TSTP Solution File: LCL660+1.010 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL660+1.010 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 04:57:33 EDT 2022
% Result : Theorem 1.12s 0.93s
% Output : Proof 1.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL660+1.010 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 23:25:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 1.12/0.93 % SZS status Theorem
% 1.12/0.93 % SZS output start Proof
% 1.12/0.93 tff(r1_type, type, (
% 1.12/0.93 r1: ( $i * $i ) > $o)).
% 1.12/0.93 tff(tptp_fun_Y_12_type, type, (
% 1.12/0.93 tptp_fun_Y_12: $i > $i)).
% 1.12/0.93 tff(tptp_fun_X_17_type, type, (
% 1.12/0.93 tptp_fun_X_17: $i)).
% 1.12/0.93 tff(p2_type, type, (
% 1.12/0.93 p2: $i > $o)).
% 1.12/0.93 tff(tptp_fun_X_13_type, type, (
% 1.12/0.93 tptp_fun_X_13: $i > $i)).
% 1.12/0.93 tff(tptp_fun_X_5_type, type, (
% 1.12/0.93 tptp_fun_X_5: $i > $i)).
% 1.12/0.93 tff(tptp_fun_Y_18_type, type, (
% 1.12/0.93 tptp_fun_Y_18: $i)).
% 1.12/0.93 tff(tptp_fun_Y_6_type, type, (
% 1.12/0.93 tptp_fun_Y_6: $i > $i)).
% 1.12/0.93 tff(tptp_fun_Y_16_type, type, (
% 1.12/0.93 tptp_fun_Y_16: $i)).
% 1.12/0.93 tff(tptp_fun_X_19_type, type, (
% 1.12/0.93 tptp_fun_X_19: $i > $i)).
% 1.12/0.93 tff(tptp_fun_X_21_type, type, (
% 1.12/0.93 tptp_fun_X_21: $i > $i)).
% 1.12/0.93 tff(tptp_fun_Y_20_type, type, (
% 1.12/0.93 tptp_fun_Y_20: $i > $i)).
% 1.12/0.93 tff(tptp_fun_X_0_type, type, (
% 1.12/0.93 tptp_fun_X_0: $i)).
% 1.12/0.93 tff(tptp_fun_Y_11_type, type, (
% 1.12/0.93 tptp_fun_Y_11: $i)).
% 1.12/0.93 tff(tptp_fun_X_15_type, type, (
% 1.12/0.93 tptp_fun_X_15: $i)).
% 1.12/0.93 tff(tptp_fun_Y_14_type, type, (
% 1.12/0.93 tptp_fun_Y_14: $i)).
% 1.12/0.93 tff(tptp_fun_Y_4_type, type, (
% 1.12/0.93 tptp_fun_Y_4: $i)).
% 1.12/0.93 tff(tptp_fun_X_3_type, type, (
% 1.12/0.93 tptp_fun_X_3: $i > $i)).
% 1.12/0.93 tff(p5_type, type, (
% 1.12/0.93 p5: $i > $o)).
% 1.12/0.93 tff(tptp_fun_Y_45_type, type, (
% 1.12/0.93 tptp_fun_Y_45: $i > $i)).
% 1.12/0.93 tff(p1_type, type, (
% 1.12/0.93 p1: $i > $o)).
% 1.12/0.93 tff(tptp_fun_Y_50_type, type, (
% 1.12/0.93 tptp_fun_Y_50: $i)).
% 1.12/0.93 tff(tptp_fun_X_51_type, type, (
% 1.12/0.93 tptp_fun_X_51: $i)).
% 1.12/0.93 tff(tptp_fun_Y_48_type, type, (
% 1.12/0.93 tptp_fun_Y_48: $i)).
% 1.12/0.93 tff(tptp_fun_X_49_type, type, (
% 1.12/0.93 tptp_fun_X_49: $i)).
% 1.12/0.93 tff(p3_type, type, (
% 1.12/0.93 p3: $i > $o)).
% 1.12/0.93 tff(tptp_fun_Y_46_type, type, (
% 1.12/0.93 tptp_fun_Y_46: $i)).
% 1.12/0.93 tff(tptp_fun_X_47_type, type, (
% 1.12/0.93 tptp_fun_X_47: $i)).
% 1.12/0.93 tff(p4_type, type, (
% 1.12/0.93 p4: $i > $o)).
% 1.12/0.93 tff(tptp_fun_Y_43_type, type, (
% 1.12/0.93 tptp_fun_Y_43: $i)).
% 1.12/0.93 tff(tptp_fun_X_44_type, type, (
% 1.12/0.93 tptp_fun_X_44: $i)).
% 1.12/0.93 tff(tptp_fun_X_33_type, type, (
% 1.12/0.93 tptp_fun_X_33: $i > $i)).
% 1.12/0.93 tff(tptp_fun_Y_32_type, type, (
% 1.12/0.93 tptp_fun_Y_32: $i > $i)).
% 1.12/0.93 tff(tptp_fun_Y_40_type, type, (
% 1.12/0.93 tptp_fun_Y_40: $i)).
% 1.12/0.93 tff(tptp_fun_Y_42_type, type, (
% 1.12/0.93 tptp_fun_Y_42: $i)).
% 1.12/0.93 tff(tptp_fun_X_41_type, type, (
% 1.12/0.93 tptp_fun_X_41: $i)).
% 1.12/0.93 tff(tptp_fun_Y_37_type, type, (
% 1.12/0.93 tptp_fun_Y_37: $i)).
% 1.12/0.93 tff(tptp_fun_Y_39_type, type, (
% 1.12/0.93 tptp_fun_Y_39: $i)).
% 1.12/0.93 tff(tptp_fun_X_38_type, type, (
% 1.12/0.93 tptp_fun_X_38: $i)).
% 1.12/0.93 tff(tptp_fun_Y_34_type, type, (
% 1.12/0.93 tptp_fun_Y_34: $i)).
% 1.12/0.93 tff(tptp_fun_Y_36_type, type, (
% 1.12/0.93 tptp_fun_Y_36: $i)).
% 1.12/0.93 tff(tptp_fun_X_35_type, type, (
% 1.12/0.93 tptp_fun_X_35: $i)).
% 1.12/0.93 tff(tptp_fun_Y_29_type, type, (
% 1.12/0.93 tptp_fun_Y_29: $i)).
% 1.12/0.93 tff(tptp_fun_Y_31_type, type, (
% 1.12/0.93 tptp_fun_Y_31: $i)).
% 1.12/0.93 tff(tptp_fun_X_30_type, type, (
% 1.12/0.93 tptp_fun_X_30: $i)).
% 1.12/0.93 tff(tptp_fun_Y_28_type, type, (
% 1.12/0.93 tptp_fun_Y_28: $i > $i)).
% 1.12/0.93 tff(tptp_fun_X_27_type, type, (
% 1.12/0.93 tptp_fun_X_27: $i > $i)).
% 1.12/0.93 tff(tptp_fun_Y_26_type, type, (
% 1.12/0.93 tptp_fun_Y_26: $i > $i)).
% 1.12/0.93 tff(tptp_fun_Y_22_type, type, (
% 1.12/0.93 tptp_fun_Y_22: $i)).
% 1.12/0.93 tff(tptp_fun_X_25_type, type, (
% 1.12/0.93 tptp_fun_X_25: $i)).
% 1.12/0.93 tff(tptp_fun_Y_24_type, type, (
% 1.12/0.93 tptp_fun_Y_24: $i)).
% 1.12/0.93 tff(tptp_fun_X_23_type, type, (
% 1.12/0.93 tptp_fun_X_23: $i)).
% 1.12/0.93 tff(tptp_fun_Y_10_type, type, (
% 1.12/0.93 tptp_fun_Y_10: $i > $i)).
% 1.12/0.93 tff(tptp_fun_X_9_type, type, (
% 1.12/0.93 tptp_fun_X_9: $i > $i)).
% 1.12/0.93 tff(tptp_fun_Y_8_type, type, (
% 1.12/0.93 tptp_fun_Y_8: $i > $i)).
% 1.12/0.93 tff(tptp_fun_X_7_type, type, (
% 1.12/0.93 tptp_fun_X_7: $i > $i)).
% 1.12/0.93 tff(tptp_fun_Y_2_type, type, (
% 1.12/0.93 tptp_fun_Y_2: $i)).
% 1.12/0.93 tff(tptp_fun_Y_1_type, type, (
% 1.12/0.93 tptp_fun_Y_1: $i)).
% 1.12/0.93 tff(1,assumption,(~(p2(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p2(tptp_fun_X_5(Y!18))))), introduced(assumption)).
% 1.12/0.93 tff(2,plain,
% 1.12/0.93 ((p2(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p2(tptp_fun_X_5(Y!18)))) | (~p2(tptp_fun_Y_6(Y!18)))),
% 1.12/0.93 inference(tautology,[status(thm)],[])).
% 1.12/0.93 tff(3,plain,
% 1.12/0.93 (~p2(tptp_fun_Y_6(Y!18))),
% 1.12/0.93 inference(unit_resolution,[status(thm)],[2, 1])).
% 1.12/0.93 tff(4,plain,
% 1.12/0.93 ((p2(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p2(tptp_fun_X_5(Y!18)))) | p2(tptp_fun_X_5(Y!18))),
% 1.12/0.93 inference(tautology,[status(thm)],[])).
% 1.12/0.93 tff(5,plain,
% 1.12/0.93 (p2(tptp_fun_X_5(Y!18))),
% 1.12/0.93 inference(unit_resolution,[status(thm)],[4, 1])).
% 1.12/0.93 tff(6,plain,
% 1.12/0.93 ((p2(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p2(tptp_fun_X_5(Y!18)))) | r1(Y!18, tptp_fun_X_5(Y!18))),
% 1.12/0.93 inference(tautology,[status(thm)],[])).
% 1.12/0.93 tff(7,plain,
% 1.12/0.93 (r1(Y!18, tptp_fun_X_5(Y!18))),
% 1.12/0.93 inference(unit_resolution,[status(thm)],[6, 1])).
% 1.12/0.93 tff(8,assumption,(~(p2(Y!11) | (~r1(X!0, Y!11)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))), introduced(assumption)).
% 1.12/0.93 tff(9,plain,
% 1.12/0.93 ((p2(Y!11) | (~r1(X!0, Y!11)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) | r1(X!0, Y!11)),
% 1.12/0.93 inference(tautology,[status(thm)],[])).
% 1.12/0.93 tff(10,plain,
% 1.12/0.93 (r1(X!0, Y!11)),
% 1.12/0.93 inference(unit_resolution,[status(thm)],[9, 8])).
% 1.12/0.93 tff(11,plain,
% 1.12/0.93 ((p2(Y!11) | (~r1(X!0, Y!11)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) | (~p2(Y!11))),
% 1.12/0.93 inference(tautology,[status(thm)],[])).
% 1.12/0.93 tff(12,plain,
% 1.12/0.93 (~p2(Y!11)),
% 1.12/0.93 inference(unit_resolution,[status(thm)],[11, 8])).
% 1.12/0.93 tff(13,plain,
% 1.12/0.93 (^[X: $i] : refl(r1(X, X) <=> r1(X, X))),
% 1.12/0.93 inference(bind,[status(th)],[])).
% 1.12/0.93 tff(14,plain,
% 1.12/0.93 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 1.12/0.93 inference(quant_intro,[status(thm)],[13])).
% 1.12/0.93 tff(15,plain,
% 1.12/0.93 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 1.12/0.93 inference(rewrite,[status(thm)],[])).
% 1.12/0.93 tff(16,axiom,(![X: $i] : r1(X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity')).
% 1.12/0.93 tff(17,plain,
% 1.12/0.93 (![X: $i] : r1(X, X)),
% 1.12/0.93 inference(modus_ponens,[status(thm)],[16, 15])).
% 1.12/0.93 tff(18,plain,(
% 1.12/0.93 ![X: $i] : r1(X, X)),
% 1.12/0.93 inference(skolemize,[status(sab)],[17])).
% 1.12/0.93 tff(19,plain,
% 1.12/0.93 (![X: $i] : r1(X, X)),
% 1.12/0.93 inference(modus_ponens,[status(thm)],[18, 14])).
% 1.12/0.93 tff(20,plain,
% 1.12/0.93 ((~![X: $i] : r1(X, X)) | r1(X!0, X!0)),
% 1.12/0.93 inference(quant_inst,[status(thm)],[])).
% 1.12/0.93 tff(21,plain,
% 1.12/0.93 (r1(X!0, X!0)),
% 1.12/0.93 inference(unit_resolution,[status(thm)],[20, 19])).
% 1.12/0.93 tff(22,assumption,((~r1(X!0, Y!4)) | p2(Y!4) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))), introduced(assumption)).
% 1.12/0.93 tff(23,plain,
% 1.12/0.93 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~((~r1(X!0, Y!4)) | p2(Y!4) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~((~r1(X!0, Y!4)) | p2(Y!4) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))),
% 1.12/0.93 inference(rewrite,[status(thm)],[])).
% 1.12/0.93 tff(24,plain,
% 1.12/0.93 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~((~r1(X!0, Y!4)) | p2(Y!4) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~((~r1(X!0, Y!4)) | p2(Y!4) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))),
% 1.12/0.93 inference(rewrite,[status(thm)],[])).
% 1.12/0.93 tff(25,plain,
% 1.12/0.93 (((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) <=> (~((~r1(X!0, Y!4)) | p2(Y!4) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))))),
% 1.12/0.93 inference(rewrite,[status(thm)],[])).
% 1.12/0.93 tff(26,plain,
% 1.12/0.93 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))),
% 1.12/0.94 inference(bind,[status(th)],[])).
% 1.12/0.94 tff(27,plain,
% 1.12/0.94 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))),
% 1.12/0.94 inference(quant_intro,[status(thm)],[26])).
% 1.12/0.94 tff(28,plain,
% 1.12/0.94 (((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) <=> ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))),
% 1.12/0.94 inference(monotonicity,[status(thm)],[27])).
% 1.12/0.94 tff(29,plain,
% 1.12/0.94 (((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) <=> (~((~r1(X!0, Y!4)) | p2(Y!4) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))))),
% 1.12/0.94 inference(transitivity,[status(thm)],[28, 25])).
% 1.12/0.94 tff(30,plain,
% 1.12/0.94 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~((~r1(X!0, Y!4)) | p2(Y!4) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))),
% 1.12/0.94 inference(monotonicity,[status(thm)],[29])).
% 1.12/0.94 tff(31,plain,
% 1.12/0.94 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~((~r1(X!0, Y!4)) | p2(Y!4) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))),
% 1.12/0.94 inference(transitivity,[status(thm)],[30, 24])).
% 1.12/0.94 tff(32,plain,
% 1.12/0.94 (((~(p3(Y!1) | (~r1(X!0, Y!1)))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) & (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_7(Y)) & p3(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y)))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))) & ((((((~p2(Y!11)) & r1(X!0, Y!11) & ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (p2(tptp_fun_Y_12(X)) & r1(X, tptp_fun_Y_12(X)) & (~(p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))) & (p2(X!0) | (p2(Y!14) & r1(X!0, Y!14) & (~(p2(X!15) | (~r1(Y!14, X!15))))))) | (r1(X!0, Y!16) & (((~p2(Y!16)) & ![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (r1(Y!16, X!17) & (~p2(Y!18)) & r1(X!17, Y!18) & ![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))) & ![X: $i] : (p2(X) | (~r1(Y!16, X)) | (p2(tptp_fun_Y_12(X)) & r1(X, tptp_fun_Y_12(X)) & (~(p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))) & ![X: $i] : ((~r1(Y!16, X)) | ((~p2(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))) & r1(X, tptp_fun_Y_20(X)) & (~p2(tptp_fun_X_21(X))) & r1(tptp_fun_Y_20(X), tptp_fun_X_21(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) | ((~p2(tptp_fun_X_19(Y))) & r1(Y, tptp_fun_X_19(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) & (p2(Y) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~r1(X!0, Y))) | (r1(X!0, Y!22) & (~p1(Y!22)) & (~p2(X!23)) & r1(Y!22, X!23) & (~p3(X!23)) & (~p1(X!23)) & (~p4(X!23)) & (~p2(Y!24)) & r1(X!23, Y!24) & (~p3(Y!24)) & (~p1(Y!24)) & (~p4(Y!24)) & r1(Y!24, X!25) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~r1(Y!22, X)) | ((~p1(X)) & (~p2(tptp_fun_Y_26(X))) & r1(X, tptp_fun_Y_26(X)) & (~p3(tptp_fun_Y_26(X))) & (~p1(tptp_fun_Y_26(X))) & (~p4(tptp_fun_Y_26(X))) & (~p2(tptp_fun_X_27(X))) & r1(tptp_fun_Y_26(X), tptp_fun_X_27(X)) & (~p3(tptp_fun_X_27(X))) & (~p1(tptp_fun_X_27(X))) & (~p4(tptp_fun_X_27(X))) & r1(tptp_fun_X_27(X), tptp_fun_Y_28(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | ((~p2(Y!29)) & r1(X!0, Y!29) & (~p3(Y!29)) & (~p1(Y!29)) & (~p4(Y!29)) & (~p2(X!30)) & r1(Y!29, X!30) & (~p3(X!30)) & (~p1(X!30)) & (~p4(X!30)) & r1(X!30, Y!31) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!29, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | ((~p2(Y!34)) & r1(X!0, Y!34) & (~p3(Y!34)) & (~p1(Y!34)) & (~p2(X!35)) & r1(Y!34, X!35) & (~p3(X!35)) & (~p1(X!35)) & (~p4(X!35)) & r1(X!35, Y!36) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!34, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | ((~p2(Y!37)) & r1(X!0, Y!37) & (~p1(Y!37)) & (~p2(X!38)) & r1(Y!37, X!38) & (~p3(X!38)) & (~p1(X!38)) & (~p4(X!38)) & r1(X!38, Y!39) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!37, X)) | ((~p2(X)) & (~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | (r1(X!0, Y!40) & (~p1(Y!40)) & (~p2(X!41)) & r1(Y!40, X!41) & (~p3(X!41)) & (~p1(X!41)) & (~p4(X!41)) & r1(X!41, Y!42) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!40, X)) | ((~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | p4(X!0) | ((~p2(Y!43)) & r1(X!0, Y!43) & (~p3(Y!43)) & (~p1(Y!43)) & (~p4(Y!43)) & r1(Y!43, X!44) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!43, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | ((~p2(Y!46)) & r1(X!0, Y!46) & (~p3(Y!46)) & (~p1(Y!46)) & r1(Y!46, X!47) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!46, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!48)) & r1(X!0, Y!48) & (~p1(Y!48)) & r1(Y!48, X!49) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!48, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!50) & (~p1(Y!50)) & r1(Y!50, X!51) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!50, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~p2(tptp_fun_X_19(Y))) & r1(Y, tptp_fun_X_19(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) <=> ((~(p3(Y!1) | (~r1(X!0, Y!1)))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) & (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_7(Y)) & p3(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y)))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))) & (((((~p2(Y!11)) & r1(X!0, Y!11) & ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (p2(tptp_fun_Y_12(X)) & r1(X, tptp_fun_Y_12(X)) & (~(p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))) & (p2(X!0) | (p2(Y!14) & r1(X!0, Y!14) & (~(p2(X!15) | (~r1(Y!14, X!15))))))) | (r1(X!0, Y!16) & (((~p2(Y!16)) & ![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (r1(Y!16, X!17) & (~p2(Y!18)) & r1(X!17, Y!18) & ![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))) & ![X: $i] : (p2(X) | (~r1(Y!16, X)) | (p2(tptp_fun_Y_12(X)) & r1(X, tptp_fun_Y_12(X)) & (~(p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))) & ![X: $i] : ((~r1(Y!16, X)) | ((~p2(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))) & r1(X, tptp_fun_Y_20(X)) & (~p2(tptp_fun_X_21(X))) & r1(tptp_fun_Y_20(X), tptp_fun_X_21(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) | ((~p2(tptp_fun_X_19(Y))) & r1(Y, tptp_fun_X_19(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) & (p2(Y) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~r1(X!0, Y))) | (r1(X!0, Y!22) & (~p1(Y!22)) & (~p2(X!23)) & r1(Y!22, X!23) & (~p3(X!23)) & (~p1(X!23)) & (~p4(X!23)) & (~p2(Y!24)) & r1(X!23, Y!24) & (~p3(Y!24)) & (~p1(Y!24)) & (~p4(Y!24)) & r1(Y!24, X!25) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~r1(Y!22, X)) | ((~p1(X)) & (~p2(tptp_fun_Y_26(X))) & r1(X, tptp_fun_Y_26(X)) & (~p3(tptp_fun_Y_26(X))) & (~p1(tptp_fun_Y_26(X))) & (~p4(tptp_fun_Y_26(X))) & (~p2(tptp_fun_X_27(X))) & r1(tptp_fun_Y_26(X), tptp_fun_X_27(X)) & (~p3(tptp_fun_X_27(X))) & (~p1(tptp_fun_X_27(X))) & (~p4(tptp_fun_X_27(X))) & r1(tptp_fun_X_27(X), tptp_fun_Y_28(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | ((~p2(Y!29)) & r1(X!0, Y!29) & (~p3(Y!29)) & (~p1(Y!29)) & (~p4(Y!29)) & (~p2(X!30)) & r1(Y!29, X!30) & (~p3(X!30)) & (~p1(X!30)) & (~p4(X!30)) & r1(X!30, Y!31) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!29, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | ((~p2(Y!34)) & r1(X!0, Y!34) & (~p3(Y!34)) & (~p1(Y!34)) & (~p2(X!35)) & r1(Y!34, X!35) & (~p3(X!35)) & (~p1(X!35)) & (~p4(X!35)) & r1(X!35, Y!36) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!34, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | ((~p2(Y!37)) & r1(X!0, Y!37) & (~p1(Y!37)) & (~p2(X!38)) & r1(Y!37, X!38) & (~p3(X!38)) & (~p1(X!38)) & (~p4(X!38)) & r1(X!38, Y!39) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!37, X)) | ((~p2(X)) & (~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | (r1(X!0, Y!40) & (~p1(Y!40)) & (~p2(X!41)) & r1(Y!40, X!41) & (~p3(X!41)) & (~p1(X!41)) & (~p4(X!41)) & r1(X!41, Y!42) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!40, X)) | ((~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | p4(X!0) | ((~p2(Y!43)) & r1(X!0, Y!43) & (~p3(Y!43)) & (~p1(Y!43)) & (~p4(Y!43)) & r1(Y!43, X!44) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!43, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | ((~p2(Y!46)) & r1(X!0, Y!46) & (~p3(Y!46)) & (~p1(Y!46)) & r1(Y!46, X!47) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!46, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!48)) & r1(X!0, Y!48) & (~p1(Y!48)) & r1(Y!48, X!49) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!48, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!50) & (~p1(Y!50)) & r1(Y!50, X!51) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!50, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~p2(tptp_fun_X_19(Y))) & r1(Y, tptp_fun_X_19(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))),
% 1.12/0.94 inference(rewrite,[status(thm)],[])).
% 1.12/0.94 tff(33,plain,
% 1.12/0.94 (((((((~p2(Y!11)) & (~(~r1(X!0, Y!11))) & ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | ((~(~p2(tptp_fun_Y_12(X)))) & (~(~r1(X, tptp_fun_Y_12(X)))) & (~(p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))) & (p2(X!0) | ((~(~p2(Y!14))) & (~(~r1(X!0, Y!14))) & (~(p2(X!15) | (~r1(Y!14, X!15))))))) | ((~(~r1(X!0, Y!16))) & ((((~(~r1(Y!16, X!17))) & ((~p2(Y!18)) & (~(~r1(X!17, Y!18))) & ![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) & ![X: $i] : (p2(X) | (~r1(Y!16, X)) | ((~(~p2(tptp_fun_Y_12(X)))) & (~(~r1(X, tptp_fun_Y_12(X)))) & (~(p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X)))))))) | ((~p2(Y!16)) & ![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y!16, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | ((~(~p2(tptp_fun_X_5(Y)))) & (~(~r1(Y, tptp_fun_X_5(Y)))) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) | ((~p2(tptp_fun_X_19(Y))) & (~(~r1(Y, tptp_fun_X_19(Y)))) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) & (p2(Y) | ((~(~p2(tptp_fun_X_5(Y)))) & (~(~r1(Y, tptp_fun_X_5(Y)))) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) | ((![Y: $i] : (p2(Y) | (~r1(X, Y)) | ((~(~p2(tptp_fun_X_5(Y)))) & (~(~r1(Y, tptp_fun_X_5(Y)))) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))) & ((~(~r1(X, tptp_fun_Y_20(X)))) & ((~p2(tptp_fun_X_21(X))) & (~(~r1(tptp_fun_Y_20(X), tptp_fun_X_21(X)))) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ((~p2(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~(~r1(X!0, Y!22))) & (~p1(Y!22)) & ((~p2(X!23)) & (~(~r1(Y!22, X!23))) & (~p3(X!23)) & (~p1(X!23)) & (~p4(X!23)) & ((~p2(Y!24)) & (~(~r1(X!23, Y!24))) & (~p3(Y!24)) & (~p1(Y!24)) & (~p4(Y!24)) & (~(~r1(Y!24, X!25))))) & ![X: $i] : ((~r1(Y!22, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | ((~p1(X)) & ((~p2(tptp_fun_Y_26(X))) & (~(~r1(X, tptp_fun_Y_26(X)))) & (~p3(tptp_fun_Y_26(X))) & (~p1(tptp_fun_Y_26(X))) & (~p4(tptp_fun_Y_26(X))) & ((~p2(tptp_fun_X_27(X))) & (~(~r1(tptp_fun_Y_26(X), tptp_fun_X_27(X)))) & (~p3(tptp_fun_X_27(X))) & (~p1(tptp_fun_X_27(X))) & (~p4(tptp_fun_X_27(X))) & (~(~r1(tptp_fun_X_27(X), tptp_fun_Y_28(X)))))))))) & (p2(X!0) | p3(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!29)) & (~(~r1(X!0, Y!29))) & (~p3(Y!29)) & (~p1(Y!29)) & (~p4(Y!29)) & ((~p2(X!30)) & (~(~r1(Y!29, X!30))) & (~p3(X!30)) & (~p1(X!30)) & (~p4(X!30)) & (~(~r1(X!30, Y!31)))) & ![X: $i] : ((~r1(Y!29, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & ((~p2(tptp_fun_Y_32(X))) & (~(~r1(X, tptp_fun_Y_32(X)))) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & (~(~r1(tptp_fun_Y_32(X), tptp_fun_X_33(X))))))))) & (p2(X!0) | p3(X!0) | p1(X!0) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!34)) & (~(~r1(X!0, Y!34))) & (~p3(Y!34)) & (~p1(Y!34)) & ((~p2(X!35)) & (~(~r1(Y!34, X!35))) & (~p3(X!35)) & (~p1(X!35)) & (~p4(X!35)) & (~(~r1(X!35, Y!36)))) & ![X: $i] : ((~r1(Y!34, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & ((~p2(tptp_fun_Y_32(X))) & (~(~r1(X, tptp_fun_Y_32(X)))) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & (~(~r1(tptp_fun_Y_32(X), tptp_fun_X_33(X))))))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!37)) & (~(~r1(X!0, Y!37))) & (~p1(Y!37)) & ((~p2(X!38)) & (~(~r1(Y!37, X!38))) & (~p3(X!38)) & (~p1(X!38)) & (~p4(X!38)) & (~(~r1(X!38, Y!39)))) & ![X: $i] : ((~r1(Y!37, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p2(X)) & (~p1(X)) & ((~p2(tptp_fun_Y_32(X))) & (~(~r1(X, tptp_fun_Y_32(X)))) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & (~(~r1(tptp_fun_Y_32(X), tptp_fun_X_33(X))))))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~(~r1(X!0, Y!40))) & (~p1(Y!40)) & ((~p2(X!41)) & (~(~r1(Y!40, X!41))) & (~p3(X!41)) & (~p1(X!41)) & (~p4(X!41)) & (~(~r1(X!41, Y!42)))) & ![X: $i] : ((~r1(Y!40, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p1(X)) & ((~p2(tptp_fun_Y_32(X))) & (~(~r1(X, tptp_fun_Y_32(X)))) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & (~(~r1(tptp_fun_Y_32(X), tptp_fun_X_33(X))))))))) & (p2(X!0) | p3(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!43)) & (~(~r1(X!0, Y!43))) & (~p3(Y!43)) & (~p1(Y!43)) & (~p4(Y!43)) & (~(~r1(Y!43, X!44))) & ![X: $i] : ((~r1(Y!43, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & (~(~r1(X, tptp_fun_Y_45(X)))))))) & (p2(X!0) | p3(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!46)) & (~(~r1(X!0, Y!46))) & (~p3(Y!46)) & (~p1(Y!46)) & (~(~r1(Y!46, X!47))) & ![X: $i] : ((~r1(Y!46, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~(~r1(X, tptp_fun_Y_45(X)))))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!48)) & (~(~r1(X!0, Y!48))) & (~p1(Y!48)) & (~(~r1(Y!48, X!49))) & ![X: $i] : ((~r1(Y!48, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(X)) & (~p1(X)) & (~(~r1(X, tptp_fun_Y_45(X)))))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~(~r1(X!0, Y!50))) & (~p1(Y!50)) & (~(~r1(Y!50, X!51))) & ![X: $i] : ((~r1(Y!50, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & (~(~r1(X, tptp_fun_Y_45(X)))))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~p2(tptp_fun_X_19(Y))) & (~(~r1(Y, tptp_fun_X_19(Y)))) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) <=> ((((((~p2(Y!11)) & r1(X!0, Y!11) & ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (p2(tptp_fun_Y_12(X)) & r1(X, tptp_fun_Y_12(X)) & (~(p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))) & (p2(X!0) | (p2(Y!14) & r1(X!0, Y!14) & (~(p2(X!15) | (~r1(Y!14, X!15))))))) | (r1(X!0, Y!16) & (((~p2(Y!16)) & ![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (r1(Y!16, X!17) & (~p2(Y!18)) & r1(X!17, Y!18) & ![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))) & ![X: $i] : (p2(X) | (~r1(Y!16, X)) | (p2(tptp_fun_Y_12(X)) & r1(X, tptp_fun_Y_12(X)) & (~(p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))) & ![X: $i] : ((~r1(Y!16, X)) | ((~p2(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))) & r1(X, tptp_fun_Y_20(X)) & (~p2(tptp_fun_X_21(X))) & r1(tptp_fun_Y_20(X), tptp_fun_X_21(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) | ((~p2(tptp_fun_X_19(Y))) & r1(Y, tptp_fun_X_19(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) & (p2(Y) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~r1(X!0, Y))) | (r1(X!0, Y!22) & (~p1(Y!22)) & (~p2(X!23)) & r1(Y!22, X!23) & (~p3(X!23)) & (~p1(X!23)) & (~p4(X!23)) & (~p2(Y!24)) & r1(X!23, Y!24) & (~p3(Y!24)) & (~p1(Y!24)) & (~p4(Y!24)) & r1(Y!24, X!25) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~r1(Y!22, X)) | ((~p1(X)) & (~p2(tptp_fun_Y_26(X))) & r1(X, tptp_fun_Y_26(X)) & (~p3(tptp_fun_Y_26(X))) & (~p1(tptp_fun_Y_26(X))) & (~p4(tptp_fun_Y_26(X))) & (~p2(tptp_fun_X_27(X))) & r1(tptp_fun_Y_26(X), tptp_fun_X_27(X)) & (~p3(tptp_fun_X_27(X))) & (~p1(tptp_fun_X_27(X))) & (~p4(tptp_fun_X_27(X))) & r1(tptp_fun_X_27(X), tptp_fun_Y_28(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | ((~p2(Y!29)) & r1(X!0, Y!29) & (~p3(Y!29)) & (~p1(Y!29)) & (~p4(Y!29)) & (~p2(X!30)) & r1(Y!29, X!30) & (~p3(X!30)) & (~p1(X!30)) & (~p4(X!30)) & r1(X!30, Y!31) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!29, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | ((~p2(Y!34)) & r1(X!0, Y!34) & (~p3(Y!34)) & (~p1(Y!34)) & (~p2(X!35)) & r1(Y!34, X!35) & (~p3(X!35)) & (~p1(X!35)) & (~p4(X!35)) & r1(X!35, Y!36) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!34, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | ((~p2(Y!37)) & r1(X!0, Y!37) & (~p1(Y!37)) & (~p2(X!38)) & r1(Y!37, X!38) & (~p3(X!38)) & (~p1(X!38)) & (~p4(X!38)) & r1(X!38, Y!39) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!37, X)) | ((~p2(X)) & (~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | (r1(X!0, Y!40) & (~p1(Y!40)) & (~p2(X!41)) & r1(Y!40, X!41) & (~p3(X!41)) & (~p1(X!41)) & (~p4(X!41)) & r1(X!41, Y!42) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!40, X)) | ((~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | p4(X!0) | ((~p2(Y!43)) & r1(X!0, Y!43) & (~p3(Y!43)) & (~p1(Y!43)) & (~p4(Y!43)) & r1(Y!43, X!44) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!43, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | ((~p2(Y!46)) & r1(X!0, Y!46) & (~p3(Y!46)) & (~p1(Y!46)) & r1(Y!46, X!47) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!46, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!48)) & r1(X!0, Y!48) & (~p1(Y!48)) & r1(Y!48, X!49) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!48, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!50) & (~p1(Y!50)) & r1(Y!50, X!51) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!50, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~p2(tptp_fun_X_19(Y))) & r1(Y, tptp_fun_X_19(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(34,plain,
% 1.12/0.95 (^[Y: $i] : trans(monotonicity(rewrite(((~(~r1(Y, tptp_fun_X_9(Y)))) & (~(~p1(tptp_fun_X_9(Y)))) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y))))) <=> (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))), (((~r1(X!0, Y)) | p1(Y) | ((~(~r1(Y, tptp_fun_X_9(Y)))) & (~(~p1(tptp_fun_X_9(Y)))) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))) <=> ((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))))), rewrite(((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))) <=> (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y))))))), (((~r1(X!0, Y)) | p1(Y) | ((~(~r1(Y, tptp_fun_X_9(Y)))) & (~(~p1(tptp_fun_X_9(Y)))) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))) <=> (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y))))))))),
% 1.12/0.95 inference(bind,[status(th)],[])).
% 1.12/0.95 tff(35,plain,
% 1.12/0.95 (![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | ((~(~r1(Y, tptp_fun_X_9(Y)))) & (~(~p1(tptp_fun_X_9(Y)))) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))) <=> ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y))))))),
% 1.12/0.95 inference(quant_intro,[status(thm)],[34])).
% 1.12/0.95 tff(36,plain,
% 1.12/0.95 (^[Y: $i] : trans(monotonicity(rewrite(((~(~r1(Y, tptp_fun_X_7(Y)))) & (~(~p3(tptp_fun_X_7(Y)))) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y))))) <=> (r1(Y, tptp_fun_X_7(Y)) & p3(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y)))))), (((~r1(X!0, Y)) | p3(Y) | ((~(~r1(Y, tptp_fun_X_7(Y)))) & (~(~p3(tptp_fun_X_7(Y)))) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y)))))) <=> ((~r1(X!0, Y)) | p3(Y) | (r1(Y, tptp_fun_X_7(Y)) & p3(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y)))))))), rewrite(((~r1(X!0, Y)) | p3(Y) | (r1(Y, tptp_fun_X_7(Y)) & p3(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y)))))) <=> (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_7(Y)) & p3(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y))))))), (((~r1(X!0, Y)) | p3(Y) | ((~(~r1(Y, tptp_fun_X_7(Y)))) & (~(~p3(tptp_fun_X_7(Y)))) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y)))))) <=> (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_7(Y)) & p3(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y))))))))),
% 1.12/0.95 inference(bind,[status(th)],[])).
% 1.12/0.95 tff(37,plain,
% 1.12/0.95 (![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | ((~(~r1(Y, tptp_fun_X_7(Y)))) & (~(~p3(tptp_fun_X_7(Y)))) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y)))))) <=> ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_7(Y)) & p3(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y))))))),
% 1.12/0.95 inference(quant_intro,[status(thm)],[36])).
% 1.12/0.95 tff(38,plain,
% 1.12/0.95 ((![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) <=> (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(39,plain,
% 1.12/0.95 (((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~(~p2(tptp_fun_X_5(Y)))) & (~(~r1(Y, tptp_fun_X_5(Y)))) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) <=> ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(40,plain,
% 1.12/0.95 ((![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~(~p2(tptp_fun_X_5(Y)))) & (~(~r1(Y, tptp_fun_X_5(Y)))) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) <=> (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))))),
% 1.12/0.95 inference(monotonicity,[status(thm)],[39])).
% 1.12/0.95 tff(41,plain,
% 1.12/0.95 ((![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~(~p2(tptp_fun_X_5(Y)))) & (~(~r1(Y, tptp_fun_X_5(Y)))) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) <=> (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))))),
% 1.12/0.95 inference(transitivity,[status(thm)],[40, 38])).
% 1.12/0.95 tff(42,plain,
% 1.12/0.95 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(43,plain,
% 1.12/0.95 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~(~p2(tptp_fun_X_5(Y)))) & (~(~r1(Y, tptp_fun_X_5(Y)))) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))))),
% 1.12/0.95 inference(monotonicity,[status(thm)],[39])).
% 1.12/0.95 tff(44,plain,
% 1.12/0.95 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~(~p2(tptp_fun_X_5(Y)))) & (~(~r1(Y, tptp_fun_X_5(Y)))) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))))),
% 1.12/0.95 inference(transitivity,[status(thm)],[43, 42])).
% 1.12/0.95 tff(45,plain,
% 1.12/0.95 ((~((~r1(X!0, Y!2)) | p1(Y!2))) <=> (~((~r1(X!0, Y!2)) | p1(Y!2)))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(46,plain,
% 1.12/0.95 ((~((~r1(X!0, Y!1)) | p3(Y!1))) <=> (~(p3(Y!1) | (~r1(X!0, Y!1))))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(47,plain,
% 1.12/0.95 (((~((~r1(X!0, Y!1)) | p3(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~(~p2(tptp_fun_X_5(Y)))) & (~(~r1(Y, tptp_fun_X_5(Y)))) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) & (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~(~p2(tptp_fun_X_5(Y)))) & (~(~r1(Y, tptp_fun_X_5(Y)))) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | ((~(~r1(Y, tptp_fun_X_7(Y)))) & (~(~p3(tptp_fun_X_7(Y)))) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | ((~(~r1(Y, tptp_fun_X_9(Y)))) & (~(~p1(tptp_fun_X_9(Y)))) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))) & ((((((~p2(Y!11)) & (~(~r1(X!0, Y!11))) & ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | ((~(~p2(tptp_fun_Y_12(X)))) & (~(~r1(X, tptp_fun_Y_12(X)))) & (~(p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))) & (p2(X!0) | ((~(~p2(Y!14))) & (~(~r1(X!0, Y!14))) & (~(p2(X!15) | (~r1(Y!14, X!15))))))) | ((~(~r1(X!0, Y!16))) & ((((~(~r1(Y!16, X!17))) & ((~p2(Y!18)) & (~(~r1(X!17, Y!18))) & ![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) & ![X: $i] : (p2(X) | (~r1(Y!16, X)) | ((~(~p2(tptp_fun_Y_12(X)))) & (~(~r1(X, tptp_fun_Y_12(X)))) & (~(p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X)))))))) | ((~p2(Y!16)) & ![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y!16, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | ((~(~p2(tptp_fun_X_5(Y)))) & (~(~r1(Y, tptp_fun_X_5(Y)))) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) | ((~p2(tptp_fun_X_19(Y))) & (~(~r1(Y, tptp_fun_X_19(Y)))) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) & (p2(Y) | ((~(~p2(tptp_fun_X_5(Y)))) & (~(~r1(Y, tptp_fun_X_5(Y)))) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) | ((![Y: $i] : (p2(Y) | (~r1(X, Y)) | ((~(~p2(tptp_fun_X_5(Y)))) & (~(~r1(Y, tptp_fun_X_5(Y)))) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))) & ((~(~r1(X, tptp_fun_Y_20(X)))) & ((~p2(tptp_fun_X_21(X))) & (~(~r1(tptp_fun_Y_20(X), tptp_fun_X_21(X)))) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ((~p2(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~(~r1(X!0, Y!22))) & (~p1(Y!22)) & ((~p2(X!23)) & (~(~r1(Y!22, X!23))) & (~p3(X!23)) & (~p1(X!23)) & (~p4(X!23)) & ((~p2(Y!24)) & (~(~r1(X!23, Y!24))) & (~p3(Y!24)) & (~p1(Y!24)) & (~p4(Y!24)) & (~(~r1(Y!24, X!25))))) & ![X: $i] : ((~r1(Y!22, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | ((~p1(X)) & ((~p2(tptp_fun_Y_26(X))) & (~(~r1(X, tptp_fun_Y_26(X)))) & (~p3(tptp_fun_Y_26(X))) & (~p1(tptp_fun_Y_26(X))) & (~p4(tptp_fun_Y_26(X))) & ((~p2(tptp_fun_X_27(X))) & (~(~r1(tptp_fun_Y_26(X), tptp_fun_X_27(X)))) & (~p3(tptp_fun_X_27(X))) & (~p1(tptp_fun_X_27(X))) & (~p4(tptp_fun_X_27(X))) & (~(~r1(tptp_fun_X_27(X), tptp_fun_Y_28(X)))))))))) & (p2(X!0) | p3(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!29)) & (~(~r1(X!0, Y!29))) & (~p3(Y!29)) & (~p1(Y!29)) & (~p4(Y!29)) & ((~p2(X!30)) & (~(~r1(Y!29, X!30))) & (~p3(X!30)) & (~p1(X!30)) & (~p4(X!30)) & (~(~r1(X!30, Y!31)))) & ![X: $i] : ((~r1(Y!29, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & ((~p2(tptp_fun_Y_32(X))) & (~(~r1(X, tptp_fun_Y_32(X)))) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & (~(~r1(tptp_fun_Y_32(X), tptp_fun_X_33(X))))))))) & (p2(X!0) | p3(X!0) | p1(X!0) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!34)) & (~(~r1(X!0, Y!34))) & (~p3(Y!34)) & (~p1(Y!34)) & ((~p2(X!35)) & (~(~r1(Y!34, X!35))) & (~p3(X!35)) & (~p1(X!35)) & (~p4(X!35)) & (~(~r1(X!35, Y!36)))) & ![X: $i] : ((~r1(Y!34, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & ((~p2(tptp_fun_Y_32(X))) & (~(~r1(X, tptp_fun_Y_32(X)))) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & (~(~r1(tptp_fun_Y_32(X), tptp_fun_X_33(X))))))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!37)) & (~(~r1(X!0, Y!37))) & (~p1(Y!37)) & ((~p2(X!38)) & (~(~r1(Y!37, X!38))) & (~p3(X!38)) & (~p1(X!38)) & (~p4(X!38)) & (~(~r1(X!38, Y!39)))) & ![X: $i] : ((~r1(Y!37, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p2(X)) & (~p1(X)) & ((~p2(tptp_fun_Y_32(X))) & (~(~r1(X, tptp_fun_Y_32(X)))) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & (~(~r1(tptp_fun_Y_32(X), tptp_fun_X_33(X))))))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~(~r1(X!0, Y!40))) & (~p1(Y!40)) & ((~p2(X!41)) & (~(~r1(Y!40, X!41))) & (~p3(X!41)) & (~p1(X!41)) & (~p4(X!41)) & (~(~r1(X!41, Y!42)))) & ![X: $i] : ((~r1(Y!40, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p1(X)) & ((~p2(tptp_fun_Y_32(X))) & (~(~r1(X, tptp_fun_Y_32(X)))) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & (~(~r1(tptp_fun_Y_32(X), tptp_fun_X_33(X))))))))) & (p2(X!0) | p3(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!43)) & (~(~r1(X!0, Y!43))) & (~p3(Y!43)) & (~p1(Y!43)) & (~p4(Y!43)) & (~(~r1(Y!43, X!44))) & ![X: $i] : ((~r1(Y!43, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & (~(~r1(X, tptp_fun_Y_45(X)))))))) & (p2(X!0) | p3(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!46)) & (~(~r1(X!0, Y!46))) & (~p3(Y!46)) & (~p1(Y!46)) & (~(~r1(Y!46, X!47))) & ![X: $i] : ((~r1(Y!46, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~(~r1(X, tptp_fun_Y_45(X)))))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!48)) & (~(~r1(X!0, Y!48))) & (~p1(Y!48)) & (~(~r1(Y!48, X!49))) & ![X: $i] : ((~r1(Y!48, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(X)) & (~p1(X)) & (~(~r1(X, tptp_fun_Y_45(X)))))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~(~r1(X!0, Y!50))) & (~p1(Y!50)) & (~(~r1(Y!50, X!51))) & ![X: $i] : ((~r1(Y!50, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & (~(~r1(X, tptp_fun_Y_45(X)))))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~p2(tptp_fun_X_19(Y))) & (~(~r1(Y, tptp_fun_X_19(Y)))) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) <=> ((~(p3(Y!1) | (~r1(X!0, Y!1)))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) & (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_7(Y)) & p3(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y)))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))) & ((((((~p2(Y!11)) & r1(X!0, Y!11) & ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (p2(tptp_fun_Y_12(X)) & r1(X, tptp_fun_Y_12(X)) & (~(p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))) & (p2(X!0) | (p2(Y!14) & r1(X!0, Y!14) & (~(p2(X!15) | (~r1(Y!14, X!15))))))) | (r1(X!0, Y!16) & (((~p2(Y!16)) & ![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (r1(Y!16, X!17) & (~p2(Y!18)) & r1(X!17, Y!18) & ![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))) & ![X: $i] : (p2(X) | (~r1(Y!16, X)) | (p2(tptp_fun_Y_12(X)) & r1(X, tptp_fun_Y_12(X)) & (~(p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))) & ![X: $i] : ((~r1(Y!16, X)) | ((~p2(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))) & r1(X, tptp_fun_Y_20(X)) & (~p2(tptp_fun_X_21(X))) & r1(tptp_fun_Y_20(X), tptp_fun_X_21(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) | ((~p2(tptp_fun_X_19(Y))) & r1(Y, tptp_fun_X_19(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) & (p2(Y) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~r1(X!0, Y))) | (r1(X!0, Y!22) & (~p1(Y!22)) & (~p2(X!23)) & r1(Y!22, X!23) & (~p3(X!23)) & (~p1(X!23)) & (~p4(X!23)) & (~p2(Y!24)) & r1(X!23, Y!24) & (~p3(Y!24)) & (~p1(Y!24)) & (~p4(Y!24)) & r1(Y!24, X!25) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~r1(Y!22, X)) | ((~p1(X)) & (~p2(tptp_fun_Y_26(X))) & r1(X, tptp_fun_Y_26(X)) & (~p3(tptp_fun_Y_26(X))) & (~p1(tptp_fun_Y_26(X))) & (~p4(tptp_fun_Y_26(X))) & (~p2(tptp_fun_X_27(X))) & r1(tptp_fun_Y_26(X), tptp_fun_X_27(X)) & (~p3(tptp_fun_X_27(X))) & (~p1(tptp_fun_X_27(X))) & (~p4(tptp_fun_X_27(X))) & r1(tptp_fun_X_27(X), tptp_fun_Y_28(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | ((~p2(Y!29)) & r1(X!0, Y!29) & (~p3(Y!29)) & (~p1(Y!29)) & (~p4(Y!29)) & (~p2(X!30)) & r1(Y!29, X!30) & (~p3(X!30)) & (~p1(X!30)) & (~p4(X!30)) & r1(X!30, Y!31) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!29, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | ((~p2(Y!34)) & r1(X!0, Y!34) & (~p3(Y!34)) & (~p1(Y!34)) & (~p2(X!35)) & r1(Y!34, X!35) & (~p3(X!35)) & (~p1(X!35)) & (~p4(X!35)) & r1(X!35, Y!36) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!34, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | ((~p2(Y!37)) & r1(X!0, Y!37) & (~p1(Y!37)) & (~p2(X!38)) & r1(Y!37, X!38) & (~p3(X!38)) & (~p1(X!38)) & (~p4(X!38)) & r1(X!38, Y!39) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!37, X)) | ((~p2(X)) & (~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | (r1(X!0, Y!40) & (~p1(Y!40)) & (~p2(X!41)) & r1(Y!40, X!41) & (~p3(X!41)) & (~p1(X!41)) & (~p4(X!41)) & r1(X!41, Y!42) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!40, X)) | ((~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | p4(X!0) | ((~p2(Y!43)) & r1(X!0, Y!43) & (~p3(Y!43)) & (~p1(Y!43)) & (~p4(Y!43)) & r1(Y!43, X!44) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!43, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | ((~p2(Y!46)) & r1(X!0, Y!46) & (~p3(Y!46)) & (~p1(Y!46)) & r1(Y!46, X!47) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!46, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!48)) & r1(X!0, Y!48) & (~p1(Y!48)) & r1(Y!48, X!49) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!48, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!50) & (~p1(Y!50)) & r1(Y!50, X!51) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!50, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~p2(tptp_fun_X_19(Y))) & r1(Y, tptp_fun_X_19(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))),
% 1.12/0.95 inference(monotonicity,[status(thm)],[46, 45, 44, 41, 37, 35, 33])).
% 1.12/0.95 tff(48,plain,
% 1.12/0.95 (((~((~r1(X!0, Y!1)) | p3(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~(~p2(tptp_fun_X_5(Y)))) & (~(~r1(Y, tptp_fun_X_5(Y)))) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) & (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~(~p2(tptp_fun_X_5(Y)))) & (~(~r1(Y, tptp_fun_X_5(Y)))) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | ((~(~r1(Y, tptp_fun_X_7(Y)))) & (~(~p3(tptp_fun_X_7(Y)))) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | ((~(~r1(Y, tptp_fun_X_9(Y)))) & (~(~p1(tptp_fun_X_9(Y)))) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))) & ((((((~p2(Y!11)) & (~(~r1(X!0, Y!11))) & ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | ((~(~p2(tptp_fun_Y_12(X)))) & (~(~r1(X, tptp_fun_Y_12(X)))) & (~(p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))) & (p2(X!0) | ((~(~p2(Y!14))) & (~(~r1(X!0, Y!14))) & (~(p2(X!15) | (~r1(Y!14, X!15))))))) | ((~(~r1(X!0, Y!16))) & ((((~(~r1(Y!16, X!17))) & ((~p2(Y!18)) & (~(~r1(X!17, Y!18))) & ![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) & ![X: $i] : (p2(X) | (~r1(Y!16, X)) | ((~(~p2(tptp_fun_Y_12(X)))) & (~(~r1(X, tptp_fun_Y_12(X)))) & (~(p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X)))))))) | ((~p2(Y!16)) & ![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y!16, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | ((~(~p2(tptp_fun_X_5(Y)))) & (~(~r1(Y, tptp_fun_X_5(Y)))) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) | ((~p2(tptp_fun_X_19(Y))) & (~(~r1(Y, tptp_fun_X_19(Y)))) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) & (p2(Y) | ((~(~p2(tptp_fun_X_5(Y)))) & (~(~r1(Y, tptp_fun_X_5(Y)))) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) | ((![Y: $i] : (p2(Y) | (~r1(X, Y)) | ((~(~p2(tptp_fun_X_5(Y)))) & (~(~r1(Y, tptp_fun_X_5(Y)))) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))) & ((~(~r1(X, tptp_fun_Y_20(X)))) & ((~p2(tptp_fun_X_21(X))) & (~(~r1(tptp_fun_Y_20(X), tptp_fun_X_21(X)))) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ((~p2(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~(~r1(X!0, Y!22))) & (~p1(Y!22)) & ((~p2(X!23)) & (~(~r1(Y!22, X!23))) & (~p3(X!23)) & (~p1(X!23)) & (~p4(X!23)) & ((~p2(Y!24)) & (~(~r1(X!23, Y!24))) & (~p3(Y!24)) & (~p1(Y!24)) & (~p4(Y!24)) & (~(~r1(Y!24, X!25))))) & ![X: $i] : ((~r1(Y!22, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | ((~p1(X)) & ((~p2(tptp_fun_Y_26(X))) & (~(~r1(X, tptp_fun_Y_26(X)))) & (~p3(tptp_fun_Y_26(X))) & (~p1(tptp_fun_Y_26(X))) & (~p4(tptp_fun_Y_26(X))) & ((~p2(tptp_fun_X_27(X))) & (~(~r1(tptp_fun_Y_26(X), tptp_fun_X_27(X)))) & (~p3(tptp_fun_X_27(X))) & (~p1(tptp_fun_X_27(X))) & (~p4(tptp_fun_X_27(X))) & (~(~r1(tptp_fun_X_27(X), tptp_fun_Y_28(X)))))))))) & (p2(X!0) | p3(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!29)) & (~(~r1(X!0, Y!29))) & (~p3(Y!29)) & (~p1(Y!29)) & (~p4(Y!29)) & ((~p2(X!30)) & (~(~r1(Y!29, X!30))) & (~p3(X!30)) & (~p1(X!30)) & (~p4(X!30)) & (~(~r1(X!30, Y!31)))) & ![X: $i] : ((~r1(Y!29, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & ((~p2(tptp_fun_Y_32(X))) & (~(~r1(X, tptp_fun_Y_32(X)))) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & (~(~r1(tptp_fun_Y_32(X), tptp_fun_X_33(X))))))))) & (p2(X!0) | p3(X!0) | p1(X!0) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!34)) & (~(~r1(X!0, Y!34))) & (~p3(Y!34)) & (~p1(Y!34)) & ((~p2(X!35)) & (~(~r1(Y!34, X!35))) & (~p3(X!35)) & (~p1(X!35)) & (~p4(X!35)) & (~(~r1(X!35, Y!36)))) & ![X: $i] : ((~r1(Y!34, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & ((~p2(tptp_fun_Y_32(X))) & (~(~r1(X, tptp_fun_Y_32(X)))) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & (~(~r1(tptp_fun_Y_32(X), tptp_fun_X_33(X))))))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!37)) & (~(~r1(X!0, Y!37))) & (~p1(Y!37)) & ((~p2(X!38)) & (~(~r1(Y!37, X!38))) & (~p3(X!38)) & (~p1(X!38)) & (~p4(X!38)) & (~(~r1(X!38, Y!39)))) & ![X: $i] : ((~r1(Y!37, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p2(X)) & (~p1(X)) & ((~p2(tptp_fun_Y_32(X))) & (~(~r1(X, tptp_fun_Y_32(X)))) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & (~(~r1(tptp_fun_Y_32(X), tptp_fun_X_33(X))))))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~(~r1(X!0, Y!40))) & (~p1(Y!40)) & ((~p2(X!41)) & (~(~r1(Y!40, X!41))) & (~p3(X!41)) & (~p1(X!41)) & (~p4(X!41)) & (~(~r1(X!41, Y!42)))) & ![X: $i] : ((~r1(Y!40, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p1(X)) & ((~p2(tptp_fun_Y_32(X))) & (~(~r1(X, tptp_fun_Y_32(X)))) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & (~(~r1(tptp_fun_Y_32(X), tptp_fun_X_33(X))))))))) & (p2(X!0) | p3(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!43)) & (~(~r1(X!0, Y!43))) & (~p3(Y!43)) & (~p1(Y!43)) & (~p4(Y!43)) & (~(~r1(Y!43, X!44))) & ![X: $i] : ((~r1(Y!43, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & (~(~r1(X, tptp_fun_Y_45(X)))))))) & (p2(X!0) | p3(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!46)) & (~(~r1(X!0, Y!46))) & (~p3(Y!46)) & (~p1(Y!46)) & (~(~r1(Y!46, X!47))) & ![X: $i] : ((~r1(Y!46, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~(~r1(X, tptp_fun_Y_45(X)))))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!48)) & (~(~r1(X!0, Y!48))) & (~p1(Y!48)) & (~(~r1(Y!48, X!49))) & ![X: $i] : ((~r1(Y!48, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(X)) & (~p1(X)) & (~(~r1(X, tptp_fun_Y_45(X)))))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~(~r1(X!0, Y!50))) & (~p1(Y!50)) & (~(~r1(Y!50, X!51))) & ![X: $i] : ((~r1(Y!50, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & (~(~r1(X, tptp_fun_Y_45(X)))))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~p2(tptp_fun_X_19(Y))) & (~(~r1(Y, tptp_fun_X_19(Y)))) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) <=> ((~(p3(Y!1) | (~r1(X!0, Y!1)))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) & (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_7(Y)) & p3(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y)))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))) & (((((~p2(Y!11)) & r1(X!0, Y!11) & ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (p2(tptp_fun_Y_12(X)) & r1(X, tptp_fun_Y_12(X)) & (~(p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))) & (p2(X!0) | (p2(Y!14) & r1(X!0, Y!14) & (~(p2(X!15) | (~r1(Y!14, X!15))))))) | (r1(X!0, Y!16) & (((~p2(Y!16)) & ![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (r1(Y!16, X!17) & (~p2(Y!18)) & r1(X!17, Y!18) & ![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))) & ![X: $i] : (p2(X) | (~r1(Y!16, X)) | (p2(tptp_fun_Y_12(X)) & r1(X, tptp_fun_Y_12(X)) & (~(p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))) & ![X: $i] : ((~r1(Y!16, X)) | ((~p2(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))) & r1(X, tptp_fun_Y_20(X)) & (~p2(tptp_fun_X_21(X))) & r1(tptp_fun_Y_20(X), tptp_fun_X_21(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) | ((~p2(tptp_fun_X_19(Y))) & r1(Y, tptp_fun_X_19(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) & (p2(Y) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~r1(X!0, Y))) | (r1(X!0, Y!22) & (~p1(Y!22)) & (~p2(X!23)) & r1(Y!22, X!23) & (~p3(X!23)) & (~p1(X!23)) & (~p4(X!23)) & (~p2(Y!24)) & r1(X!23, Y!24) & (~p3(Y!24)) & (~p1(Y!24)) & (~p4(Y!24)) & r1(Y!24, X!25) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~r1(Y!22, X)) | ((~p1(X)) & (~p2(tptp_fun_Y_26(X))) & r1(X, tptp_fun_Y_26(X)) & (~p3(tptp_fun_Y_26(X))) & (~p1(tptp_fun_Y_26(X))) & (~p4(tptp_fun_Y_26(X))) & (~p2(tptp_fun_X_27(X))) & r1(tptp_fun_Y_26(X), tptp_fun_X_27(X)) & (~p3(tptp_fun_X_27(X))) & (~p1(tptp_fun_X_27(X))) & (~p4(tptp_fun_X_27(X))) & r1(tptp_fun_X_27(X), tptp_fun_Y_28(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | ((~p2(Y!29)) & r1(X!0, Y!29) & (~p3(Y!29)) & (~p1(Y!29)) & (~p4(Y!29)) & (~p2(X!30)) & r1(Y!29, X!30) & (~p3(X!30)) & (~p1(X!30)) & (~p4(X!30)) & r1(X!30, Y!31) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!29, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | ((~p2(Y!34)) & r1(X!0, Y!34) & (~p3(Y!34)) & (~p1(Y!34)) & (~p2(X!35)) & r1(Y!34, X!35) & (~p3(X!35)) & (~p1(X!35)) & (~p4(X!35)) & r1(X!35, Y!36) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!34, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | ((~p2(Y!37)) & r1(X!0, Y!37) & (~p1(Y!37)) & (~p2(X!38)) & r1(Y!37, X!38) & (~p3(X!38)) & (~p1(X!38)) & (~p4(X!38)) & r1(X!38, Y!39) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!37, X)) | ((~p2(X)) & (~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | (r1(X!0, Y!40) & (~p1(Y!40)) & (~p2(X!41)) & r1(Y!40, X!41) & (~p3(X!41)) & (~p1(X!41)) & (~p4(X!41)) & r1(X!41, Y!42) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!40, X)) | ((~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | p4(X!0) | ((~p2(Y!43)) & r1(X!0, Y!43) & (~p3(Y!43)) & (~p1(Y!43)) & (~p4(Y!43)) & r1(Y!43, X!44) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!43, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | ((~p2(Y!46)) & r1(X!0, Y!46) & (~p3(Y!46)) & (~p1(Y!46)) & r1(Y!46, X!47) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!46, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!48)) & r1(X!0, Y!48) & (~p1(Y!48)) & r1(Y!48, X!49) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!48, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!50) & (~p1(Y!50)) & r1(Y!50, X!51) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!50, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~p2(tptp_fun_X_19(Y))) & r1(Y, tptp_fun_X_19(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))),
% 1.12/0.96 inference(transitivity,[status(thm)],[47, 32])).
% 1.12/0.96 tff(49,plain,
% 1.12/0.96 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p5(X)) | (~r1(Y, X)))))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | ((~![Y: $i] : ((~p5(Y)) | (~r1(X, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))))) | (~(((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, 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))))))))) & ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p5(X)) | (~r1(Y, X)))))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | ((~![Y: $i] : ((~p5(Y)) | (~r1(X, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))))) | (~(((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, 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))))))))) & ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))))))),
% 1.16/0.96 inference(rewrite,[status(thm)],[])).
% 1.16/0.96 tff(50,plain,
% 1.16/0.96 ((~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p5(X)) | (~r1(Y, X)))))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | ((~![Y: $i] : ((~p5(Y)) | (~r1(X, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))))) | (~(((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, 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))))))))) & ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p5(X)) | (~r1(Y, X)))))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | ((~![Y: $i] : ((~p5(Y)) | (~r1(X, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))))) | (~(((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, 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))))))))) & ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))))))),
% 1.16/0.97 inference(rewrite,[status(thm)],[])).
% 1.16/0.97 tff(51,plain,
% 1.16/0.97 ((~?[X: $i] : (~((((((((~![Y: $i] : ((~r1(X, Y)) | (~p5(Y)))) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p3(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p3(X))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p5(X)))))) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~![Y: $i] : (((~r1(X, Y)) | 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)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | (~((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) <=> (~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p5(X)) | (~r1(Y, X)))))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | ((~![Y: $i] : ((~p5(Y)) | (~r1(X, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))))) | (~(((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, 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))))))))) & ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))))))))),
% 1.16/0.97 inference(rewrite,[status(thm)],[])).
% 1.16/0.97 tff(52,plain,
% 1.16/0.97 ((~(~?[X: $i] : (~((((((((~![Y: $i] : ((~r1(X, Y)) | (~p5(Y)))) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p3(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p3(X))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p5(X)))))) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~![Y: $i] : (((~r1(X, Y)) | 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)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | (~((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))))))))) <=> (~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p5(X)) | (~r1(Y, X)))))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | ((~![Y: $i] : ((~p5(Y)) | (~r1(X, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))))) | (~(((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, 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))))))))) & ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))))))))),
% 1.16/0.98 inference(monotonicity,[status(thm)],[51])).
% 1.16/0.98 tff(53,plain,
% 1.16/0.98 ((~(~?[X: $i] : (~((((((((~![Y: $i] : ((~r1(X, Y)) | (~p5(Y)))) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p3(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p3(X))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p5(X)))))) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~![Y: $i] : (((~r1(X, Y)) | 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)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | (~((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p5(X)) | (~r1(Y, X)))))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | ((~![Y: $i] : ((~p5(Y)) | (~r1(X, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))))) | (~(((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, 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))))))))) & ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))))))),
% 1.16/0.98 inference(transitivity,[status(thm)],[52, 50])).
% 1.16/0.98 tff(54,axiom,(~(~?[X: $i] : (~((((((((~![Y: $i] : ((~r1(X, Y)) | (~p5(Y)))) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p3(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p3(X))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p5(X)))))) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~![Y: $i] : (((~r1(X, Y)) | 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)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | (~((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','main')).
% 1.16/0.98 tff(55,plain,
% 1.16/0.98 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p5(X)) | (~r1(Y, X)))))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | ((~![Y: $i] : ((~p5(Y)) | (~r1(X, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))))) | (~(((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, 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))))))))) & ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))))))),
% 1.16/0.99 inference(modus_ponens,[status(thm)],[54, 53])).
% 1.16/0.99 tff(56,plain,
% 1.16/0.99 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p5(X)) | (~r1(Y, X)))))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | ((~![Y: $i] : ((~p5(Y)) | (~r1(X, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))))) | (~(((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, 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))))))))) & ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))))))),
% 1.16/0.99 inference(modus_ponens,[status(thm)],[55, 49])).
% 1.16/0.99 tff(57,plain,
% 1.16/0.99 ((~(p3(Y!1) | (~r1(X!0, Y!1)))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) & (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_7(Y)) & p3(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y)))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))) & (((((~p2(Y!11)) & r1(X!0, Y!11) & ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (p2(tptp_fun_Y_12(X)) & r1(X, tptp_fun_Y_12(X)) & (~(p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))) & (p2(X!0) | (p2(Y!14) & r1(X!0, Y!14) & (~(p2(X!15) | (~r1(Y!14, X!15))))))) | (r1(X!0, Y!16) & (((~p2(Y!16)) & ![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (r1(Y!16, X!17) & (~p2(Y!18)) & r1(X!17, Y!18) & ![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))) & ![X: $i] : (p2(X) | (~r1(Y!16, X)) | (p2(tptp_fun_Y_12(X)) & r1(X, tptp_fun_Y_12(X)) & (~(p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))) & ![X: $i] : ((~r1(Y!16, X)) | ((~p2(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))) & r1(X, tptp_fun_Y_20(X)) & (~p2(tptp_fun_X_21(X))) & r1(tptp_fun_Y_20(X), tptp_fun_X_21(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) | ((~p2(tptp_fun_X_19(Y))) & r1(Y, tptp_fun_X_19(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) & (p2(Y) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~r1(X!0, Y))) | (r1(X!0, Y!22) & (~p1(Y!22)) & (~p2(X!23)) & r1(Y!22, X!23) & (~p3(X!23)) & (~p1(X!23)) & (~p4(X!23)) & (~p2(Y!24)) & r1(X!23, Y!24) & (~p3(Y!24)) & (~p1(Y!24)) & (~p4(Y!24)) & r1(Y!24, X!25) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~r1(Y!22, X)) | ((~p1(X)) & (~p2(tptp_fun_Y_26(X))) & r1(X, tptp_fun_Y_26(X)) & (~p3(tptp_fun_Y_26(X))) & (~p1(tptp_fun_Y_26(X))) & (~p4(tptp_fun_Y_26(X))) & (~p2(tptp_fun_X_27(X))) & r1(tptp_fun_Y_26(X), tptp_fun_X_27(X)) & (~p3(tptp_fun_X_27(X))) & (~p1(tptp_fun_X_27(X))) & (~p4(tptp_fun_X_27(X))) & r1(tptp_fun_X_27(X), tptp_fun_Y_28(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | ((~p2(Y!29)) & r1(X!0, Y!29) & (~p3(Y!29)) & (~p1(Y!29)) & (~p4(Y!29)) & (~p2(X!30)) & r1(Y!29, X!30) & (~p3(X!30)) & (~p1(X!30)) & (~p4(X!30)) & r1(X!30, Y!31) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!29, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | ((~p2(Y!34)) & r1(X!0, Y!34) & (~p3(Y!34)) & (~p1(Y!34)) & (~p2(X!35)) & r1(Y!34, X!35) & (~p3(X!35)) & (~p1(X!35)) & (~p4(X!35)) & r1(X!35, Y!36) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!34, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | ((~p2(Y!37)) & r1(X!0, Y!37) & (~p1(Y!37)) & (~p2(X!38)) & r1(Y!37, X!38) & (~p3(X!38)) & (~p1(X!38)) & (~p4(X!38)) & r1(X!38, Y!39) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!37, X)) | ((~p2(X)) & (~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | (r1(X!0, Y!40) & (~p1(Y!40)) & (~p2(X!41)) & r1(Y!40, X!41) & (~p3(X!41)) & (~p1(X!41)) & (~p4(X!41)) & r1(X!41, Y!42) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!40, X)) | ((~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | p4(X!0) | ((~p2(Y!43)) & r1(X!0, Y!43) & (~p3(Y!43)) & (~p1(Y!43)) & (~p4(Y!43)) & r1(Y!43, X!44) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!43, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | ((~p2(Y!46)) & r1(X!0, Y!46) & (~p3(Y!46)) & (~p1(Y!46)) & r1(Y!46, X!47) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!46, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!48)) & r1(X!0, Y!48) & (~p1(Y!48)) & r1(Y!48, X!49) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!48, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!50) & (~p1(Y!50)) & r1(Y!50, X!51) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!50, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~p2(tptp_fun_X_19(Y))) & r1(Y, tptp_fun_X_19(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))),
% 1.16/0.99 inference(modus_ponens,[status(thm)],[56, 48])).
% 1.16/0.99 tff(58,plain,
% 1.16/0.99 (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))),
% 1.16/0.99 inference(and_elim,[status(thm)],[57])).
% 1.16/0.99 tff(59,plain,
% 1.16/0.99 (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~((~r1(X!0, Y!4)) | p2(Y!4) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))))),
% 1.16/0.99 inference(modus_ponens,[status(thm)],[58, 31])).
% 1.16/0.99 tff(60,plain,
% 1.16/0.99 (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~((~r1(X!0, Y!4)) | p2(Y!4) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))))),
% 1.16/0.99 inference(modus_ponens,[status(thm)],[59, 23])).
% 1.16/0.99 tff(61,plain,
% 1.16/0.99 (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))),
% 1.16/0.99 inference(unit_resolution,[status(thm)],[60, 22])).
% 1.16/0.99 tff(62,plain,
% 1.16/0.99 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | ((~r1(X!0, X!0)) | (~((~p5(tptp_fun_X_3(X!0))) | (~r1(X!0, tptp_fun_X_3(X!0))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (~r1(X!0, X!0)) | (~((~p5(tptp_fun_X_3(X!0))) | (~r1(X!0, tptp_fun_X_3(X!0))))))),
% 1.16/0.99 inference(rewrite,[status(thm)],[])).
% 1.16/0.99 tff(63,plain,
% 1.16/0.99 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | ((~r1(X!0, X!0)) | (~((~p5(tptp_fun_X_3(X!0))) | (~r1(X!0, tptp_fun_X_3(X!0))))))),
% 1.16/0.99 inference(quant_inst,[status(thm)],[])).
% 1.16/0.99 tff(64,plain,
% 1.16/0.99 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (~r1(X!0, X!0)) | (~((~p5(tptp_fun_X_3(X!0))) | (~r1(X!0, tptp_fun_X_3(X!0)))))),
% 1.16/0.99 inference(modus_ponens,[status(thm)],[63, 62])).
% 1.16/0.99 tff(65,plain,
% 1.16/0.99 (~((~p5(tptp_fun_X_3(X!0))) | (~r1(X!0, tptp_fun_X_3(X!0))))),
% 1.16/0.99 inference(unit_resolution,[status(thm)],[64, 61, 21])).
% 1.16/0.99 tff(66,plain,
% 1.16/0.99 (((~p5(tptp_fun_X_3(X!0))) | (~r1(X!0, tptp_fun_X_3(X!0)))) | r1(X!0, tptp_fun_X_3(X!0))),
% 1.16/0.99 inference(tautology,[status(thm)],[])).
% 1.16/0.99 tff(67,plain,
% 1.16/0.99 (r1(X!0, tptp_fun_X_3(X!0))),
% 1.16/0.99 inference(unit_resolution,[status(thm)],[66, 65])).
% 1.16/0.99 tff(68,plain,
% 1.16/0.99 (((~p5(tptp_fun_X_3(X!0))) | (~r1(X!0, tptp_fun_X_3(X!0)))) | p5(tptp_fun_X_3(X!0))),
% 1.16/0.99 inference(tautology,[status(thm)],[])).
% 1.16/0.99 tff(69,plain,
% 1.16/0.99 (p5(tptp_fun_X_3(X!0))),
% 1.16/0.99 inference(unit_resolution,[status(thm)],[68, 65])).
% 1.16/0.99 tff(70,plain,
% 1.16/0.99 ((![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | (~((~r1(X!0, Y!4)) | p2(Y!4) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))))) <=> ((~((~r1(X!0, Y!4)) | p2(Y!4) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))))),
% 1.16/0.99 inference(rewrite,[status(thm)],[])).
% 1.16/0.99 tff(71,plain,
% 1.16/0.99 ((~((~r1(X!0, Y!4)) | p2(Y!4) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) <=> (~((~r1(X!0, Y!4)) | p2(Y!4) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))))),
% 1.16/0.99 inference(rewrite,[status(thm)],[])).
% 1.16/0.99 tff(72,plain,
% 1.16/0.99 ((![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | (~((~r1(X!0, Y!4)) | p2(Y!4) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))))) <=> (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | (~((~r1(X!0, Y!4)) | p2(Y!4) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))),
% 1.16/0.99 inference(monotonicity,[status(thm)],[71])).
% 1.16/0.99 tff(73,plain,
% 1.16/0.99 ((![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | (~((~r1(X!0, Y!4)) | p2(Y!4) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))))) <=> ((~((~r1(X!0, Y!4)) | p2(Y!4) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))))),
% 1.16/0.99 inference(transitivity,[status(thm)],[72, 70])).
% 1.16/0.99 tff(74,plain,
% 1.16/0.99 ((![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | (~((~r1(X!0, Y!4)) | p2(Y!4) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))))) <=> (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | (~((~r1(X!0, Y!4)) | p2(Y!4) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))),
% 1.16/0.99 inference(rewrite,[status(thm)],[])).
% 1.16/0.99 tff(75,plain,
% 1.16/0.99 ((![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | (~((~r1(X!0, Y!4)) | p2(Y!4) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))))) <=> (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | (~((~r1(X!0, Y!4)) | p2(Y!4) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))),
% 1.16/0.99 inference(rewrite,[status(thm)],[])).
% 1.16/0.99 tff(76,plain,
% 1.16/0.99 ((![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) <=> (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | (~((~r1(X!0, Y!4)) | p2(Y!4) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))),
% 1.16/0.99 inference(monotonicity,[status(thm)],[29])).
% 1.16/0.99 tff(77,plain,
% 1.16/0.99 ((![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) <=> (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | (~((~r1(X!0, Y!4)) | p2(Y!4) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))),
% 1.16/0.99 inference(transitivity,[status(thm)],[76, 75])).
% 1.16/0.99 tff(78,plain,
% 1.16/0.99 (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!4) | (~r1(X!0, Y!4)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))),
% 1.16/0.99 inference(and_elim,[status(thm)],[57])).
% 1.16/0.99 tff(79,plain,
% 1.16/0.99 (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | (~((~r1(X!0, Y!4)) | p2(Y!4) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))))),
% 1.16/0.99 inference(modus_ponens,[status(thm)],[78, 77])).
% 1.16/0.99 tff(80,plain,
% 1.16/0.99 (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | (~((~r1(X!0, Y!4)) | p2(Y!4) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))))),
% 1.16/0.99 inference(modus_ponens,[status(thm)],[79, 74])).
% 1.16/0.99 tff(81,plain,
% 1.16/0.99 ((~((~r1(X!0, Y!4)) | p2(Y!4) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y)))),
% 1.16/0.99 inference(modus_ponens,[status(thm)],[80, 73])).
% 1.16/0.99 tff(82,plain,
% 1.16/0.99 (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y)))),
% 1.16/0.99 inference(unit_resolution,[status(thm)],[81, 22])).
% 1.16/0.99 tff(83,plain,
% 1.16/0.99 (((~![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y)))) | ((~p5(tptp_fun_X_3(X!0))) | (~r1(X!0, tptp_fun_X_3(X!0))))) <=> ((~![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y)))) | (~p5(tptp_fun_X_3(X!0))) | (~r1(X!0, tptp_fun_X_3(X!0))))),
% 1.16/0.99 inference(rewrite,[status(thm)],[])).
% 1.16/0.99 tff(84,plain,
% 1.16/0.99 ((~![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y)))) | ((~p5(tptp_fun_X_3(X!0))) | (~r1(X!0, tptp_fun_X_3(X!0))))),
% 1.16/0.99 inference(quant_inst,[status(thm)],[])).
% 1.16/0.99 tff(85,plain,
% 1.16/0.99 ((~![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y)))) | (~p5(tptp_fun_X_3(X!0))) | (~r1(X!0, tptp_fun_X_3(X!0)))),
% 1.16/0.99 inference(modus_ponens,[status(thm)],[84, 83])).
% 1.16/0.99 tff(86,plain,
% 1.16/0.99 ($false),
% 1.16/0.99 inference(unit_resolution,[status(thm)],[85, 82, 69, 67])).
% 1.16/0.99 tff(87,plain,(~((~r1(X!0, Y!4)) | p2(Y!4) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))), inference(lemma,lemma(discharge,[]))).
% 1.16/0.99 tff(88,plain,
% 1.16/0.99 (((~r1(X!0, Y!4)) | p2(Y!4) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))),
% 1.16/0.99 inference(tautology,[status(thm)],[])).
% 1.16/0.99 tff(89,plain,
% 1.16/0.99 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))),
% 1.16/0.99 inference(unit_resolution,[status(thm)],[88, 87])).
% 1.16/0.99 tff(90,plain,
% 1.16/0.99 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (p2(Y!11) | (~r1(X!0, Y!11)) | (~((~p2(tptp_fun_X_5(Y!11))) | (~r1(tptp_fun_X_5(Y!11), tptp_fun_Y_6(Y!11))) | p2(tptp_fun_Y_6(Y!11)) | (~r1(Y!11, tptp_fun_X_5(Y!11))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | p2(Y!11) | (~r1(X!0, Y!11)) | (~((~p2(tptp_fun_X_5(Y!11))) | (~r1(tptp_fun_X_5(Y!11), tptp_fun_Y_6(Y!11))) | p2(tptp_fun_Y_6(Y!11)) | (~r1(Y!11, tptp_fun_X_5(Y!11))))))),
% 1.16/0.99 inference(rewrite,[status(thm)],[])).
% 1.16/0.99 tff(91,plain,
% 1.16/0.99 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (p2(Y!11) | (~r1(X!0, Y!11)) | (~((~p2(tptp_fun_X_5(Y!11))) | (~r1(tptp_fun_X_5(Y!11), tptp_fun_Y_6(Y!11))) | p2(tptp_fun_Y_6(Y!11)) | (~r1(Y!11, tptp_fun_X_5(Y!11))))))),
% 1.16/0.99 inference(quant_inst,[status(thm)],[])).
% 1.16/0.99 tff(92,plain,
% 1.16/0.99 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | p2(Y!11) | (~r1(X!0, Y!11)) | (~((~p2(tptp_fun_X_5(Y!11))) | (~r1(tptp_fun_X_5(Y!11), tptp_fun_Y_6(Y!11))) | p2(tptp_fun_Y_6(Y!11)) | (~r1(Y!11, tptp_fun_X_5(Y!11)))))),
% 1.16/0.99 inference(modus_ponens,[status(thm)],[91, 90])).
% 1.16/0.99 tff(93,plain,
% 1.16/0.99 (~((~p2(tptp_fun_X_5(Y!11))) | (~r1(tptp_fun_X_5(Y!11), tptp_fun_Y_6(Y!11))) | p2(tptp_fun_Y_6(Y!11)) | (~r1(Y!11, tptp_fun_X_5(Y!11))))),
% 1.16/0.99 inference(unit_resolution,[status(thm)],[92, 89, 12, 10])).
% 1.16/0.99 tff(94,plain,
% 1.16/0.99 (((~p2(tptp_fun_X_5(Y!11))) | (~r1(tptp_fun_X_5(Y!11), tptp_fun_Y_6(Y!11))) | p2(tptp_fun_Y_6(Y!11)) | (~r1(Y!11, tptp_fun_X_5(Y!11)))) | r1(Y!11, tptp_fun_X_5(Y!11))),
% 1.16/0.99 inference(tautology,[status(thm)],[])).
% 1.16/0.99 tff(95,plain,
% 1.16/0.99 (r1(Y!11, tptp_fun_X_5(Y!11))),
% 1.16/0.99 inference(unit_resolution,[status(thm)],[94, 93])).
% 1.16/0.99 tff(96,plain,
% 1.16/0.99 (((~p2(tptp_fun_X_5(Y!11))) | (~r1(tptp_fun_X_5(Y!11), tptp_fun_Y_6(Y!11))) | p2(tptp_fun_Y_6(Y!11)) | (~r1(Y!11, tptp_fun_X_5(Y!11)))) | p2(tptp_fun_X_5(Y!11))),
% 1.16/1.00 inference(tautology,[status(thm)],[])).
% 1.16/1.00 tff(97,plain,
% 1.16/1.00 (p2(tptp_fun_X_5(Y!11))),
% 1.16/1.00 inference(unit_resolution,[status(thm)],[96, 93])).
% 1.16/1.00 tff(98,plain,
% 1.16/1.00 ((p2(Y!11) | (~r1(X!0, Y!11)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) | ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))),
% 1.16/1.00 inference(tautology,[status(thm)],[])).
% 1.16/1.00 tff(99,plain,
% 1.16/1.00 (![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))),
% 1.16/1.00 inference(unit_resolution,[status(thm)],[98, 8])).
% 1.16/1.00 tff(100,plain,
% 1.16/1.00 (((~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ((~p2(tptp_fun_X_5(Y!11))) | (~r1(Y!11, tptp_fun_X_5(Y!11))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_5(Y!11), Y))))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~p2(tptp_fun_X_5(Y!11))) | (~r1(Y!11, tptp_fun_X_5(Y!11))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_5(Y!11), Y))))),
% 1.16/1.00 inference(rewrite,[status(thm)],[])).
% 1.16/1.00 tff(101,plain,
% 1.16/1.00 ((~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ((~p2(tptp_fun_X_5(Y!11))) | (~r1(Y!11, tptp_fun_X_5(Y!11))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_5(Y!11), Y))))),
% 1.16/1.00 inference(quant_inst,[status(thm)],[])).
% 1.16/1.00 tff(102,plain,
% 1.16/1.00 ((~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~p2(tptp_fun_X_5(Y!11))) | (~r1(Y!11, tptp_fun_X_5(Y!11))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_5(Y!11), Y)))),
% 1.16/1.00 inference(modus_ponens,[status(thm)],[101, 100])).
% 1.16/1.00 tff(103,plain,
% 1.16/1.00 (![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_5(Y!11), Y)))),
% 1.16/1.00 inference(unit_resolution,[status(thm)],[102, 99, 97, 95])).
% 1.16/1.00 tff(104,plain,
% 1.16/1.00 (((~p2(tptp_fun_X_5(Y!11))) | (~r1(tptp_fun_X_5(Y!11), tptp_fun_Y_6(Y!11))) | p2(tptp_fun_Y_6(Y!11)) | (~r1(Y!11, tptp_fun_X_5(Y!11)))) | (~p2(tptp_fun_Y_6(Y!11)))),
% 1.16/1.00 inference(tautology,[status(thm)],[])).
% 1.16/1.00 tff(105,plain,
% 1.16/1.00 (~p2(tptp_fun_Y_6(Y!11))),
% 1.16/1.00 inference(unit_resolution,[status(thm)],[104, 93])).
% 1.16/1.00 tff(106,plain,
% 1.16/1.00 (((~p2(tptp_fun_X_5(Y!11))) | (~r1(tptp_fun_X_5(Y!11), tptp_fun_Y_6(Y!11))) | p2(tptp_fun_Y_6(Y!11)) | (~r1(Y!11, tptp_fun_X_5(Y!11)))) | r1(tptp_fun_X_5(Y!11), tptp_fun_Y_6(Y!11))),
% 1.16/1.00 inference(tautology,[status(thm)],[])).
% 1.16/1.00 tff(107,plain,
% 1.16/1.00 (r1(tptp_fun_X_5(Y!11), tptp_fun_Y_6(Y!11))),
% 1.16/1.00 inference(unit_resolution,[status(thm)],[106, 93])).
% 1.16/1.00 tff(108,plain,
% 1.16/1.00 (((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_5(Y!11), Y)))) | (p2(tptp_fun_Y_6(Y!11)) | (~r1(tptp_fun_X_5(Y!11), tptp_fun_Y_6(Y!11))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_5(Y!11), Y)))) | p2(tptp_fun_Y_6(Y!11)) | (~r1(tptp_fun_X_5(Y!11), tptp_fun_Y_6(Y!11))))),
% 1.16/1.00 inference(rewrite,[status(thm)],[])).
% 1.16/1.00 tff(109,plain,
% 1.16/1.00 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_5(Y!11), Y)))) | (p2(tptp_fun_Y_6(Y!11)) | (~r1(tptp_fun_X_5(Y!11), tptp_fun_Y_6(Y!11))))),
% 1.16/1.00 inference(quant_inst,[status(thm)],[])).
% 1.16/1.00 tff(110,plain,
% 1.16/1.00 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_5(Y!11), Y)))) | p2(tptp_fun_Y_6(Y!11)) | (~r1(tptp_fun_X_5(Y!11), tptp_fun_Y_6(Y!11)))),
% 1.16/1.00 inference(modus_ponens,[status(thm)],[109, 108])).
% 1.16/1.00 tff(111,plain,
% 1.16/1.00 ($false),
% 1.16/1.00 inference(unit_resolution,[status(thm)],[110, 107, 105, 103])).
% 1.16/1.00 tff(112,plain,(p2(Y!11) | (~r1(X!0, Y!11)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))), inference(lemma,lemma(discharge,[]))).
% 1.16/1.00 tff(113,assumption,(![X: $i] : (p2(X) | (~r1(Y!4, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))), introduced(assumption)).
% 1.16/1.00 tff(114,assumption,(~((~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!4)), tptp_fun_X_13(tptp_fun_X_19(Y!4)))) | (~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | (~r1(tptp_fun_X_19(Y!4), tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!4))))), introduced(assumption)).
% 1.16/1.00 tff(115,plain,
% 1.16/1.00 (((~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!4)), tptp_fun_X_13(tptp_fun_X_19(Y!4)))) | (~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | (~r1(tptp_fun_X_19(Y!4), tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!4)))) | r1(tptp_fun_X_19(Y!4), tptp_fun_Y_12(tptp_fun_X_19(Y!4)))),
% 1.16/1.00 inference(tautology,[status(thm)],[])).
% 1.16/1.00 tff(116,plain,
% 1.16/1.00 (r1(tptp_fun_X_19(Y!4), tptp_fun_Y_12(tptp_fun_X_19(Y!4)))),
% 1.16/1.00 inference(unit_resolution,[status(thm)],[115, 114])).
% 1.16/1.00 tff(117,plain,
% 1.16/1.00 (((~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!4)), tptp_fun_X_13(tptp_fun_X_19(Y!4)))) | (~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | (~r1(tptp_fun_X_19(Y!4), tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!4)))) | p2(tptp_fun_Y_12(tptp_fun_X_19(Y!4)))),
% 1.16/1.00 inference(tautology,[status(thm)],[])).
% 1.16/1.00 tff(118,plain,
% 1.16/1.00 (p2(tptp_fun_Y_12(tptp_fun_X_19(Y!4)))),
% 1.16/1.00 inference(unit_resolution,[status(thm)],[117, 114])).
% 1.16/1.00 tff(119,plain,
% 1.16/1.00 (^[Y: $i] : refl((p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))))),
% 1.16/1.00 inference(bind,[status(th)],[])).
% 1.16/1.00 tff(120,plain,
% 1.16/1.00 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))),
% 1.16/1.00 inference(quant_intro,[status(thm)],[119])).
% 1.16/1.00 tff(121,plain,
% 1.16/1.00 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))))),
% 1.16/1.00 inference(bind,[status(th)],[])).
% 1.16/1.00 tff(122,plain,
% 1.16/1.00 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))),
% 1.16/1.00 inference(quant_intro,[status(thm)],[121])).
% 1.16/1.00 tff(123,plain,
% 1.16/1.00 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))),
% 1.16/1.00 inference(transitivity,[status(thm)],[122, 120])).
% 1.16/1.00 tff(124,plain,
% 1.16/1.00 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | ((~p2(tptp_fun_X_19(Y))) & r1(Y, tptp_fun_X_19(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))))),
% 1.16/1.00 inference(bind,[status(th)],[])).
% 1.16/1.00 tff(125,plain,
% 1.16/1.00 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~p2(tptp_fun_X_19(Y))) & r1(Y, tptp_fun_X_19(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))),
% 1.16/1.00 inference(quant_intro,[status(thm)],[124])).
% 1.16/1.00 tff(126,plain,
% 1.16/1.00 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~p2(tptp_fun_X_19(Y))) & r1(Y, tptp_fun_X_19(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))),
% 1.16/1.00 inference(and_elim,[status(thm)],[57])).
% 1.16/1.00 tff(127,plain,
% 1.16/1.00 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))),
% 1.16/1.00 inference(modus_ponens,[status(thm)],[126, 125])).
% 1.16/1.00 tff(128,plain,
% 1.16/1.00 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))),
% 1.16/1.00 inference(modus_ponens,[status(thm)],[127, 123])).
% 1.16/1.00 tff(129,plain,
% 1.16/1.00 (((~r1(X!0, Y!4)) | p2(Y!4) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))) | (~p2(Y!4))),
% 1.16/1.00 inference(tautology,[status(thm)],[])).
% 1.16/1.00 tff(130,plain,
% 1.16/1.00 (~p2(Y!4)),
% 1.16/1.00 inference(unit_resolution,[status(thm)],[129, 87])).
% 1.16/1.00 tff(131,plain,
% 1.16/1.00 (((~r1(X!0, Y!4)) | p2(Y!4) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))) | r1(X!0, Y!4)),
% 1.16/1.00 inference(tautology,[status(thm)],[])).
% 1.16/1.00 tff(132,plain,
% 1.16/1.00 (r1(X!0, Y!4)),
% 1.16/1.00 inference(unit_resolution,[status(thm)],[131, 87])).
% 1.16/1.00 tff(133,plain,
% 1.16/1.00 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))) | (p2(Y!4) | (~r1(X!0, Y!4)) | (~(p2(tptp_fun_X_19(Y!4)) | (~r1(Y!4, tptp_fun_X_19(Y!4))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!4), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))) | p2(Y!4) | (~r1(X!0, Y!4)) | (~(p2(tptp_fun_X_19(Y!4)) | (~r1(Y!4, tptp_fun_X_19(Y!4))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!4), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))),
% 1.16/1.00 inference(rewrite,[status(thm)],[])).
% 1.16/1.00 tff(134,plain,
% 1.16/1.00 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))) | (p2(Y!4) | (~r1(X!0, Y!4)) | (~(p2(tptp_fun_X_19(Y!4)) | (~r1(Y!4, tptp_fun_X_19(Y!4))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!4), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))),
% 1.16/1.00 inference(quant_inst,[status(thm)],[])).
% 1.16/1.00 tff(135,plain,
% 1.16/1.00 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))) | p2(Y!4) | (~r1(X!0, Y!4)) | (~(p2(tptp_fun_X_19(Y!4)) | (~r1(Y!4, tptp_fun_X_19(Y!4))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!4), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))),
% 1.16/1.00 inference(modus_ponens,[status(thm)],[134, 133])).
% 1.16/1.00 tff(136,plain,
% 1.16/1.00 (~(p2(tptp_fun_X_19(Y!4)) | (~r1(Y!4, tptp_fun_X_19(Y!4))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!4), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))),
% 1.16/1.00 inference(unit_resolution,[status(thm)],[135, 132, 130, 128])).
% 1.16/1.00 tff(137,plain,
% 1.16/1.00 ((p2(tptp_fun_X_19(Y!4)) | (~r1(Y!4, tptp_fun_X_19(Y!4))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!4), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) | ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!4), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))),
% 1.16/1.00 inference(tautology,[status(thm)],[])).
% 1.16/1.00 tff(138,plain,
% 1.16/1.00 (![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!4), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))),
% 1.16/1.00 inference(unit_resolution,[status(thm)],[137, 136])).
% 1.16/1.00 tff(139,plain,
% 1.16/1.00 (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!4), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | ((~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | (~r1(tptp_fun_X_19(Y!4), tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!4)), X))))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!4), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | (~r1(tptp_fun_X_19(Y!4), tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!4)), X))))),
% 1.16/1.00 inference(rewrite,[status(thm)],[])).
% 1.16/1.00 tff(140,plain,
% 1.16/1.00 ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!4), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | ((~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | (~r1(tptp_fun_X_19(Y!4), tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!4)), X))))),
% 1.16/1.00 inference(quant_inst,[status(thm)],[])).
% 1.16/1.00 tff(141,plain,
% 1.16/1.00 ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!4), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | (~r1(tptp_fun_X_19(Y!4), tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!4)), X)))),
% 1.16/1.00 inference(modus_ponens,[status(thm)],[140, 139])).
% 1.16/1.00 tff(142,plain,
% 1.16/1.00 (![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!4)), X)))),
% 1.16/1.00 inference(unit_resolution,[status(thm)],[141, 138, 118, 116])).
% 1.16/1.00 tff(143,plain,
% 1.16/1.00 (((~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!4)), tptp_fun_X_13(tptp_fun_X_19(Y!4)))) | (~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | (~r1(tptp_fun_X_19(Y!4), tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!4)))) | (~p2(tptp_fun_X_13(tptp_fun_X_19(Y!4))))),
% 1.16/1.00 inference(tautology,[status(thm)],[])).
% 1.16/1.00 tff(144,plain,
% 1.16/1.00 (~p2(tptp_fun_X_13(tptp_fun_X_19(Y!4)))),
% 1.16/1.00 inference(unit_resolution,[status(thm)],[143, 114])).
% 1.16/1.00 tff(145,plain,
% 1.16/1.00 (((~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!4)), tptp_fun_X_13(tptp_fun_X_19(Y!4)))) | (~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | (~r1(tptp_fun_X_19(Y!4), tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!4)))) | r1(tptp_fun_Y_12(tptp_fun_X_19(Y!4)), tptp_fun_X_13(tptp_fun_X_19(Y!4)))),
% 1.16/1.00 inference(tautology,[status(thm)],[])).
% 1.16/1.00 tff(146,plain,
% 1.16/1.00 (r1(tptp_fun_Y_12(tptp_fun_X_19(Y!4)), tptp_fun_X_13(tptp_fun_X_19(Y!4)))),
% 1.16/1.00 inference(unit_resolution,[status(thm)],[145, 114])).
% 1.16/1.00 tff(147,plain,
% 1.16/1.00 (((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!4)), X)))) | (p2(tptp_fun_X_13(tptp_fun_X_19(Y!4))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!4)), tptp_fun_X_13(tptp_fun_X_19(Y!4)))))) <=> ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!4)), X)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!4))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!4)), tptp_fun_X_13(tptp_fun_X_19(Y!4)))))),
% 1.16/1.00 inference(rewrite,[status(thm)],[])).
% 1.16/1.00 tff(148,plain,
% 1.16/1.00 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!4)), X)))) | (p2(tptp_fun_X_13(tptp_fun_X_19(Y!4))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!4)), tptp_fun_X_13(tptp_fun_X_19(Y!4)))))),
% 1.16/1.00 inference(quant_inst,[status(thm)],[])).
% 1.16/1.00 tff(149,plain,
% 1.16/1.00 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!4)), X)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!4))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!4)), tptp_fun_X_13(tptp_fun_X_19(Y!4))))),
% 1.16/1.00 inference(modus_ponens,[status(thm)],[148, 147])).
% 1.16/1.00 tff(150,plain,
% 1.16/1.00 ($false),
% 1.16/1.00 inference(unit_resolution,[status(thm)],[149, 146, 144, 142])).
% 1.16/1.00 tff(151,plain,((~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!4)), tptp_fun_X_13(tptp_fun_X_19(Y!4)))) | (~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | (~r1(tptp_fun_X_19(Y!4), tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!4)))), inference(lemma,lemma(discharge,[]))).
% 1.16/1.00 tff(152,plain,
% 1.16/1.00 ((p2(tptp_fun_X_19(Y!4)) | (~r1(Y!4, tptp_fun_X_19(Y!4))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!4), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) | r1(Y!4, tptp_fun_X_19(Y!4))),
% 1.16/1.00 inference(tautology,[status(thm)],[])).
% 1.16/1.00 tff(153,plain,
% 1.16/1.00 (r1(Y!4, tptp_fun_X_19(Y!4))),
% 1.16/1.00 inference(unit_resolution,[status(thm)],[152, 136])).
% 1.16/1.00 tff(154,plain,
% 1.16/1.00 ((p2(tptp_fun_X_19(Y!4)) | (~r1(Y!4, tptp_fun_X_19(Y!4))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!4), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) | (~p2(tptp_fun_X_19(Y!4)))),
% 1.16/1.00 inference(tautology,[status(thm)],[])).
% 1.16/1.00 tff(155,plain,
% 1.16/1.00 (~p2(tptp_fun_X_19(Y!4))),
% 1.16/1.00 inference(unit_resolution,[status(thm)],[154, 136])).
% 1.16/1.00 tff(156,plain,
% 1.16/1.00 (((~![X: $i] : (p2(X) | (~r1(Y!4, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))) | (p2(tptp_fun_X_19(Y!4)) | (~r1(Y!4, tptp_fun_X_19(Y!4))) | (~((~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!4)), tptp_fun_X_13(tptp_fun_X_19(Y!4)))) | (~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | (~r1(tptp_fun_X_19(Y!4), tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!4))))))) <=> ((~![X: $i] : (p2(X) | (~r1(Y!4, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))) | p2(tptp_fun_X_19(Y!4)) | (~r1(Y!4, tptp_fun_X_19(Y!4))) | (~((~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!4)), tptp_fun_X_13(tptp_fun_X_19(Y!4)))) | (~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | (~r1(tptp_fun_X_19(Y!4), tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!4))))))),
% 1.16/1.00 inference(rewrite,[status(thm)],[])).
% 1.16/1.00 tff(157,plain,
% 1.16/1.00 ((p2(tptp_fun_X_19(Y!4)) | (~r1(Y!4, tptp_fun_X_19(Y!4))) | (~((~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | (~r1(tptp_fun_X_19(Y!4), tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!4))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!4)), tptp_fun_X_13(tptp_fun_X_19(Y!4))))))) <=> (p2(tptp_fun_X_19(Y!4)) | (~r1(Y!4, tptp_fun_X_19(Y!4))) | (~((~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!4)), tptp_fun_X_13(tptp_fun_X_19(Y!4)))) | (~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | (~r1(tptp_fun_X_19(Y!4), tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!4))))))),
% 1.16/1.00 inference(rewrite,[status(thm)],[])).
% 1.16/1.00 tff(158,plain,
% 1.16/1.00 (((~![X: $i] : (p2(X) | (~r1(Y!4, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))) | (p2(tptp_fun_X_19(Y!4)) | (~r1(Y!4, tptp_fun_X_19(Y!4))) | (~((~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | (~r1(tptp_fun_X_19(Y!4), tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!4))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!4)), tptp_fun_X_13(tptp_fun_X_19(Y!4)))))))) <=> ((~![X: $i] : (p2(X) | (~r1(Y!4, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))) | (p2(tptp_fun_X_19(Y!4)) | (~r1(Y!4, tptp_fun_X_19(Y!4))) | (~((~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!4)), tptp_fun_X_13(tptp_fun_X_19(Y!4)))) | (~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | (~r1(tptp_fun_X_19(Y!4), tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!4)))))))),
% 1.16/1.00 inference(monotonicity,[status(thm)],[157])).
% 1.16/1.00 tff(159,plain,
% 1.16/1.00 (((~![X: $i] : (p2(X) | (~r1(Y!4, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))) | (p2(tptp_fun_X_19(Y!4)) | (~r1(Y!4, tptp_fun_X_19(Y!4))) | (~((~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | (~r1(tptp_fun_X_19(Y!4), tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!4))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!4)), tptp_fun_X_13(tptp_fun_X_19(Y!4)))))))) <=> ((~![X: $i] : (p2(X) | (~r1(Y!4, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))) | p2(tptp_fun_X_19(Y!4)) | (~r1(Y!4, tptp_fun_X_19(Y!4))) | (~((~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!4)), tptp_fun_X_13(tptp_fun_X_19(Y!4)))) | (~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | (~r1(tptp_fun_X_19(Y!4), tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!4))))))),
% 1.16/1.00 inference(transitivity,[status(thm)],[158, 156])).
% 1.16/1.00 tff(160,plain,
% 1.16/1.00 ((~![X: $i] : (p2(X) | (~r1(Y!4, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))) | (p2(tptp_fun_X_19(Y!4)) | (~r1(Y!4, tptp_fun_X_19(Y!4))) | (~((~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | (~r1(tptp_fun_X_19(Y!4), tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!4))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!4)), tptp_fun_X_13(tptp_fun_X_19(Y!4)))))))),
% 1.16/1.00 inference(quant_inst,[status(thm)],[])).
% 1.16/1.00 tff(161,plain,
% 1.16/1.00 ((~![X: $i] : (p2(X) | (~r1(Y!4, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))) | p2(tptp_fun_X_19(Y!4)) | (~r1(Y!4, tptp_fun_X_19(Y!4))) | (~((~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!4)), tptp_fun_X_13(tptp_fun_X_19(Y!4)))) | (~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | (~r1(tptp_fun_X_19(Y!4), tptp_fun_Y_12(tptp_fun_X_19(Y!4)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!4)))))),
% 1.16/1.00 inference(modus_ponens,[status(thm)],[160, 159])).
% 1.16/1.00 tff(162,plain,
% 1.16/1.00 ($false),
% 1.16/1.00 inference(unit_resolution,[status(thm)],[161, 155, 153, 151, 113])).
% 1.16/1.00 tff(163,plain,(~![X: $i] : (p2(X) | (~r1(Y!4, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))), inference(lemma,lemma(discharge,[]))).
% 1.16/1.00 tff(164,assumption,(![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X)))))))), introduced(assumption)).
% 1.16/1.00 tff(165,plain,
% 1.16/1.00 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X)))))))) | ((~r1(X!0, Y!4)) | ![X: $i] : (p2(X) | (~r1(Y!4, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X)))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X)))))))) | (~r1(X!0, Y!4)) | ![X: $i] : (p2(X) | (~r1(Y!4, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X)))))))),
% 1.16/1.00 inference(rewrite,[status(thm)],[])).
% 1.16/1.00 tff(166,plain,
% 1.16/1.00 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X)))))))) | ((~r1(X!0, Y!4)) | ![X: $i] : (p2(X) | (~r1(Y!4, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X)))))))),
% 1.16/1.00 inference(quant_inst,[status(thm)],[])).
% 1.16/1.00 tff(167,plain,
% 1.16/1.00 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X)))))))) | (~r1(X!0, Y!4)) | ![X: $i] : (p2(X) | (~r1(Y!4, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))),
% 1.16/1.00 inference(modus_ponens,[status(thm)],[166, 165])).
% 1.16/1.00 tff(168,plain,
% 1.16/1.00 ($false),
% 1.16/1.00 inference(unit_resolution,[status(thm)],[167, 132, 164, 163])).
% 1.16/1.00 tff(169,plain,(~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X)))))))), inference(lemma,lemma(discharge,[]))).
% 1.16/1.00 tff(170,plain,
% 1.16/1.00 ((~((~(p2(Y!11) | (~r1(X!0, Y!11)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))) | (~(p2(Y!11) | (~r1(X!0, Y!11)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X)))))))),
% 1.16/1.00 inference(tautology,[status(thm)],[])).
% 1.16/1.00 tff(171,plain,
% 1.16/1.00 (~((~(p2(Y!11) | (~r1(X!0, Y!11)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))),
% 1.16/1.00 inference(unit_resolution,[status(thm)],[170, 169, 112])).
% 1.16/1.00 tff(172,plain,
% 1.16/1.00 (((~(p2(X!0) | (~((~p2(Y!14)) | (~r1(X!0, Y!14)) | p2(X!15) | (~r1(Y!14, X!15)))))) | (~((~(p2(Y!11) | (~r1(X!0, Y!11)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X)))))))))) | ((~(p2(Y!11) | (~r1(X!0, Y!11)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))),
% 1.16/1.00 inference(tautology,[status(thm)],[])).
% 1.16/1.00 tff(173,plain,
% 1.16/1.00 ((~(p2(X!0) | (~((~p2(Y!14)) | (~r1(X!0, Y!14)) | p2(X!15) | (~r1(Y!14, X!15)))))) | (~((~(p2(Y!11) | (~r1(X!0, Y!11)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X)))))))))),
% 1.16/1.00 inference(unit_resolution,[status(thm)],[172, 171])).
% 1.16/1.00 tff(174,plain,
% 1.16/1.00 (((~((~((~(p2(Y!11) | (~r1(X!0, Y!11)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))) | (~(p2(X!0) | (~((~p2(Y!14)) | (~r1(X!0, Y!14)) | p2(X!15) | (~r1(Y!14, X!15)))))))) | (~((~r1(X!0, Y!16)) | (~((~(p2(Y!16) | (~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!16, X!17)) | p2(Y!18) | (~r1(X!17, Y!18)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))))) | (~![X: $i] : ((~r1(Y!16, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_20(X))) | p2(tptp_fun_X_21(X)) | (~r1(tptp_fun_Y_20(X), tptp_fun_X_21(X))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | (~(p2(Y) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))))))) <=> ((~((~(p2(X!0) | (~((~p2(Y!14)) | (~r1(X!0, Y!14)) | p2(X!15) | (~r1(Y!14, X!15)))))) | (~((~(p2(Y!11) | (~r1(X!0, Y!11)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))))) | (~((~r1(X!0, Y!16)) | (~((~(p2(Y!16) | (~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!16, X!17)) | p2(Y!18) | (~r1(X!17, Y!18)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))))) | (~![X: $i] : ((~r1(Y!16, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_20(X))) | p2(tptp_fun_X_21(X)) | (~r1(tptp_fun_Y_20(X), tptp_fun_X_21(X))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (~((~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))))))))))))),
% 1.16/1.00 inference(rewrite,[status(thm)],[])).
% 1.16/1.00 tff(175,plain,
% 1.16/1.00 (((~((~((~(p2(Y!11) | (~r1(X!0, Y!11)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))) | (~(p2(X!0) | (~((~p2(Y!14)) | (~r1(X!0, Y!14)) | p2(X!15) | (~r1(Y!14, X!15)))))))) | (~((~r1(X!0, Y!16)) | (~((~(p2(Y!16) | (~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!16, X!17)) | p2(Y!18) | (~r1(X!17, Y!18)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))))) | (~![X: $i] : ((~r1(Y!16, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_20(X))) | p2(tptp_fun_X_21(X)) | (~r1(tptp_fun_Y_20(X), tptp_fun_X_21(X))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | (~(p2(Y) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))))))) <=> ((~((~((~(p2(Y!11) | (~r1(X!0, Y!11)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))) | (~(p2(X!0) | (~((~p2(Y!14)) | (~r1(X!0, Y!14)) | p2(X!15) | (~r1(Y!14, X!15)))))))) | (~((~r1(X!0, Y!16)) | (~((~(p2(Y!16) | (~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!16, X!17)) | p2(Y!18) | (~r1(X!17, Y!18)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))))) | (~![X: $i] : ((~r1(Y!16, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_20(X))) | p2(tptp_fun_X_21(X)) | (~r1(tptp_fun_Y_20(X), tptp_fun_X_21(X))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | (~(p2(Y) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))))))))))),
% 1.16/1.00 inference(rewrite,[status(thm)],[])).
% 1.16/1.00 tff(176,plain,
% 1.16/1.00 ((((((~p2(Y!11)) & r1(X!0, Y!11) & ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (p2(tptp_fun_Y_12(X)) & r1(X, tptp_fun_Y_12(X)) & (~(p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))) & (p2(X!0) | (p2(Y!14) & r1(X!0, Y!14) & (~(p2(X!15) | (~r1(Y!14, X!15))))))) | (r1(X!0, Y!16) & (((~p2(Y!16)) & ![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (r1(Y!16, X!17) & (~p2(Y!18)) & r1(X!17, Y!18) & ![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))) & ![X: $i] : (p2(X) | (~r1(Y!16, X)) | (p2(tptp_fun_Y_12(X)) & r1(X, tptp_fun_Y_12(X)) & (~(p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))) & ![X: $i] : ((~r1(Y!16, X)) | ((~p2(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))) & r1(X, tptp_fun_Y_20(X)) & (~p2(tptp_fun_X_21(X))) & r1(tptp_fun_Y_20(X), tptp_fun_X_21(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) | ((~p2(tptp_fun_X_19(Y))) & r1(Y, tptp_fun_X_19(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) & (p2(Y) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))))))) <=> ((~((~((~(p2(Y!11) | (~r1(X!0, Y!11)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))) | (~(p2(X!0) | (~((~p2(Y!14)) | (~r1(X!0, Y!14)) | p2(X!15) | (~r1(Y!14, X!15)))))))) | (~((~r1(X!0, Y!16)) | (~((~(p2(Y!16) | (~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!16, X!17)) | p2(Y!18) | (~r1(X!17, Y!18)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))))) | (~![X: $i] : ((~r1(Y!16, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_20(X))) | p2(tptp_fun_X_21(X)) | (~r1(tptp_fun_Y_20(X), tptp_fun_X_21(X))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | (~(p2(Y) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))))))))))),
% 1.16/1.00 inference(rewrite,[status(thm)],[])).
% 1.16/1.00 tff(177,plain,
% 1.16/1.00 (((((~p2(Y!11)) & r1(X!0, Y!11) & ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (p2(tptp_fun_Y_12(X)) & r1(X, tptp_fun_Y_12(X)) & (~(p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))) & (p2(X!0) | (p2(Y!14) & r1(X!0, Y!14) & (~(p2(X!15) | (~r1(Y!14, X!15))))))) | (r1(X!0, Y!16) & (((~p2(Y!16)) & ![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (r1(Y!16, X!17) & (~p2(Y!18)) & r1(X!17, Y!18) & ![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))) & ![X: $i] : (p2(X) | (~r1(Y!16, X)) | (p2(tptp_fun_Y_12(X)) & r1(X, tptp_fun_Y_12(X)) & (~(p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))) & ![X: $i] : ((~r1(Y!16, X)) | ((~p2(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))) & r1(X, tptp_fun_Y_20(X)) & (~p2(tptp_fun_X_21(X))) & r1(tptp_fun_Y_20(X), tptp_fun_X_21(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) | ((~p2(tptp_fun_X_19(Y))) & r1(Y, tptp_fun_X_19(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) & (p2(Y) | (p2(tptp_fun_X_5(Y)) & r1(Y, tptp_fun_X_5(Y)) & (~(p2(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))))))),
% 1.16/1.01 inference(and_elim,[status(thm)],[57])).
% 1.16/1.01 tff(178,plain,
% 1.16/1.01 ((~((~((~(p2(Y!11) | (~r1(X!0, Y!11)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))) | (~(p2(X!0) | (~((~p2(Y!14)) | (~r1(X!0, Y!14)) | p2(X!15) | (~r1(Y!14, X!15)))))))) | (~((~r1(X!0, Y!16)) | (~((~(p2(Y!16) | (~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!16, X!17)) | p2(Y!18) | (~r1(X!17, Y!18)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))))) | (~![X: $i] : ((~r1(Y!16, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_20(X))) | p2(tptp_fun_X_21(X)) | (~r1(tptp_fun_Y_20(X), tptp_fun_X_21(X))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | (~(p2(Y) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))))))),
% 1.16/1.01 inference(modus_ponens,[status(thm)],[177, 176])).
% 1.16/1.01 tff(179,plain,
% 1.16/1.01 ((~((~((~(p2(Y!11) | (~r1(X!0, Y!11)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))) | (~(p2(X!0) | (~((~p2(Y!14)) | (~r1(X!0, Y!14)) | p2(X!15) | (~r1(Y!14, X!15)))))))) | (~((~r1(X!0, Y!16)) | (~((~(p2(Y!16) | (~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!16, X!17)) | p2(Y!18) | (~r1(X!17, Y!18)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))))) | (~![X: $i] : ((~r1(Y!16, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_20(X))) | p2(tptp_fun_X_21(X)) | (~r1(tptp_fun_Y_20(X), tptp_fun_X_21(X))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | (~(p2(Y) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))))))),
% 1.16/1.01 inference(modus_ponens,[status(thm)],[178, 175])).
% 1.16/1.01 tff(180,plain,
% 1.16/1.01 ((~((~(p2(X!0) | (~((~p2(Y!14)) | (~r1(X!0, Y!14)) | p2(X!15) | (~r1(Y!14, X!15)))))) | (~((~(p2(Y!11) | (~r1(X!0, Y!11)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))))) | (~((~r1(X!0, Y!16)) | (~((~(p2(Y!16) | (~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!16, X!17)) | p2(Y!18) | (~r1(X!17, Y!18)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))))) | (~![X: $i] : ((~r1(Y!16, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_20(X))) | p2(tptp_fun_X_21(X)) | (~r1(tptp_fun_Y_20(X), tptp_fun_X_21(X))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (~((~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))))))))),
% 1.16/1.01 inference(modus_ponens,[status(thm)],[179, 174])).
% 1.16/1.01 tff(181,plain,
% 1.16/1.01 (~((~r1(X!0, Y!16)) | (~((~(p2(Y!16) | (~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!16, X!17)) | p2(Y!18) | (~r1(X!17, Y!18)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))))) | (~![X: $i] : ((~r1(Y!16, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_20(X))) | p2(tptp_fun_X_21(X)) | (~r1(tptp_fun_Y_20(X), tptp_fun_X_21(X))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (~((~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))))))))))),
% 1.16/1.01 inference(unit_resolution,[status(thm)],[180, 173])).
% 1.16/1.01 tff(182,plain,
% 1.16/1.01 (((~r1(X!0, Y!16)) | (~((~(p2(Y!16) | (~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!16, X!17)) | p2(Y!18) | (~r1(X!17, Y!18)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))))) | (~![X: $i] : ((~r1(Y!16, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_20(X))) | p2(tptp_fun_X_21(X)) | (~r1(tptp_fun_Y_20(X), tptp_fun_X_21(X))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (~((~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))))))) | ((~(p2(Y!16) | (~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!16, X!17)) | p2(Y!18) | (~r1(X!17, Y!18)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))))),
% 1.16/1.01 inference(tautology,[status(thm)],[])).
% 1.16/1.01 tff(183,plain,
% 1.16/1.01 ((~(p2(Y!16) | (~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!16, X!17)) | p2(Y!18) | (~r1(X!17, Y!18)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X)))))))))),
% 1.16/1.01 inference(unit_resolution,[status(thm)],[182, 181])).
% 1.16/1.01 tff(184,plain,
% 1.16/1.01 (((~r1(X!0, Y!16)) | (~((~(p2(Y!16) | (~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!16, X!17)) | p2(Y!18) | (~r1(X!17, Y!18)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))))) | (~![X: $i] : ((~r1(Y!16, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_20(X))) | p2(tptp_fun_X_21(X)) | (~r1(tptp_fun_Y_20(X), tptp_fun_X_21(X))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (~((~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))))))) | r1(X!0, Y!16)),
% 1.16/1.01 inference(tautology,[status(thm)],[])).
% 1.16/1.01 tff(185,plain,
% 1.16/1.01 (r1(X!0, Y!16)),
% 1.16/1.01 inference(unit_resolution,[status(thm)],[184, 181])).
% 1.16/1.01 tff(186,assumption,((~(p2(Y!16) | (~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!16, X!17)) | p2(Y!18) | (~r1(X!17, Y!18)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X)))))))))), introduced(assumption)).
% 1.16/1.01 tff(187,assumption,(r1(X!0, Y!16)), introduced(assumption)).
% 1.16/1.01 tff(188,assumption,(~p2(Y!16)), introduced(assumption)).
% 1.16/1.01 tff(189,assumption,((~r1(tptp_fun_X_5(Y!16), tptp_fun_Y_6(Y!16))) | p2(tptp_fun_Y_6(Y!16)) | (~r1(Y!16, tptp_fun_X_5(Y!16))) | (~p2(tptp_fun_X_5(Y!16)))), introduced(assumption)).
% 1.16/1.01 tff(190,assumption,(![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))), introduced(assumption)).
% 1.16/1.01 tff(191,plain,
% 1.16/1.01 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (p2(Y!16) | (~r1(X!0, Y!16)) | (~((~r1(tptp_fun_X_5(Y!16), tptp_fun_Y_6(Y!16))) | p2(tptp_fun_Y_6(Y!16)) | (~r1(Y!16, tptp_fun_X_5(Y!16))) | (~p2(tptp_fun_X_5(Y!16))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | p2(Y!16) | (~r1(X!0, Y!16)) | (~((~r1(tptp_fun_X_5(Y!16), tptp_fun_Y_6(Y!16))) | p2(tptp_fun_Y_6(Y!16)) | (~r1(Y!16, tptp_fun_X_5(Y!16))) | (~p2(tptp_fun_X_5(Y!16))))))),
% 1.16/1.01 inference(rewrite,[status(thm)],[])).
% 1.16/1.01 tff(192,plain,
% 1.16/1.01 ((p2(Y!16) | (~r1(X!0, Y!16)) | (~((~p2(tptp_fun_X_5(Y!16))) | (~r1(tptp_fun_X_5(Y!16), tptp_fun_Y_6(Y!16))) | p2(tptp_fun_Y_6(Y!16)) | (~r1(Y!16, tptp_fun_X_5(Y!16)))))) <=> (p2(Y!16) | (~r1(X!0, Y!16)) | (~((~r1(tptp_fun_X_5(Y!16), tptp_fun_Y_6(Y!16))) | p2(tptp_fun_Y_6(Y!16)) | (~r1(Y!16, tptp_fun_X_5(Y!16))) | (~p2(tptp_fun_X_5(Y!16))))))),
% 1.16/1.01 inference(rewrite,[status(thm)],[])).
% 1.16/1.01 tff(193,plain,
% 1.16/1.01 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (p2(Y!16) | (~r1(X!0, Y!16)) | (~((~p2(tptp_fun_X_5(Y!16))) | (~r1(tptp_fun_X_5(Y!16), tptp_fun_Y_6(Y!16))) | p2(tptp_fun_Y_6(Y!16)) | (~r1(Y!16, tptp_fun_X_5(Y!16))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (p2(Y!16) | (~r1(X!0, Y!16)) | (~((~r1(tptp_fun_X_5(Y!16), tptp_fun_Y_6(Y!16))) | p2(tptp_fun_Y_6(Y!16)) | (~r1(Y!16, tptp_fun_X_5(Y!16))) | (~p2(tptp_fun_X_5(Y!16)))))))),
% 1.16/1.01 inference(monotonicity,[status(thm)],[192])).
% 1.16/1.01 tff(194,plain,
% 1.16/1.01 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (p2(Y!16) | (~r1(X!0, Y!16)) | (~((~p2(tptp_fun_X_5(Y!16))) | (~r1(tptp_fun_X_5(Y!16), tptp_fun_Y_6(Y!16))) | p2(tptp_fun_Y_6(Y!16)) | (~r1(Y!16, tptp_fun_X_5(Y!16))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | p2(Y!16) | (~r1(X!0, Y!16)) | (~((~r1(tptp_fun_X_5(Y!16), tptp_fun_Y_6(Y!16))) | p2(tptp_fun_Y_6(Y!16)) | (~r1(Y!16, tptp_fun_X_5(Y!16))) | (~p2(tptp_fun_X_5(Y!16))))))),
% 1.16/1.01 inference(transitivity,[status(thm)],[193, 191])).
% 1.16/1.01 tff(195,plain,
% 1.16/1.01 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (p2(Y!16) | (~r1(X!0, Y!16)) | (~((~p2(tptp_fun_X_5(Y!16))) | (~r1(tptp_fun_X_5(Y!16), tptp_fun_Y_6(Y!16))) | p2(tptp_fun_Y_6(Y!16)) | (~r1(Y!16, tptp_fun_X_5(Y!16))))))),
% 1.16/1.01 inference(quant_inst,[status(thm)],[])).
% 1.16/1.01 tff(196,plain,
% 1.16/1.01 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | p2(Y!16) | (~r1(X!0, Y!16)) | (~((~r1(tptp_fun_X_5(Y!16), tptp_fun_Y_6(Y!16))) | p2(tptp_fun_Y_6(Y!16)) | (~r1(Y!16, tptp_fun_X_5(Y!16))) | (~p2(tptp_fun_X_5(Y!16)))))),
% 1.16/1.01 inference(modus_ponens,[status(thm)],[195, 194])).
% 1.16/1.01 tff(197,plain,
% 1.16/1.01 ($false),
% 1.16/1.01 inference(unit_resolution,[status(thm)],[196, 190, 187, 188, 189])).
% 1.16/1.01 tff(198,plain,((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (~r1(X!0, Y!16)) | p2(Y!16) | (~((~r1(tptp_fun_X_5(Y!16), tptp_fun_Y_6(Y!16))) | p2(tptp_fun_Y_6(Y!16)) | (~r1(Y!16, tptp_fun_X_5(Y!16))) | (~p2(tptp_fun_X_5(Y!16)))))), inference(lemma,lemma(discharge,[]))).
% 1.16/1.01 tff(199,plain,
% 1.16/1.01 (~((~r1(tptp_fun_X_5(Y!16), tptp_fun_Y_6(Y!16))) | p2(tptp_fun_Y_6(Y!16)) | (~r1(Y!16, tptp_fun_X_5(Y!16))) | (~p2(tptp_fun_X_5(Y!16))))),
% 1.16/1.01 inference(unit_resolution,[status(thm)],[198, 188, 89, 187])).
% 1.16/1.01 tff(200,assumption,(~((~r1(tptp_fun_X_5(Y!16), tptp_fun_Y_6(Y!16))) | p2(tptp_fun_Y_6(Y!16)) | (~r1(Y!16, tptp_fun_X_5(Y!16))) | (~p2(tptp_fun_X_5(Y!16))))), introduced(assumption)).
% 1.16/1.01 tff(201,plain,
% 1.16/1.01 (((~r1(tptp_fun_X_5(Y!16), tptp_fun_Y_6(Y!16))) | p2(tptp_fun_Y_6(Y!16)) | (~r1(Y!16, tptp_fun_X_5(Y!16))) | (~p2(tptp_fun_X_5(Y!16)))) | p2(tptp_fun_X_5(Y!16))),
% 1.16/1.01 inference(tautology,[status(thm)],[])).
% 1.16/1.01 tff(202,plain,
% 1.16/1.01 (p2(tptp_fun_X_5(Y!16))),
% 1.16/1.01 inference(unit_resolution,[status(thm)],[201, 200])).
% 1.16/1.01 tff(203,plain,
% 1.16/1.01 (((~r1(tptp_fun_X_5(Y!16), tptp_fun_Y_6(Y!16))) | p2(tptp_fun_Y_6(Y!16)) | (~r1(Y!16, tptp_fun_X_5(Y!16))) | (~p2(tptp_fun_X_5(Y!16)))) | r1(Y!16, tptp_fun_X_5(Y!16))),
% 1.16/1.01 inference(tautology,[status(thm)],[])).
% 1.16/1.01 tff(204,plain,
% 1.16/1.01 (r1(Y!16, tptp_fun_X_5(Y!16))),
% 1.16/1.01 inference(unit_resolution,[status(thm)],[203, 200])).
% 1.16/1.01 tff(205,assumption,(![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))), introduced(assumption)).
% 1.16/1.01 tff(206,plain,
% 1.16/1.01 (((~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ((~p2(tptp_fun_X_5(Y!16))) | (~r1(Y!16, tptp_fun_X_5(Y!16))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_5(Y!16), Y))))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~p2(tptp_fun_X_5(Y!16))) | (~r1(Y!16, tptp_fun_X_5(Y!16))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_5(Y!16), Y))))),
% 1.16/1.01 inference(rewrite,[status(thm)],[])).
% 1.16/1.01 tff(207,plain,
% 1.16/1.01 ((~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ((~p2(tptp_fun_X_5(Y!16))) | (~r1(Y!16, tptp_fun_X_5(Y!16))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_5(Y!16), Y))))),
% 1.16/1.01 inference(quant_inst,[status(thm)],[])).
% 1.16/1.01 tff(208,plain,
% 1.16/1.01 ((~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~p2(tptp_fun_X_5(Y!16))) | (~r1(Y!16, tptp_fun_X_5(Y!16))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_5(Y!16), Y)))),
% 1.16/1.01 inference(modus_ponens,[status(thm)],[207, 206])).
% 1.16/1.01 tff(209,plain,
% 1.16/1.01 (![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_5(Y!16), Y)))),
% 1.16/1.01 inference(unit_resolution,[status(thm)],[208, 205, 204, 202])).
% 1.16/1.01 tff(210,plain,
% 1.16/1.01 (((~r1(tptp_fun_X_5(Y!16), tptp_fun_Y_6(Y!16))) | p2(tptp_fun_Y_6(Y!16)) | (~r1(Y!16, tptp_fun_X_5(Y!16))) | (~p2(tptp_fun_X_5(Y!16)))) | (~p2(tptp_fun_Y_6(Y!16)))),
% 1.16/1.01 inference(tautology,[status(thm)],[])).
% 1.16/1.01 tff(211,plain,
% 1.16/1.01 (~p2(tptp_fun_Y_6(Y!16))),
% 1.16/1.01 inference(unit_resolution,[status(thm)],[210, 200])).
% 1.16/1.01 tff(212,plain,
% 1.16/1.01 (((~r1(tptp_fun_X_5(Y!16), tptp_fun_Y_6(Y!16))) | p2(tptp_fun_Y_6(Y!16)) | (~r1(Y!16, tptp_fun_X_5(Y!16))) | (~p2(tptp_fun_X_5(Y!16)))) | r1(tptp_fun_X_5(Y!16), tptp_fun_Y_6(Y!16))),
% 1.16/1.01 inference(tautology,[status(thm)],[])).
% 1.16/1.01 tff(213,plain,
% 1.16/1.01 (r1(tptp_fun_X_5(Y!16), tptp_fun_Y_6(Y!16))),
% 1.16/1.01 inference(unit_resolution,[status(thm)],[212, 200])).
% 1.16/1.01 tff(214,plain,
% 1.16/1.01 (((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_5(Y!16), Y)))) | (p2(tptp_fun_Y_6(Y!16)) | (~r1(tptp_fun_X_5(Y!16), tptp_fun_Y_6(Y!16))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_5(Y!16), Y)))) | p2(tptp_fun_Y_6(Y!16)) | (~r1(tptp_fun_X_5(Y!16), tptp_fun_Y_6(Y!16))))),
% 1.16/1.01 inference(rewrite,[status(thm)],[])).
% 1.16/1.01 tff(215,plain,
% 1.16/1.01 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_5(Y!16), Y)))) | (p2(tptp_fun_Y_6(Y!16)) | (~r1(tptp_fun_X_5(Y!16), tptp_fun_Y_6(Y!16))))),
% 1.16/1.01 inference(quant_inst,[status(thm)],[])).
% 1.16/1.01 tff(216,plain,
% 1.16/1.01 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_5(Y!16), Y)))) | p2(tptp_fun_Y_6(Y!16)) | (~r1(tptp_fun_X_5(Y!16), tptp_fun_Y_6(Y!16)))),
% 1.16/1.01 inference(modus_ponens,[status(thm)],[215, 214])).
% 1.16/1.01 tff(217,plain,
% 1.16/1.01 ($false),
% 1.16/1.01 inference(unit_resolution,[status(thm)],[216, 213, 211, 209])).
% 1.16/1.01 tff(218,plain,(((~r1(tptp_fun_X_5(Y!16), tptp_fun_Y_6(Y!16))) | p2(tptp_fun_Y_6(Y!16)) | (~r1(Y!16, tptp_fun_X_5(Y!16))) | (~p2(tptp_fun_X_5(Y!16)))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))), inference(lemma,lemma(discharge,[]))).
% 1.16/1.01 tff(219,plain,
% 1.16/1.01 (~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))),
% 1.16/1.01 inference(unit_resolution,[status(thm)],[218, 199])).
% 1.16/1.01 tff(220,plain,
% 1.16/1.01 ((p2(Y!16) | (~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) | ![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))),
% 1.16/1.01 inference(tautology,[status(thm)],[])).
% 1.16/1.01 tff(221,plain,
% 1.16/1.01 (p2(Y!16) | (~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))),
% 1.16/1.01 inference(unit_resolution,[status(thm)],[220, 219])).
% 1.16/1.01 tff(222,plain,
% 1.16/1.01 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))) | (p2(Y!16) | (~r1(X!0, Y!16)) | (~(p2(tptp_fun_X_19(Y!16)) | (~r1(Y!16, tptp_fun_X_19(Y!16))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!16), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))) | p2(Y!16) | (~r1(X!0, Y!16)) | (~(p2(tptp_fun_X_19(Y!16)) | (~r1(Y!16, tptp_fun_X_19(Y!16))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!16), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))),
% 1.16/1.01 inference(rewrite,[status(thm)],[])).
% 1.16/1.01 tff(223,plain,
% 1.16/1.01 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))) | (p2(Y!16) | (~r1(X!0, Y!16)) | (~(p2(tptp_fun_X_19(Y!16)) | (~r1(Y!16, tptp_fun_X_19(Y!16))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!16), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))),
% 1.16/1.01 inference(quant_inst,[status(thm)],[])).
% 1.16/1.01 tff(224,plain,
% 1.16/1.01 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))) | p2(Y!16) | (~r1(X!0, Y!16)) | (~(p2(tptp_fun_X_19(Y!16)) | (~r1(Y!16, tptp_fun_X_19(Y!16))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!16), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))),
% 1.16/1.01 inference(modus_ponens,[status(thm)],[223, 222])).
% 1.16/1.01 tff(225,plain,
% 1.16/1.01 (p2(Y!16) | (~(p2(tptp_fun_X_19(Y!16)) | (~r1(Y!16, tptp_fun_X_19(Y!16))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!16), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))),
% 1.16/1.01 inference(unit_resolution,[status(thm)],[224, 187, 128])).
% 1.16/1.01 tff(226,plain,
% 1.16/1.01 (~(p2(tptp_fun_X_19(Y!16)) | (~r1(Y!16, tptp_fun_X_19(Y!16))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!16), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))),
% 1.16/1.01 inference(unit_resolution,[status(thm)],[225, 188])).
% 1.16/1.01 tff(227,assumption,(~(p2(tptp_fun_X_19(Y!16)) | (~r1(Y!16, tptp_fun_X_19(Y!16))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!16), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))), introduced(assumption)).
% 1.16/1.01 tff(228,plain,
% 1.16/1.01 ((p2(tptp_fun_X_19(Y!16)) | (~r1(Y!16, tptp_fun_X_19(Y!16))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!16), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) | r1(Y!16, tptp_fun_X_19(Y!16))),
% 1.16/1.01 inference(tautology,[status(thm)],[])).
% 1.16/1.01 tff(229,plain,
% 1.16/1.01 (r1(Y!16, tptp_fun_X_19(Y!16))),
% 1.16/1.01 inference(unit_resolution,[status(thm)],[228, 227])).
% 1.16/1.01 tff(230,plain,
% 1.16/1.01 ((p2(tptp_fun_X_19(Y!16)) | (~r1(Y!16, tptp_fun_X_19(Y!16))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!16), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) | (~p2(tptp_fun_X_19(Y!16)))),
% 1.16/1.01 inference(tautology,[status(thm)],[])).
% 1.16/1.01 tff(231,plain,
% 1.16/1.01 (~p2(tptp_fun_X_19(Y!16))),
% 1.16/1.01 inference(unit_resolution,[status(thm)],[230, 227])).
% 1.16/1.01 tff(232,assumption,(![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))), introduced(assumption)).
% 1.16/1.01 tff(233,plain,
% 1.16/1.01 (((~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))) | (p2(tptp_fun_X_19(Y!16)) | (~r1(Y!16, tptp_fun_X_19(Y!16))) | (~((~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!16)))) | (~r1(tptp_fun_X_19(Y!16), tptp_fun_Y_12(tptp_fun_X_19(Y!16)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!16))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!16)), tptp_fun_X_13(tptp_fun_X_19(Y!16)))))))) <=> ((~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))) | p2(tptp_fun_X_19(Y!16)) | (~r1(Y!16, tptp_fun_X_19(Y!16))) | (~((~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!16)))) | (~r1(tptp_fun_X_19(Y!16), tptp_fun_Y_12(tptp_fun_X_19(Y!16)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!16))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!16)), tptp_fun_X_13(tptp_fun_X_19(Y!16)))))))),
% 1.16/1.01 inference(rewrite,[status(thm)],[])).
% 1.16/1.01 tff(234,plain,
% 1.16/1.01 ((~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))) | (p2(tptp_fun_X_19(Y!16)) | (~r1(Y!16, tptp_fun_X_19(Y!16))) | (~((~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!16)))) | (~r1(tptp_fun_X_19(Y!16), tptp_fun_Y_12(tptp_fun_X_19(Y!16)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!16))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!16)), tptp_fun_X_13(tptp_fun_X_19(Y!16)))))))),
% 1.16/1.01 inference(quant_inst,[status(thm)],[])).
% 1.16/1.01 tff(235,plain,
% 1.16/1.01 ((~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))) | p2(tptp_fun_X_19(Y!16)) | (~r1(Y!16, tptp_fun_X_19(Y!16))) | (~((~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!16)))) | (~r1(tptp_fun_X_19(Y!16), tptp_fun_Y_12(tptp_fun_X_19(Y!16)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!16))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!16)), tptp_fun_X_13(tptp_fun_X_19(Y!16))))))),
% 1.16/1.01 inference(modus_ponens,[status(thm)],[234, 233])).
% 1.16/1.01 tff(236,plain,
% 1.16/1.01 (~((~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!16)))) | (~r1(tptp_fun_X_19(Y!16), tptp_fun_Y_12(tptp_fun_X_19(Y!16)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!16))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!16)), tptp_fun_X_13(tptp_fun_X_19(Y!16)))))),
% 1.16/1.01 inference(unit_resolution,[status(thm)],[235, 232, 231, 229])).
% 1.16/1.01 tff(237,plain,
% 1.16/1.01 (((~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!16)))) | (~r1(tptp_fun_X_19(Y!16), tptp_fun_Y_12(tptp_fun_X_19(Y!16)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!16))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!16)), tptp_fun_X_13(tptp_fun_X_19(Y!16))))) | r1(tptp_fun_X_19(Y!16), tptp_fun_Y_12(tptp_fun_X_19(Y!16)))),
% 1.16/1.01 inference(tautology,[status(thm)],[])).
% 1.16/1.01 tff(238,plain,
% 1.16/1.01 (r1(tptp_fun_X_19(Y!16), tptp_fun_Y_12(tptp_fun_X_19(Y!16)))),
% 1.16/1.01 inference(unit_resolution,[status(thm)],[237, 236])).
% 1.16/1.01 tff(239,plain,
% 1.16/1.01 (((~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!16)))) | (~r1(tptp_fun_X_19(Y!16), tptp_fun_Y_12(tptp_fun_X_19(Y!16)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!16))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!16)), tptp_fun_X_13(tptp_fun_X_19(Y!16))))) | p2(tptp_fun_Y_12(tptp_fun_X_19(Y!16)))),
% 1.16/1.01 inference(tautology,[status(thm)],[])).
% 1.16/1.01 tff(240,plain,
% 1.16/1.01 (p2(tptp_fun_Y_12(tptp_fun_X_19(Y!16)))),
% 1.16/1.01 inference(unit_resolution,[status(thm)],[239, 236])).
% 1.16/1.01 tff(241,plain,
% 1.16/1.01 ((p2(tptp_fun_X_19(Y!16)) | (~r1(Y!16, tptp_fun_X_19(Y!16))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!16), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) | ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!16), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))),
% 1.16/1.01 inference(tautology,[status(thm)],[])).
% 1.16/1.01 tff(242,plain,
% 1.16/1.01 (![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!16), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))),
% 1.16/1.01 inference(unit_resolution,[status(thm)],[241, 227])).
% 1.16/1.01 tff(243,plain,
% 1.16/1.01 (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!16), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | ((~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!16)))) | (~r1(tptp_fun_X_19(Y!16), tptp_fun_Y_12(tptp_fun_X_19(Y!16)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!16)), X))))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!16), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!16)))) | (~r1(tptp_fun_X_19(Y!16), tptp_fun_Y_12(tptp_fun_X_19(Y!16)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!16)), X))))),
% 1.16/1.01 inference(rewrite,[status(thm)],[])).
% 1.16/1.01 tff(244,plain,
% 1.16/1.01 ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!16), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | ((~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!16)))) | (~r1(tptp_fun_X_19(Y!16), tptp_fun_Y_12(tptp_fun_X_19(Y!16)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!16)), X))))),
% 1.16/1.01 inference(quant_inst,[status(thm)],[])).
% 1.16/1.01 tff(245,plain,
% 1.16/1.01 ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!16), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!16)))) | (~r1(tptp_fun_X_19(Y!16), tptp_fun_Y_12(tptp_fun_X_19(Y!16)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!16)), X)))),
% 1.16/1.01 inference(modus_ponens,[status(thm)],[244, 243])).
% 1.16/1.01 tff(246,plain,
% 1.16/1.01 (![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!16)), X)))),
% 1.16/1.01 inference(unit_resolution,[status(thm)],[245, 242, 240, 238])).
% 1.16/1.01 tff(247,plain,
% 1.16/1.01 (((~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!16)))) | (~r1(tptp_fun_X_19(Y!16), tptp_fun_Y_12(tptp_fun_X_19(Y!16)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!16))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!16)), tptp_fun_X_13(tptp_fun_X_19(Y!16))))) | r1(tptp_fun_Y_12(tptp_fun_X_19(Y!16)), tptp_fun_X_13(tptp_fun_X_19(Y!16)))),
% 1.16/1.01 inference(tautology,[status(thm)],[])).
% 1.16/1.01 tff(248,plain,
% 1.16/1.01 (r1(tptp_fun_Y_12(tptp_fun_X_19(Y!16)), tptp_fun_X_13(tptp_fun_X_19(Y!16)))),
% 1.16/1.01 inference(unit_resolution,[status(thm)],[247, 236])).
% 1.16/1.01 tff(249,plain,
% 1.16/1.01 (((~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!16)))) | (~r1(tptp_fun_X_19(Y!16), tptp_fun_Y_12(tptp_fun_X_19(Y!16)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!16))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!16)), tptp_fun_X_13(tptp_fun_X_19(Y!16))))) | (~p2(tptp_fun_X_13(tptp_fun_X_19(Y!16))))),
% 1.16/1.01 inference(tautology,[status(thm)],[])).
% 1.16/1.01 tff(250,plain,
% 1.16/1.01 (~p2(tptp_fun_X_13(tptp_fun_X_19(Y!16)))),
% 1.16/1.01 inference(unit_resolution,[status(thm)],[249, 236])).
% 1.16/1.01 tff(251,plain,
% 1.16/1.01 (((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!16)), X)))) | (p2(tptp_fun_X_13(tptp_fun_X_19(Y!16))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!16)), tptp_fun_X_13(tptp_fun_X_19(Y!16)))))) <=> ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!16)), X)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!16))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!16)), tptp_fun_X_13(tptp_fun_X_19(Y!16)))))),
% 1.16/1.01 inference(rewrite,[status(thm)],[])).
% 1.16/1.01 tff(252,plain,
% 1.16/1.01 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!16)), X)))) | (p2(tptp_fun_X_13(tptp_fun_X_19(Y!16))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!16)), tptp_fun_X_13(tptp_fun_X_19(Y!16)))))),
% 1.16/1.01 inference(quant_inst,[status(thm)],[])).
% 1.16/1.01 tff(253,plain,
% 1.16/1.01 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!16)), X)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!16))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!16)), tptp_fun_X_13(tptp_fun_X_19(Y!16))))),
% 1.16/1.01 inference(modus_ponens,[status(thm)],[252, 251])).
% 1.16/1.02 tff(254,plain,
% 1.16/1.02 ($false),
% 1.16/1.02 inference(unit_resolution,[status(thm)],[253, 250, 248, 246])).
% 1.16/1.02 tff(255,plain,((p2(tptp_fun_X_19(Y!16)) | (~r1(Y!16, tptp_fun_X_19(Y!16))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!16), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) | (~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X)))))))), inference(lemma,lemma(discharge,[]))).
% 1.16/1.02 tff(256,plain,
% 1.16/1.02 (~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))),
% 1.16/1.02 inference(unit_resolution,[status(thm)],[255, 226])).
% 1.16/1.02 tff(257,plain,
% 1.16/1.02 (((~r1(Y!16, X!17)) | p2(Y!18) | (~r1(X!17, Y!18)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X)))))))) | ![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))),
% 1.16/1.02 inference(tautology,[status(thm)],[])).
% 1.16/1.02 tff(258,plain,
% 1.16/1.02 ((~r1(Y!16, X!17)) | p2(Y!18) | (~r1(X!17, Y!18)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X)))))))),
% 1.16/1.02 inference(unit_resolution,[status(thm)],[257, 256])).
% 1.16/1.02 tff(259,plain,
% 1.16/1.02 ((~((~(p2(Y!16) | (~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!16, X!17)) | p2(Y!18) | (~r1(X!17, Y!18)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))))) | (~(p2(Y!16) | (~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!16, X!17)) | p2(Y!18) | (~r1(X!17, Y!18)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X)))))))))),
% 1.16/1.02 inference(tautology,[status(thm)],[])).
% 1.16/1.02 tff(260,plain,
% 1.16/1.02 ($false),
% 1.16/1.02 inference(unit_resolution,[status(thm)],[259, 258, 221, 186])).
% 1.16/1.02 tff(261,plain,(p2(Y!16) | (~((~(p2(Y!16) | (~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!16, X!17)) | p2(Y!18) | (~r1(X!17, Y!18)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))))) | (~r1(X!0, Y!16))), inference(lemma,lemma(discharge,[]))).
% 1.16/1.02 tff(262,plain,
% 1.16/1.02 (p2(Y!16)),
% 1.16/1.02 inference(unit_resolution,[status(thm)],[261, 183, 185])).
% 1.16/1.02 tff(263,plain,
% 1.16/1.02 ((p2(Y!16) | (~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) | (~p2(Y!16))),
% 1.16/1.02 inference(tautology,[status(thm)],[])).
% 1.16/1.02 tff(264,plain,
% 1.16/1.02 (p2(Y!16) | (~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))),
% 1.16/1.02 inference(unit_resolution,[status(thm)],[263, 262])).
% 1.16/1.02 tff(265,plain,
% 1.16/1.02 (~((~r1(Y!16, X!17)) | p2(Y!18) | (~r1(X!17, Y!18)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))),
% 1.16/1.02 inference(unit_resolution,[status(thm)],[259, 264, 183])).
% 1.16/1.02 tff(266,plain,
% 1.16/1.02 (((~r1(Y!16, X!17)) | p2(Y!18) | (~r1(X!17, Y!18)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X)))))))) | ![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))),
% 1.16/1.02 inference(tautology,[status(thm)],[])).
% 1.16/1.02 tff(267,plain,
% 1.16/1.02 (![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))),
% 1.16/1.02 inference(unit_resolution,[status(thm)],[266, 265])).
% 1.16/1.02 tff(268,plain,
% 1.16/1.02 (((~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ((~p2(tptp_fun_X_5(Y!18))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_5(Y!18), Y))))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~p2(tptp_fun_X_5(Y!18))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_5(Y!18), Y))))),
% 1.16/1.02 inference(rewrite,[status(thm)],[])).
% 1.16/1.02 tff(269,plain,
% 1.16/1.02 ((~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ((~p2(tptp_fun_X_5(Y!18))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_5(Y!18), Y))))),
% 1.16/1.02 inference(quant_inst,[status(thm)],[])).
% 1.16/1.02 tff(270,plain,
% 1.16/1.02 ((~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~p2(tptp_fun_X_5(Y!18))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_5(Y!18), Y)))),
% 1.16/1.02 inference(modus_ponens,[status(thm)],[269, 268])).
% 1.16/1.02 tff(271,plain,
% 1.16/1.02 (![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_5(Y!18), Y)))),
% 1.16/1.02 inference(unit_resolution,[status(thm)],[270, 267, 7, 5])).
% 1.16/1.02 tff(272,plain,
% 1.16/1.02 ((p2(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p2(tptp_fun_X_5(Y!18)))) | r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))),
% 1.16/1.02 inference(tautology,[status(thm)],[])).
% 1.16/1.02 tff(273,plain,
% 1.16/1.02 (r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))),
% 1.16/1.02 inference(unit_resolution,[status(thm)],[272, 1])).
% 1.16/1.02 tff(274,assumption,(~p2(tptp_fun_Y_6(Y!18))), introduced(assumption)).
% 1.16/1.02 tff(275,plain,
% 1.16/1.02 (((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_5(Y!18), Y)))) | (p2(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_5(Y!18), Y)))) | p2(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))))),
% 1.16/1.02 inference(rewrite,[status(thm)],[])).
% 1.16/1.02 tff(276,plain,
% 1.16/1.02 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_5(Y!18), Y)))) | (p2(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))))),
% 1.16/1.02 inference(quant_inst,[status(thm)],[])).
% 1.16/1.02 tff(277,plain,
% 1.16/1.02 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_5(Y!18), Y)))) | p2(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18)))),
% 1.16/1.02 inference(modus_ponens,[status(thm)],[276, 275])).
% 1.16/1.02 tff(278,plain,
% 1.16/1.02 ($false),
% 1.16/1.02 inference(unit_resolution,[status(thm)],[277, 274, 273, 271])).
% 1.16/1.02 tff(279,plain,((p2(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p2(tptp_fun_X_5(Y!18)))) | p2(tptp_fun_Y_6(Y!18))), inference(lemma,lemma(discharge,[]))).
% 1.16/1.02 tff(280,plain,
% 1.16/1.02 ($false),
% 1.16/1.02 inference(unit_resolution,[status(thm)],[279, 3, 1])).
% 1.16/1.02 tff(281,plain,(p2(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p2(tptp_fun_X_5(Y!18)))), inference(lemma,lemma(discharge,[]))).
% 1.16/1.02 tff(282,assumption,(p2(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p2(tptp_fun_X_5(Y!18)))), introduced(assumption)).
% 1.16/1.02 tff(283,plain,
% 1.16/1.02 (((~r1(Y!16, X!17)) | p2(Y!18) | (~r1(X!17, Y!18)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X)))))))) | (~p2(Y!18))),
% 1.16/1.02 inference(tautology,[status(thm)],[])).
% 1.16/1.02 tff(284,plain,
% 1.16/1.02 (~p2(Y!18)),
% 1.16/1.02 inference(unit_resolution,[status(thm)],[283, 265])).
% 1.16/1.02 tff(285,plain,
% 1.16/1.02 ((~(p2(Y!18) | (~(p2(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p2(tptp_fun_X_5(Y!18))))))) | p2(Y!18) | (~(p2(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p2(tptp_fun_X_5(Y!18)))))),
% 1.16/1.02 inference(tautology,[status(thm)],[])).
% 1.16/1.02 tff(286,plain,
% 1.16/1.02 (~(p2(Y!18) | (~(p2(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p2(tptp_fun_X_5(Y!18))))))),
% 1.16/1.02 inference(unit_resolution,[status(thm)],[285, 284, 282])).
% 1.16/1.02 tff(287,plain,
% 1.16/1.02 (((~(p2(Y!18) | (~(p2(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p2(tptp_fun_X_5(Y!18))))))) | (~((~(p2(tptp_fun_X_19(Y!18)) | (~r1(Y!18, tptp_fun_X_19(Y!18))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!18), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))))) | (p2(Y!18) | (~(p2(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p2(tptp_fun_X_5(Y!18))))))),
% 1.16/1.02 inference(tautology,[status(thm)],[])).
% 1.16/1.02 tff(288,plain,
% 1.16/1.02 ((~(p2(Y!18) | (~(p2(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p2(tptp_fun_X_5(Y!18))))))) | (~((~(p2(tptp_fun_X_19(Y!18)) | (~r1(Y!18, tptp_fun_X_19(Y!18))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!18), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))))),
% 1.16/1.02 inference(unit_resolution,[status(thm)],[287, 286])).
% 1.16/1.02 tff(289,assumption,(p2(X!17) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!17, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))), introduced(assumption)).
% 1.16/1.02 tff(290,assumption,(![Y: $i] : (p2(Y) | (~r1(X!17, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))), introduced(assumption)).
% 1.16/1.02 tff(291,plain,
% 1.16/1.02 (((~r1(Y!16, X!17)) | p2(Y!18) | (~r1(X!17, Y!18)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X)))))))) | r1(X!17, Y!18)),
% 1.16/1.02 inference(tautology,[status(thm)],[])).
% 1.16/1.02 tff(292,plain,
% 1.16/1.02 (r1(X!17, Y!18)),
% 1.16/1.02 inference(unit_resolution,[status(thm)],[291, 265])).
% 1.16/1.02 tff(293,plain,
% 1.16/1.02 (((~![Y: $i] : (p2(Y) | (~r1(X!17, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (p2(Y!18) | (~r1(X!17, Y!18)) | (~(p2(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p2(tptp_fun_X_5(Y!18))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!17, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | p2(Y!18) | (~r1(X!17, Y!18)) | (~(p2(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p2(tptp_fun_X_5(Y!18))))))),
% 1.16/1.02 inference(rewrite,[status(thm)],[])).
% 1.16/1.02 tff(294,plain,
% 1.16/1.02 ((p2(Y!18) | (~r1(X!17, Y!18)) | (~((~p2(tptp_fun_X_5(Y!18))) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | p2(tptp_fun_Y_6(Y!18)) | (~r1(Y!18, tptp_fun_X_5(Y!18)))))) <=> (p2(Y!18) | (~r1(X!17, Y!18)) | (~(p2(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p2(tptp_fun_X_5(Y!18))))))),
% 1.16/1.02 inference(rewrite,[status(thm)],[])).
% 1.16/1.02 tff(295,plain,
% 1.16/1.02 (((~![Y: $i] : (p2(Y) | (~r1(X!17, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (p2(Y!18) | (~r1(X!17, Y!18)) | (~((~p2(tptp_fun_X_5(Y!18))) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | p2(tptp_fun_Y_6(Y!18)) | (~r1(Y!18, tptp_fun_X_5(Y!18))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!17, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (p2(Y!18) | (~r1(X!17, Y!18)) | (~(p2(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p2(tptp_fun_X_5(Y!18)))))))),
% 1.16/1.02 inference(monotonicity,[status(thm)],[294])).
% 1.16/1.02 tff(296,plain,
% 1.16/1.02 (((~![Y: $i] : (p2(Y) | (~r1(X!17, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (p2(Y!18) | (~r1(X!17, Y!18)) | (~((~p2(tptp_fun_X_5(Y!18))) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | p2(tptp_fun_Y_6(Y!18)) | (~r1(Y!18, tptp_fun_X_5(Y!18))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!17, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | p2(Y!18) | (~r1(X!17, Y!18)) | (~(p2(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p2(tptp_fun_X_5(Y!18))))))),
% 1.16/1.02 inference(transitivity,[status(thm)],[295, 293])).
% 1.16/1.02 tff(297,plain,
% 1.16/1.02 ((~![Y: $i] : (p2(Y) | (~r1(X!17, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (p2(Y!18) | (~r1(X!17, Y!18)) | (~((~p2(tptp_fun_X_5(Y!18))) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | p2(tptp_fun_Y_6(Y!18)) | (~r1(Y!18, tptp_fun_X_5(Y!18))))))),
% 1.16/1.02 inference(quant_inst,[status(thm)],[])).
% 1.16/1.02 tff(298,plain,
% 1.16/1.02 ((~![Y: $i] : (p2(Y) | (~r1(X!17, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | p2(Y!18) | (~r1(X!17, Y!18)) | (~(p2(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p2(tptp_fun_X_5(Y!18)))))),
% 1.16/1.02 inference(modus_ponens,[status(thm)],[297, 296])).
% 1.16/1.02 tff(299,plain,
% 1.16/1.02 ($false),
% 1.16/1.02 inference(unit_resolution,[status(thm)],[298, 284, 292, 290, 282])).
% 1.16/1.02 tff(300,plain,((~![Y: $i] : (p2(Y) | (~r1(X!17, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (~(p2(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p2(tptp_fun_X_5(Y!18)))))), inference(lemma,lemma(discharge,[]))).
% 1.16/1.02 tff(301,plain,
% 1.16/1.02 (~![Y: $i] : (p2(Y) | (~r1(X!17, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))),
% 1.16/1.02 inference(unit_resolution,[status(thm)],[300, 282])).
% 1.16/1.02 tff(302,plain,
% 1.16/1.02 (((~r1(X!17, tptp_fun_Y_20(X!17))) | p2(tptp_fun_X_21(X!17)) | (~r1(tptp_fun_Y_20(X!17), tptp_fun_X_21(X!17))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X!17), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X!17, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))) | ![Y: $i] : (p2(Y) | (~r1(X!17, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))),
% 1.16/1.02 inference(tautology,[status(thm)],[])).
% 1.16/1.02 tff(303,plain,
% 1.16/1.02 ((~r1(X!17, tptp_fun_Y_20(X!17))) | p2(tptp_fun_X_21(X!17)) | (~r1(tptp_fun_Y_20(X!17), tptp_fun_X_21(X!17))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X!17), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X!17, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))),
% 1.16/1.02 inference(unit_resolution,[status(thm)],[302, 301])).
% 1.16/1.02 tff(304,plain,
% 1.16/1.02 (((~r1(X!0, Y!16)) | (~((~(p2(Y!16) | (~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!16, X!17)) | p2(Y!18) | (~r1(X!17, Y!18)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))))))) | (~![X: $i] : ((~r1(Y!16, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_20(X))) | p2(tptp_fun_X_21(X)) | (~r1(tptp_fun_Y_20(X), tptp_fun_X_21(X))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (~((~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))))))) | ![X: $i] : ((~r1(Y!16, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_20(X))) | p2(tptp_fun_X_21(X)) | (~r1(tptp_fun_Y_20(X), tptp_fun_X_21(X))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (~((~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))))))))),
% 1.16/1.02 inference(tautology,[status(thm)],[])).
% 1.16/1.02 tff(305,plain,
% 1.16/1.02 (![X: $i] : ((~r1(Y!16, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_20(X))) | p2(tptp_fun_X_21(X)) | (~r1(tptp_fun_Y_20(X), tptp_fun_X_21(X))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (~((~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))))))))),
% 1.16/1.02 inference(unit_resolution,[status(thm)],[304, 181])).
% 1.16/1.02 tff(306,plain,
% 1.16/1.02 (((~r1(Y!16, X!17)) | p2(Y!18) | (~r1(X!17, Y!18)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X)))))))) | r1(Y!16, X!17)),
% 1.16/1.02 inference(tautology,[status(thm)],[])).
% 1.16/1.02 tff(307,plain,
% 1.16/1.02 (r1(Y!16, X!17)),
% 1.16/1.02 inference(unit_resolution,[status(thm)],[306, 265])).
% 1.16/1.02 tff(308,plain,
% 1.16/1.02 (((~![X: $i] : ((~r1(Y!16, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_20(X))) | p2(tptp_fun_X_21(X)) | (~r1(tptp_fun_Y_20(X), tptp_fun_X_21(X))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (~((~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))))))))) | ((~r1(Y!16, X!17)) | (~(p2(X!17) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!17, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X!17, tptp_fun_Y_20(X!17))) | p2(tptp_fun_X_21(X!17)) | (~r1(tptp_fun_Y_20(X!17), tptp_fun_X_21(X!17))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X!17), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X!17, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![Y: $i] : ((~r1(X!17, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (~((~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))))))))) <=> ((~![X: $i] : ((~r1(Y!16, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_20(X))) | p2(tptp_fun_X_21(X)) | (~r1(tptp_fun_Y_20(X), tptp_fun_X_21(X))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (~((~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))))))))) | (~r1(Y!16, X!17)) | (~(p2(X!17) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!17, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X!17, tptp_fun_Y_20(X!17))) | p2(tptp_fun_X_21(X!17)) | (~r1(tptp_fun_Y_20(X!17), tptp_fun_X_21(X!17))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X!17), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X!17, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![Y: $i] : ((~r1(X!17, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (~((~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))))))))),
% 1.16/1.02 inference(rewrite,[status(thm)],[])).
% 1.16/1.02 tff(309,plain,
% 1.16/1.02 ((~![X: $i] : ((~r1(Y!16, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_20(X))) | p2(tptp_fun_X_21(X)) | (~r1(tptp_fun_Y_20(X), tptp_fun_X_21(X))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (~((~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))))))))) | ((~r1(Y!16, X!17)) | (~(p2(X!17) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!17, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X!17, tptp_fun_Y_20(X!17))) | p2(tptp_fun_X_21(X!17)) | (~r1(tptp_fun_Y_20(X!17), tptp_fun_X_21(X!17))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X!17), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X!17, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![Y: $i] : ((~r1(X!17, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (~((~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))))))))),
% 1.16/1.02 inference(quant_inst,[status(thm)],[])).
% 1.16/1.02 tff(310,plain,
% 1.16/1.02 ((~![X: $i] : ((~r1(Y!16, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_20(X))) | p2(tptp_fun_X_21(X)) | (~r1(tptp_fun_Y_20(X), tptp_fun_X_21(X))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (~((~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))))))))) | (~r1(Y!16, X!17)) | (~(p2(X!17) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!17, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X!17, tptp_fun_Y_20(X!17))) | p2(tptp_fun_X_21(X!17)) | (~r1(tptp_fun_Y_20(X!17), tptp_fun_X_21(X!17))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X!17), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X!17, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![Y: $i] : ((~r1(X!17, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (~((~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))))),
% 1.16/1.02 inference(modus_ponens,[status(thm)],[309, 308])).
% 1.16/1.02 tff(311,plain,
% 1.16/1.02 ((~(p2(X!17) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!17, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X!17, tptp_fun_Y_20(X!17))) | p2(tptp_fun_X_21(X!17)) | (~r1(tptp_fun_Y_20(X!17), tptp_fun_X_21(X!17))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(X!17), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X!17, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) | ![Y: $i] : ((~r1(X!17, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (~((~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))))),
% 1.16/1.02 inference(unit_resolution,[status(thm)],[310, 307, 305])).
% 1.16/1.02 tff(312,plain,
% 1.16/1.02 (![Y: $i] : ((~r1(X!17, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (~((~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))))),
% 1.16/1.02 inference(unit_resolution,[status(thm)],[311, 303, 289])).
% 1.16/1.02 tff(313,plain,
% 1.16/1.02 (((~![Y: $i] : ((~r1(X!17, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (~((~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))))) | ((~r1(X!17, Y!18)) | (~((~(p2(Y!18) | (~(p2(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p2(tptp_fun_X_5(Y!18))))))) | (~((~(p2(tptp_fun_X_19(Y!18)) | (~r1(Y!18, tptp_fun_X_19(Y!18))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!18), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))))) <=> ((~![Y: $i] : ((~r1(X!17, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (~((~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))))) | (~r1(X!17, Y!18)) | (~((~(p2(Y!18) | (~(p2(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p2(tptp_fun_X_5(Y!18))))))) | (~((~(p2(tptp_fun_X_19(Y!18)) | (~r1(Y!18, tptp_fun_X_19(Y!18))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!18), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))))),
% 1.16/1.02 inference(rewrite,[status(thm)],[])).
% 1.16/1.02 tff(314,plain,
% 1.16/1.02 (((~r1(X!17, Y!18)) | (~((~(p2(Y!18) | (~((~p2(tptp_fun_X_5(Y!18))) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | p2(tptp_fun_Y_6(Y!18)) | (~r1(Y!18, tptp_fun_X_5(Y!18))))))) | (~((~(p2(tptp_fun_X_19(Y!18)) | (~r1(Y!18, tptp_fun_X_19(Y!18))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!18), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))))))) <=> ((~r1(X!17, Y!18)) | (~((~(p2(Y!18) | (~(p2(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p2(tptp_fun_X_5(Y!18))))))) | (~((~(p2(tptp_fun_X_19(Y!18)) | (~r1(Y!18, tptp_fun_X_19(Y!18))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!18), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))))),
% 1.16/1.03 inference(rewrite,[status(thm)],[])).
% 1.16/1.03 tff(315,plain,
% 1.16/1.03 (((~![Y: $i] : ((~r1(X!17, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (~((~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))))) | ((~r1(X!17, Y!18)) | (~((~(p2(Y!18) | (~((~p2(tptp_fun_X_5(Y!18))) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | p2(tptp_fun_Y_6(Y!18)) | (~r1(Y!18, tptp_fun_X_5(Y!18))))))) | (~((~(p2(tptp_fun_X_19(Y!18)) | (~r1(Y!18, tptp_fun_X_19(Y!18))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!18), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))))) <=> ((~![Y: $i] : ((~r1(X!17, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (~((~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))))) | ((~r1(X!17, Y!18)) | (~((~(p2(Y!18) | (~(p2(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p2(tptp_fun_X_5(Y!18))))))) | (~((~(p2(tptp_fun_X_19(Y!18)) | (~r1(Y!18, tptp_fun_X_19(Y!18))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!18), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))))))))),
% 1.16/1.03 inference(monotonicity,[status(thm)],[314])).
% 1.16/1.03 tff(316,plain,
% 1.16/1.03 (((~![Y: $i] : ((~r1(X!17, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (~((~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))))) | ((~r1(X!17, Y!18)) | (~((~(p2(Y!18) | (~((~p2(tptp_fun_X_5(Y!18))) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | p2(tptp_fun_Y_6(Y!18)) | (~r1(Y!18, tptp_fun_X_5(Y!18))))))) | (~((~(p2(tptp_fun_X_19(Y!18)) | (~r1(Y!18, tptp_fun_X_19(Y!18))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!18), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))))) <=> ((~![Y: $i] : ((~r1(X!17, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (~((~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))))) | (~r1(X!17, Y!18)) | (~((~(p2(Y!18) | (~(p2(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p2(tptp_fun_X_5(Y!18))))))) | (~((~(p2(tptp_fun_X_19(Y!18)) | (~r1(Y!18, tptp_fun_X_19(Y!18))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!18), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))))),
% 1.16/1.03 inference(transitivity,[status(thm)],[315, 313])).
% 1.16/1.03 tff(317,plain,
% 1.16/1.03 ((~![Y: $i] : ((~r1(X!17, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (~((~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))))) | ((~r1(X!17, Y!18)) | (~((~(p2(Y!18) | (~((~p2(tptp_fun_X_5(Y!18))) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | p2(tptp_fun_Y_6(Y!18)) | (~r1(Y!18, tptp_fun_X_5(Y!18))))))) | (~((~(p2(tptp_fun_X_19(Y!18)) | (~r1(Y!18, tptp_fun_X_19(Y!18))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!18), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))))),
% 1.16/1.03 inference(quant_inst,[status(thm)],[])).
% 1.16/1.03 tff(318,plain,
% 1.16/1.03 ((~![Y: $i] : ((~r1(X!17, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) | (~((~(p2(tptp_fun_X_19(Y)) | (~r1(Y, tptp_fun_X_19(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))))) | (~r1(X!17, Y!18)) | (~((~(p2(Y!18) | (~(p2(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p2(tptp_fun_X_5(Y!18))))))) | (~((~(p2(tptp_fun_X_19(Y!18)) | (~r1(Y!18, tptp_fun_X_19(Y!18))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!18), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_5(Y))) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))) | p2(tptp_fun_Y_6(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))))))))),
% 1.16/1.03 inference(modus_ponens,[status(thm)],[317, 316])).
% 1.16/1.03 tff(319,plain,
% 1.16/1.03 ($false),
% 1.16/1.03 inference(unit_resolution,[status(thm)],[318, 292, 312, 288])).
% 1.16/1.03 tff(320,plain,((~(p2(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p2(tptp_fun_X_5(Y!18))))) | (~(p2(X!17) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!17, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))), inference(lemma,lemma(discharge,[]))).
% 1.16/1.03 tff(321,plain,
% 1.16/1.03 (~(p2(X!17) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!17, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))),
% 1.16/1.03 inference(unit_resolution,[status(thm)],[320, 281])).
% 1.16/1.03 tff(322,plain,
% 1.16/1.03 ((p2(X!17) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!17, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) | (~p2(X!17))),
% 1.16/1.03 inference(tautology,[status(thm)],[])).
% 1.16/1.03 tff(323,plain,
% 1.16/1.03 (~p2(X!17)),
% 1.16/1.03 inference(unit_resolution,[status(thm)],[322, 321])).
% 1.16/1.03 tff(324,plain,
% 1.16/1.03 (![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))),
% 1.16/1.03 inference(unit_resolution,[status(thm)],[257, 265])).
% 1.16/1.03 tff(325,plain,
% 1.16/1.03 (((~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))) | (p2(X!17) | (~r1(Y!16, X!17)) | (~((~p2(tptp_fun_Y_12(X!17))) | (~r1(X!17, tptp_fun_Y_12(X!17))) | p2(tptp_fun_X_13(X!17)) | (~r1(tptp_fun_Y_12(X!17), tptp_fun_X_13(X!17))))))) <=> ((~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))) | p2(X!17) | (~r1(Y!16, X!17)) | (~((~p2(tptp_fun_Y_12(X!17))) | (~r1(X!17, tptp_fun_Y_12(X!17))) | p2(tptp_fun_X_13(X!17)) | (~r1(tptp_fun_Y_12(X!17), tptp_fun_X_13(X!17))))))),
% 1.16/1.03 inference(rewrite,[status(thm)],[])).
% 1.16/1.03 tff(326,plain,
% 1.16/1.03 ((~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))) | (p2(X!17) | (~r1(Y!16, X!17)) | (~((~p2(tptp_fun_Y_12(X!17))) | (~r1(X!17, tptp_fun_Y_12(X!17))) | p2(tptp_fun_X_13(X!17)) | (~r1(tptp_fun_Y_12(X!17), tptp_fun_X_13(X!17))))))),
% 1.16/1.03 inference(quant_inst,[status(thm)],[])).
% 1.16/1.03 tff(327,plain,
% 1.16/1.03 ((~![X: $i] : (p2(X) | (~r1(Y!16, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))) | p2(X!17) | (~r1(Y!16, X!17)) | (~((~p2(tptp_fun_Y_12(X!17))) | (~r1(X!17, tptp_fun_Y_12(X!17))) | p2(tptp_fun_X_13(X!17)) | (~r1(tptp_fun_Y_12(X!17), tptp_fun_X_13(X!17)))))),
% 1.16/1.03 inference(modus_ponens,[status(thm)],[326, 325])).
% 1.16/1.03 tff(328,plain,
% 1.16/1.03 (p2(X!17) | (~((~p2(tptp_fun_Y_12(X!17))) | (~r1(X!17, tptp_fun_Y_12(X!17))) | p2(tptp_fun_X_13(X!17)) | (~r1(tptp_fun_Y_12(X!17), tptp_fun_X_13(X!17)))))),
% 1.16/1.03 inference(unit_resolution,[status(thm)],[327, 307, 324])).
% 1.16/1.03 tff(329,plain,
% 1.16/1.03 (~((~p2(tptp_fun_Y_12(X!17))) | (~r1(X!17, tptp_fun_Y_12(X!17))) | p2(tptp_fun_X_13(X!17)) | (~r1(tptp_fun_Y_12(X!17), tptp_fun_X_13(X!17))))),
% 1.16/1.03 inference(unit_resolution,[status(thm)],[328, 323])).
% 1.16/1.03 tff(330,plain,
% 1.16/1.03 (((~p2(tptp_fun_Y_12(X!17))) | (~r1(X!17, tptp_fun_Y_12(X!17))) | p2(tptp_fun_X_13(X!17)) | (~r1(tptp_fun_Y_12(X!17), tptp_fun_X_13(X!17)))) | r1(X!17, tptp_fun_Y_12(X!17))),
% 1.16/1.03 inference(tautology,[status(thm)],[])).
% 1.16/1.03 tff(331,plain,
% 1.16/1.03 (r1(X!17, tptp_fun_Y_12(X!17))),
% 1.16/1.03 inference(unit_resolution,[status(thm)],[330, 329])).
% 1.16/1.03 tff(332,plain,
% 1.16/1.03 (((~p2(tptp_fun_Y_12(X!17))) | (~r1(X!17, tptp_fun_Y_12(X!17))) | p2(tptp_fun_X_13(X!17)) | (~r1(tptp_fun_Y_12(X!17), tptp_fun_X_13(X!17)))) | p2(tptp_fun_Y_12(X!17))),
% 1.16/1.03 inference(tautology,[status(thm)],[])).
% 1.16/1.03 tff(333,plain,
% 1.16/1.03 (p2(tptp_fun_Y_12(X!17))),
% 1.16/1.03 inference(unit_resolution,[status(thm)],[332, 329])).
% 1.16/1.03 tff(334,plain,
% 1.16/1.03 ((p2(X!17) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!17, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) | ![Y: $i] : ((~p2(Y)) | (~r1(X!17, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))),
% 1.16/1.03 inference(tautology,[status(thm)],[])).
% 1.16/1.03 tff(335,plain,
% 1.16/1.03 (![Y: $i] : ((~p2(Y)) | (~r1(X!17, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))),
% 1.16/1.03 inference(unit_resolution,[status(thm)],[334, 321])).
% 1.16/1.03 tff(336,plain,
% 1.16/1.03 (((~![Y: $i] : ((~p2(Y)) | (~r1(X!17, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | ((~p2(tptp_fun_Y_12(X!17))) | (~r1(X!17, tptp_fun_Y_12(X!17))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(X!17), X))))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(X!17, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~p2(tptp_fun_Y_12(X!17))) | (~r1(X!17, tptp_fun_Y_12(X!17))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(X!17), X))))),
% 1.16/1.03 inference(rewrite,[status(thm)],[])).
% 1.16/1.03 tff(337,plain,
% 1.16/1.03 ((~![Y: $i] : ((~p2(Y)) | (~r1(X!17, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | ((~p2(tptp_fun_Y_12(X!17))) | (~r1(X!17, tptp_fun_Y_12(X!17))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(X!17), X))))),
% 1.16/1.03 inference(quant_inst,[status(thm)],[])).
% 1.16/1.03 tff(338,plain,
% 1.16/1.03 ((~![Y: $i] : ((~p2(Y)) | (~r1(X!17, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~p2(tptp_fun_Y_12(X!17))) | (~r1(X!17, tptp_fun_Y_12(X!17))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(X!17), X)))),
% 1.16/1.03 inference(modus_ponens,[status(thm)],[337, 336])).
% 1.16/1.03 tff(339,plain,
% 1.16/1.03 (![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(X!17), X)))),
% 1.16/1.03 inference(unit_resolution,[status(thm)],[338, 335, 333, 331])).
% 1.16/1.03 tff(340,plain,
% 1.16/1.03 (((~p2(tptp_fun_Y_12(X!17))) | (~r1(X!17, tptp_fun_Y_12(X!17))) | p2(tptp_fun_X_13(X!17)) | (~r1(tptp_fun_Y_12(X!17), tptp_fun_X_13(X!17)))) | r1(tptp_fun_Y_12(X!17), tptp_fun_X_13(X!17))),
% 1.16/1.03 inference(tautology,[status(thm)],[])).
% 1.16/1.03 tff(341,plain,
% 1.16/1.03 (r1(tptp_fun_Y_12(X!17), tptp_fun_X_13(X!17))),
% 1.16/1.03 inference(unit_resolution,[status(thm)],[340, 329])).
% 1.16/1.03 tff(342,plain,
% 1.16/1.03 (((~p2(tptp_fun_Y_12(X!17))) | (~r1(X!17, tptp_fun_Y_12(X!17))) | p2(tptp_fun_X_13(X!17)) | (~r1(tptp_fun_Y_12(X!17), tptp_fun_X_13(X!17)))) | (~p2(tptp_fun_X_13(X!17)))),
% 1.16/1.03 inference(tautology,[status(thm)],[])).
% 1.16/1.03 tff(343,plain,
% 1.16/1.03 (~p2(tptp_fun_X_13(X!17))),
% 1.16/1.03 inference(unit_resolution,[status(thm)],[342, 329])).
% 1.16/1.03 tff(344,plain,
% 1.16/1.03 (((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(X!17), X)))) | (p2(tptp_fun_X_13(X!17)) | (~r1(tptp_fun_Y_12(X!17), tptp_fun_X_13(X!17))))) <=> ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(X!17), X)))) | p2(tptp_fun_X_13(X!17)) | (~r1(tptp_fun_Y_12(X!17), tptp_fun_X_13(X!17))))),
% 1.16/1.03 inference(rewrite,[status(thm)],[])).
% 1.16/1.03 tff(345,plain,
% 1.16/1.03 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(X!17), X)))) | (p2(tptp_fun_X_13(X!17)) | (~r1(tptp_fun_Y_12(X!17), tptp_fun_X_13(X!17))))),
% 1.16/1.03 inference(quant_inst,[status(thm)],[])).
% 1.16/1.03 tff(346,plain,
% 1.16/1.03 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(X!17), X)))) | p2(tptp_fun_X_13(X!17)) | (~r1(tptp_fun_Y_12(X!17), tptp_fun_X_13(X!17)))),
% 1.16/1.03 inference(modus_ponens,[status(thm)],[345, 344])).
% 1.16/1.03 tff(347,plain,
% 1.16/1.03 ($false),
% 1.16/1.03 inference(unit_resolution,[status(thm)],[346, 343, 341, 339])).
% 1.16/1.03 % SZS output end Proof
%------------------------------------------------------------------------------