TSTP Solution File: LCL658+1.005 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL658+1.005 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 04:57:31 EDT 2022
% Result : Theorem 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL658+1.005 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Sep 1 23:43:49 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 % SZS output start Proof
% 0.19/0.44 tff(p1_type, type, (
% 0.19/0.44 p1: $i > $o)).
% 0.19/0.44 tff(tptp_fun_Y_1_type, type, (
% 0.19/0.44 tptp_fun_Y_1: $i > $i)).
% 0.19/0.44 tff(tptp_fun_X_6_type, type, (
% 0.19/0.44 tptp_fun_X_6: $i)).
% 0.19/0.44 tff(r1_type, type, (
% 0.19/0.44 r1: ( $i * $i ) > $o)).
% 0.19/0.44 tff(tptp_fun_X_8_type, type, (
% 0.19/0.44 tptp_fun_X_8: $i > $i)).
% 0.19/0.44 tff(tptp_fun_Y_7_type, type, (
% 0.19/0.44 tptp_fun_Y_7: $i > $i)).
% 0.19/0.44 tff(tptp_fun_Y_4_type, type, (
% 0.19/0.44 tptp_fun_Y_4: $i)).
% 0.19/0.44 tff(tptp_fun_Y_14_type, type, (
% 0.19/0.44 tptp_fun_Y_14: $i > $i)).
% 0.19/0.44 tff(tptp_fun_X_13_type, type, (
% 0.19/0.44 tptp_fun_X_13: $i > $i)).
% 0.19/0.44 tff(tptp_fun_X_12_type, type, (
% 0.19/0.44 tptp_fun_X_12: $i > $i)).
% 0.19/0.44 tff(tptp_fun_X_9_type, type, (
% 0.19/0.44 tptp_fun_X_9: $i > $i)).
% 0.19/0.44 tff(tptp_fun_X_10_type, type, (
% 0.19/0.44 tptp_fun_X_10: $i > $i)).
% 0.19/0.44 tff(tptp_fun_Y_11_type, type, (
% 0.19/0.44 tptp_fun_Y_11: $i > $i)).
% 0.19/0.44 tff(tptp_fun_X_0_type, type, (
% 0.19/0.44 tptp_fun_X_0: $i)).
% 0.19/0.44 tff(tptp_fun_X_5_type, type, (
% 0.19/0.44 tptp_fun_X_5: $i)).
% 0.19/0.44 tff(tptp_fun_X_3_type, type, (
% 0.19/0.44 tptp_fun_X_3: $i)).
% 0.19/0.44 tff(tptp_fun_Y_2_type, type, (
% 0.19/0.44 tptp_fun_Y_2: $i)).
% 0.19/0.44 tff(1,assumption,(p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6)))), introduced(assumption)).
% 0.19/0.44 tff(2,assumption,(![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))), introduced(assumption)).
% 0.19/0.44 tff(3,plain,
% 0.19/0.44 ((![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & (r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (r1(Y, tptp_fun_X_10(Y)) & p1(tptp_fun_X_10(Y)) & (~(p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & (((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_13(Y)) & p1(tptp_fun_X_13(Y)) & (~(p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (r1(Y, tptp_fun_X_10(Y)) & p1(tptp_fun_X_10(Y)) & (~(p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & (((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_13(Y)) & p1(tptp_fun_X_13(Y)) & (~(p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(4,plain,
% 0.19/0.44 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_7(X)))) & (~(~p1(tptp_fun_Y_7(X)))) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | ((~(~r1(Y, tptp_fun_X_10(Y)))) & (~(~p1(tptp_fun_X_10(Y)))) & (~(p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))))) & ![Y: $i] : ((~r1(tptp_fun_X_10(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ((~(~p1(Y))) & (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | ((~p1(tptp_fun_X_12(Y))) & (~(~r1(Y, tptp_fun_X_12(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_13(Y)))) & (~(~p1(tptp_fun_X_13(Y)))) & (~(p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))) | ((~p1(tptp_fun_X_12(Y))) & (~(~r1(Y, tptp_fun_X_12(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (r1(Y, tptp_fun_X_10(Y)) & p1(tptp_fun_X_10(Y)) & (~(p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & (((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_13(Y)) & p1(tptp_fun_X_13(Y)) & (~(p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(5,plain,
% 0.19/0.45 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_7(X)))) & (~(~p1(tptp_fun_Y_7(X)))) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | ((~(~r1(Y, tptp_fun_X_10(Y)))) & (~(~p1(tptp_fun_X_10(Y)))) & (~(p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))))) & ![Y: $i] : ((~r1(tptp_fun_X_10(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ((~(~p1(Y))) & (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | ((~p1(tptp_fun_X_12(Y))) & (~(~r1(Y, tptp_fun_X_12(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_13(Y)))) & (~(~p1(tptp_fun_X_13(Y)))) & (~(p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))) | ((~p1(tptp_fun_X_12(Y))) & (~(~r1(Y, tptp_fun_X_12(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (r1(Y, tptp_fun_X_10(Y)) & p1(tptp_fun_X_10(Y)) & (~(p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & (((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_13(Y)) & p1(tptp_fun_X_13(Y)) & (~(p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.45 tff(6,plain,
% 0.19/0.45 (((r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) <=> (r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y)))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(7,plain,
% 0.19/0.45 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y)))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y)))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(8,plain,
% 0.19/0.45 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y)))))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[7])).
% 0.19/0.45 tff(9,plain,
% 0.19/0.45 ((r1(X!0, Y!2) & (r1(Y!2, X!3) & r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))))) <=> (r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(10,plain,
% 0.19/0.45 ((r1(Y!2, X!3) & (r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))))) <=> (r1(Y!2, X!3) & r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(11,plain,
% 0.19/0.45 ((r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & (r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) <=> (r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(12,plain,
% 0.19/0.45 (^[X: $i] : rewrite((p1(X) | (~r1(Y!4, X)) | ((~(~r1(X, tptp_fun_Y_7(X)))) & (~(~p1(tptp_fun_Y_7(X)))) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) <=> (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(13,plain,
% 0.19/0.45 (![X: $i] : (p1(X) | (~r1(Y!4, X)) | ((~(~r1(X, tptp_fun_Y_7(X)))) & (~(~p1(tptp_fun_Y_7(X)))) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) <=> ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.45 tff(14,plain,
% 0.19/0.45 (((~(~r1(Y!4, X!6))) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) <=> (r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(15,plain,
% 0.19/0.45 ((~(~r1(X!3, Y!4))) <=> r1(X!3, Y!4)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(16,plain,
% 0.19/0.45 (((~(~r1(X!3, Y!4))) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & ((~(~r1(Y!4, X!6))) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | ((~(~r1(X, tptp_fun_Y_7(X)))) & (~(~p1(tptp_fun_Y_7(X)))) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) <=> (r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & (r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[15, 14, 13])).
% 0.19/0.45 tff(17,plain,
% 0.19/0.45 (((~(~r1(X!3, Y!4))) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & ((~(~r1(Y!4, X!6))) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | ((~(~r1(X, tptp_fun_Y_7(X)))) & (~(~p1(tptp_fun_Y_7(X)))) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) <=> (r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[16, 11])).
% 0.19/0.45 tff(18,plain,
% 0.19/0.45 ((~(~r1(Y!2, X!3))) <=> r1(Y!2, X!3)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(19,plain,
% 0.19/0.45 (((~(~r1(Y!2, X!3))) & ((~(~r1(X!3, Y!4))) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & ((~(~r1(Y!4, X!6))) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | ((~(~r1(X, tptp_fun_Y_7(X)))) & (~(~p1(tptp_fun_Y_7(X)))) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))))) <=> (r1(Y!2, X!3) & (r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[18, 17])).
% 0.19/0.45 tff(20,plain,
% 0.19/0.45 (((~(~r1(Y!2, X!3))) & ((~(~r1(X!3, Y!4))) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & ((~(~r1(Y!4, X!6))) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | ((~(~r1(X, tptp_fun_Y_7(X)))) & (~(~p1(tptp_fun_Y_7(X)))) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))))) <=> (r1(Y!2, X!3) & r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[19, 10])).
% 0.19/0.45 tff(21,plain,
% 0.19/0.45 ((~(~r1(X!0, Y!2))) <=> r1(X!0, Y!2)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(22,plain,
% 0.19/0.45 (((~(~r1(X!0, Y!2))) & ((~(~r1(Y!2, X!3))) & ((~(~r1(X!3, Y!4))) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & ((~(~r1(Y!4, X!6))) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | ((~(~r1(X, tptp_fun_Y_7(X)))) & (~(~p1(tptp_fun_Y_7(X)))) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))))) <=> (r1(X!0, Y!2) & (r1(Y!2, X!3) & r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[21, 20])).
% 0.19/0.45 tff(23,plain,
% 0.19/0.45 (((~(~r1(X!0, Y!2))) & ((~(~r1(Y!2, X!3))) & ((~(~r1(X!3, Y!4))) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & ((~(~r1(Y!4, X!6))) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | ((~(~r1(X, tptp_fun_Y_7(X)))) & (~(~p1(tptp_fun_Y_7(X)))) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))))) <=> (r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[22, 9])).
% 0.19/0.45 tff(24,plain,
% 0.19/0.45 ((((~(~r1(X!0, Y!2))) & ((~(~r1(Y!2, X!3))) & ((~(~r1(X!3, Y!4))) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & ((~(~r1(Y!4, X!6))) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | ((~(~r1(X, tptp_fun_Y_7(X)))) & (~(~p1(tptp_fun_Y_7(X)))) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) <=> ((r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y)))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[23, 8])).
% 0.19/0.46 tff(25,plain,
% 0.19/0.46 ((((~(~r1(X!0, Y!2))) & ((~(~r1(Y!2, X!3))) & ((~(~r1(X!3, Y!4))) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & ((~(~r1(Y!4, X!6))) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | ((~(~r1(X, tptp_fun_Y_7(X)))) & (~(~p1(tptp_fun_Y_7(X)))) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) <=> (r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y)))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[24, 6])).
% 0.19/0.46 tff(26,plain,
% 0.19/0.46 ((![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & (((~(~r1(X!0, Y!2))) & ((~(~r1(Y!2, X!3))) & ((~(~r1(X!3, Y!4))) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & ((~(~r1(Y!4, X!6))) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | ((~(~r1(X, tptp_fun_Y_7(X)))) & (~(~p1(tptp_fun_Y_7(X)))) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_7(X)))) & (~(~p1(tptp_fun_Y_7(X)))) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | ((~(~r1(Y, tptp_fun_X_10(Y)))) & (~(~p1(tptp_fun_X_10(Y)))) & (~(p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))))) & ![Y: $i] : ((~r1(tptp_fun_X_10(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ((~(~p1(Y))) & (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | ((~p1(tptp_fun_X_12(Y))) & (~(~r1(Y, tptp_fun_X_12(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_13(Y)))) & (~(~p1(tptp_fun_X_13(Y)))) & (~(p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))) | ((~p1(tptp_fun_X_12(Y))) & (~(~r1(Y, tptp_fun_X_12(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & (r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (r1(Y, tptp_fun_X_10(Y)) & p1(tptp_fun_X_10(Y)) & (~(p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & (((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_13(Y)) & p1(tptp_fun_X_13(Y)) & (~(p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[25, 5])).
% 0.19/0.46 tff(27,plain,
% 0.19/0.46 ((![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & (((~(~r1(X!0, Y!2))) & ((~(~r1(Y!2, X!3))) & ((~(~r1(X!3, Y!4))) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & ((~(~r1(Y!4, X!6))) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | ((~(~r1(X, tptp_fun_Y_7(X)))) & (~(~p1(tptp_fun_Y_7(X)))) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_7(X)))) & (~(~p1(tptp_fun_Y_7(X)))) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | ((~(~r1(Y, tptp_fun_X_10(Y)))) & (~(~p1(tptp_fun_X_10(Y)))) & (~(p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))))) & ![Y: $i] : ((~r1(tptp_fun_X_10(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ((~(~p1(Y))) & (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | ((~p1(tptp_fun_X_12(Y))) & (~(~r1(Y, tptp_fun_X_12(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_13(Y)))) & (~(~p1(tptp_fun_X_13(Y)))) & (~(p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))) | ((~p1(tptp_fun_X_12(Y))) & (~(~r1(Y, tptp_fun_X_12(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (r1(Y, tptp_fun_X_10(Y)) & p1(tptp_fun_X_10(Y)) & (~(p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & (((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_13(Y)) & p1(tptp_fun_X_13(Y)) & (~(p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[26, 3])).
% 0.19/0.46 tff(28,plain,
% 0.19/0.46 (?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))))) <=> ?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(29,plain,
% 0.19/0.46 ((~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))))))) <=> ?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(30,plain,
% 0.19/0.46 ((~?[X: $i] : (~(((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((((((![X: $i] : ((~r1(Y, X)) | p1(X)) | (~p1(Y))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y)))))) | (~![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))) | (~(![X: $i] : ((~r1(Y, X)) | p1(X)) | (~p1(Y))))))))) & ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (~![X: $i] : (((~r1(Y, X)) | p1(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(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))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p1(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y))))))))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (~![X: $i] : (((~r1(Y, X)) | p1(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y)))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) <=> (~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(31,plain,
% 0.19/0.46 ((~(~?[X: $i] : (~(((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((((((![X: $i] : ((~r1(Y, X)) | p1(X)) | (~p1(Y))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y)))))) | (~![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))) | (~(![X: $i] : ((~r1(Y, X)) | p1(X)) | (~p1(Y))))))))) & ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (~![X: $i] : (((~r1(Y, X)) | p1(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(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))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p1(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y))))))))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (~![X: $i] : (((~r1(Y, X)) | p1(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y)))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))) <=> (~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[30])).
% 0.19/0.47 tff(32,plain,
% 0.19/0.47 ((~(~?[X: $i] : (~(((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((((((![X: $i] : ((~r1(Y, X)) | p1(X)) | (~p1(Y))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y)))))) | (~![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))) | (~(![X: $i] : ((~r1(Y, X)) | p1(X)) | (~p1(Y))))))))) & ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (~![X: $i] : (((~r1(Y, X)) | p1(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(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))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p1(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y))))))))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (~![X: $i] : (((~r1(Y, X)) | p1(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y)))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))) <=> ?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[31, 29])).
% 0.19/0.47 tff(33,axiom,(~(~?[X: $i] : (~(((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((((((![X: $i] : ((~r1(Y, X)) | p1(X)) | (~p1(Y))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y)))))) | (~![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))) | (~(![X: $i] : ((~r1(Y, X)) | p1(X)) | (~p1(Y))))))))) & ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (~![X: $i] : (((~r1(Y, X)) | p1(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(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))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p1(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y))))))))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (~![X: $i] : (((~r1(Y, X)) | p1(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y)))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','main')).
% 0.19/0.47 tff(34,plain,
% 0.19/0.47 (?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.19/0.47 tff(35,plain,
% 0.19/0.47 (?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[34, 28])).
% 0.19/0.47 tff(36,plain,
% 0.19/0.47 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (r1(Y, tptp_fun_X_10(Y)) & p1(tptp_fun_X_10(Y)) & (~(p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & (((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_13(Y)) & p1(tptp_fun_X_13(Y)) & (~(p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[35, 27])).
% 0.19/0.47 tff(37,plain,
% 0.19/0.47 (r1(Y!4, X!6)),
% 0.19/0.47 inference(and_elim,[status(thm)],[36])).
% 0.19/0.47 tff(38,plain,
% 0.19/0.47 (((~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) | ((~r1(Y!4, X!6)) | (~(p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6))))))) <=> ((~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) | (~r1(Y!4, X!6)) | (~(p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(39,plain,
% 0.19/0.47 ((~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) | ((~r1(Y!4, X!6)) | (~(p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(40,plain,
% 0.19/0.47 ((~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) | (~r1(Y!4, X!6)) | (~(p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.19/0.47 tff(41,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[40, 37, 2, 1])).
% 0.19/0.47 tff(42,plain,((~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) | (~(p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6)))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(43,plain,
% 0.19/0.47 (~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[42, 1])).
% 0.19/0.47 tff(44,assumption,(~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))), introduced(assumption)).
% 0.19/0.47 tff(45,plain,
% 0.19/0.47 ((p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | r1(Y!4, tptp_fun_X_12(Y!4))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(46,plain,
% 0.19/0.47 (r1(Y!4, tptp_fun_X_12(Y!4))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.19/0.47 tff(47,plain,
% 0.19/0.47 ((p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~p1(tptp_fun_X_12(Y!4)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(48,plain,
% 0.19/0.47 (~p1(tptp_fun_X_12(Y!4))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[47, 44])).
% 0.19/0.47 tff(49,plain,
% 0.19/0.47 (^[X: $i] : refl((p1(X) | (~r1(Y!4, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) <=> (p1(X) | (~r1(Y!4, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(50,plain,
% 0.19/0.47 (![X: $i] : (p1(X) | (~r1(Y!4, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) <=> ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.47 tff(51,plain,
% 0.19/0.47 (^[X: $i] : rewrite((p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) <=> (p1(X) | (~r1(Y!4, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(52,plain,
% 0.19/0.47 (![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) <=> ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[51])).
% 0.19/0.47 tff(53,plain,
% 0.19/0.47 (![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))),
% 0.19/0.47 inference(and_elim,[status(thm)],[36])).
% 0.19/0.47 tff(54,plain,
% 0.19/0.47 (![X: $i] : (p1(X) | (~r1(Y!4, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.19/0.47 tff(55,plain,
% 0.19/0.47 (![X: $i] : (p1(X) | (~r1(Y!4, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.19/0.47 tff(56,plain,
% 0.19/0.47 (((~![X: $i] : (p1(X) | (~r1(Y!4, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | (p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~((~r1(tptp_fun_X_12(Y!4), tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | (~p1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | p1(tptp_fun_X_8(tptp_fun_X_12(Y!4))) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), tptp_fun_X_8(tptp_fun_X_12(Y!4)))))))) <=> ((~![X: $i] : (p1(X) | (~r1(Y!4, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~((~r1(tptp_fun_X_12(Y!4), tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | (~p1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | p1(tptp_fun_X_8(tptp_fun_X_12(Y!4))) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), tptp_fun_X_8(tptp_fun_X_12(Y!4)))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(57,plain,
% 0.19/0.47 ((~![X: $i] : (p1(X) | (~r1(Y!4, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | (p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~((~r1(tptp_fun_X_12(Y!4), tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | (~p1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | p1(tptp_fun_X_8(tptp_fun_X_12(Y!4))) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), tptp_fun_X_8(tptp_fun_X_12(Y!4)))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(58,plain,
% 0.19/0.47 ((~![X: $i] : (p1(X) | (~r1(Y!4, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~((~r1(tptp_fun_X_12(Y!4), tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | (~p1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | p1(tptp_fun_X_8(tptp_fun_X_12(Y!4))) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), tptp_fun_X_8(tptp_fun_X_12(Y!4))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.19/0.47 tff(59,plain,
% 0.19/0.47 (~((~r1(tptp_fun_X_12(Y!4), tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | (~p1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | p1(tptp_fun_X_8(tptp_fun_X_12(Y!4))) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), tptp_fun_X_8(tptp_fun_X_12(Y!4)))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[58, 55, 48, 46])).
% 0.19/0.47 tff(60,plain,
% 0.19/0.47 (((~r1(tptp_fun_X_12(Y!4), tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | (~p1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | p1(tptp_fun_X_8(tptp_fun_X_12(Y!4))) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), tptp_fun_X_8(tptp_fun_X_12(Y!4))))) | p1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(61,plain,
% 0.19/0.47 (p1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.19/0.47 tff(62,plain,
% 0.19/0.47 (((~r1(tptp_fun_X_12(Y!4), tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | (~p1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | p1(tptp_fun_X_8(tptp_fun_X_12(Y!4))) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), tptp_fun_X_8(tptp_fun_X_12(Y!4))))) | r1(tptp_fun_X_12(Y!4), tptp_fun_Y_7(tptp_fun_X_12(Y!4)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(63,plain,
% 0.19/0.47 (r1(tptp_fun_X_12(Y!4), tptp_fun_Y_7(tptp_fun_X_12(Y!4)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[62, 59])).
% 0.19/0.47 tff(64,plain,
% 0.19/0.47 ((p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(65,plain,
% 0.19/0.47 (![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[64, 44])).
% 0.19/0.47 tff(66,plain,
% 0.19/0.47 (((~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ((~p1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | (~r1(tptp_fun_X_12(Y!4), tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), X))))) <=> ((~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | (~p1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | (~r1(tptp_fun_X_12(Y!4), tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), X))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(67,plain,
% 0.19/0.47 ((~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ((~p1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | (~r1(tptp_fun_X_12(Y!4), tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), X))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(68,plain,
% 0.19/0.47 ((~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | (~p1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | (~r1(tptp_fun_X_12(Y!4), tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), X)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.19/0.47 tff(69,plain,
% 0.19/0.47 (![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), X)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[68, 65, 63, 61])).
% 0.19/0.47 tff(70,plain,
% 0.19/0.47 (((~r1(tptp_fun_X_12(Y!4), tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | (~p1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | p1(tptp_fun_X_8(tptp_fun_X_12(Y!4))) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), tptp_fun_X_8(tptp_fun_X_12(Y!4))))) | r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), tptp_fun_X_8(tptp_fun_X_12(Y!4)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(71,plain,
% 0.19/0.47 (r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), tptp_fun_X_8(tptp_fun_X_12(Y!4)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[70, 59])).
% 0.19/0.47 tff(72,plain,
% 0.19/0.47 (((~r1(tptp_fun_X_12(Y!4), tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | (~p1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | p1(tptp_fun_X_8(tptp_fun_X_12(Y!4))) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), tptp_fun_X_8(tptp_fun_X_12(Y!4))))) | (~p1(tptp_fun_X_8(tptp_fun_X_12(Y!4))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(73,plain,
% 0.19/0.47 (~p1(tptp_fun_X_8(tptp_fun_X_12(Y!4)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[72, 59])).
% 0.19/0.47 tff(74,plain,
% 0.19/0.47 (((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), X)))) | (p1(tptp_fun_X_8(tptp_fun_X_12(Y!4))) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), tptp_fun_X_8(tptp_fun_X_12(Y!4)))))) <=> ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), X)))) | p1(tptp_fun_X_8(tptp_fun_X_12(Y!4))) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), tptp_fun_X_8(tptp_fun_X_12(Y!4)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(75,plain,
% 0.19/0.47 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), X)))) | (p1(tptp_fun_X_8(tptp_fun_X_12(Y!4))) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), tptp_fun_X_8(tptp_fun_X_12(Y!4)))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(76,plain,
% 0.19/0.47 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), X)))) | p1(tptp_fun_X_8(tptp_fun_X_12(Y!4))) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), tptp_fun_X_8(tptp_fun_X_12(Y!4))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.48 tff(77,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[76, 73, 71, 69])).
% 0.19/0.48 tff(78,plain,(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(79,plain,
% 0.19/0.48 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(80,plain,
% 0.19/0.48 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[79])).
% 0.19/0.48 tff(81,plain,
% 0.19/0.48 (^[Y: $i] : refl(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(82,plain,
% 0.19/0.48 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[81])).
% 0.19/0.48 tff(83,plain,
% 0.19/0.48 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(84,plain,
% 0.19/0.48 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[83])).
% 0.19/0.48 tff(85,plain,
% 0.19/0.48 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[84, 82])).
% 0.19/0.48 tff(86,plain,
% 0.19/0.48 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (r1(Y, tptp_fun_X_10(Y)) & p1(tptp_fun_X_10(Y)) & (~(p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & (((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_13(Y)) & p1(tptp_fun_X_13(Y)) & (~(p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(87,plain,
% 0.19/0.48 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (r1(Y, tptp_fun_X_10(Y)) & p1(tptp_fun_X_10(Y)) & (~(p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & (((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_13(Y)) & p1(tptp_fun_X_13(Y)) & (~(p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[86])).
% 0.19/0.48 tff(88,plain,
% 0.19/0.48 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (r1(Y, tptp_fun_X_10(Y)) & p1(tptp_fun_X_10(Y)) & (~(p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & (((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_13(Y)) & p1(tptp_fun_X_13(Y)) & (~(p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))),
% 0.19/0.48 inference(and_elim,[status(thm)],[36])).
% 0.19/0.48 tff(89,plain,
% 0.19/0.48 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.19/0.48 tff(90,plain,
% 0.19/0.48 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.19/0.48 tff(91,plain,
% 0.19/0.48 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[90, 80])).
% 0.19/0.48 tff(92,plain,
% 0.19/0.48 (r1(X!0, Y!2)),
% 0.19/0.48 inference(and_elim,[status(thm)],[36])).
% 0.19/0.48 tff(93,plain,
% 0.19/0.48 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))))) | ((~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))))) | (~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(94,plain,
% 0.19/0.49 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))))) | ((~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(95,plain,
% 0.19/0.49 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))))) | (~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.19/0.49 tff(96,plain,
% 0.19/0.49 (![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[95, 92, 91])).
% 0.19/0.49 tff(97,plain,
% 0.19/0.49 (r1(Y!2, X!3)),
% 0.19/0.49 inference(and_elim,[status(thm)],[36])).
% 0.19/0.49 tff(98,plain,
% 0.19/0.49 (((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))) | ((~r1(Y!2, X!3)) | ![Y: $i] : ((~r1(X!3, Y)) | (~((~(p1(Y) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))) <=> ((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))) | (~r1(Y!2, X!3)) | ![Y: $i] : ((~r1(X!3, Y)) | (~((~(p1(Y) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(99,plain,
% 0.19/0.49 ((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))) | ((~r1(Y!2, X!3)) | ![Y: $i] : ((~r1(X!3, Y)) | (~((~(p1(Y) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(100,plain,
% 0.19/0.49 ((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))) | (~r1(Y!2, X!3)) | ![Y: $i] : ((~r1(X!3, Y)) | (~((~(p1(Y) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.19/0.49 tff(101,plain,
% 0.19/0.49 (![Y: $i] : ((~r1(X!3, Y)) | (~((~(p1(Y) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[100, 97, 96])).
% 0.19/0.49 tff(102,plain,
% 0.19/0.49 (r1(X!3, Y!4)),
% 0.19/0.49 inference(and_elim,[status(thm)],[36])).
% 0.19/0.49 tff(103,plain,
% 0.19/0.49 (((~![Y: $i] : ((~r1(X!3, Y)) | (~((~(p1(Y) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))) | ((~r1(X!3, Y!4)) | (~((~(p1(Y!4) | (~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~((~p1(Y!4)) | ![X: $i] : (p1(X) | (~r1(Y!4, X))) | ![X: $i] : ((~r1(Y!4, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))) <=> ((~![Y: $i] : ((~r1(X!3, Y)) | (~((~(p1(Y) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))) | (~r1(X!3, Y!4)) | (~((~(p1(Y!4) | (~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~((~p1(Y!4)) | ![X: $i] : (p1(X) | (~r1(Y!4, X))) | ![X: $i] : ((~r1(Y!4, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(104,plain,
% 0.19/0.49 ((~![Y: $i] : ((~r1(X!3, Y)) | (~((~(p1(Y) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))) | ((~r1(X!3, Y!4)) | (~((~(p1(Y!4) | (~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~((~p1(Y!4)) | ![X: $i] : (p1(X) | (~r1(Y!4, X))) | ![X: $i] : ((~r1(Y!4, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(105,plain,
% 0.19/0.49 ((~![Y: $i] : ((~r1(X!3, Y)) | (~((~(p1(Y) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p1(tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))) | (~r1(X!3, Y!4)) | (~((~(p1(Y!4) | (~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~((~p1(Y!4)) | ![X: $i] : (p1(X) | (~r1(Y!4, X))) | ![X: $i] : ((~r1(Y!4, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.49 tff(106,plain,
% 0.19/0.50 (~((~(p1(Y!4) | (~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~((~p1(Y!4)) | ![X: $i] : (p1(X) | (~r1(Y!4, X))) | ![X: $i] : ((~r1(Y!4, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[105, 102, 101])).
% 0.19/0.50 tff(107,plain,
% 0.19/0.50 (((~(p1(Y!4) | (~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~((~p1(Y!4)) | ![X: $i] : (p1(X) | (~r1(Y!4, X))) | ![X: $i] : ((~r1(Y!4, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))) | (p1(Y!4) | (~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(108,plain,
% 0.19/0.50 (p1(Y!4) | (~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.19/0.50 tff(109,plain,
% 0.19/0.50 ((~(p1(Y!4) | (~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | p1(Y!4) | (~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(110,plain,
% 0.19/0.50 (p1(Y!4) | (~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.19/0.50 tff(111,plain,
% 0.19/0.50 (p1(Y!4) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[110, 78])).
% 0.19/0.50 tff(112,plain,
% 0.19/0.50 (p1(Y!4)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[111, 43])).
% 0.19/0.50 tff(113,plain,
% 0.19/0.50 (((~(p1(Y!4) | (~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~((~p1(Y!4)) | ![X: $i] : (p1(X) | (~r1(Y!4, X))) | ![X: $i] : ((~r1(Y!4, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))) | ((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(114,plain,
% 0.19/0.50 ((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[113, 106])).
% 0.19/0.50 tff(115,plain,
% 0.19/0.50 ((~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))) | (~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(116,plain,
% 0.19/0.50 ((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.19/0.50 tff(117,plain,
% 0.19/0.50 (![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[116, 78])).
% 0.19/0.50 tff(118,assumption,(~((~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))), introduced(assumption)).
% 0.19/0.50 tff(119,plain,
% 0.19/0.50 (((~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | r1(Y!4, tptp_fun_X_10(Y!4))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(120,plain,
% 0.19/0.50 (r1(Y!4, tptp_fun_X_10(Y!4))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.19/0.50 tff(121,plain,
% 0.19/0.50 (((~![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))) | ((~r1(Y!4, tptp_fun_X_10(Y!4))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_10(Y!4), Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))) <=> ((~![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))) | (~r1(Y!4, tptp_fun_X_10(Y!4))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_10(Y!4), Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(122,plain,
% 0.19/0.50 ((~![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))) | ((~r1(Y!4, tptp_fun_X_10(Y!4))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_10(Y!4), Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(123,plain,
% 0.19/0.50 ((~![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))) | (~r1(Y!4, tptp_fun_X_10(Y!4))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_10(Y!4), Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.19/0.50 tff(124,plain,
% 0.19/0.50 (![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_10(Y!4), Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[123, 120, 117])).
% 0.19/0.50 tff(125,plain,
% 0.19/0.50 (((~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(126,plain,
% 0.19/0.50 (r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[125, 118])).
% 0.19/0.50 tff(127,plain,
% 0.19/0.50 (((~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~p1(tptp_fun_Y_11(Y!4)))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(128,plain,
% 0.19/0.50 (~p1(tptp_fun_Y_11(Y!4))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[127, 118])).
% 0.19/0.50 tff(129,plain,
% 0.19/0.50 (((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_10(Y!4), Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))) | (p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~((~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4)))))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_10(Y!4), Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~((~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4)))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(130,plain,
% 0.19/0.50 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_10(Y!4), Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))) | (p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~((~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4)))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(131,plain,
% 0.19/0.50 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_10(Y!4), Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~((~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.19/0.50 tff(132,plain,
% 0.19/0.50 (~((~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4)))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[131, 128, 126, 124])).
% 0.19/0.50 tff(133,plain,
% 0.19/0.50 (((~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4))))) | p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(134,plain,
% 0.19/0.50 (p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.19/0.50 tff(135,plain,
% 0.19/0.50 (((~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4))))) | r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(136,plain,
% 0.19/0.50 (r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[135, 132])).
% 0.19/0.50 tff(137,plain,
% 0.19/0.50 (((~p1(tptp_fun_Y_11(Y!4))) | p1(tptp_fun_X_9(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_9(tptp_fun_Y_11(Y!4))))) | p1(tptp_fun_Y_11(Y!4))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(138,plain,
% 0.19/0.50 ((~p1(tptp_fun_Y_11(Y!4))) | p1(tptp_fun_X_9(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_9(tptp_fun_Y_11(Y!4))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[137, 128])).
% 0.19/0.50 tff(139,plain,
% 0.19/0.50 (((~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(140,plain,
% 0.19/0.50 (![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[139, 118])).
% 0.19/0.50 tff(141,plain,
% 0.19/0.50 (((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | ((~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~((~p1(tptp_fun_Y_11(Y!4))) | p1(tptp_fun_X_9(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_9(tptp_fun_Y_11(Y!4)))))) | ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_11(Y!4), X))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~((~p1(tptp_fun_Y_11(Y!4))) | p1(tptp_fun_X_9(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_9(tptp_fun_Y_11(Y!4)))))) | ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_11(Y!4), X))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(142,plain,
% 0.19/0.50 (((~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~((~p1(tptp_fun_Y_11(Y!4))) | p1(tptp_fun_X_9(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_9(tptp_fun_Y_11(Y!4)))))) | ![X: $i] : ((~r1(tptp_fun_Y_11(Y!4), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) <=> ((~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~((~p1(tptp_fun_Y_11(Y!4))) | p1(tptp_fun_X_9(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_9(tptp_fun_Y_11(Y!4)))))) | ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_11(Y!4), X))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(143,plain,
% 0.19/0.50 (((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | ((~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~((~p1(tptp_fun_Y_11(Y!4))) | p1(tptp_fun_X_9(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_9(tptp_fun_Y_11(Y!4)))))) | ![X: $i] : ((~r1(tptp_fun_Y_11(Y!4), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | ((~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~((~p1(tptp_fun_Y_11(Y!4))) | p1(tptp_fun_X_9(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_9(tptp_fun_Y_11(Y!4)))))) | ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_11(Y!4), X)))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[142])).
% 0.19/0.50 tff(144,plain,
% 0.19/0.50 (((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | ((~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~((~p1(tptp_fun_Y_11(Y!4))) | p1(tptp_fun_X_9(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_9(tptp_fun_Y_11(Y!4)))))) | ![X: $i] : ((~r1(tptp_fun_Y_11(Y!4), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~((~p1(tptp_fun_Y_11(Y!4))) | p1(tptp_fun_X_9(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_9(tptp_fun_Y_11(Y!4)))))) | ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_11(Y!4), X))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[143, 141])).
% 0.19/0.50 tff(145,plain,
% 0.19/0.50 ((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | ((~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~((~p1(tptp_fun_Y_11(Y!4))) | p1(tptp_fun_X_9(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_9(tptp_fun_Y_11(Y!4)))))) | ![X: $i] : ((~r1(tptp_fun_Y_11(Y!4), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(146,plain,
% 0.19/0.50 ((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~((~p1(tptp_fun_Y_11(Y!4))) | p1(tptp_fun_X_9(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_9(tptp_fun_Y_11(Y!4)))))) | ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_11(Y!4), X)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.19/0.50 tff(147,plain,
% 0.19/0.50 (![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_11(Y!4), X)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[146, 126, 140, 138])).
% 0.19/0.50 tff(148,plain,
% 0.19/0.50 (((~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_11(Y!4), X)))) | ((~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), Y))))) <=> ((~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_11(Y!4), X)))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), Y))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(149,plain,
% 0.19/0.50 (((~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), Y))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4))))) <=> ((~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), Y))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(150,plain,
% 0.19/0.50 (((~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_11(Y!4), X)))) | ((~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), Y))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))))) <=> ((~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_11(Y!4), X)))) | ((~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), Y)))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[149])).
% 0.19/0.50 tff(151,plain,
% 0.19/0.50 (((~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_11(Y!4), X)))) | ((~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), Y))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))))) <=> ((~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_11(Y!4), X)))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), Y))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[150, 148])).
% 0.19/0.50 tff(152,plain,
% 0.19/0.50 ((~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_11(Y!4), X)))) | ((~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), Y))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(153,plain,
% 0.19/0.50 ((~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_11(Y!4), X)))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), Y)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.19/0.50 tff(154,plain,
% 0.19/0.50 (![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), Y)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[153, 147, 136, 134])).
% 0.19/0.50 tff(155,plain,
% 0.19/0.50 (((~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4))))) | r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4)))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(156,plain,
% 0.19/0.50 (r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[155, 132])).
% 0.19/0.50 tff(157,plain,
% 0.19/0.50 (((~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4))))) | (~p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(158,plain,
% 0.19/0.50 (~p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[157, 132])).
% 0.19/0.50 tff(159,plain,
% 0.19/0.50 (((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), Y)))) | (p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4)))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), Y)))) | p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(160,plain,
% 0.19/0.50 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), Y)))) | (p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4)))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(161,plain,
% 0.19/0.50 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), Y)))) | p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.19/0.50 tff(162,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[161, 158, 156, 154])).
% 0.19/0.50 tff(163,plain,((~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(164,assumption,(![X: $i] : (p1(X) | (~r1(Y!4, X)))), introduced(assumption)).
% 0.19/0.50 tff(165,plain,
% 0.19/0.50 (~(p1(X!5) | (~r1(Y!4, X!5)))),
% 0.19/0.50 inference(and_elim,[status(thm)],[36])).
% 0.19/0.50 tff(166,plain,
% 0.19/0.50 (r1(Y!4, X!5)),
% 0.19/0.50 inference(or_elim,[status(thm)],[165])).
% 0.19/0.50 tff(167,plain,
% 0.19/0.50 (~p1(X!5)),
% 0.19/0.50 inference(or_elim,[status(thm)],[165])).
% 0.19/0.50 tff(168,plain,
% 0.19/0.50 (((~![X: $i] : (p1(X) | (~r1(Y!4, X)))) | (p1(X!5) | (~r1(Y!4, X!5)))) <=> ((~![X: $i] : (p1(X) | (~r1(Y!4, X)))) | p1(X!5) | (~r1(Y!4, X!5)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(169,plain,
% 0.19/0.50 ((~![X: $i] : (p1(X) | (~r1(Y!4, X)))) | (p1(X!5) | (~r1(Y!4, X!5)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(170,plain,
% 0.19/0.50 ((~![X: $i] : (p1(X) | (~r1(Y!4, X)))) | p1(X!5) | (~r1(Y!4, X!5))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.19/0.50 tff(171,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[170, 167, 166, 164])).
% 0.19/0.50 tff(172,plain,(~![X: $i] : (p1(X) | (~r1(Y!4, X)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(173,plain,
% 0.19/0.50 (((~(p1(Y!4) | (~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~((~p1(Y!4)) | ![X: $i] : (p1(X) | (~r1(Y!4, X))) | ![X: $i] : ((~r1(Y!4, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | (~p1(tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))) | ((~p1(Y!4)) | ![X: $i] : (p1(X) | (~r1(Y!4, X))) | ![X: $i] : ((~r1(Y!4, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(174,plain,
% 0.19/0.51 ((~p1(Y!4)) | ![X: $i] : (p1(X) | (~r1(Y!4, X))) | ![X: $i] : ((~r1(Y!4, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[173, 106])).
% 0.19/0.51 tff(175,plain,
% 0.19/0.51 ((~((~p1(Y!4)) | ![X: $i] : (p1(X) | (~r1(Y!4, X))) | ![X: $i] : ((~r1(Y!4, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~p1(Y!4)) | ![X: $i] : (p1(X) | (~r1(Y!4, X))) | ![X: $i] : ((~r1(Y!4, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(176,plain,
% 0.19/0.51 ((~p1(Y!4)) | ![X: $i] : (p1(X) | (~r1(Y!4, X))) | ![X: $i] : ((~r1(Y!4, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[175, 174])).
% 0.19/0.51 tff(177,plain,
% 0.19/0.51 ((~p1(Y!4)) | ![X: $i] : ((~r1(Y!4, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[176, 172, 163])).
% 0.19/0.51 tff(178,plain,
% 0.19/0.51 (![X: $i] : ((~r1(Y!4, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[177, 112])).
% 0.19/0.51 tff(179,plain,
% 0.19/0.51 (^[Y: $i] : refl(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(180,plain,
% 0.19/0.51 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[179])).
% 0.19/0.51 tff(181,plain,
% 0.19/0.51 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(182,plain,
% 0.19/0.51 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[181])).
% 0.19/0.51 tff(183,plain,
% 0.19/0.51 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[182, 180])).
% 0.19/0.51 tff(184,plain,
% 0.19/0.51 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))),
% 0.19/0.51 inference(and_elim,[status(thm)],[36])).
% 0.19/0.51 tff(185,plain,
% 0.19/0.51 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.19/0.51 tff(186,plain,
% 0.19/0.51 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | ((~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(187,plain,
% 0.19/0.51 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | ((~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(188,plain,
% 0.19/0.51 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.19/0.51 tff(189,plain,
% 0.19/0.51 (![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[188, 185, 92])).
% 0.19/0.51 tff(190,plain,
% 0.19/0.51 (((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) | ((~r1(Y!2, X!3)) | ![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) <=> ((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) | (~r1(Y!2, X!3)) | ![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(191,plain,
% 0.19/0.51 ((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) | ((~r1(Y!2, X!3)) | ![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(192,plain,
% 0.19/0.51 ((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) | (~r1(Y!2, X!3)) | ![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.19/0.51 tff(193,plain,
% 0.19/0.51 (![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[192, 97, 189])).
% 0.19/0.51 tff(194,plain,
% 0.19/0.51 (((~![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ((~r1(X!3, Y!4)) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) <=> ((~![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~r1(X!3, Y!4)) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(195,plain,
% 0.19/0.51 ((~![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ((~r1(X!3, Y!4)) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(196,plain,
% 0.19/0.51 ((~![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~r1(X!3, Y!4)) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.19/0.51 tff(197,plain,
% 0.19/0.51 (![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[196, 102, 193])).
% 0.19/0.51 tff(198,plain,
% 0.19/0.51 (((~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | ((~r1(Y!4, X!6)) | (~(p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6))))) | ![Y: $i] : ((~r1(X!6, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) <=> ((~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(Y!4, X!6)) | (~(p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6))))) | ![Y: $i] : ((~r1(X!6, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(199,plain,
% 0.19/0.51 ((~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | ((~r1(Y!4, X!6)) | (~(p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6))))) | ![Y: $i] : ((~r1(X!6, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(200,plain,
% 0.19/0.51 ((~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(Y!4, X!6)) | (~(p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6))))) | ![Y: $i] : ((~r1(X!6, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.19/0.51 tff(201,plain,
% 0.19/0.51 ((~(p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6))))) | ![Y: $i] : ((~r1(X!6, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[200, 37, 197])).
% 0.19/0.51 tff(202,plain,
% 0.19/0.51 (![Y: $i] : ((~r1(X!6, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[201, 1])).
% 0.19/0.51 tff(203,assumption,(![Y: $i] : ((~r1(X!6, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))), introduced(assumption)).
% 0.19/0.51 tff(204,assumption,(~((~r1(X!6, tptp_fun_Y_7(X!6))) | (~p1(tptp_fun_Y_7(X!6))) | p1(tptp_fun_X_8(X!6)) | (~r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6))))), introduced(assumption)).
% 0.19/0.51 tff(205,plain,
% 0.19/0.51 (((~r1(X!6, tptp_fun_Y_7(X!6))) | (~p1(tptp_fun_Y_7(X!6))) | p1(tptp_fun_X_8(X!6)) | (~r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6)))) | r1(X!6, tptp_fun_Y_7(X!6))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(206,plain,
% 0.19/0.51 (r1(X!6, tptp_fun_Y_7(X!6))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[205, 204])).
% 0.19/0.51 tff(207,plain,
% 0.19/0.51 (((~![Y: $i] : ((~r1(X!6, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ((~r1(X!6, tptp_fun_Y_7(X!6))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(X!6), X))))) <=> ((~![Y: $i] : ((~r1(X!6, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | (~r1(X!6, tptp_fun_Y_7(X!6))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(X!6), X))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(208,plain,
% 0.19/0.51 ((~![Y: $i] : ((~r1(X!6, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ((~r1(X!6, tptp_fun_Y_7(X!6))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(X!6), X))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(209,plain,
% 0.19/0.51 ((~![Y: $i] : ((~r1(X!6, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | (~r1(X!6, tptp_fun_Y_7(X!6))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(X!6), X)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.19/0.51 tff(210,plain,
% 0.19/0.51 (![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(X!6), X)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[209, 206, 203])).
% 0.19/0.51 tff(211,plain,
% 0.19/0.51 (((~r1(X!6, tptp_fun_Y_7(X!6))) | (~p1(tptp_fun_Y_7(X!6))) | p1(tptp_fun_X_8(X!6)) | (~r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6)))) | r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(212,plain,
% 0.19/0.51 (r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[211, 204])).
% 0.19/0.51 tff(213,plain,
% 0.19/0.51 (((~r1(X!6, tptp_fun_Y_7(X!6))) | (~p1(tptp_fun_Y_7(X!6))) | p1(tptp_fun_X_8(X!6)) | (~r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6)))) | (~p1(tptp_fun_X_8(X!6)))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(214,plain,
% 0.19/0.51 (~p1(tptp_fun_X_8(X!6))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[213, 204])).
% 0.19/0.51 tff(215,plain,
% 0.19/0.51 (((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(X!6), X)))) | (p1(tptp_fun_X_8(X!6)) | (~r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6))))) <=> ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(X!6), X)))) | p1(tptp_fun_X_8(X!6)) | (~r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(216,plain,
% 0.19/0.51 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(X!6), X)))) | (p1(tptp_fun_X_8(X!6)) | (~r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(217,plain,
% 0.19/0.51 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(X!6), X)))) | p1(tptp_fun_X_8(X!6)) | (~r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.19/0.51 tff(218,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[217, 214, 212, 210])).
% 0.19/0.51 tff(219,plain,(((~r1(X!6, tptp_fun_Y_7(X!6))) | (~p1(tptp_fun_Y_7(X!6))) | p1(tptp_fun_X_8(X!6)) | (~r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6)))) | (~![Y: $i] : ((~r1(X!6, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51 tff(220,plain,
% 0.19/0.51 ((~r1(X!6, tptp_fun_Y_7(X!6))) | (~p1(tptp_fun_Y_7(X!6))) | p1(tptp_fun_X_8(X!6)) | (~r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[219, 202])).
% 0.19/0.51 tff(221,plain,
% 0.19/0.51 (((~![X: $i] : ((~r1(Y!4, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | ((~r1(Y!4, X!6)) | (~((~r1(X!6, tptp_fun_Y_7(X!6))) | (~p1(tptp_fun_Y_7(X!6))) | p1(tptp_fun_X_8(X!6)) | (~r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6))))))) <=> ((~![X: $i] : ((~r1(Y!4, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | (~r1(Y!4, X!6)) | (~((~r1(X!6, tptp_fun_Y_7(X!6))) | (~p1(tptp_fun_Y_7(X!6))) | p1(tptp_fun_X_8(X!6)) | (~r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(222,plain,
% 0.19/0.51 ((~![X: $i] : ((~r1(Y!4, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | ((~r1(Y!4, X!6)) | (~((~r1(X!6, tptp_fun_Y_7(X!6))) | (~p1(tptp_fun_Y_7(X!6))) | p1(tptp_fun_X_8(X!6)) | (~r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6))))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(223,plain,
% 0.19/0.51 ((~![X: $i] : ((~r1(Y!4, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | (~r1(Y!4, X!6)) | (~((~r1(X!6, tptp_fun_Y_7(X!6))) | (~p1(tptp_fun_Y_7(X!6))) | p1(tptp_fun_X_8(X!6)) | (~r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6)))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.19/0.51 tff(224,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[223, 37, 220, 178])).
% 0.19/0.51 tff(225,plain,(~(p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51 tff(226,plain,
% 0.19/0.51 ((p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6)))) | (~p1(tptp_fun_Y_1(X!6)))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(227,plain,
% 0.19/0.51 (~p1(tptp_fun_Y_1(X!6))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[226, 225])).
% 0.19/0.52 tff(228,plain,
% 0.19/0.52 ((p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6)))) | r1(X!6, tptp_fun_Y_1(X!6))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(229,plain,
% 0.19/0.52 (r1(X!6, tptp_fun_Y_1(X!6))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[228, 225])).
% 0.19/0.52 tff(230,assumption,(r1(X!6, tptp_fun_Y_1(X!6))), introduced(assumption)).
% 0.19/0.52 tff(231,assumption,(~p1(tptp_fun_Y_1(X!6))), introduced(assumption)).
% 0.19/0.52 tff(232,plain,
% 0.19/0.52 (^[Y: $i] : refl((p1(Y) | (~r1(X!6, Y))) <=> (p1(Y) | (~r1(X!6, Y))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(233,plain,
% 0.19/0.52 (![Y: $i] : (p1(Y) | (~r1(X!6, Y))) <=> ![Y: $i] : (p1(Y) | (~r1(X!6, Y)))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[232])).
% 0.19/0.52 tff(234,plain,
% 0.19/0.52 (![Y: $i] : (p1(Y) | (~r1(X!6, Y)))),
% 0.19/0.52 inference(and_elim,[status(thm)],[36])).
% 0.19/0.52 tff(235,plain,
% 0.19/0.52 (![Y: $i] : (p1(Y) | (~r1(X!6, Y)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.19/0.52 tff(236,plain,
% 0.19/0.52 (((~![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) | (p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) | p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(237,plain,
% 0.19/0.52 ((~![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) | (p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(238,plain,
% 0.19/0.52 ((~![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) | p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.19/0.52 tff(239,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[238, 235, 231, 230])).
% 0.19/0.52 tff(240,plain,((~r1(X!6, tptp_fun_Y_1(X!6))) | p1(tptp_fun_Y_1(X!6))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.52 tff(241,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[240, 229, 227])).
% 0.19/0.52 % SZS output end Proof
%------------------------------------------------------------------------------