TSTP Solution File: LCL658+1.001 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL658+1.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.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 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL658+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n010.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Sep 1 23:12:28 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(r1_type, type, (
% 0.20/0.41 r1: ( $i * $i ) > $o)).
% 0.20/0.41 tff(tptp_fun_Y_1_type, type, (
% 0.20/0.41 tptp_fun_Y_1: $i > $i)).
% 0.20/0.41 tff(tptp_fun_X_12_type, type, (
% 0.20/0.41 tptp_fun_X_12: $i)).
% 0.20/0.41 tff(p1_type, type, (
% 0.20/0.41 p1: $i > $o)).
% 0.20/0.41 tff(tptp_fun_Y_6_type, type, (
% 0.20/0.41 tptp_fun_Y_6: $i > $i)).
% 0.20/0.41 tff(tptp_fun_X_2_type, type, (
% 0.20/0.41 tptp_fun_X_2: $i > $i)).
% 0.20/0.41 tff(tptp_fun_Y_10_type, type, (
% 0.20/0.41 tptp_fun_Y_10: $i)).
% 0.20/0.41 tff(tptp_fun_X_11_type, type, (
% 0.20/0.41 tptp_fun_X_11: $i)).
% 0.20/0.41 tff(tptp_fun_X_0_type, type, (
% 0.20/0.41 tptp_fun_X_0: $i)).
% 0.20/0.41 tff(tptp_fun_Y_9_type, type, (
% 0.20/0.41 tptp_fun_Y_9: $i > $i)).
% 0.20/0.41 tff(tptp_fun_X_8_type, type, (
% 0.20/0.41 tptp_fun_X_8: $i > $i)).
% 0.20/0.41 tff(tptp_fun_X_7_type, type, (
% 0.20/0.41 tptp_fun_X_7: $i > $i)).
% 0.20/0.41 tff(tptp_fun_X_5_type, type, (
% 0.20/0.41 tptp_fun_X_5: $i > $i)).
% 0.20/0.41 tff(tptp_fun_X_3_type, type, (
% 0.20/0.41 tptp_fun_X_3: $i > $i)).
% 0.20/0.41 tff(tptp_fun_Y_4_type, type, (
% 0.20/0.41 tptp_fun_Y_4: $i > $i)).
% 0.20/0.41 tff(1,assumption,(~(p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12))))), introduced(assumption)).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 ((p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12)))) | r1(X!12, tptp_fun_Y_6(X!12))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 (r1(X!12, tptp_fun_Y_6(X!12))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.20/0.41 tff(4,plain,
% 0.20/0.41 ((p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12)))) | (~p1(tptp_fun_Y_6(X!12)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 (~p1(tptp_fun_Y_6(X!12))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.20/0.41 tff(6,plain,
% 0.20/0.41 (^[Y: $i] : refl((p1(Y) | (~r1(X!12, Y))) <=> (p1(Y) | (~r1(X!12, Y))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(7,plain,
% 0.20/0.41 (![Y: $i] : (p1(Y) | (~r1(X!12, Y))) <=> ![Y: $i] : (p1(Y) | (~r1(X!12, Y)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 ((![Y: $i] : ((~r1(X!0, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | ((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) & (((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (p1(tptp_fun_X_8(Y)) & r1(Y, tptp_fun_X_8(Y)) & (~(p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))) & (r1(X!0, Y!10) & (~(p1(X!11) | (~r1(Y!10, X!11)))) & r1(Y!10, X!12) & ![Y: $i] : (p1(Y) | (~r1(X!12, Y))) & ![X: $i] : (p1(X) | (~r1(Y!10, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | ((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) & (((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (p1(tptp_fun_X_8(Y)) & r1(Y, tptp_fun_X_8(Y)) & (~(p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))) & r1(X!0, Y!10) & (~(p1(X!11) | (~r1(Y!10, X!11)))) & r1(Y!10, X!12) & ![Y: $i] : (p1(Y) | (~r1(X!12, Y))) & ![X: $i] : (p1(X) | (~r1(Y!10, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(9,plain,
% 0.20/0.42 ((r1(X!0, Y!10) & (~(p1(X!11) | (~r1(Y!10, X!11)))) & (r1(Y!10, X!12) & ![Y: $i] : (p1(Y) | (~r1(X!12, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!10, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))) <=> (r1(X!0, Y!10) & (~(p1(X!11) | (~r1(Y!10, X!11)))) & r1(Y!10, X!12) & ![Y: $i] : (p1(Y) | (~r1(X!12, Y))) & ![X: $i] : (p1(X) | (~r1(Y!10, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(10,plain,
% 0.20/0.42 (^[X: $i] : rewrite((p1(X) | (~r1(Y!10, X)) | ((~(~p1(tptp_fun_Y_1(X)))) & (~(~r1(X, tptp_fun_Y_1(X)))) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))) <=> (p1(X) | (~r1(Y!10, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(11,plain,
% 0.20/0.42 (![X: $i] : (p1(X) | (~r1(Y!10, X)) | ((~(~p1(tptp_fun_Y_1(X)))) & (~(~r1(X, tptp_fun_Y_1(X)))) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))) <=> ![X: $i] : (p1(X) | (~r1(Y!10, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.42 tff(12,plain,
% 0.20/0.42 (((~(~r1(Y!10, X!12))) & ![Y: $i] : (p1(Y) | (~r1(X!12, Y)))) <=> (r1(Y!10, X!12) & ![Y: $i] : (p1(Y) | (~r1(X!12, Y))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 ((~(~r1(X!0, Y!10))) <=> r1(X!0, Y!10)),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 (((~(~r1(X!0, Y!10))) & (~(p1(X!11) | (~r1(Y!10, X!11)))) & ((~(~r1(Y!10, X!12))) & ![Y: $i] : (p1(Y) | (~r1(X!12, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!10, X)) | ((~(~p1(tptp_fun_Y_1(X)))) & (~(~r1(X, tptp_fun_Y_1(X)))) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))) <=> (r1(X!0, Y!10) & (~(p1(X!11) | (~r1(Y!10, X!11)))) & (r1(Y!10, X!12) & ![Y: $i] : (p1(Y) | (~r1(X!12, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!10, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[13, 12, 11])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 (((~(~r1(X!0, Y!10))) & (~(p1(X!11) | (~r1(Y!10, X!11)))) & ((~(~r1(Y!10, X!12))) & ![Y: $i] : (p1(Y) | (~r1(X!12, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!10, X)) | ((~(~p1(tptp_fun_Y_1(X)))) & (~(~r1(X, tptp_fun_Y_1(X)))) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))) <=> (r1(X!0, Y!10) & (~(p1(X!11) | (~r1(Y!10, X!11)))) & r1(Y!10, X!12) & ![Y: $i] : (p1(Y) | (~r1(X!12, Y))) & ![X: $i] : (p1(X) | (~r1(Y!10, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[14, 9])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 (^[Y: $i] : rewrite(((~r1(X!0, 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)))) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))) | ((~(~p1(tptp_fun_X_3(Y)))) & (~(~r1(Y, tptp_fun_X_3(Y)))) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ((~(~p1(Y))) & (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | ((~p1(tptp_fun_X_7(Y))) & (~(~r1(Y, tptp_fun_X_7(Y)))) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ((~(~p1(tptp_fun_X_8(Y)))) & (~(~r1(Y, tptp_fun_X_8(Y)))) & (~(p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))) | ((~p1(tptp_fun_X_7(Y))) & (~(~r1(Y, tptp_fun_X_7(Y)))) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) <=> ((~r1(X!0, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | ((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) & (((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (p1(tptp_fun_X_8(Y)) & r1(Y, tptp_fun_X_8(Y)) & (~(p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 (![Y: $i] : ((~r1(X!0, 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)))) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))) | ((~(~p1(tptp_fun_X_3(Y)))) & (~(~r1(Y, tptp_fun_X_3(Y)))) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ((~(~p1(Y))) & (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | ((~p1(tptp_fun_X_7(Y))) & (~(~r1(Y, tptp_fun_X_7(Y)))) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ((~(~p1(tptp_fun_X_8(Y)))) & (~(~r1(Y, tptp_fun_X_8(Y)))) & (~(p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))) | ((~p1(tptp_fun_X_7(Y))) & (~(~r1(Y, tptp_fun_X_7(Y)))) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | ((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) & (((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (p1(tptp_fun_X_8(Y)) & r1(Y, tptp_fun_X_8(Y)) & (~(p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 ((![Y: $i] : ((~r1(X!0, 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)))) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))) | ((~(~p1(tptp_fun_X_3(Y)))) & (~(~r1(Y, tptp_fun_X_3(Y)))) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ((~(~p1(Y))) & (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | ((~p1(tptp_fun_X_7(Y))) & (~(~r1(Y, tptp_fun_X_7(Y)))) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ((~(~p1(tptp_fun_X_8(Y)))) & (~(~r1(Y, tptp_fun_X_8(Y)))) & (~(p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))) | ((~p1(tptp_fun_X_7(Y))) & (~(~r1(Y, tptp_fun_X_7(Y)))) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ((~(~r1(X!0, Y!10))) & (~(p1(X!11) | (~r1(Y!10, X!11)))) & ((~(~r1(Y!10, X!12))) & ![Y: $i] : (p1(Y) | (~r1(X!12, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!10, X)) | ((~(~p1(tptp_fun_Y_1(X)))) & (~(~r1(X, tptp_fun_Y_1(X)))) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | ((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) & (((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (p1(tptp_fun_X_8(Y)) & r1(Y, tptp_fun_X_8(Y)) & (~(p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))) & (r1(X!0, Y!10) & (~(p1(X!11) | (~r1(Y!10, X!11)))) & r1(Y!10, X!12) & ![Y: $i] : (p1(Y) | (~r1(X!12, Y))) & ![X: $i] : (p1(X) | (~r1(Y!10, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[17, 15])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 ((![Y: $i] : ((~r1(X!0, 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)))) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))) | ((~(~p1(tptp_fun_X_3(Y)))) & (~(~r1(Y, tptp_fun_X_3(Y)))) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ((~(~p1(Y))) & (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | ((~p1(tptp_fun_X_7(Y))) & (~(~r1(Y, tptp_fun_X_7(Y)))) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ((~(~p1(tptp_fun_X_8(Y)))) & (~(~r1(Y, tptp_fun_X_8(Y)))) & (~(p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))) | ((~p1(tptp_fun_X_7(Y))) & (~(~r1(Y, tptp_fun_X_7(Y)))) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ((~(~r1(X!0, Y!10))) & (~(p1(X!11) | (~r1(Y!10, X!11)))) & ((~(~r1(Y!10, X!12))) & ![Y: $i] : (p1(Y) | (~r1(X!12, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!10, X)) | ((~(~p1(tptp_fun_Y_1(X)))) & (~(~r1(X, tptp_fun_Y_1(X)))) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | ((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) & (((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (p1(tptp_fun_X_8(Y)) & r1(Y, tptp_fun_X_8(Y)) & (~(p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))) & r1(X!0, Y!10) & (~(p1(X!11) | (~r1(Y!10, X!11)))) & r1(Y!10, X!12) & ![Y: $i] : (p1(Y) | (~r1(X!12, Y))) & ![X: $i] : (p1(X) | (~r1(Y!10, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[18, 8])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (?[X: $i] : (~((~![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)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, 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] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~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] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) <=> ?[X: $i] : (~((~![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)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, 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] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~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] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(21,plain,
% 0.20/0.43 ((~(~?[X: $i] : (~((~![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)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, 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] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~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] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))) <=> ?[X: $i] : (~((~![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)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, 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] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~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] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(22,plain,
% 0.20/0.43 ((~?[X: $i] : (~((~![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)) | 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)))))))))))) <=> (~?[X: $i] : (~((~![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)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, 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] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~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] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(23,plain,
% 0.20/0.43 ((~(~?[X: $i] : (~((~![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)) | 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))))))))))))) <=> (~(~?[X: $i] : (~((~![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)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, 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] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~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] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[22])).
% 0.20/0.43 tff(24,plain,
% 0.20/0.43 ((~(~?[X: $i] : (~((~![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)) | 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))))))))))))) <=> ?[X: $i] : (~((~![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)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, 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] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~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] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[23, 21])).
% 0.20/0.43 tff(25,axiom,(~(~?[X: $i] : (~((~![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)) | 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))))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','main')).
% 0.20/0.44 tff(26,plain,
% 0.20/0.44 (?[X: $i] : (~((~![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)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, 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] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~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] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.20/0.44 tff(27,plain,
% 0.20/0.44 (?[X: $i] : (~((~![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)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, 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] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~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] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[26, 20])).
% 0.20/0.44 tff(28,plain,
% 0.20/0.44 (![Y: $i] : ((~r1(X!0, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | ((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) & (((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (p1(tptp_fun_X_8(Y)) & r1(Y, tptp_fun_X_8(Y)) & (~(p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))) & r1(X!0, Y!10) & (~(p1(X!11) | (~r1(Y!10, X!11)))) & r1(Y!10, X!12) & ![Y: $i] : (p1(Y) | (~r1(X!12, Y))) & ![X: $i] : (p1(X) | (~r1(Y!10, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[27, 19])).
% 0.20/0.44 tff(29,plain,
% 0.20/0.44 (![Y: $i] : (p1(Y) | (~r1(X!12, Y)))),
% 0.20/0.44 inference(and_elim,[status(thm)],[28])).
% 0.20/0.44 tff(30,plain,
% 0.20/0.44 (![Y: $i] : (p1(Y) | (~r1(X!12, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[29, 7])).
% 0.20/0.44 tff(31,plain,
% 0.20/0.44 (((~![Y: $i] : (p1(Y) | (~r1(X!12, Y)))) | (p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(X!12, Y)))) | p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(32,plain,
% 0.20/0.44 ((~![Y: $i] : (p1(Y) | (~r1(X!12, Y)))) | (p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(33,plain,
% 0.20/0.44 ((~![Y: $i] : (p1(Y) | (~r1(X!12, Y)))) | p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.44 tff(34,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[33, 30, 5, 3])).
% 0.20/0.44 tff(35,plain,(p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(36,plain,
% 0.20/0.44 (r1(X!0, Y!10)),
% 0.20/0.44 inference(and_elim,[status(thm)],[28])).
% 0.20/0.44 tff(37,plain,
% 0.20/0.44 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))))))) <=> ((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(38,plain,
% 0.20/0.44 (![Y: $i] : ((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.44 tff(39,plain,
% 0.20/0.44 (^[Y: $i] : refl(((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))))))) <=> ((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(40,plain,
% 0.20/0.44 (![Y: $i] : ((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.44 tff(41,plain,
% 0.20/0.44 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))))))) <=> ((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(42,plain,
% 0.20/0.44 (![Y: $i] : ((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.45 tff(43,plain,
% 0.20/0.45 (![Y: $i] : ((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[42, 40])).
% 0.20/0.45 tff(44,plain,
% 0.20/0.45 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | ((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) & (((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (p1(tptp_fun_X_8(Y)) & r1(Y, tptp_fun_X_8(Y)) & (~(p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))) <=> ((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(45,plain,
% 0.20/0.45 (![Y: $i] : ((~r1(X!0, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | ((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) & (((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (p1(tptp_fun_X_8(Y)) & r1(Y, tptp_fun_X_8(Y)) & (~(p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[44])).
% 0.20/0.45 tff(46,plain,
% 0.20/0.45 (![Y: $i] : ((~r1(X!0, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | ((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) & (((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (p1(tptp_fun_X_8(Y)) & r1(Y, tptp_fun_X_8(Y)) & (~(p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))))))),
% 0.20/0.45 inference(and_elim,[status(thm)],[28])).
% 0.20/0.45 tff(47,plain,
% 0.20/0.45 (![Y: $i] : ((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.45 tff(48,plain,
% 0.20/0.45 (![Y: $i] : ((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.20/0.45 tff(49,plain,
% 0.20/0.45 (![Y: $i] : ((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[48, 38])).
% 0.20/0.45 tff(50,plain,
% 0.20/0.45 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))) | ((~r1(X!0, Y!10)) | (~((~((~p1(Y!10)) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | ![X: $i] : ((~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))) | (~((~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(p1(Y!10) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))) | (~r1(X!0, Y!10)) | (~((~((~p1(Y!10)) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | ![X: $i] : ((~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))) | (~((~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(p1(Y!10) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(51,plain,
% 0.20/0.45 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))) | ((~r1(X!0, Y!10)) | (~((~((~p1(Y!10)) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | ![X: $i] : ((~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))) | (~((~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(p1(Y!10) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(52,plain,
% 0.20/0.45 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))) | (~r1(X!0, Y!10)) | (~((~((~p1(Y!10)) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | ![X: $i] : ((~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))) | (~((~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(p1(Y!10) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.45 tff(53,plain,
% 0.20/0.45 (~((~((~p1(Y!10)) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | ![X: $i] : ((~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))) | (~((~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(p1(Y!10) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[52, 49, 36])).
% 0.20/0.46 tff(54,plain,
% 0.20/0.46 (((~((~p1(Y!10)) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | ![X: $i] : ((~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))) | (~((~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(p1(Y!10) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))))) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(55,plain,
% 0.20/0.46 (![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.20/0.46 tff(56,plain,
% 0.20/0.46 (r1(Y!10, X!12)),
% 0.20/0.46 inference(and_elim,[status(thm)],[28])).
% 0.20/0.46 tff(57,plain,
% 0.20/0.46 (((~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | ((~r1(Y!10, X!12)) | (~(p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12))))) | ![Y: $i] : ((~r1(X!12, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) <=> ((~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(Y!10, X!12)) | (~(p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12))))) | ![Y: $i] : ((~r1(X!12, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(58,plain,
% 0.20/0.46 ((~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | ((~r1(Y!10, X!12)) | (~(p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12))))) | ![Y: $i] : ((~r1(X!12, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(59,plain,
% 0.20/0.46 ((~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(Y!10, X!12)) | (~(p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12))))) | ![Y: $i] : ((~r1(X!12, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.46 tff(60,plain,
% 0.20/0.46 ((~(p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12))))) | ![Y: $i] : ((~r1(X!12, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[59, 56, 55])).
% 0.20/0.46 tff(61,plain,
% 0.20/0.46 (![Y: $i] : ((~r1(X!12, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[60, 35])).
% 0.20/0.46 tff(62,assumption,(![X: $i] : (p1(X) | (~r1(Y!10, X)))), introduced(assumption)).
% 0.20/0.46 tff(63,plain,
% 0.20/0.46 (~(p1(X!11) | (~r1(Y!10, X!11)))),
% 0.20/0.46 inference(and_elim,[status(thm)],[28])).
% 0.20/0.46 tff(64,plain,
% 0.20/0.46 (r1(Y!10, X!11)),
% 0.20/0.46 inference(or_elim,[status(thm)],[63])).
% 0.20/0.46 tff(65,plain,
% 0.20/0.46 (~p1(X!11)),
% 0.20/0.46 inference(or_elim,[status(thm)],[63])).
% 0.20/0.46 tff(66,plain,
% 0.20/0.46 (((~![X: $i] : (p1(X) | (~r1(Y!10, X)))) | (p1(X!11) | (~r1(Y!10, X!11)))) <=> ((~![X: $i] : (p1(X) | (~r1(Y!10, X)))) | p1(X!11) | (~r1(Y!10, X!11)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(67,plain,
% 0.20/0.46 ((~![X: $i] : (p1(X) | (~r1(Y!10, X)))) | (p1(X!11) | (~r1(Y!10, X!11)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(68,plain,
% 0.20/0.46 ((~![X: $i] : (p1(X) | (~r1(Y!10, X)))) | p1(X!11) | (~r1(Y!10, X!11))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.20/0.46 tff(69,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[68, 65, 64, 62])).
% 0.20/0.46 tff(70,plain,(~![X: $i] : (p1(X) | (~r1(Y!10, X)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(71,assumption,(~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))), introduced(assumption)).
% 0.20/0.46 tff(72,plain,
% 0.20/0.46 ((p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | r1(Y!10, tptp_fun_X_7(Y!10))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(73,plain,
% 0.20/0.46 (r1(Y!10, tptp_fun_X_7(Y!10))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.20/0.46 tff(74,plain,
% 0.20/0.46 ((p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~p1(tptp_fun_X_7(Y!10)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(75,plain,
% 0.20/0.46 (~p1(tptp_fun_X_7(Y!10))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[74, 71])).
% 0.20/0.46 tff(76,plain,
% 0.20/0.46 (^[X: $i] : refl((p1(X) | (~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))) <=> (p1(X) | (~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(77,plain,
% 0.20/0.46 (![X: $i] : (p1(X) | (~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))) <=> ![X: $i] : (p1(X) | (~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[76])).
% 0.20/0.46 tff(78,plain,
% 0.20/0.46 (^[X: $i] : rewrite((p1(X) | (~r1(Y!10, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))) <=> (p1(X) | (~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(79,plain,
% 0.20/0.46 (![X: $i] : (p1(X) | (~r1(Y!10, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))) <=> ![X: $i] : (p1(X) | (~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[78])).
% 0.20/0.46 tff(80,plain,
% 0.20/0.46 (![X: $i] : (p1(X) | (~r1(Y!10, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))),
% 0.20/0.46 inference(and_elim,[status(thm)],[28])).
% 0.20/0.46 tff(81,plain,
% 0.20/0.46 (![X: $i] : (p1(X) | (~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.20/0.46 tff(82,plain,
% 0.20/0.46 (![X: $i] : (p1(X) | (~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.20/0.46 tff(83,plain,
% 0.20/0.46 (((~![X: $i] : (p1(X) | (~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))) | (p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~((~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | (~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10)))))))) <=> ((~![X: $i] : (p1(X) | (~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))) | p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~((~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | (~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10)))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(84,plain,
% 0.20/0.46 ((~![X: $i] : (p1(X) | (~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))) | (p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~((~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | (~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10)))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(85,plain,
% 0.20/0.46 ((~![X: $i] : (p1(X) | (~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))) | p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~((~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | (~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.20/0.46 tff(86,plain,
% 0.20/0.46 (~((~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | (~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10)))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[85, 82, 75, 73])).
% 0.20/0.46 tff(87,plain,
% 0.20/0.46 (((~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | (~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10))))) | p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(88,plain,
% 0.20/0.46 (p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.20/0.46 tff(89,plain,
% 0.20/0.46 (((~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | (~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10))))) | r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(90,plain,
% 0.20/0.46 (r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[89, 86])).
% 0.20/0.46 tff(91,plain,
% 0.20/0.46 ((p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(92,plain,
% 0.20/0.46 (![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[91, 71])).
% 0.20/0.46 tff(93,plain,
% 0.20/0.46 (((~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ((~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | (~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), X))))) <=> ((~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | (~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | (~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), X))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(94,plain,
% 0.20/0.46 ((~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ((~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | (~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), X))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(95,plain,
% 0.20/0.46 ((~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | (~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | (~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), X)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.46 tff(96,plain,
% 0.20/0.46 (![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), X)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[95, 92, 90, 88])).
% 0.20/0.46 tff(97,plain,
% 0.20/0.46 (((~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | (~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10))))) | r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(98,plain,
% 0.20/0.46 (r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[97, 86])).
% 0.20/0.46 tff(99,plain,
% 0.20/0.46 (((~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | (~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10))))) | (~p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(100,plain,
% 0.20/0.46 (~p1(tptp_fun_X_2(tptp_fun_X_7(Y!10)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[99, 86])).
% 0.20/0.46 tff(101,plain,
% 0.20/0.46 (((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), X)))) | (p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10)))))) <=> ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), X)))) | p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(102,plain,
% 0.20/0.46 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), X)))) | (p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10)))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(103,plain,
% 0.20/0.46 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), X)))) | p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.20/0.46 tff(104,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[103, 100, 98, 96])).
% 0.20/0.46 tff(105,plain,(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(106,assumption,(![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))), introduced(assumption)).
% 0.20/0.46 tff(107,plain,
% 0.20/0.46 (((~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | ((~r1(Y!10, X!12)) | (~(p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12))))))) <=> ((~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~r1(Y!10, X!12)) | (~(p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(108,plain,
% 0.20/0.46 ((~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | ((~r1(Y!10, X!12)) | (~(p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(109,plain,
% 0.20/0.46 ((~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~r1(Y!10, X!12)) | (~(p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.20/0.46 tff(110,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[109, 56, 106, 35])).
% 0.20/0.46 tff(111,plain,(~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(112,plain,
% 0.20/0.46 (((~((~p1(Y!10)) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | ![X: $i] : ((~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))) | (~((~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(p1(Y!10) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))))) | (p1(Y!10) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(113,plain,
% 0.20/0.46 (p1(Y!10) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[112, 53])).
% 0.20/0.46 tff(114,plain,
% 0.20/0.46 ((~(p1(Y!10) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | p1(Y!10) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(115,plain,
% 0.20/0.46 (p1(Y!10) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.20/0.46 tff(116,plain,
% 0.20/0.46 (p1(Y!10)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[115, 111, 105])).
% 0.20/0.46 tff(117,plain,
% 0.20/0.46 (((~((~p1(Y!10)) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | ![X: $i] : ((~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))) | (~((~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(p1(Y!10) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))))) | ((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(118,plain,
% 0.20/0.46 ((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[117, 53])).
% 0.20/0.46 tff(119,plain,
% 0.20/0.46 ((~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))) | (~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(120,plain,
% 0.20/0.46 ((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.20/0.46 tff(121,plain,
% 0.20/0.46 (![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[120, 105])).
% 0.20/0.46 tff(122,assumption,(~((~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))), introduced(assumption)).
% 0.20/0.46 tff(123,plain,
% 0.20/0.46 (((~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | r1(Y!10, tptp_fun_X_3(Y!10))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(124,plain,
% 0.20/0.47 (r1(Y!10, tptp_fun_X_3(Y!10))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.20/0.47 tff(125,plain,
% 0.20/0.47 (((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))) | ((~r1(Y!10, tptp_fun_X_3(Y!10))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))) <=> ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))) | (~r1(Y!10, tptp_fun_X_3(Y!10))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(126,plain,
% 0.20/0.47 ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))) | ((~r1(Y!10, tptp_fun_X_3(Y!10))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(127,plain,
% 0.20/0.47 ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))) | (~r1(Y!10, tptp_fun_X_3(Y!10))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.20/0.47 tff(128,plain,
% 0.20/0.47 (![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[127, 124, 121])).
% 0.20/0.47 tff(129,plain,
% 0.20/0.47 (((~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(130,plain,
% 0.20/0.47 (r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[129, 122])).
% 0.20/0.47 tff(131,plain,
% 0.20/0.47 (((~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~p1(tptp_fun_Y_4(Y!10)))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(132,plain,
% 0.20/0.47 (~p1(tptp_fun_Y_4(Y!10))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[131, 122])).
% 0.20/0.47 tff(133,plain,
% 0.20/0.47 (((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))) | (p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~((~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10)))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))) | (~p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)))))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))) | p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~((~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10)))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))) | (~p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(134,plain,
% 0.20/0.47 ((p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~((~p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10))))))) <=> (p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~((~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10)))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))) | (~p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(135,plain,
% 0.20/0.47 (((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))) | (p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~((~p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10)))))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))) | (p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~((~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10)))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))) | (~p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10))))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[134])).
% 0.20/0.47 tff(136,plain,
% 0.20/0.47 (((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))) | (p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~((~p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10)))))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))) | p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~((~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10)))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))) | (~p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[135, 133])).
% 0.20/0.47 tff(137,plain,
% 0.20/0.47 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))) | (p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~((~p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10)))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(138,plain,
% 0.20/0.47 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))) | p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~((~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10)))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))) | (~p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.20/0.47 tff(139,plain,
% 0.20/0.47 (~((~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10)))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))) | (~p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[138, 132, 130, 128])).
% 0.20/0.47 tff(140,plain,
% 0.20/0.47 (((~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10)))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))) | (~p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10))))) | p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(141,plain,
% 0.20/0.47 (p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.20/0.47 tff(142,plain,
% 0.20/0.47 (((~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10)))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))) | (~p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10))))) | r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(143,plain,
% 0.20/0.47 (r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[142, 139])).
% 0.20/0.47 tff(144,plain,
% 0.20/0.47 (((~p1(tptp_fun_Y_4(Y!10))) | p1(tptp_fun_X_5(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_5(tptp_fun_Y_4(Y!10))))) | p1(tptp_fun_Y_4(Y!10))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(145,plain,
% 0.20/0.47 ((~p1(tptp_fun_Y_4(Y!10))) | p1(tptp_fun_X_5(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_5(tptp_fun_Y_4(Y!10))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[144, 132])).
% 0.20/0.47 tff(146,plain,
% 0.20/0.47 (((~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(147,plain,
% 0.20/0.47 (![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[146, 122])).
% 0.20/0.47 tff(148,plain,
% 0.20/0.47 (((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | ((~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~((~p1(tptp_fun_Y_4(Y!10))) | p1(tptp_fun_X_5(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_5(tptp_fun_Y_4(Y!10)))))) | ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(Y!10), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~((~p1(tptp_fun_Y_4(Y!10))) | p1(tptp_fun_X_5(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_5(tptp_fun_Y_4(Y!10)))))) | ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(Y!10), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(149,plain,
% 0.20/0.47 ((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | ((~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~((~p1(tptp_fun_Y_4(Y!10))) | p1(tptp_fun_X_5(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_5(tptp_fun_Y_4(Y!10)))))) | ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(Y!10), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(150,plain,
% 0.20/0.47 ((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~((~p1(tptp_fun_Y_4(Y!10))) | p1(tptp_fun_X_5(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_5(tptp_fun_Y_4(Y!10)))))) | ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(Y!10), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.20/0.47 tff(151,plain,
% 0.20/0.47 (![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(Y!10), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[150, 130, 147, 145])).
% 0.20/0.47 tff(152,plain,
% 0.20/0.47 (((~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(Y!10), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ((~p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), Y))))) <=> ((~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(Y!10), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), Y))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(153,plain,
% 0.20/0.47 ((~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(Y!10), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ((~p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), Y))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(154,plain,
% 0.20/0.47 ((~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(Y!10), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), Y)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.20/0.47 tff(155,plain,
% 0.20/0.47 (![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), Y)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[154, 151, 143, 141])).
% 0.20/0.47 tff(156,plain,
% 0.20/0.47 (((~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10)))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))) | (~p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10))))) | (~p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(157,plain,
% 0.20/0.47 (~p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[156, 139])).
% 0.20/0.47 tff(158,plain,
% 0.20/0.47 (((~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10)))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))) | (~p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10))))) | r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10)))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(159,plain,
% 0.20/0.47 (r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[158, 139])).
% 0.20/0.47 tff(160,plain,
% 0.20/0.47 (((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), Y)))) | (p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10)))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), Y)))) | p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(161,plain,
% 0.20/0.47 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), Y)))) | (p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10)))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(162,plain,
% 0.20/0.47 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), Y)))) | p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.20/0.47 tff(163,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[162, 159, 157, 155])).
% 0.20/0.47 tff(164,plain,((~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(165,plain,
% 0.20/0.47 (((~((~p1(Y!10)) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | ![X: $i] : ((~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))) | (~((~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(p1(Y!10) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))))) | ((~p1(Y!10)) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | ![X: $i] : ((~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))) | (~((~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(166,plain,
% 0.20/0.47 ((~p1(Y!10)) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | ![X: $i] : ((~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))) | (~((~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[165, 53])).
% 0.20/0.47 tff(167,plain,
% 0.20/0.47 ((~((~p1(Y!10)) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | ![X: $i] : ((~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))) | (~((~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~p1(Y!10)) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | ![X: $i] : ((~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))) | (~((~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(168,plain,
% 0.20/0.47 ((~p1(Y!10)) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | ![X: $i] : ((~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))) | (~((~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.20/0.47 tff(169,plain,
% 0.20/0.47 (![X: $i] : ((~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[168, 164, 116, 70])).
% 0.20/0.47 tff(170,plain,
% 0.20/0.47 (((~![X: $i] : ((~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))) | ((~r1(Y!10, X!12)) | (~((~r1(X!12, tptp_fun_Y_1(X!12))) | (~p1(tptp_fun_Y_1(X!12))) | p1(tptp_fun_X_2(X!12)) | (~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12))))))) <=> ((~![X: $i] : ((~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))) | (~r1(Y!10, X!12)) | (~((~r1(X!12, tptp_fun_Y_1(X!12))) | (~p1(tptp_fun_Y_1(X!12))) | p1(tptp_fun_X_2(X!12)) | (~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(171,plain,
% 0.20/0.47 ((~![X: $i] : ((~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))) | ((~r1(Y!10, X!12)) | (~((~r1(X!12, tptp_fun_Y_1(X!12))) | (~p1(tptp_fun_Y_1(X!12))) | p1(tptp_fun_X_2(X!12)) | (~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(172,plain,
% 0.20/0.47 ((~![X: $i] : ((~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_1(X))) | (~p1(tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))) | (~r1(Y!10, X!12)) | (~((~r1(X!12, tptp_fun_Y_1(X!12))) | (~p1(tptp_fun_Y_1(X!12))) | p1(tptp_fun_X_2(X!12)) | (~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.20/0.47 tff(173,plain,
% 0.20/0.47 (~((~r1(X!12, tptp_fun_Y_1(X!12))) | (~p1(tptp_fun_Y_1(X!12))) | p1(tptp_fun_X_2(X!12)) | (~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[172, 56, 169])).
% 0.20/0.47 tff(174,plain,
% 0.20/0.47 (((~r1(X!12, tptp_fun_Y_1(X!12))) | (~p1(tptp_fun_Y_1(X!12))) | p1(tptp_fun_X_2(X!12)) | (~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12)))) | r1(X!12, tptp_fun_Y_1(X!12))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(175,plain,
% 0.20/0.47 (r1(X!12, tptp_fun_Y_1(X!12))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[174, 173])).
% 0.20/0.47 tff(176,plain,
% 0.20/0.47 (((~![Y: $i] : ((~r1(X!12, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ((~r1(X!12, tptp_fun_Y_1(X!12))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(X!12), X))))) <=> ((~![Y: $i] : ((~r1(X!12, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | (~r1(X!12, tptp_fun_Y_1(X!12))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(X!12), X))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(177,plain,
% 0.20/0.47 ((~![Y: $i] : ((~r1(X!12, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ((~r1(X!12, tptp_fun_Y_1(X!12))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(X!12), X))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(178,plain,
% 0.20/0.47 ((~![Y: $i] : ((~r1(X!12, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | (~r1(X!12, tptp_fun_Y_1(X!12))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(X!12), X)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.20/0.47 tff(179,plain,
% 0.20/0.47 (![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(X!12), X)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[178, 175, 61])).
% 0.20/0.47 tff(180,plain,
% 0.20/0.47 (((~r1(X!12, tptp_fun_Y_1(X!12))) | (~p1(tptp_fun_Y_1(X!12))) | p1(tptp_fun_X_2(X!12)) | (~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12)))) | r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(181,plain,
% 0.20/0.47 (r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[180, 173])).
% 0.20/0.47 tff(182,plain,
% 0.20/0.47 (((~r1(X!12, tptp_fun_Y_1(X!12))) | (~p1(tptp_fun_Y_1(X!12))) | p1(tptp_fun_X_2(X!12)) | (~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12)))) | (~p1(tptp_fun_X_2(X!12)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(183,plain,
% 0.20/0.48 (~p1(tptp_fun_X_2(X!12))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[182, 173])).
% 0.20/0.48 tff(184,plain,
% 0.20/0.48 (((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(X!12), X)))) | (p1(tptp_fun_X_2(X!12)) | (~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12))))) <=> ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(X!12), X)))) | p1(tptp_fun_X_2(X!12)) | (~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(185,plain,
% 0.20/0.48 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(X!12), X)))) | (p1(tptp_fun_X_2(X!12)) | (~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(186,plain,
% 0.20/0.48 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(X!12), X)))) | p1(tptp_fun_X_2(X!12)) | (~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.20/0.48 tff(187,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[186, 183, 181, 179])).
% 0.20/0.48 % SZS output end Proof
%------------------------------------------------------------------------------