).
% 5.37/3.65 tff(338,plain,
% 5.37/3.65 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 5.37/3.65 inference(rewrite,[status(thm)],[])).
% 5.37/3.65 tff(339,plain,
% 5.37/3.65 ((r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9))))) <=> ((~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 5.37/3.65 inference(rewrite,[status(thm)],[])).
% 5.37/3.65 tff(340,plain,
% 5.37/3.65 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 5.37/3.65 inference(monotonicity,[status(thm)],[339])).
% 5.37/3.65 tff(341,plain,
% 5.37/3.65 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 5.37/3.65 inference(transitivity,[status(thm)],[340, 338])).
% 5.37/3.65 tff(342,plain,
% 5.37/3.65 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 5.37/3.65 inference(quant_inst,[status(thm)],[])).
% 5.44/3.65 tff(343,plain,
% 5.44/3.65 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 5.44/3.65 inference(modus_ponens,[status(thm)],[342, 341])).
% 5.44/3.65 tff(344,plain,
% 5.44/3.65 (r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 5.44/3.65 inference(unit_resolution,[status(thm)],[343, 73, 337, 319])).
% 5.44/3.65 tff(345,plain,
% 5.44/3.65 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 5.44/3.65 inference(rewrite,[status(thm)],[])).
% 5.44/3.65 tff(346,plain,
% 5.44/3.65 ((r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) <=> ((~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 5.44/3.65 inference(rewrite,[status(thm)],[])).
% 5.44/3.65 tff(347,plain,
% 5.44/3.65 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))),
% 5.44/3.65 inference(monotonicity,[status(thm)],[346])).
% 5.44/3.65 tff(348,plain,
% 5.44/3.65 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 5.44/3.65 inference(transitivity,[status(thm)],[347, 345])).
% 5.44/3.65 tff(349,plain,
% 5.44/3.65 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 5.44/3.65 inference(quant_inst,[status(thm)],[])).
% 5.44/3.65 tff(350,plain,
% 5.44/3.65 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 5.44/3.65 inference(modus_ponens,[status(thm)],[349, 348])).
% 5.44/3.65 tff(351,plain,
% 5.44/3.65 (r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 5.44/3.65 inference(unit_resolution,[status(thm)],[350, 73, 344, 330])).
% 5.44/3.66 tff(352,assumption,(![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))), introduced(assumption)).
% 5.44/3.66 tff(353,plain,
% 5.44/3.66 (((~![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))) | ((~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))))) <=> ((~![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))) | (~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))))),
% 5.44/3.66 inference(rewrite,[status(thm)],[])).
% 5.44/3.66 tff(354,plain,
% 5.44/3.66 ((~![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))) | ((~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))))),
% 5.44/3.66 inference(quant_inst,[status(thm)],[])).
% 5.44/3.66 tff(355,plain,
% 5.44/3.66 ((~![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))) | (~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))),
% 5.44/3.66 inference(modus_ponens,[status(thm)],[354, 353])).
% 5.44/3.66 tff(356,plain,
% 5.44/3.66 ($false),
% 5.44/3.66 inference(unit_resolution,[status(thm)],[355, 352, 351, 286])).
% 5.44/3.66 tff(357,plain,((~![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))), inference(lemma,lemma(discharge,[]))).
% 5.44/3.66 tff(358,plain,
% 5.44/3.66 (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))),
% 5.44/3.66 inference(unit_resolution,[status(thm)],[357, 285])).
% 5.44/3.66 tff(359,assumption,(![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))), introduced(assumption)).
% 5.44/3.66 tff(360,assumption,(~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))), introduced(assumption)).
% 5.44/3.66 tff(361,plain,
% 5.44/3.66 (((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 5.44/3.66 inference(tautology,[status(thm)],[])).
% 5.44/3.66 tff(362,plain,
% 5.44/3.66 (r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 5.44/3.66 inference(unit_resolution,[status(thm)],[361, 360])).
% 5.44/3.66 tff(363,plain,
% 5.44/3.66 (((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))),
% 5.44/3.66 inference(tautology,[status(thm)],[])).
% 5.44/3.66 tff(364,plain,
% 5.44/3.66 (~p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 5.44/3.66 inference(unit_resolution,[status(thm)],[363, 360])).
% 5.44/3.66 tff(365,assumption,(~p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))), introduced(assumption)).
% 5.44/3.66 tff(366,assumption,(r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))), introduced(assumption)).
% 5.44/3.66 tff(367,plain,
% 5.44/3.66 (((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))) | (p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))) | p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))),
% 5.44/3.66 inference(rewrite,[status(thm)],[])).
% 5.44/3.66 tff(368,plain,
% 5.44/3.66 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))) | (p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))),
% 5.44/3.66 inference(quant_inst,[status(thm)],[])).
% 5.44/3.66 tff(369,plain,
% 5.44/3.66 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))) | p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))),
% 5.44/3.66 inference(modus_ponens,[status(thm)],[368, 367])).
% 5.44/3.66 tff(370,plain,
% 5.44/3.66 ($false),
% 5.44/3.66 inference(unit_resolution,[status(thm)],[369, 359, 366, 365])).
% 5.44/3.66 tff(371,plain,((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))), inference(lemma,lemma(discharge,[]))).
% 5.44/3.66 tff(372,plain,
% 5.44/3.66 ($false),
% 5.44/3.66 inference(unit_resolution,[status(thm)],[371, 364, 362, 359])).
% 5.44/3.66 tff(373,plain,(((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))))), inference(lemma,lemma(discharge,[]))).
% 5.44/3.66 tff(374,plain,
% 5.44/3.66 (~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))),
% 5.44/3.66 inference(unit_resolution,[status(thm)],[373, 358])).
% 5.44/3.66 tff(375,plain,
% 5.44/3.66 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X))))),
% 5.44/3.66 inference(rewrite,[status(thm)],[])).
% 5.44/3.66 tff(376,plain,
% 5.44/3.66 (((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | ![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) <=> ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X))))),
% 5.44/3.66 inference(rewrite,[status(thm)],[])).
% 5.44/3.66 tff(377,plain,
% 5.44/3.66 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | ![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X)))))),
% 5.44/3.66 inference(monotonicity,[status(thm)],[376])).
% 5.44/3.66 tff(378,plain,
% 5.44/3.66 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | ![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X))))),
% 5.44/3.66 inference(transitivity,[status(thm)],[377, 375])).
% 5.44/3.66 tff(379,plain,
% 5.44/3.66 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | ![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))),
% 5.44/3.66 inference(quant_inst,[status(thm)],[])).
% 5.44/3.66 tff(380,plain,
% 5.44/3.66 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X)))),
% 5.44/3.66 inference(modus_ponens,[status(thm)],[379, 378])).
% 5.44/3.66 tff(381,plain,
% 5.44/3.66 (![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X)))),
% 5.44/3.66 inference(unit_resolution,[status(thm)],[380, 202, 326])).
% 5.44/3.66 tff(382,plain,
% 5.44/3.66 (((~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X)))) | ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))))) <=> ((~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))))),
% 5.44/3.66 inference(rewrite,[status(thm)],[])).
% 5.44/3.66 tff(383,plain,
% 5.44/3.66 ((![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) <=> ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))))),
% 5.44/3.66 inference(rewrite,[status(thm)],[])).
% 5.44/3.66 tff(384,plain,
% 5.44/3.66 (^[Y: $i] : trans(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) <=> (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))), (((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) <=> ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))), rewrite(((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) <=> ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))), (((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) <=> ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))))),
% 5.44/3.66 inference(bind,[status(th)],[])).
% 5.44/3.66 tff(385,plain,
% 5.44/3.66 (![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) <=> ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))),
% 5.44/3.66 inference(quant_intro,[status(thm)],[384])).
% 5.44/3.66 tff(386,plain,
% 5.44/3.66 (^[Y: $i] : rewrite(((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | p1(Y)) <=> (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))))),
% 5.44/3.66 inference(bind,[status(th)],[])).
% 5.44/3.66 tff(387,plain,
% 5.44/3.66 (![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | p1(Y)) <=> ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))),
% 5.44/3.66 inference(quant_intro,[status(thm)],[386])).
% 5.44/3.66 tff(388,plain,
% 5.44/3.66 ((![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | p1(Y)) | ![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) <=> (![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))),
% 5.44/3.66 inference(monotonicity,[status(thm)],[387, 385])).
% 5.44/3.66 tff(389,plain,
% 5.44/3.66 ((![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | p1(Y)) | ![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) <=> ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))))),
% 5.44/3.66 inference(transitivity,[status(thm)],[388, 383])).
% 5.44/3.66 tff(390,plain,
% 5.44/3.66 (((~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X)))) | (![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | p1(Y)) | ![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) <=> ((~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X)))) | ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))))),
% 5.44/3.66 inference(monotonicity,[status(thm)],[389])).
% 5.44/3.66 tff(391,plain,
% 5.44/3.66 (((~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X)))) | (![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | p1(Y)) | ![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) <=> ((~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))))),
% 5.44/3.66 inference(transitivity,[status(thm)],[390, 382])).
% 5.44/3.66 tff(392,plain,
% 5.44/3.66 ((~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X)))) | (![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | p1(Y)) | ![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))),
% 5.44/3.66 inference(quant_inst,[status(thm)],[])).
% 5.44/3.66 tff(393,plain,
% 5.44/3.66 ((~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))),
% 5.44/3.67 inference(modus_ponens,[status(thm)],[392, 391])).
% 5.44/3.67 tff(394,plain,
% 5.44/3.67 (![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))),
% 5.44/3.67 inference(unit_resolution,[status(thm)],[393, 330, 381])).
% 5.44/3.67 tff(395,plain,
% 5.44/3.67 (![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))),
% 5.44/3.67 inference(unit_resolution,[status(thm)],[394, 374])).
% 5.44/3.67 tff(396,assumption,(~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), X)))))), introduced(assumption)).
% 5.44/3.67 tff(397,plain,
% 5.44/3.67 (((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), X))))) | r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 5.44/3.67 inference(tautology,[status(thm)],[])).
% 5.44/3.67 tff(398,plain,
% 5.44/3.67 (r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 5.44/3.67 inference(unit_resolution,[status(thm)],[397, 396])).
% 5.44/3.67 tff(399,assumption,(![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))), introduced(assumption)).
% 5.44/3.67 tff(400,plain,
% 5.44/3.67 (((~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))) | ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))))) <=> ((~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))))),
% 5.44/3.67 inference(rewrite,[status(thm)],[])).
% 5.44/3.67 tff(401,plain,
% 5.44/3.67 (((~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) <=> ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))))),
% 5.44/3.67 inference(rewrite,[status(thm)],[])).
% 5.44/3.67 tff(402,plain,
% 5.44/3.67 ((~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))) <=> (~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))))),
% 5.44/3.67 inference(rewrite,[status(thm)],[])).
% 5.44/3.67 tff(403,plain,
% 5.44/3.67 (((~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) <=> ((~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))),
% 5.44/3.67 inference(monotonicity,[status(thm)],[402])).
% 5.44/3.67 tff(404,plain,
% 5.44/3.67 (((~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) <=> ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))))),
% 5.44/3.67 inference(transitivity,[status(thm)],[403, 401])).
% 5.44/3.67 tff(405,plain,
% 5.44/3.67 (((~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))) | ((~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))) <=> ((~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))) | ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))))))),
% 5.44/3.67 inference(monotonicity,[status(thm)],[404])).
% 5.44/3.67 tff(406,plain,
% 5.44/3.67 (((~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))) | ((~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))) <=> ((~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))))),
% 5.44/3.67 inference(transitivity,[status(thm)],[405, 400])).
% 5.44/3.67 tff(407,plain,
% 5.44/3.67 ((~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))) | ((~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))),
% 5.44/3.67 inference(quant_inst,[status(thm)],[])).
% 5.44/3.67 tff(408,plain,
% 5.44/3.67 ((~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))))),
% 5.44/3.67 inference(modus_ponens,[status(thm)],[407, 406])).
% 5.44/3.67 tff(409,plain,
% 5.44/3.67 (~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))),
% 5.44/3.67 inference(unit_resolution,[status(thm)],[408, 399, 398])).
% 5.44/3.67 tff(410,plain,
% 5.44/3.67 (((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | (~p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))),
% 5.44/3.67 inference(tautology,[status(thm)],[])).
% 5.44/3.67 tff(411,plain,
% 5.44/3.67 (~p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))),
% 5.44/3.67 inference(unit_resolution,[status(thm)],[410, 409])).
% 5.44/3.67 tff(412,plain,
% 5.44/3.67 (((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))),
% 5.44/3.67 inference(tautology,[status(thm)],[])).
% 5.44/3.67 tff(413,plain,
% 5.44/3.67 (r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))),
% 5.44/3.67 inference(unit_resolution,[status(thm)],[412, 409])).
% 5.44/3.67 tff(414,plain,
% 5.44/3.67 (((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), X))))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), X)))),
% 5.44/3.67 inference(tautology,[status(thm)],[])).
% 5.44/3.67 tff(415,plain,
% 5.44/3.67 (![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), X)))),
% 5.46/3.67 inference(unit_resolution,[status(thm)],[414, 396])).
% 5.46/3.67 tff(416,plain,
% 5.46/3.67 (((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), X)))) | (p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))))) <=> ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), X)))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))))),
% 5.46/3.67 inference(rewrite,[status(thm)],[])).
% 5.46/3.67 tff(417,plain,
% 5.46/3.67 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), X)))) | (p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))))),
% 5.46/3.67 inference(quant_inst,[status(thm)],[])).
% 5.46/3.67 tff(418,plain,
% 5.46/3.67 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), X)))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))),
% 5.46/3.67 inference(modus_ponens,[status(thm)],[417, 416])).
% 5.46/3.67 tff(419,plain,
% 5.46/3.67 ($false),
% 5.46/3.67 inference(unit_resolution,[status(thm)],[418, 415, 413, 411])).
% 5.46/3.67 tff(420,plain,(((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), X))))) | (~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))))), inference(lemma,lemma(discharge,[]))).
% 5.46/3.67 tff(421,plain,
% 5.46/3.67 ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), X))))),
% 5.46/3.67 inference(unit_resolution,[status(thm)],[420, 395])).
% 5.46/3.67 tff(422,plain,
% 5.46/3.67 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!8, X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | r1(Y!8, tptp_fun_X_7(X!9)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | r1(Y!8, tptp_fun_X_7(X!9)))),
% 5.46/3.67 inference(rewrite,[status(thm)],[])).
% 5.46/3.67 tff(423,plain,
% 5.46/3.67 ((r1(Y!8, tptp_fun_X_7(X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | (~r1(Y!8, X!9))) <=> ((~r1(Y!8, X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | r1(Y!8, tptp_fun_X_7(X!9)))),
% 5.46/3.67 inference(rewrite,[status(thm)],[])).
% 5.46/3.67 tff(424,plain,
% 5.46/3.67 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | (~r1(Y!8, X!9)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!8, X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | r1(Y!8, tptp_fun_X_7(X!9))))),
% 5.46/3.67 inference(monotonicity,[status(thm)],[423])).
% 5.46/3.67 tff(425,plain,
% 5.46/3.67 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | (~r1(Y!8, X!9)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | r1(Y!8, tptp_fun_X_7(X!9)))),
% 5.46/3.67 inference(transitivity,[status(thm)],[424, 422])).
% 5.46/3.67 tff(426,plain,
% 5.46/3.67 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | (~r1(Y!8, X!9)))),
% 5.46/3.67 inference(quant_inst,[status(thm)],[])).
% 5.46/3.67 tff(427,plain,
% 5.46/3.67 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | r1(Y!8, tptp_fun_X_7(X!9))),
% 5.46/3.67 inference(modus_ponens,[status(thm)],[426, 425])).
% 5.46/3.67 tff(428,plain,
% 5.46/3.67 (r1(Y!8, tptp_fun_X_7(X!9))),
% 5.46/3.67 inference(unit_resolution,[status(thm)],[427, 73, 273, 297])).
% 5.46/3.67 tff(429,plain,
% 5.46/3.67 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!8, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 5.46/3.67 inference(rewrite,[status(thm)],[])).
% 5.46/3.67 tff(430,plain,
% 5.46/3.67 ((r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(Y!8, tptp_fun_X_7(X!9)))) <=> ((~r1(Y!8, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 5.46/3.67 inference(rewrite,[status(thm)],[])).
% 5.46/3.67 tff(431,plain,
% 5.46/3.67 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(Y!8, tptp_fun_X_7(X!9))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!8, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 5.46/3.67 inference(monotonicity,[status(thm)],[430])).
% 5.46/3.67 tff(432,plain,
% 5.46/3.67 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(Y!8, tptp_fun_X_7(X!9))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 5.46/3.67 inference(transitivity,[status(thm)],[431, 429])).
% 5.46/3.67 tff(433,plain,
% 5.46/3.67 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(Y!8, tptp_fun_X_7(X!9))))),
% 5.46/3.67 inference(quant_inst,[status(thm)],[])).
% 5.46/3.67 tff(434,plain,
% 5.46/3.67 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9)))),
% 5.46/3.67 inference(modus_ponens,[status(thm)],[433, 432])).
% 5.46/3.67 tff(435,plain,
% 5.46/3.67 (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9)))),
% 5.46/3.67 inference(unit_resolution,[status(thm)],[434, 73, 428, 308])).
% 5.46/3.67 tff(436,plain,
% 5.46/3.67 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 5.46/3.67 inference(rewrite,[status(thm)],[])).
% 5.46/3.67 tff(437,plain,
% 5.46/3.67 ((r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9))))) <=> ((~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 5.46/3.67 inference(rewrite,[status(thm)],[])).
% 5.46/3.67 tff(438,plain,
% 5.46/3.67 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 5.46/3.68 inference(monotonicity,[status(thm)],[437])).
% 5.46/3.68 tff(439,plain,
% 5.46/3.68 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 5.46/3.68 inference(transitivity,[status(thm)],[438, 436])).
% 5.46/3.68 tff(440,plain,
% 5.46/3.68 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 5.46/3.68 inference(quant_inst,[status(thm)],[])).
% 5.46/3.68 tff(441,plain,
% 5.46/3.68 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 5.46/3.68 inference(modus_ponens,[status(thm)],[440, 439])).
% 5.46/3.68 tff(442,plain,
% 5.46/3.68 (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 5.46/3.68 inference(unit_resolution,[status(thm)],[441, 73, 435, 319])).
% 5.46/3.68 tff(443,plain,
% 5.46/3.68 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 5.46/3.68 inference(rewrite,[status(thm)],[])).
% 5.46/3.68 tff(444,plain,
% 5.46/3.68 ((r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) <=> ((~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 5.46/3.68 inference(rewrite,[status(thm)],[])).
% 5.46/3.68 tff(445,plain,
% 5.46/3.68 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))),
% 5.46/3.68 inference(monotonicity,[status(thm)],[444])).
% 5.46/3.68 tff(446,plain,
% 5.46/3.68 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 5.46/3.68 inference(transitivity,[status(thm)],[445, 443])).
% 5.46/3.68 tff(447,plain,
% 5.46/3.68 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 5.46/3.68 inference(quant_inst,[status(thm)],[])).
% 5.46/3.68 tff(448,plain,
% 5.46/3.68 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 5.46/3.68 inference(modus_ponens,[status(thm)],[447, 446])).
% 5.46/3.68 tff(449,plain,
% 5.46/3.68 (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 5.46/3.68 inference(unit_resolution,[status(thm)],[448, 73, 442, 330])).
% 5.46/3.68 tff(450,assumption,(![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))), introduced(assumption)).
% 5.46/3.68 tff(451,plain,
% 5.46/3.68 (((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))) | ((~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), X)))))))) <=> ((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), X)))))))),
% 5.46/3.68 inference(rewrite,[status(thm)],[])).
% 5.46/3.68 tff(452,plain,
% 5.46/3.68 ((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))) | ((~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), X)))))))),
% 5.46/3.68 inference(quant_inst,[status(thm)],[])).
% 5.46/3.68 tff(453,plain,
% 5.46/3.68 ((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), X))))))),
% 5.46/3.68 inference(modus_ponens,[status(thm)],[452, 451])).
% 5.46/3.68 tff(454,plain,
% 5.46/3.68 ($false),
% 5.46/3.68 inference(unit_resolution,[status(thm)],[453, 450, 449, 421])).
% 5.46/3.68 tff(455,plain,(~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))), inference(lemma,lemma(discharge,[]))).
% 5.46/3.68 tff(456,plain,
% 5.46/3.68 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))))),
% 5.46/3.68 inference(rewrite,[status(thm)],[])).
% 5.46/3.68 tff(457,plain,
% 5.46/3.68 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))))),
% 5.46/3.68 inference(rewrite,[status(thm)],[])).
% 5.46/3.68 tff(458,plain,
% 5.46/3.68 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))))),
% 5.46/3.68 inference(bind,[status(th)],[])).
% 5.46/3.68 tff(459,plain,
% 5.46/3.68 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))),
% 5.46/3.68 inference(quant_intro,[status(thm)],[458])).
% 5.46/3.68 tff(460,plain,
% 5.46/3.68 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))))),
% 5.46/3.68 inference(monotonicity,[status(thm)],[459])).
% 5.46/3.68 tff(461,plain,
% 5.46/3.68 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))))),
% 5.46/3.68 inference(transitivity,[status(thm)],[460, 457])).
% 5.46/3.68 tff(462,plain,
% 5.46/3.68 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))),
% 5.46/3.68 inference(and_elim,[status(thm)],[51])).
% 5.46/3.68 tff(463,plain,
% 5.46/3.68 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))),
% 5.46/3.68 inference(modus_ponens,[status(thm)],[462, 461])).
% 5.46/3.68 tff(464,plain,
% 5.46/3.68 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))),
% 5.46/3.68 inference(modus_ponens,[status(thm)],[463, 456])).
% 5.46/3.68 tff(465,plain,
% 5.46/3.68 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))),
% 5.46/3.68 inference(unit_resolution,[status(thm)],[464, 98, 89])).
% 5.46/3.68 tff(466,plain,
% 5.46/3.68 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))) | ((~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))) | (~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))),
% 5.46/3.68 inference(rewrite,[status(thm)],[])).
% 5.46/3.68 tff(467,plain,
% 5.46/3.68 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))) | ((~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))),
% 5.46/3.68 inference(quant_inst,[status(thm)],[])).
% 5.46/3.68 tff(468,plain,
% 5.46/3.68 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))) | (~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))),
% 5.46/3.68 inference(modus_ponens,[status(thm)],[467, 466])).
% 5.46/3.68 tff(469,plain,
% 5.46/3.68 (![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))),
% 5.46/3.68 inference(unit_resolution,[status(thm)],[468, 465, 61])).
% 5.46/3.68 tff(470,plain,
% 5.46/3.68 (![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))),
% 5.46/3.68 inference(unit_resolution,[status(thm)],[469, 455])).
% 5.46/3.68 tff(471,plain,
% 5.46/3.68 (((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))) | ((~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | p1(tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))))) <=> ((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | p1(tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))))),
% 5.46/3.68 inference(rewrite,[status(thm)],[])).
% 5.46/3.68 tff(472,plain,
% 5.46/3.68 ((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))) | ((~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | p1(tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))))),
% 5.46/3.69 inference(quant_inst,[status(thm)],[])).
% 5.46/3.69 tff(473,plain,
% 5.46/3.69 ((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | p1(tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))),
% 5.46/3.69 inference(modus_ponens,[status(thm)],[472, 471])).
% 5.46/3.69 tff(474,plain,
% 5.46/3.69 ($false),
% 5.46/3.69 inference(unit_resolution,[status(thm)],[473, 470, 249, 228])).
% 5.46/3.69 % SZS output end Proof
%------------------------------------------------------------------------------