TSTP Solution File: LCL660+1.001 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL660+1.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 0.70s 0.69s
% Output : Proof 0.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL660+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Sep 1 23:21:49 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.70/0.69 % SZS status Theorem
% 0.70/0.69 % SZS output start Proof
% 0.70/0.69 tff(p2_type, type, (
% 0.70/0.69 p2: $i > $o)).
% 0.70/0.69 tff(tptp_fun_X_4_type, type, (
% 0.70/0.69 tptp_fun_X_4: $i > $i)).
% 0.70/0.69 tff(tptp_fun_Y_16_type, type, (
% 0.70/0.69 tptp_fun_Y_16: $i)).
% 0.70/0.69 tff(tptp_fun_Y_5_type, type, (
% 0.70/0.69 tptp_fun_Y_5: $i > $i)).
% 0.70/0.69 tff(r1_type, type, (
% 0.70/0.69 r1: ( $i * $i ) > $o)).
% 0.70/0.69 tff(tptp_fun_X_13_type, type, (
% 0.70/0.69 tptp_fun_X_13: $i > $i)).
% 0.70/0.69 tff(tptp_fun_Y_12_type, type, (
% 0.70/0.69 tptp_fun_Y_12: $i > $i)).
% 0.70/0.69 tff(tptp_fun_Y_18_type, type, (
% 0.70/0.69 tptp_fun_Y_18: $i)).
% 0.70/0.69 tff(tptp_fun_X_17_type, type, (
% 0.70/0.69 tptp_fun_X_17: $i)).
% 0.70/0.69 tff(tptp_fun_X_19_type, type, (
% 0.70/0.69 tptp_fun_X_19: $i > $i)).
% 0.70/0.69 tff(tptp_fun_X_21_type, type, (
% 0.70/0.69 tptp_fun_X_21: $i > $i)).
% 0.70/0.69 tff(tptp_fun_Y_20_type, type, (
% 0.70/0.69 tptp_fun_Y_20: $i > $i)).
% 0.70/0.69 tff(tptp_fun_X_0_type, type, (
% 0.70/0.69 tptp_fun_X_0: $i)).
% 0.70/0.69 tff(tptp_fun_Y_11_type, type, (
% 0.70/0.69 tptp_fun_Y_11: $i)).
% 0.70/0.69 tff(tptp_fun_X_15_type, type, (
% 0.70/0.69 tptp_fun_X_15: $i)).
% 0.70/0.69 tff(tptp_fun_Y_14_type, type, (
% 0.70/0.69 tptp_fun_Y_14: $i)).
% 0.70/0.69 tff(tptp_fun_Y_3_type, type, (
% 0.70/0.69 tptp_fun_Y_3: $i)).
% 0.70/0.69 tff(tptp_fun_X_6_type, type, (
% 0.70/0.69 tptp_fun_X_6: $i > $i)).
% 0.70/0.69 tff(p3_type, type, (
% 0.70/0.69 p3: $i > $o)).
% 0.70/0.69 tff(p1_type, type, (
% 0.70/0.69 p1: $i > $o)).
% 0.70/0.69 tff(tptp_fun_Y_10_type, type, (
% 0.70/0.69 tptp_fun_Y_10: $i > $i)).
% 0.70/0.69 tff(tptp_fun_X_9_type, type, (
% 0.70/0.69 tptp_fun_X_9: $i > $i)).
% 0.70/0.69 tff(p4_type, type, (
% 0.70/0.69 p4: $i > $o)).
% 0.70/0.69 tff(tptp_fun_Y_8_type, type, (
% 0.70/0.69 tptp_fun_Y_8: $i > $i)).
% 0.70/0.69 tff(tptp_fun_X_7_type, type, (
% 0.70/0.69 tptp_fun_X_7: $i > $i)).
% 0.70/0.69 tff(tptp_fun_Y_2_type, type, (
% 0.70/0.69 tptp_fun_Y_2: $i)).
% 0.70/0.69 tff(tptp_fun_Y_1_type, type, (
% 0.70/0.69 tptp_fun_Y_1: $i)).
% 0.70/0.69 tff(1,plain,
% 0.70/0.69 (^[X: $i] : refl(r1(X, X) <=> r1(X, X))),
% 0.70/0.69 inference(bind,[status(th)],[])).
% 0.70/0.69 tff(2,plain,
% 0.70/0.69 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 0.70/0.69 inference(quant_intro,[status(thm)],[1])).
% 0.70/0.69 tff(3,plain,
% 0.70/0.69 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 0.70/0.69 inference(rewrite,[status(thm)],[])).
% 0.70/0.69 tff(4,axiom,(![X: $i] : r1(X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reflexivity')).
% 0.70/0.69 tff(5,plain,
% 0.70/0.69 (![X: $i] : r1(X, X)),
% 0.70/0.69 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.70/0.69 tff(6,plain,(
% 0.70/0.69 ![X: $i] : r1(X, X)),
% 0.70/0.69 inference(skolemize,[status(sab)],[5])).
% 0.70/0.69 tff(7,plain,
% 0.70/0.69 (![X: $i] : r1(X, X)),
% 0.70/0.69 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.70/0.69 tff(8,plain,
% 0.70/0.69 ((~![X: $i] : r1(X, X)) | r1(X!0, X!0)),
% 0.70/0.69 inference(quant_inst,[status(thm)],[])).
% 0.70/0.69 tff(9,plain,
% 0.70/0.69 (r1(X!0, X!0)),
% 0.70/0.69 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.70/0.69 tff(10,assumption,(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))), introduced(assumption)).
% 0.70/0.69 tff(11,plain,
% 0.70/0.69 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))) <=> ((~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))),
% 0.70/0.69 inference(rewrite,[status(thm)],[])).
% 0.70/0.69 tff(12,plain,
% 0.70/0.69 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) <=> (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))),
% 0.70/0.69 inference(rewrite,[status(thm)],[])).
% 0.70/0.69 tff(13,plain,
% 0.70/0.69 ((p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) <=> (p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))),
% 0.70/0.69 inference(monotonicity,[status(thm)],[12])).
% 0.70/0.69 tff(14,plain,
% 0.70/0.69 ((~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) <=> (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.70/0.69 inference(monotonicity,[status(thm)],[13])).
% 0.70/0.69 tff(15,plain,
% 0.70/0.69 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))),
% 0.70/0.69 inference(monotonicity,[status(thm)],[14])).
% 0.70/0.69 tff(16,plain,
% 0.70/0.69 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))) <=> ((~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))),
% 0.70/0.69 inference(transitivity,[status(thm)],[15, 11])).
% 0.70/0.69 tff(17,plain,
% 0.70/0.69 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))),
% 0.70/0.69 inference(rewrite,[status(thm)],[])).
% 0.70/0.69 tff(18,plain,
% 0.70/0.69 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))),
% 0.70/0.69 inference(rewrite,[status(thm)],[])).
% 0.70/0.69 tff(19,plain,
% 0.70/0.69 (((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) <=> (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.70/0.69 inference(rewrite,[status(thm)],[])).
% 0.70/0.69 tff(20,plain,
% 0.70/0.69 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))),
% 0.70/0.69 inference(bind,[status(th)],[])).
% 0.70/0.69 tff(21,plain,
% 0.70/0.69 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))),
% 0.70/0.70 inference(quant_intro,[status(thm)],[20])).
% 0.70/0.70 tff(22,plain,
% 0.70/0.70 (((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) <=> ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))),
% 0.70/0.70 inference(monotonicity,[status(thm)],[21])).
% 0.70/0.70 tff(23,plain,
% 0.70/0.70 (((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) <=> (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.70/0.70 inference(transitivity,[status(thm)],[22, 19])).
% 0.70/0.70 tff(24,plain,
% 0.70/0.70 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))),
% 0.70/0.70 inference(monotonicity,[status(thm)],[23])).
% 0.70/0.70 tff(25,plain,
% 0.70/0.70 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))),
% 0.70/0.70 inference(transitivity,[status(thm)],[24, 18])).
% 0.70/0.70 tff(26,plain,
% 0.70/0.70 (((~((~r1(X!0, Y!1)) | p4(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & ![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_7(Y)) & p4(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(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_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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)))))) & (p2(Y) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))) & ![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)))))))) <=> ((~((~r1(X!0, Y!1)) | p4(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & ![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_7(Y)) & p4(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(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_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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)))))) & (p2(Y) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))) & ![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)))))))),
% 0.70/0.70 inference(rewrite,[status(thm)],[])).
% 0.70/0.70 tff(27,plain,
% 0.70/0.70 (((((((~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_4(Y)))) & (~(~r1(Y, tptp_fun_X_4(Y)))) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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)))))) & (p2(Y) | ((~(~p2(tptp_fun_X_4(Y)))) & (~(~r1(Y, tptp_fun_X_4(Y)))) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ((![Y: $i] : (p2(Y) | (~r1(X, Y)) | ((~(~p2(tptp_fun_X_4(Y)))) & (~(~r1(Y, tptp_fun_X_4(Y)))) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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))))))))) & ![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_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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)))))) & (p2(Y) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))) & ![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)))))))),
% 0.70/0.70 inference(rewrite,[status(thm)],[])).
% 0.70/0.70 tff(28,plain,
% 0.70/0.70 (^[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))))))))),
% 0.70/0.70 inference(bind,[status(th)],[])).
% 0.70/0.70 tff(29,plain,
% 0.70/0.70 (![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))))))),
% 0.70/0.70 inference(quant_intro,[status(thm)],[28])).
% 0.70/0.70 tff(30,plain,
% 0.70/0.70 (^[Y: $i] : trans(monotonicity(rewrite(((~(~r1(Y, tptp_fun_X_7(Y)))) & (~(~p4(tptp_fun_X_7(Y)))) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(tptp_fun_Y_8(Y))))) <=> (r1(Y, tptp_fun_X_7(Y)) & p4(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(tptp_fun_Y_8(Y)))))), (((~r1(X!0, Y)) | p4(Y) | ((~(~r1(Y, tptp_fun_X_7(Y)))) & (~(~p4(tptp_fun_X_7(Y)))) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(tptp_fun_Y_8(Y)))))) <=> ((~r1(X!0, Y)) | p4(Y) | (r1(Y, tptp_fun_X_7(Y)) & p4(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(tptp_fun_Y_8(Y)))))))), rewrite(((~r1(X!0, Y)) | p4(Y) | (r1(Y, tptp_fun_X_7(Y)) & p4(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(tptp_fun_Y_8(Y)))))) <=> (p4(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_7(Y)) & p4(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(tptp_fun_Y_8(Y))))))), (((~r1(X!0, Y)) | p4(Y) | ((~(~r1(Y, tptp_fun_X_7(Y)))) & (~(~p4(tptp_fun_X_7(Y)))) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(tptp_fun_Y_8(Y)))))) <=> (p4(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_7(Y)) & p4(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(tptp_fun_Y_8(Y))))))))),
% 0.70/0.70 inference(bind,[status(th)],[])).
% 0.70/0.70 tff(31,plain,
% 0.70/0.70 (![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | ((~(~r1(Y, tptp_fun_X_7(Y)))) & (~(~p4(tptp_fun_X_7(Y)))) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(tptp_fun_Y_8(Y)))))) <=> ![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_7(Y)) & p4(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(tptp_fun_Y_8(Y))))))),
% 0.70/0.70 inference(quant_intro,[status(thm)],[30])).
% 0.70/0.70 tff(32,plain,
% 0.70/0.70 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.70/0.70 inference(rewrite,[status(thm)],[])).
% 0.70/0.70 tff(33,plain,
% 0.70/0.70 (((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~(~p2(tptp_fun_X_4(Y)))) & (~(~r1(Y, tptp_fun_X_4(Y)))) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) <=> ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))),
% 0.70/0.70 inference(rewrite,[status(thm)],[])).
% 0.70/0.70 tff(34,plain,
% 0.70/0.70 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~(~p2(tptp_fun_X_4(Y)))) & (~(~r1(Y, tptp_fun_X_4(Y)))) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.70/0.70 inference(monotonicity,[status(thm)],[33])).
% 0.70/0.70 tff(35,plain,
% 0.70/0.70 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~(~p2(tptp_fun_X_4(Y)))) & (~(~r1(Y, tptp_fun_X_4(Y)))) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.70/0.70 inference(transitivity,[status(thm)],[34, 32])).
% 0.70/0.70 tff(36,plain,
% 0.70/0.70 ((![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) <=> (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.70/0.70 inference(rewrite,[status(thm)],[])).
% 0.70/0.70 tff(37,plain,
% 0.70/0.70 ((![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~(~p2(tptp_fun_X_4(Y)))) & (~(~r1(Y, tptp_fun_X_4(Y)))) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) <=> (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.70/0.70 inference(monotonicity,[status(thm)],[33])).
% 0.70/0.70 tff(38,plain,
% 0.70/0.70 ((![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~(~p2(tptp_fun_X_4(Y)))) & (~(~r1(Y, tptp_fun_X_4(Y)))) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) <=> (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.70/0.70 inference(transitivity,[status(thm)],[37, 36])).
% 0.70/0.70 tff(39,plain,
% 0.70/0.70 ((~((~r1(X!0, Y!2)) | p1(Y!2))) <=> (~((~r1(X!0, Y!2)) | p1(Y!2)))),
% 0.70/0.70 inference(rewrite,[status(thm)],[])).
% 0.70/0.70 tff(40,plain,
% 0.70/0.70 ((~((~r1(X!0, Y!1)) | p4(Y!1))) <=> (~((~r1(X!0, Y!1)) | p4(Y!1)))),
% 0.70/0.70 inference(rewrite,[status(thm)],[])).
% 0.70/0.70 tff(41,plain,
% 0.70/0.70 (((~((~r1(X!0, Y!1)) | p4(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~(~p2(tptp_fun_X_4(Y)))) & (~(~r1(Y, tptp_fun_X_4(Y)))) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~(~p2(tptp_fun_X_4(Y)))) & (~(~r1(Y, tptp_fun_X_4(Y)))) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | ((~(~r1(Y, tptp_fun_X_7(Y)))) & (~(~p4(tptp_fun_X_7(Y)))) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(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_4(Y)))) & (~(~r1(Y, tptp_fun_X_4(Y)))) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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)))))) & (p2(Y) | ((~(~p2(tptp_fun_X_4(Y)))) & (~(~r1(Y, tptp_fun_X_4(Y)))) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ((![Y: $i] : (p2(Y) | (~r1(X, Y)) | ((~(~p2(tptp_fun_X_4(Y)))) & (~(~r1(Y, tptp_fun_X_4(Y)))) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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))))))))) & ![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)))))))) <=> ((~((~r1(X!0, Y!1)) | p4(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & ![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_7(Y)) & p4(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(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_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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)))))) & (p2(Y) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))) & ![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))))))))),
% 0.70/0.71 inference(monotonicity,[status(thm)],[40, 39, 38, 35, 31, 29, 27])).
% 0.70/0.71 tff(42,plain,
% 0.70/0.71 (((~((~r1(X!0, Y!1)) | p4(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~(~p2(tptp_fun_X_4(Y)))) & (~(~r1(Y, tptp_fun_X_4(Y)))) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~(~p2(tptp_fun_X_4(Y)))) & (~(~r1(Y, tptp_fun_X_4(Y)))) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | ((~(~r1(Y, tptp_fun_X_7(Y)))) & (~(~p4(tptp_fun_X_7(Y)))) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(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_4(Y)))) & (~(~r1(Y, tptp_fun_X_4(Y)))) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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)))))) & (p2(Y) | ((~(~p2(tptp_fun_X_4(Y)))) & (~(~r1(Y, tptp_fun_X_4(Y)))) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ((![Y: $i] : (p2(Y) | (~r1(X, Y)) | ((~(~p2(tptp_fun_X_4(Y)))) & (~(~r1(Y, tptp_fun_X_4(Y)))) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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))))))))) & ![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)))))))) <=> ((~((~r1(X!0, Y!1)) | p4(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & ![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_7(Y)) & p4(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(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_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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)))))) & (p2(Y) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))) & ![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)))))))),
% 0.70/0.71 inference(transitivity,[status(thm)],[41, 26])).
% 0.70/0.71 tff(43,plain,
% 0.70/0.71 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~p3(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)) | (~![X: $i] : ((~p3(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)) | p4(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p4(X)) | ![Y: $i] : ((~r1(X, Y)) | p4(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))))))))))))) & ![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)) | p4(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~p3(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)) | (~![X: $i] : ((~p3(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)) | p4(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p4(X)) | ![Y: $i] : ((~r1(X, Y)) | p4(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))))))))))))) & ![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))))))))))))),
% 0.70/0.71 inference(rewrite,[status(thm)],[])).
% 0.70/0.71 tff(44,plain,
% 0.70/0.71 ((~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~p3(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)) | (~![X: $i] : ((~p3(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)) | p4(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p4(X)) | ![Y: $i] : ((~r1(X, Y)) | p4(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))))))))))))) & ![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)) | p4(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~p3(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)) | (~![X: $i] : ((~p3(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)) | p4(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p4(X)) | ![Y: $i] : ((~r1(X, Y)) | p4(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))))))))))))) & ![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))))))))))))),
% 0.70/0.71 inference(rewrite,[status(thm)],[])).
% 0.70/0.71 tff(45,plain,
% 0.70/0.71 ((~?[X: $i] : (~((((((((~![Y: $i] : ((~r1(X, Y)) | (~p3(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)) | p4(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p4(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))) | (~p4(X))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p3(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)))))))))))) & ![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)) | p4(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~p3(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)) | (~![X: $i] : ((~p3(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)) | p4(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p4(X)) | ![Y: $i] : ((~r1(X, Y)) | p4(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))))))))))))) & ![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)))))))))))))),
% 0.70/0.71 inference(rewrite,[status(thm)],[])).
% 0.70/0.71 tff(46,plain,
% 0.70/0.71 ((~(~?[X: $i] : (~((((((((~![Y: $i] : ((~r1(X, Y)) | (~p3(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)) | p4(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p4(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))) | (~p4(X))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p3(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)))))))))))) & ![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)) | p4(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~p3(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)) | (~![X: $i] : ((~p3(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)) | p4(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p4(X)) | ![Y: $i] : ((~r1(X, Y)) | p4(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))))))))))))) & ![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))))))))))))))),
% 0.70/0.72 inference(monotonicity,[status(thm)],[45])).
% 0.70/0.72 tff(47,plain,
% 0.70/0.72 ((~(~?[X: $i] : (~((((((((~![Y: $i] : ((~r1(X, Y)) | (~p3(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)) | p4(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p4(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))) | (~p4(X))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p3(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)))))))))))) & ![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)) | p4(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~p3(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)) | (~![X: $i] : ((~p3(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)) | p4(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p4(X)) | ![Y: $i] : ((~r1(X, Y)) | p4(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))))))))))))) & ![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))))))))))))),
% 0.70/0.72 inference(transitivity,[status(thm)],[46, 44])).
% 0.70/0.72 tff(48,axiom,(~(~?[X: $i] : (~((((((((~![Y: $i] : ((~r1(X, Y)) | (~p3(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)) | p4(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p4(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))) | (~p4(X))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p3(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)))))))))))) & ![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/sandbox2/benchmark/theBenchmark.p','main')).
% 0.70/0.72 tff(49,plain,
% 0.70/0.72 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~p3(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)) | (~![X: $i] : ((~p3(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)) | p4(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p4(X)) | ![Y: $i] : ((~r1(X, Y)) | p4(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))))))))))))) & ![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))))))))))))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.70/0.72 tff(50,plain,
% 0.70/0.72 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~p3(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)) | (~![X: $i] : ((~p3(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)) | p4(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p4(X)) | ![Y: $i] : ((~r1(X, Y)) | p4(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))))))))))))) & ![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))))))))))))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[49, 43])).
% 0.70/0.72 tff(51,plain,
% 0.70/0.72 ((~((~r1(X!0, Y!1)) | p4(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & ![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_7(Y)) & p4(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(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_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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)))))) & (p2(Y) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))) & ![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))))))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[50, 42])).
% 0.70/0.72 tff(52,plain,
% 0.70/0.72 (![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))),
% 0.70/0.72 inference(and_elim,[status(thm)],[51])).
% 0.70/0.72 tff(53,plain,
% 0.70/0.72 (![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[52, 25])).
% 0.70/0.72 tff(54,plain,
% 0.70/0.72 (![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[53, 17])).
% 0.70/0.72 tff(55,plain,
% 0.70/0.72 ((~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[54, 16])).
% 0.70/0.72 tff(56,plain,
% 0.70/0.72 (![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[55, 10])).
% 0.70/0.72 tff(57,plain,
% 0.70/0.72 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | ((~r1(X!0, X!0)) | (~((~p3(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~r1(X!0, X!0)) | (~((~p3(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0))))))),
% 0.70/0.72 inference(rewrite,[status(thm)],[])).
% 0.70/0.72 tff(58,plain,
% 0.70/0.72 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | ((~r1(X!0, X!0)) | (~((~p3(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0))))))),
% 0.70/0.72 inference(quant_inst,[status(thm)],[])).
% 0.70/0.72 tff(59,plain,
% 0.70/0.72 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~r1(X!0, X!0)) | (~((~p3(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0)))))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.70/0.72 tff(60,plain,
% 0.70/0.72 (~((~p3(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0))))),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[59, 56, 9])).
% 0.70/0.72 tff(61,plain,
% 0.70/0.72 (((~p3(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0)))) | r1(X!0, tptp_fun_X_6(X!0))),
% 0.70/0.72 inference(tautology,[status(thm)],[])).
% 0.70/0.72 tff(62,plain,
% 0.70/0.72 (r1(X!0, tptp_fun_X_6(X!0))),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.70/0.72 tff(63,plain,
% 0.70/0.72 (((~p3(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0)))) | p3(tptp_fun_X_6(X!0))),
% 0.70/0.72 inference(tautology,[status(thm)],[])).
% 0.70/0.72 tff(64,plain,
% 0.70/0.72 (p3(tptp_fun_X_6(X!0))),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[63, 60])).
% 0.70/0.72 tff(65,plain,
% 0.70/0.72 ((![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))) <=> (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))),
% 0.70/0.72 inference(rewrite,[status(thm)],[])).
% 0.70/0.72 tff(66,plain,
% 0.70/0.72 ((![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))) <=> (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))),
% 0.70/0.72 inference(rewrite,[status(thm)],[])).
% 0.70/0.72 tff(67,plain,
% 0.70/0.72 ((![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) <=> (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))),
% 0.70/0.72 inference(monotonicity,[status(thm)],[23])).
% 0.70/0.72 tff(68,plain,
% 0.70/0.72 ((![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) <=> (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))),
% 0.70/0.72 inference(transitivity,[status(thm)],[67, 66])).
% 0.70/0.72 tff(69,plain,
% 0.70/0.72 (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))),
% 0.70/0.72 inference(and_elim,[status(thm)],[51])).
% 0.70/0.72 tff(70,plain,
% 0.70/0.72 (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.70/0.72 tff(71,plain,
% 0.70/0.72 (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[70, 65])).
% 0.70/0.72 tff(72,plain,
% 0.70/0.72 (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y)))),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[71, 10])).
% 0.70/0.72 tff(73,plain,
% 0.70/0.72 (((~![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y)))) | ((~p3(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0))))) <=> ((~![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y)))) | (~p3(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0))))),
% 0.70/0.72 inference(rewrite,[status(thm)],[])).
% 0.70/0.72 tff(74,plain,
% 0.70/0.72 ((~![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y)))) | ((~p3(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0))))),
% 0.70/0.72 inference(quant_inst,[status(thm)],[])).
% 0.70/0.72 tff(75,plain,
% 0.70/0.72 ((~![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y)))) | (~p3(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0)))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.70/0.72 tff(76,plain,
% 0.70/0.72 ($false),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[75, 72, 64, 62])).
% 0.70/0.72 tff(77,plain,(~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.72 tff(78,plain,
% 0.70/0.72 ((p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) | (~p2(Y!3))),
% 0.70/0.72 inference(tautology,[status(thm)],[])).
% 0.70/0.72 tff(79,plain,
% 0.70/0.72 (~p2(Y!3)),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.70/0.72 tff(80,assumption,((~(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)))))))), introduced(assumption)).
% 0.70/0.72 tff(81,assumption,(~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))), introduced(assumption)).
% 0.70/0.72 tff(82,plain,
% 0.70/0.72 ((p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))),
% 0.70/0.73 inference(tautology,[status(thm)],[])).
% 0.70/0.73 tff(83,plain,
% 0.70/0.73 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.70/0.73 tff(84,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)).
% 0.70/0.73 tff(85,plain,
% 0.70/0.73 ((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)),
% 0.70/0.73 inference(tautology,[status(thm)],[])).
% 0.70/0.73 tff(86,plain,
% 0.70/0.73 (r1(X!0, Y!11)),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.70/0.73 tff(87,plain,
% 0.70/0.73 ((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))),
% 0.70/0.73 inference(tautology,[status(thm)],[])).
% 0.70/0.73 tff(88,plain,
% 0.70/0.73 (~p2(Y!11)),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[87, 84])).
% 0.70/0.73 tff(89,assumption,(![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))), introduced(assumption)).
% 0.70/0.73 tff(90,plain,
% 0.70/0.73 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!11) | (~r1(X!0, Y!11)) | (~(p2(tptp_fun_Y_5(Y!11)) | (~r1(Y!11, tptp_fun_X_4(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!11) | (~r1(X!0, Y!11)) | (~(p2(tptp_fun_Y_5(Y!11)) | (~r1(Y!11, tptp_fun_X_4(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))))))),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(91,plain,
% 0.70/0.73 ((p2(Y!11) | (~r1(X!0, Y!11)) | (~((~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11)))))) <=> (p2(Y!11) | (~r1(X!0, Y!11)) | (~(p2(tptp_fun_Y_5(Y!11)) | (~r1(Y!11, tptp_fun_X_4(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))))))),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(92,plain,
% 0.70/0.73 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!11) | (~r1(X!0, Y!11)) | (~((~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!11) | (~r1(X!0, Y!11)) | (~(p2(tptp_fun_Y_5(Y!11)) | (~r1(Y!11, tptp_fun_X_4(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11)))))))),
% 0.70/0.73 inference(monotonicity,[status(thm)],[91])).
% 0.70/0.73 tff(93,plain,
% 0.70/0.73 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!11) | (~r1(X!0, Y!11)) | (~((~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!11) | (~r1(X!0, Y!11)) | (~(p2(tptp_fun_Y_5(Y!11)) | (~r1(Y!11, tptp_fun_X_4(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))))))),
% 0.70/0.73 inference(transitivity,[status(thm)],[92, 90])).
% 0.70/0.73 tff(94,plain,
% 0.70/0.73 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!11) | (~r1(X!0, Y!11)) | (~((~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))))))),
% 0.70/0.73 inference(quant_inst,[status(thm)],[])).
% 0.70/0.73 tff(95,plain,
% 0.70/0.73 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!11) | (~r1(X!0, Y!11)) | (~(p2(tptp_fun_Y_5(Y!11)) | (~r1(Y!11, tptp_fun_X_4(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11)))))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.70/0.73 tff(96,plain,
% 0.70/0.73 (~(p2(tptp_fun_Y_5(Y!11)) | (~r1(Y!11, tptp_fun_X_4(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))))),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[95, 89, 88, 86])).
% 0.70/0.73 tff(97,plain,
% 0.70/0.73 ((p2(tptp_fun_Y_5(Y!11)) | (~r1(Y!11, tptp_fun_X_4(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11)))) | p2(tptp_fun_X_4(Y!11))),
% 0.70/0.73 inference(tautology,[status(thm)],[])).
% 0.70/0.73 tff(98,plain,
% 0.70/0.73 (p2(tptp_fun_X_4(Y!11))),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.70/0.73 tff(99,plain,
% 0.70/0.73 ((p2(tptp_fun_Y_5(Y!11)) | (~r1(Y!11, tptp_fun_X_4(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11)))) | r1(Y!11, tptp_fun_X_4(Y!11))),
% 0.70/0.73 inference(tautology,[status(thm)],[])).
% 0.70/0.73 tff(100,plain,
% 0.70/0.73 (r1(Y!11, tptp_fun_X_4(Y!11))),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[99, 96])).
% 0.70/0.73 tff(101,plain,
% 0.70/0.73 ((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))))),
% 0.70/0.73 inference(tautology,[status(thm)],[])).
% 0.70/0.73 tff(102,plain,
% 0.70/0.73 (![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[101, 84])).
% 0.70/0.73 tff(103,plain,
% 0.70/0.73 (((~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ((~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!11), Y))))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!11), Y))))),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(104,plain,
% 0.70/0.73 ((~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ((~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!11), Y))))),
% 0.70/0.73 inference(quant_inst,[status(thm)],[])).
% 0.70/0.73 tff(105,plain,
% 0.70/0.73 ((~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!11), Y)))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.70/0.73 tff(106,plain,
% 0.70/0.73 (![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!11), Y)))),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[105, 102, 100, 98])).
% 0.70/0.73 tff(107,plain,
% 0.70/0.73 ((p2(tptp_fun_Y_5(Y!11)) | (~r1(Y!11, tptp_fun_X_4(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11)))) | r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))),
% 0.70/0.73 inference(tautology,[status(thm)],[])).
% 0.70/0.73 tff(108,plain,
% 0.70/0.73 (r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[107, 96])).
% 0.70/0.73 tff(109,plain,
% 0.70/0.73 ((p2(tptp_fun_Y_5(Y!11)) | (~r1(Y!11, tptp_fun_X_4(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11)))) | (~p2(tptp_fun_Y_5(Y!11)))),
% 0.70/0.73 inference(tautology,[status(thm)],[])).
% 0.70/0.73 tff(110,plain,
% 0.70/0.73 (~p2(tptp_fun_Y_5(Y!11))),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[109, 96])).
% 0.70/0.73 tff(111,plain,
% 0.70/0.73 (((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!11), Y)))) | (p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!11), Y)))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))))),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(112,plain,
% 0.70/0.73 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!11), Y)))) | (p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))))),
% 0.70/0.73 inference(quant_inst,[status(thm)],[])).
% 0.70/0.73 tff(113,plain,
% 0.70/0.73 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!11), Y)))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11)))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.70/0.73 tff(114,plain,
% 0.70/0.73 ($false),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[113, 110, 108, 106])).
% 0.70/0.73 tff(115,plain,((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] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.73 tff(116,plain,
% 0.70/0.73 (p2(Y!11) | (~r1(X!0, Y!11)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[115, 83])).
% 0.70/0.73 tff(117,plain,
% 0.70/0.73 ((~((~(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)))))))),
% 0.70/0.73 inference(tautology,[status(thm)],[])).
% 0.70/0.73 tff(118,plain,
% 0.70/0.73 (![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)))))))),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[117, 116, 80])).
% 0.70/0.73 tff(119,plain,
% 0.70/0.73 ((p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) | r1(X!0, Y!3)),
% 0.70/0.73 inference(tautology,[status(thm)],[])).
% 0.70/0.73 tff(120,plain,
% 0.70/0.73 (r1(X!0, Y!3)),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[119, 81])).
% 0.70/0.73 tff(121,plain,
% 0.70/0.73 (((~![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!3)) | ![X: $i] : (p2(X) | (~r1(Y!3, 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!3)) | ![X: $i] : (p2(X) | (~r1(Y!3, 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)))))))),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(122,plain,
% 0.70/0.73 ((~![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!3)) | ![X: $i] : (p2(X) | (~r1(Y!3, 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)))))))),
% 0.70/0.73 inference(quant_inst,[status(thm)],[])).
% 0.70/0.73 tff(123,plain,
% 0.70/0.73 ((~![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!3)) | ![X: $i] : (p2(X) | (~r1(Y!3, 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))))))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.70/0.73 tff(124,plain,
% 0.70/0.73 (![X: $i] : (p2(X) | (~r1(Y!3, 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))))))),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[123, 120, 118])).
% 0.70/0.73 tff(125,plain,
% 0.70/0.73 (^[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)))))))))),
% 0.70/0.73 inference(bind,[status(th)],[])).
% 0.70/0.73 tff(126,plain,
% 0.70/0.73 (![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))))))))),
% 0.70/0.73 inference(quant_intro,[status(thm)],[125])).
% 0.70/0.73 tff(127,plain,
% 0.70/0.73 (^[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)))))))))),
% 0.70/0.73 inference(bind,[status(th)],[])).
% 0.70/0.73 tff(128,plain,
% 0.70/0.73 (![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))))))))),
% 0.70/0.73 inference(quant_intro,[status(thm)],[127])).
% 0.70/0.73 tff(129,plain,
% 0.70/0.73 (![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))))))))),
% 0.70/0.73 inference(transitivity,[status(thm)],[128, 126])).
% 0.70/0.73 tff(130,plain,
% 0.70/0.73 (^[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)))))))))),
% 0.70/0.73 inference(bind,[status(th)],[])).
% 0.70/0.73 tff(131,plain,
% 0.70/0.73 (![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))))))))),
% 0.70/0.73 inference(quant_intro,[status(thm)],[130])).
% 0.70/0.73 tff(132,plain,
% 0.70/0.73 (![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))))))),
% 0.70/0.73 inference(and_elim,[status(thm)],[51])).
% 0.70/0.73 tff(133,plain,
% 0.70/0.73 (![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))))))))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.70/0.73 tff(134,plain,
% 0.70/0.73 (![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))))))))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.70/0.73 tff(135,assumption,(~p2(Y!3)), introduced(assumption)).
% 0.70/0.73 tff(136,plain,
% 0.70/0.73 (((~![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!3) | (~r1(X!0, Y!3)) | (~(p2(tptp_fun_X_19(Y!3)) | (~r1(Y!3, tptp_fun_X_19(Y!3))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!3), 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!3) | (~r1(X!0, Y!3)) | (~(p2(tptp_fun_X_19(Y!3)) | (~r1(Y!3, tptp_fun_X_19(Y!3))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(137,plain,
% 0.70/0.73 ((~![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!3) | (~r1(X!0, Y!3)) | (~(p2(tptp_fun_X_19(Y!3)) | (~r1(Y!3, tptp_fun_X_19(Y!3))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))),
% 0.70/0.73 inference(quant_inst,[status(thm)],[])).
% 0.70/0.73 tff(138,plain,
% 0.70/0.73 ((~![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!3) | (~r1(X!0, Y!3)) | (~(p2(tptp_fun_X_19(Y!3)) | (~r1(Y!3, tptp_fun_X_19(Y!3))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.70/0.73 tff(139,plain,
% 0.70/0.73 (~(p2(tptp_fun_X_19(Y!3)) | (~r1(Y!3, tptp_fun_X_19(Y!3))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[138, 135, 120, 134])).
% 0.70/0.73 tff(140,plain,
% 0.70/0.73 ((p2(tptp_fun_X_19(Y!3)) | (~r1(Y!3, tptp_fun_X_19(Y!3))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) | ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))),
% 0.70/0.73 inference(tautology,[status(thm)],[])).
% 0.70/0.73 tff(141,plain,
% 0.70/0.73 (![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.70/0.73 tff(142,assumption,(~((~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!3)))) | (~r1(tptp_fun_X_19(Y!3), tptp_fun_Y_12(tptp_fun_X_19(Y!3)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!3))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!3)), tptp_fun_X_13(tptp_fun_X_19(Y!3)))))), introduced(assumption)).
% 0.70/0.73 tff(143,plain,
% 0.70/0.73 (((~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!3)))) | (~r1(tptp_fun_X_19(Y!3), tptp_fun_Y_12(tptp_fun_X_19(Y!3)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!3))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!3)), tptp_fun_X_13(tptp_fun_X_19(Y!3))))) | r1(tptp_fun_X_19(Y!3), tptp_fun_Y_12(tptp_fun_X_19(Y!3)))),
% 0.70/0.73 inference(tautology,[status(thm)],[])).
% 0.70/0.73 tff(144,plain,
% 0.70/0.73 (r1(tptp_fun_X_19(Y!3), tptp_fun_Y_12(tptp_fun_X_19(Y!3)))),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.70/0.73 tff(145,plain,
% 0.70/0.73 (((~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!3)))) | (~r1(tptp_fun_X_19(Y!3), tptp_fun_Y_12(tptp_fun_X_19(Y!3)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!3))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!3)), tptp_fun_X_13(tptp_fun_X_19(Y!3))))) | p2(tptp_fun_Y_12(tptp_fun_X_19(Y!3)))),
% 0.70/0.73 inference(tautology,[status(thm)],[])).
% 0.70/0.73 tff(146,plain,
% 0.70/0.73 (p2(tptp_fun_Y_12(tptp_fun_X_19(Y!3)))),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[145, 142])).
% 0.70/0.73 tff(147,assumption,(![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))), introduced(assumption)).
% 0.70/0.73 tff(148,plain,
% 0.70/0.73 (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | ((~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!3)))) | (~r1(tptp_fun_X_19(Y!3), tptp_fun_Y_12(tptp_fun_X_19(Y!3)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!3)), X))))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!3)))) | (~r1(tptp_fun_X_19(Y!3), tptp_fun_Y_12(tptp_fun_X_19(Y!3)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!3)), X))))),
% 0.78/0.73 inference(rewrite,[status(thm)],[])).
% 0.78/0.73 tff(149,plain,
% 0.78/0.73 ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | ((~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!3)))) | (~r1(tptp_fun_X_19(Y!3), tptp_fun_Y_12(tptp_fun_X_19(Y!3)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!3)), X))))),
% 0.78/0.73 inference(quant_inst,[status(thm)],[])).
% 0.78/0.73 tff(150,plain,
% 0.78/0.73 ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!3)))) | (~r1(tptp_fun_X_19(Y!3), tptp_fun_Y_12(tptp_fun_X_19(Y!3)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!3)), X)))),
% 0.78/0.73 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.78/0.73 tff(151,plain,
% 0.78/0.73 (![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!3)), X)))),
% 0.78/0.73 inference(unit_resolution,[status(thm)],[150, 147, 146, 144])).
% 0.78/0.73 tff(152,plain,
% 0.78/0.73 (((~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!3)))) | (~r1(tptp_fun_X_19(Y!3), tptp_fun_Y_12(tptp_fun_X_19(Y!3)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!3))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!3)), tptp_fun_X_13(tptp_fun_X_19(Y!3))))) | r1(tptp_fun_Y_12(tptp_fun_X_19(Y!3)), tptp_fun_X_13(tptp_fun_X_19(Y!3)))),
% 0.78/0.73 inference(tautology,[status(thm)],[])).
% 0.78/0.73 tff(153,plain,
% 0.78/0.73 (r1(tptp_fun_Y_12(tptp_fun_X_19(Y!3)), tptp_fun_X_13(tptp_fun_X_19(Y!3)))),
% 0.78/0.73 inference(unit_resolution,[status(thm)],[152, 142])).
% 0.78/0.73 tff(154,plain,
% 0.78/0.73 (((~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!3)))) | (~r1(tptp_fun_X_19(Y!3), tptp_fun_Y_12(tptp_fun_X_19(Y!3)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!3))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!3)), tptp_fun_X_13(tptp_fun_X_19(Y!3))))) | (~p2(tptp_fun_X_13(tptp_fun_X_19(Y!3))))),
% 0.78/0.73 inference(tautology,[status(thm)],[])).
% 0.78/0.73 tff(155,plain,
% 0.78/0.73 (~p2(tptp_fun_X_13(tptp_fun_X_19(Y!3)))),
% 0.78/0.73 inference(unit_resolution,[status(thm)],[154, 142])).
% 0.78/0.73 tff(156,plain,
% 0.78/0.73 (((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!3)), X)))) | (p2(tptp_fun_X_13(tptp_fun_X_19(Y!3))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!3)), tptp_fun_X_13(tptp_fun_X_19(Y!3)))))) <=> ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!3)), X)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!3))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!3)), tptp_fun_X_13(tptp_fun_X_19(Y!3)))))),
% 0.78/0.73 inference(rewrite,[status(thm)],[])).
% 0.78/0.73 tff(157,plain,
% 0.78/0.73 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!3)), X)))) | (p2(tptp_fun_X_13(tptp_fun_X_19(Y!3))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!3)), tptp_fun_X_13(tptp_fun_X_19(Y!3)))))),
% 0.78/0.73 inference(quant_inst,[status(thm)],[])).
% 0.78/0.73 tff(158,plain,
% 0.78/0.73 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!3)), X)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!3))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!3)), tptp_fun_X_13(tptp_fun_X_19(Y!3))))),
% 0.78/0.73 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.78/0.73 tff(159,plain,
% 0.78/0.73 ($false),
% 0.78/0.73 inference(unit_resolution,[status(thm)],[158, 155, 153, 151])).
% 0.78/0.73 tff(160,plain,(((~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!3)))) | (~r1(tptp_fun_X_19(Y!3), tptp_fun_Y_12(tptp_fun_X_19(Y!3)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!3))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!3)), tptp_fun_X_13(tptp_fun_X_19(Y!3))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))), inference(lemma,lemma(discharge,[]))).
% 0.78/0.73 tff(161,plain,
% 0.78/0.73 ((~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!3)))) | (~r1(tptp_fun_X_19(Y!3), tptp_fun_Y_12(tptp_fun_X_19(Y!3)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!3))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!3)), tptp_fun_X_13(tptp_fun_X_19(Y!3))))),
% 0.78/0.73 inference(unit_resolution,[status(thm)],[160, 141])).
% 0.78/0.73 tff(162,plain,
% 0.78/0.73 ((p2(tptp_fun_X_19(Y!3)) | (~r1(Y!3, tptp_fun_X_19(Y!3))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) | r1(Y!3, tptp_fun_X_19(Y!3))),
% 0.78/0.73 inference(tautology,[status(thm)],[])).
% 0.78/0.73 tff(163,plain,
% 0.78/0.73 (r1(Y!3, tptp_fun_X_19(Y!3))),
% 0.78/0.73 inference(unit_resolution,[status(thm)],[162, 139])).
% 0.78/0.73 tff(164,plain,
% 0.78/0.73 ((p2(tptp_fun_X_19(Y!3)) | (~r1(Y!3, tptp_fun_X_19(Y!3))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) | (~p2(tptp_fun_X_19(Y!3)))),
% 0.78/0.73 inference(tautology,[status(thm)],[])).
% 0.78/0.73 tff(165,plain,
% 0.78/0.73 (~p2(tptp_fun_X_19(Y!3))),
% 0.78/0.73 inference(unit_resolution,[status(thm)],[164, 139])).
% 0.78/0.73 tff(166,plain,
% 0.78/0.73 (((~![X: $i] : (p2(X) | (~r1(Y!3, 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!3)) | (~r1(Y!3, tptp_fun_X_19(Y!3))) | (~((~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!3)))) | (~r1(tptp_fun_X_19(Y!3), tptp_fun_Y_12(tptp_fun_X_19(Y!3)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!3))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!3)), tptp_fun_X_13(tptp_fun_X_19(Y!3)))))))) <=> ((~![X: $i] : (p2(X) | (~r1(Y!3, 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!3)) | (~r1(Y!3, tptp_fun_X_19(Y!3))) | (~((~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!3)))) | (~r1(tptp_fun_X_19(Y!3), tptp_fun_Y_12(tptp_fun_X_19(Y!3)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!3))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!3)), tptp_fun_X_13(tptp_fun_X_19(Y!3)))))))),
% 0.78/0.73 inference(rewrite,[status(thm)],[])).
% 0.78/0.73 tff(167,plain,
% 0.78/0.73 ((~![X: $i] : (p2(X) | (~r1(Y!3, 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!3)) | (~r1(Y!3, tptp_fun_X_19(Y!3))) | (~((~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!3)))) | (~r1(tptp_fun_X_19(Y!3), tptp_fun_Y_12(tptp_fun_X_19(Y!3)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!3))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!3)), tptp_fun_X_13(tptp_fun_X_19(Y!3)))))))),
% 0.78/0.73 inference(quant_inst,[status(thm)],[])).
% 0.78/0.73 tff(168,plain,
% 0.78/0.73 ((~![X: $i] : (p2(X) | (~r1(Y!3, X)) | (~((~p2(tptp_fun_Y_12(X))) | (~r1(X, tptp_fun_Y_12(X))) | p2(tptp_fun_X_13(X)) | (~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))))))) | p2(tptp_fun_X_19(Y!3)) | (~r1(Y!3, tptp_fun_X_19(Y!3))) | (~((~p2(tptp_fun_Y_12(tptp_fun_X_19(Y!3)))) | (~r1(tptp_fun_X_19(Y!3), tptp_fun_Y_12(tptp_fun_X_19(Y!3)))) | p2(tptp_fun_X_13(tptp_fun_X_19(Y!3))) | (~r1(tptp_fun_Y_12(tptp_fun_X_19(Y!3)), tptp_fun_X_13(tptp_fun_X_19(Y!3))))))),
% 0.78/0.73 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.78/0.73 tff(169,plain,
% 0.78/0.73 ($false),
% 0.78/0.73 inference(unit_resolution,[status(thm)],[168, 165, 163, 161, 124])).
% 0.78/0.73 tff(170,plain,((p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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(Y!3)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.73 tff(171,plain,
% 0.78/0.73 (~((~(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))))))))),
% 0.78/0.73 inference(unit_resolution,[status(thm)],[170, 79, 77])).
% 0.78/0.73 tff(172,plain,
% 0.78/0.73 (((~(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))))))))),
% 0.78/0.74 inference(tautology,[status(thm)],[])).
% 0.78/0.74 tff(173,plain,
% 0.78/0.74 ((~(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)))))))))),
% 0.78/0.74 inference(unit_resolution,[status(thm)],[172, 171])).
% 0.78/0.74 tff(174,plain,
% 0.78/0.74 (((~((~((~(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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | (~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))))))),
% 0.78/0.74 inference(rewrite,[status(thm)],[])).
% 0.78/0.74 tff(175,plain,
% 0.78/0.74 (((~((~((~(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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | (~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | (~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))))),
% 0.78/0.74 inference(rewrite,[status(thm)],[])).
% 0.78/0.74 tff(176,plain,
% 0.78/0.74 ((((((~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_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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)))))) & (p2(Y) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | (~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))))),
% 0.78/0.74 inference(rewrite,[status(thm)],[])).
% 0.78/0.74 tff(177,plain,
% 0.78/0.74 (((((~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_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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)))))) & (p2(Y) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))),
% 0.78/0.74 inference(and_elim,[status(thm)],[51])).
% 0.78/0.74 tff(178,plain,
% 0.78/0.74 ((~((~((~(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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | (~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))))),
% 0.78/0.74 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.78/0.74 tff(179,plain,
% 0.78/0.74 ((~((~((~(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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | (~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))))),
% 0.78/0.74 inference(modus_ponens,[status(thm)],[178, 175])).
% 0.78/0.74 tff(180,plain,
% 0.78/0.74 ((~((~(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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))))))),
% 0.78/0.74 inference(modus_ponens,[status(thm)],[179, 174])).
% 0.78/0.74 tff(181,plain,
% 0.78/0.74 (~((~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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))))),
% 0.78/0.74 inference(unit_resolution,[status(thm)],[180, 173])).
% 0.78/0.74 tff(182,plain,
% 0.78/0.74 (((~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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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))))))))))),
% 0.78/0.74 inference(tautology,[status(thm)],[])).
% 0.78/0.74 tff(183,plain,
% 0.78/0.74 ((~(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)))))))))),
% 0.78/0.74 inference(unit_resolution,[status(thm)],[182, 181])).
% 0.78/0.74 tff(184,plain,
% 0.78/0.74 (((~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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))),
% 0.78/0.75 inference(tautology,[status(thm)],[])).
% 0.78/0.75 tff(185,plain,
% 0.78/0.75 (![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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))),
% 0.78/0.75 inference(unit_resolution,[status(thm)],[184, 181])).
% 0.78/0.75 tff(186,assumption,(~((~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)).
% 0.78/0.75 tff(187,plain,
% 0.78/0.75 (((~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))))),
% 0.78/0.75 inference(tautology,[status(thm)],[])).
% 0.78/0.75 tff(188,plain,
% 0.78/0.75 (![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))),
% 0.78/0.75 inference(unit_resolution,[status(thm)],[187, 186])).
% 0.78/0.75 tff(189,assumption,(~(p2(tptp_fun_Y_5(Y!18)) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))) | (~p2(tptp_fun_X_4(Y!18))))), introduced(assumption)).
% 0.78/0.75 tff(190,plain,
% 0.78/0.75 ((p2(tptp_fun_Y_5(Y!18)) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))) | (~p2(tptp_fun_X_4(Y!18)))) | p2(tptp_fun_X_4(Y!18))),
% 0.78/0.75 inference(tautology,[status(thm)],[])).
% 0.78/0.75 tff(191,plain,
% 0.78/0.75 (p2(tptp_fun_X_4(Y!18))),
% 0.78/0.75 inference(unit_resolution,[status(thm)],[190, 189])).
% 0.78/0.75 tff(192,plain,
% 0.78/0.75 ((p2(tptp_fun_Y_5(Y!18)) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))) | (~p2(tptp_fun_X_4(Y!18)))) | r1(Y!18, tptp_fun_X_4(Y!18))),
% 0.78/0.75 inference(tautology,[status(thm)],[])).
% 0.78/0.75 tff(193,plain,
% 0.78/0.75 (r1(Y!18, tptp_fun_X_4(Y!18))),
% 0.78/0.75 inference(unit_resolution,[status(thm)],[192, 189])).
% 0.78/0.75 tff(194,assumption,(![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))), introduced(assumption)).
% 0.78/0.75 tff(195,plain,
% 0.78/0.75 (((~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ((~p2(tptp_fun_X_4(Y!18))) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!18), Y))))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~p2(tptp_fun_X_4(Y!18))) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!18), Y))))),
% 0.78/0.75 inference(rewrite,[status(thm)],[])).
% 0.78/0.75 tff(196,plain,
% 0.78/0.75 ((~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ((~p2(tptp_fun_X_4(Y!18))) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!18), Y))))),
% 0.78/0.75 inference(quant_inst,[status(thm)],[])).
% 0.78/0.75 tff(197,plain,
% 0.78/0.75 ((~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~p2(tptp_fun_X_4(Y!18))) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!18), Y)))),
% 0.78/0.75 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.78/0.75 tff(198,plain,
% 0.78/0.75 (![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!18), Y)))),
% 0.78/0.75 inference(unit_resolution,[status(thm)],[197, 194, 193, 191])).
% 0.78/0.75 tff(199,plain,
% 0.78/0.75 ((p2(tptp_fun_Y_5(Y!18)) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))) | (~p2(tptp_fun_X_4(Y!18)))) | r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))),
% 0.78/0.75 inference(tautology,[status(thm)],[])).
% 0.78/0.75 tff(200,plain,
% 0.78/0.75 (r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))),
% 0.78/0.75 inference(unit_resolution,[status(thm)],[199, 189])).
% 0.78/0.75 tff(201,plain,
% 0.78/0.75 ((p2(tptp_fun_Y_5(Y!18)) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))) | (~p2(tptp_fun_X_4(Y!18)))) | (~p2(tptp_fun_Y_5(Y!18)))),
% 0.78/0.75 inference(tautology,[status(thm)],[])).
% 0.78/0.75 tff(202,plain,
% 0.78/0.75 (~p2(tptp_fun_Y_5(Y!18))),
% 0.78/0.75 inference(unit_resolution,[status(thm)],[201, 189])).
% 0.78/0.75 tff(203,plain,
% 0.78/0.75 (((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!18), Y)))) | (p2(tptp_fun_Y_5(Y!18)) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!18), Y)))) | p2(tptp_fun_Y_5(Y!18)) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))))),
% 0.78/0.75 inference(rewrite,[status(thm)],[])).
% 0.78/0.75 tff(204,plain,
% 0.78/0.75 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!18), Y)))) | (p2(tptp_fun_Y_5(Y!18)) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))))),
% 0.78/0.75 inference(quant_inst,[status(thm)],[])).
% 0.78/0.75 tff(205,plain,
% 0.78/0.75 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!18), Y)))) | p2(tptp_fun_Y_5(Y!18)) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18)))),
% 0.78/0.75 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.78/0.75 tff(206,plain,
% 0.78/0.75 ($false),
% 0.78/0.75 inference(unit_resolution,[status(thm)],[205, 202, 200, 198])).
% 0.78/0.75 tff(207,plain,((p2(tptp_fun_Y_5(Y!18)) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))) | (~p2(tptp_fun_X_4(Y!18)))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!18, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))), inference(lemma,lemma(discharge,[]))).
% 0.78/0.75 tff(208,plain,
% 0.78/0.75 (p2(tptp_fun_Y_5(Y!18)) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))) | (~p2(tptp_fun_X_4(Y!18)))),
% 0.78/0.75 inference(unit_resolution,[status(thm)],[207, 188])).
% 0.78/0.75 tff(209,plain,
% 0.78/0.75 (((~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))),
% 0.78/0.75 inference(tautology,[status(thm)],[])).
% 0.78/0.75 tff(210,plain,
% 0.78/0.75 (~p2(Y!18)),
% 0.78/0.75 inference(unit_resolution,[status(thm)],[209, 186])).
% 0.78/0.75 tff(211,plain,
% 0.78/0.75 (((~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)),
% 0.78/0.75 inference(tautology,[status(thm)],[])).
% 0.78/0.75 tff(212,plain,
% 0.78/0.75 (r1(X!17, Y!18)),
% 0.78/0.75 inference(unit_resolution,[status(thm)],[211, 186])).
% 0.78/0.75 tff(213,assumption,(p2(tptp_fun_Y_5(Y!18)) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))) | (~p2(tptp_fun_X_4(Y!18)))), introduced(assumption)).
% 0.78/0.75 tff(214,assumption,(~p2(Y!18)), introduced(assumption)).
% 0.78/0.75 tff(215,plain,
% 0.78/0.75 ((~(p2(Y!18) | (~(p2(tptp_fun_Y_5(Y!18)) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))) | (~p2(tptp_fun_X_4(Y!18))))))) | p2(Y!18) | (~(p2(tptp_fun_Y_5(Y!18)) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))) | (~p2(tptp_fun_X_4(Y!18)))))),
% 0.78/0.75 inference(tautology,[status(thm)],[])).
% 0.78/0.75 tff(216,plain,
% 0.78/0.75 (~(p2(Y!18) | (~(p2(tptp_fun_Y_5(Y!18)) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))) | (~p2(tptp_fun_X_4(Y!18))))))),
% 0.78/0.75 inference(unit_resolution,[status(thm)],[215, 214, 213])).
% 0.78/0.75 tff(217,plain,
% 0.78/0.75 (((~(p2(Y!18) | (~(p2(tptp_fun_Y_5(Y!18)) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))) | (~p2(tptp_fun_X_4(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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))) | (p2(Y!18) | (~(p2(tptp_fun_Y_5(Y!18)) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))) | (~p2(tptp_fun_X_4(Y!18))))))),
% 0.78/0.75 inference(tautology,[status(thm)],[])).
% 0.78/0.75 tff(218,plain,
% 0.78/0.75 ((~(p2(Y!18) | (~(p2(tptp_fun_Y_5(Y!18)) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))) | (~p2(tptp_fun_X_4(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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.78/0.75 inference(unit_resolution,[status(thm)],[217, 216])).
% 0.78/0.75 tff(219,assumption,(![Y: $i] : ((~r1(X!17, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))), introduced(assumption)).
% 0.78/0.75 tff(220,assumption,(r1(X!17, Y!18)), introduced(assumption)).
% 0.78/0.75 tff(221,plain,
% 0.78/0.75 (((~![Y: $i] : ((~r1(X!17, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) | ((~r1(X!17, Y!18)) | (~((~(p2(Y!18) | (~(p2(tptp_fun_Y_5(Y!18)) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))) | (~p2(tptp_fun_X_4(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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) <=> ((~![Y: $i] : ((~r1(X!17, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) | (~r1(X!17, Y!18)) | (~((~(p2(Y!18) | (~(p2(tptp_fun_Y_5(Y!18)) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))) | (~p2(tptp_fun_X_4(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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))),
% 0.78/0.75 inference(rewrite,[status(thm)],[])).
% 0.78/0.75 tff(222,plain,
% 0.78/0.75 (((~r1(X!17, Y!18)) | (~((~(p2(Y!18) | (~((~p2(tptp_fun_X_4(Y!18))) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | p2(tptp_fun_Y_5(Y!18)) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))) <=> ((~r1(X!17, Y!18)) | (~((~(p2(Y!18) | (~(p2(tptp_fun_Y_5(Y!18)) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))) | (~p2(tptp_fun_X_4(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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))),
% 0.78/0.75 inference(rewrite,[status(thm)],[])).
% 0.78/0.75 tff(223,plain,
% 0.78/0.75 (((~![Y: $i] : ((~r1(X!17, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) | ((~r1(X!17, Y!18)) | (~((~(p2(Y!18) | (~((~p2(tptp_fun_X_4(Y!18))) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | p2(tptp_fun_Y_5(Y!18)) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) <=> ((~![Y: $i] : ((~r1(X!17, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) | ((~r1(X!17, Y!18)) | (~((~(p2(Y!18) | (~(p2(tptp_fun_Y_5(Y!18)) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))) | (~p2(tptp_fun_X_4(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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))),
% 0.78/0.75 inference(monotonicity,[status(thm)],[222])).
% 0.78/0.75 tff(224,plain,
% 0.78/0.75 (((~![Y: $i] : ((~r1(X!17, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) | ((~r1(X!17, Y!18)) | (~((~(p2(Y!18) | (~((~p2(tptp_fun_X_4(Y!18))) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | p2(tptp_fun_Y_5(Y!18)) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) <=> ((~![Y: $i] : ((~r1(X!17, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) | (~r1(X!17, Y!18)) | (~((~(p2(Y!18) | (~(p2(tptp_fun_Y_5(Y!18)) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))) | (~p2(tptp_fun_X_4(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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))),
% 0.78/0.75 inference(transitivity,[status(thm)],[223, 221])).
% 0.78/0.75 tff(225,plain,
% 0.78/0.75 ((~![Y: $i] : ((~r1(X!17, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) | ((~r1(X!17, Y!18)) | (~((~(p2(Y!18) | (~((~p2(tptp_fun_X_4(Y!18))) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | p2(tptp_fun_Y_5(Y!18)) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))),
% 0.78/0.75 inference(quant_inst,[status(thm)],[])).
% 0.78/0.75 tff(226,plain,
% 0.78/0.75 ((~![Y: $i] : ((~r1(X!17, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) | (~r1(X!17, Y!18)) | (~((~(p2(Y!18) | (~(p2(tptp_fun_Y_5(Y!18)) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))) | (~p2(tptp_fun_X_4(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: $i] : (p2(Y) | (~r1(X, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))),
% 0.78/0.75 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.78/0.75 tff(227,plain,
% 0.78/0.75 ($false),
% 0.78/0.75 inference(unit_resolution,[status(thm)],[226, 220, 219, 218])).
% 0.78/0.75 tff(228,plain,((~![Y: $i] : ((~r1(X!17, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) | (~r1(X!17, Y!18)) | p2(Y!18) | (~(p2(tptp_fun_Y_5(Y!18)) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))) | (~p2(tptp_fun_X_4(Y!18)))))), inference(lemma,lemma(discharge,[]))).
% 0.78/0.75 tff(229,plain,
% 0.78/0.75 (~![Y: $i] : ((~r1(X!17, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))),
% 0.78/0.75 inference(unit_resolution,[status(thm)],[228, 212, 210, 208])).
% 0.78/0.75 tff(230,assumption,(![Y: $i] : (p2(Y) | (~r1(X!17, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))), introduced(assumption)).
% 0.78/0.75 tff(231,plain,
% 0.78/0.75 (((~![Y: $i] : (p2(Y) | (~r1(X!17, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!18) | (~r1(X!17, Y!18)) | (~(p2(tptp_fun_Y_5(Y!18)) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))) | (~p2(tptp_fun_X_4(Y!18))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!17, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!18) | (~r1(X!17, Y!18)) | (~(p2(tptp_fun_Y_5(Y!18)) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))) | (~p2(tptp_fun_X_4(Y!18))))))),
% 0.78/0.75 inference(rewrite,[status(thm)],[])).
% 0.78/0.75 tff(232,plain,
% 0.78/0.75 ((p2(Y!18) | (~r1(X!17, Y!18)) | (~((~p2(tptp_fun_X_4(Y!18))) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | p2(tptp_fun_Y_5(Y!18)) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18)))))) <=> (p2(Y!18) | (~r1(X!17, Y!18)) | (~(p2(tptp_fun_Y_5(Y!18)) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))) | (~p2(tptp_fun_X_4(Y!18))))))),
% 0.78/0.75 inference(rewrite,[status(thm)],[])).
% 0.78/0.75 tff(233,plain,
% 0.78/0.75 (((~![Y: $i] : (p2(Y) | (~r1(X!17, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!18) | (~r1(X!17, Y!18)) | (~((~p2(tptp_fun_X_4(Y!18))) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | p2(tptp_fun_Y_5(Y!18)) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!17, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!18) | (~r1(X!17, Y!18)) | (~(p2(tptp_fun_Y_5(Y!18)) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))) | (~p2(tptp_fun_X_4(Y!18)))))))),
% 0.78/0.75 inference(monotonicity,[status(thm)],[232])).
% 0.78/0.75 tff(234,plain,
% 0.78/0.75 (((~![Y: $i] : (p2(Y) | (~r1(X!17, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!18) | (~r1(X!17, Y!18)) | (~((~p2(tptp_fun_X_4(Y!18))) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | p2(tptp_fun_Y_5(Y!18)) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!17, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!18) | (~r1(X!17, Y!18)) | (~(p2(tptp_fun_Y_5(Y!18)) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))) | (~p2(tptp_fun_X_4(Y!18))))))),
% 0.78/0.75 inference(transitivity,[status(thm)],[233, 231])).
% 0.78/0.75 tff(235,plain,
% 0.78/0.75 ((~![Y: $i] : (p2(Y) | (~r1(X!17, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!18) | (~r1(X!17, Y!18)) | (~((~p2(tptp_fun_X_4(Y!18))) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | p2(tptp_fun_Y_5(Y!18)) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))))))),
% 0.78/0.75 inference(quant_inst,[status(thm)],[])).
% 0.78/0.75 tff(236,plain,
% 0.78/0.75 ((~![Y: $i] : (p2(Y) | (~r1(X!17, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!18) | (~r1(X!17, Y!18)) | (~(p2(tptp_fun_Y_5(Y!18)) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))) | (~p2(tptp_fun_X_4(Y!18)))))),
% 0.78/0.75 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.78/0.75 tff(237,plain,
% 0.78/0.75 ($false),
% 0.78/0.75 inference(unit_resolution,[status(thm)],[236, 214, 220, 230, 213])).
% 0.78/0.75 tff(238,plain,((~![Y: $i] : (p2(Y) | (~r1(X!17, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!18) | (~r1(X!17, Y!18)) | (~(p2(tptp_fun_Y_5(Y!18)) | (~r1(Y!18, tptp_fun_X_4(Y!18))) | (~r1(tptp_fun_X_4(Y!18), tptp_fun_Y_5(Y!18))) | (~p2(tptp_fun_X_4(Y!18)))))), inference(lemma,lemma(discharge,[]))).
% 0.78/0.75 tff(239,plain,
% 0.78/0.75 (~![Y: $i] : (p2(Y) | (~r1(X!17, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))),
% 0.78/0.75 inference(unit_resolution,[status(thm)],[238, 210, 212, 208])).
% 0.78/0.75 tff(240,plain,
% 0.78/0.75 (((~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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) | ![Y: $i] : (p2(Y) | (~r1(X!17, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))),
% 0.78/0.75 inference(tautology,[status(thm)],[])).
% 0.78/0.75 tff(241,plain,
% 0.78/0.75 ((~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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))),
% 0.78/0.75 inference(unit_resolution,[status(thm)],[240, 239])).
% 0.78/0.75 tff(242,assumption,(![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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))), introduced(assumption)).
% 0.78/0.75 tff(243,plain,
% 0.78/0.75 (((~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)),
% 0.78/0.75 inference(tautology,[status(thm)],[])).
% 0.78/0.75 tff(244,plain,
% 0.78/0.75 (r1(Y!16, X!17)),
% 0.78/0.75 inference(unit_resolution,[status(thm)],[243, 186])).
% 0.78/0.76 tff(245,plain,
% 0.78/0.76 (((~![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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X!17, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X!17, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))),
% 0.78/0.76 inference(rewrite,[status(thm)],[])).
% 0.78/0.76 tff(246,plain,
% 0.78/0.76 ((~![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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X!17, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))),
% 0.78/0.76 inference(quant_inst,[status(thm)],[])).
% 0.78/0.76 tff(247,plain,
% 0.78/0.76 ((~![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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X!17, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))),
% 0.78/0.76 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.78/0.76 tff(248,plain,
% 0.78/0.76 ((~(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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X!17, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))),
% 0.78/0.76 inference(unit_resolution,[status(thm)],[247, 244, 242])).
% 0.78/0.76 tff(249,plain,
% 0.78/0.76 (~(p2(X!17) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!17, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))),
% 0.78/0.76 inference(unit_resolution,[status(thm)],[248, 241, 229])).
% 0.78/0.76 tff(250,plain,
% 0.78/0.76 ((p2(X!17) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!17, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) | (~p2(X!17))),
% 0.78/0.76 inference(tautology,[status(thm)],[])).
% 0.78/0.76 tff(251,plain,
% 0.78/0.76 (~p2(X!17)),
% 0.78/0.76 inference(unit_resolution,[status(thm)],[250, 249])).
% 0.78/0.76 tff(252,plain,
% 0.78/0.76 (((~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))))))),
% 0.78/0.76 inference(tautology,[status(thm)],[])).
% 0.78/0.76 tff(253,plain,
% 0.78/0.76 (![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))))))),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[252, 186])).
% 0.81/0.76 tff(254,plain,
% 0.81/0.76 (((~![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))))))),
% 0.81/0.76 inference(rewrite,[status(thm)],[])).
% 0.81/0.76 tff(255,plain,
% 0.81/0.76 ((~![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))))))),
% 0.81/0.76 inference(quant_inst,[status(thm)],[])).
% 0.81/0.76 tff(256,plain,
% 0.81/0.76 ((~![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)))))),
% 0.81/0.76 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.81/0.76 tff(257,plain,
% 0.81/0.76 (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)))))),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[256, 244, 253])).
% 0.81/0.76 tff(258,plain,
% 0.81/0.76 (~((~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))))),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[257, 251])).
% 0.81/0.76 tff(259,plain,
% 0.81/0.76 (((~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))),
% 0.81/0.76 inference(tautology,[status(thm)],[])).
% 0.81/0.76 tff(260,plain,
% 0.81/0.76 (r1(X!17, tptp_fun_Y_12(X!17))),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[259, 258])).
% 0.81/0.76 tff(261,plain,
% 0.81/0.76 (((~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))),
% 0.81/0.76 inference(tautology,[status(thm)],[])).
% 0.81/0.76 tff(262,plain,
% 0.81/0.76 (p2(tptp_fun_Y_12(X!17))),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[261, 258])).
% 0.81/0.76 tff(263,plain,
% 0.81/0.76 ((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))))),
% 0.81/0.76 inference(tautology,[status(thm)],[])).
% 0.81/0.76 tff(264,plain,
% 0.81/0.76 (![Y: $i] : ((~p2(Y)) | (~r1(X!17, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[263, 249])).
% 0.81/0.76 tff(265,plain,
% 0.81/0.76 (((~![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))))),
% 0.81/0.76 inference(rewrite,[status(thm)],[])).
% 0.81/0.76 tff(266,plain,
% 0.81/0.76 ((~![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))))),
% 0.81/0.76 inference(quant_inst,[status(thm)],[])).
% 0.81/0.76 tff(267,plain,
% 0.81/0.76 ((~![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)))),
% 0.81/0.76 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.81/0.76 tff(268,plain,
% 0.81/0.76 (![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(X!17), X)))),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[267, 264, 262, 260])).
% 0.81/0.76 tff(269,plain,
% 0.81/0.76 (((~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))),
% 0.81/0.76 inference(tautology,[status(thm)],[])).
% 0.81/0.76 tff(270,plain,
% 0.81/0.76 (r1(tptp_fun_Y_12(X!17), tptp_fun_X_13(X!17))),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[269, 258])).
% 0.81/0.76 tff(271,plain,
% 0.81/0.76 (((~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)))),
% 0.81/0.76 inference(tautology,[status(thm)],[])).
% 0.81/0.76 tff(272,plain,
% 0.81/0.76 (~p2(tptp_fun_X_13(X!17))),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[271, 258])).
% 0.81/0.76 tff(273,plain,
% 0.81/0.76 (((~![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))))),
% 0.81/0.76 inference(rewrite,[status(thm)],[])).
% 0.81/0.76 tff(274,plain,
% 0.81/0.76 ((~![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))))),
% 0.81/0.76 inference(quant_inst,[status(thm)],[])).
% 0.81/0.76 tff(275,plain,
% 0.81/0.76 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_12(X!17), X)))) | p2(tptp_fun_X_13(X!17)) | (~r1(tptp_fun_Y_12(X!17), tptp_fun_X_13(X!17)))),
% 0.81/0.76 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.81/0.76 tff(276,plain,
% 0.81/0.76 ($false),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[275, 272, 270, 268])).
% 0.81/0.76 tff(277,plain,(((~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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.81/0.76 tff(278,plain,
% 0.81/0.76 ((~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)))))))),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[277, 185])).
% 0.81/0.76 tff(279,plain,
% 0.81/0.76 ((~((~(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)))))))))),
% 0.81/0.76 inference(tautology,[status(thm)],[])).
% 0.81/0.76 tff(280,plain,
% 0.81/0.76 (~(p2(Y!16) | (~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[279, 278, 183])).
% 0.81/0.76 tff(281,plain,
% 0.81/0.76 ((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))))),
% 0.81/0.76 inference(tautology,[status(thm)],[])).
% 0.81/0.76 tff(282,plain,
% 0.81/0.76 (![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[281, 280])).
% 0.81/0.76 tff(283,assumption,(~((~r1(Y!16, tptp_fun_X_4(Y!16))) | (~r1(tptp_fun_X_4(Y!16), tptp_fun_Y_5(Y!16))) | p2(tptp_fun_Y_5(Y!16)) | (~p2(tptp_fun_X_4(Y!16))))), introduced(assumption)).
% 0.81/0.76 tff(284,plain,
% 0.81/0.76 (((~r1(Y!16, tptp_fun_X_4(Y!16))) | (~r1(tptp_fun_X_4(Y!16), tptp_fun_Y_5(Y!16))) | p2(tptp_fun_Y_5(Y!16)) | (~p2(tptp_fun_X_4(Y!16)))) | p2(tptp_fun_X_4(Y!16))),
% 0.81/0.76 inference(tautology,[status(thm)],[])).
% 0.81/0.76 tff(285,plain,
% 0.81/0.76 (p2(tptp_fun_X_4(Y!16))),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[284, 283])).
% 0.81/0.76 tff(286,plain,
% 0.81/0.76 (((~r1(Y!16, tptp_fun_X_4(Y!16))) | (~r1(tptp_fun_X_4(Y!16), tptp_fun_Y_5(Y!16))) | p2(tptp_fun_Y_5(Y!16)) | (~p2(tptp_fun_X_4(Y!16)))) | r1(Y!16, tptp_fun_X_4(Y!16))),
% 0.81/0.76 inference(tautology,[status(thm)],[])).
% 0.81/0.76 tff(287,plain,
% 0.81/0.76 (r1(Y!16, tptp_fun_X_4(Y!16))),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[286, 283])).
% 0.81/0.76 tff(288,assumption,(![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))), introduced(assumption)).
% 0.81/0.76 tff(289,plain,
% 0.81/0.76 (((~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ((~p2(tptp_fun_X_4(Y!16))) | (~r1(Y!16, tptp_fun_X_4(Y!16))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!16), Y))))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~p2(tptp_fun_X_4(Y!16))) | (~r1(Y!16, tptp_fun_X_4(Y!16))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!16), Y))))),
% 0.81/0.76 inference(rewrite,[status(thm)],[])).
% 0.81/0.76 tff(290,plain,
% 0.81/0.76 ((~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ((~p2(tptp_fun_X_4(Y!16))) | (~r1(Y!16, tptp_fun_X_4(Y!16))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!16), Y))))),
% 0.81/0.76 inference(quant_inst,[status(thm)],[])).
% 0.81/0.76 tff(291,plain,
% 0.81/0.76 ((~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~p2(tptp_fun_X_4(Y!16))) | (~r1(Y!16, tptp_fun_X_4(Y!16))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!16), Y)))),
% 0.81/0.76 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.81/0.76 tff(292,plain,
% 0.81/0.76 (![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!16), Y)))),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[291, 288, 287, 285])).
% 0.81/0.76 tff(293,plain,
% 0.81/0.76 (((~r1(Y!16, tptp_fun_X_4(Y!16))) | (~r1(tptp_fun_X_4(Y!16), tptp_fun_Y_5(Y!16))) | p2(tptp_fun_Y_5(Y!16)) | (~p2(tptp_fun_X_4(Y!16)))) | (~p2(tptp_fun_Y_5(Y!16)))),
% 0.81/0.76 inference(tautology,[status(thm)],[])).
% 0.81/0.76 tff(294,plain,
% 0.81/0.76 (~p2(tptp_fun_Y_5(Y!16))),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[293, 283])).
% 0.81/0.76 tff(295,plain,
% 0.81/0.76 (((~r1(Y!16, tptp_fun_X_4(Y!16))) | (~r1(tptp_fun_X_4(Y!16), tptp_fun_Y_5(Y!16))) | p2(tptp_fun_Y_5(Y!16)) | (~p2(tptp_fun_X_4(Y!16)))) | r1(tptp_fun_X_4(Y!16), tptp_fun_Y_5(Y!16))),
% 0.81/0.76 inference(tautology,[status(thm)],[])).
% 0.81/0.76 tff(296,plain,
% 0.81/0.76 (r1(tptp_fun_X_4(Y!16), tptp_fun_Y_5(Y!16))),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[295, 283])).
% 0.81/0.76 tff(297,plain,
% 0.81/0.76 (((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!16), Y)))) | (p2(tptp_fun_Y_5(Y!16)) | (~r1(tptp_fun_X_4(Y!16), tptp_fun_Y_5(Y!16))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!16), Y)))) | p2(tptp_fun_Y_5(Y!16)) | (~r1(tptp_fun_X_4(Y!16), tptp_fun_Y_5(Y!16))))),
% 0.81/0.76 inference(rewrite,[status(thm)],[])).
% 0.81/0.76 tff(298,plain,
% 0.81/0.76 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!16), Y)))) | (p2(tptp_fun_Y_5(Y!16)) | (~r1(tptp_fun_X_4(Y!16), tptp_fun_Y_5(Y!16))))),
% 0.81/0.76 inference(quant_inst,[status(thm)],[])).
% 0.81/0.76 tff(299,plain,
% 0.81/0.76 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!16), Y)))) | p2(tptp_fun_Y_5(Y!16)) | (~r1(tptp_fun_X_4(Y!16), tptp_fun_Y_5(Y!16)))),
% 0.81/0.76 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.81/0.76 tff(300,plain,
% 0.81/0.76 ($false),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[299, 296, 294, 292])).
% 0.81/0.76 tff(301,plain,(((~r1(Y!16, tptp_fun_X_4(Y!16))) | (~r1(tptp_fun_X_4(Y!16), tptp_fun_Y_5(Y!16))) | p2(tptp_fun_Y_5(Y!16)) | (~p2(tptp_fun_X_4(Y!16)))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))), inference(lemma,lemma(discharge,[]))).
% 0.81/0.76 tff(302,plain,
% 0.81/0.76 ((~r1(Y!16, tptp_fun_X_4(Y!16))) | (~r1(tptp_fun_X_4(Y!16), tptp_fun_Y_5(Y!16))) | p2(tptp_fun_Y_5(Y!16)) | (~p2(tptp_fun_X_4(Y!16)))),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[301, 282])).
% 0.81/0.76 tff(303,plain,
% 0.81/0.76 ((p2(Y!16) | (~![X: $i] : ((~p2(X)) | (~r1(Y!16, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) | (~p2(Y!16))),
% 0.81/0.76 inference(tautology,[status(thm)],[])).
% 0.81/0.76 tff(304,plain,
% 0.81/0.76 (~p2(Y!16)),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[303, 280])).
% 0.81/0.76 tff(305,plain,
% 0.81/0.76 (((~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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_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_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))))) | r1(X!0, Y!16)),
% 0.81/0.76 inference(tautology,[status(thm)],[])).
% 0.81/0.76 tff(306,plain,
% 0.81/0.76 (r1(X!0, Y!16)),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[305, 181])).
% 0.81/0.76 tff(307,plain,
% 0.81/0.76 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[82, 77])).
% 0.81/0.76 tff(308,plain,
% 0.81/0.76 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!16) | (~r1(X!0, Y!16)) | (~((~r1(Y!16, tptp_fun_X_4(Y!16))) | (~r1(tptp_fun_X_4(Y!16), tptp_fun_Y_5(Y!16))) | p2(tptp_fun_Y_5(Y!16)) | (~p2(tptp_fun_X_4(Y!16))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!16) | (~r1(X!0, Y!16)) | (~((~r1(Y!16, tptp_fun_X_4(Y!16))) | (~r1(tptp_fun_X_4(Y!16), tptp_fun_Y_5(Y!16))) | p2(tptp_fun_Y_5(Y!16)) | (~p2(tptp_fun_X_4(Y!16))))))),
% 0.81/0.76 inference(rewrite,[status(thm)],[])).
% 0.81/0.76 tff(309,plain,
% 0.81/0.76 ((p2(Y!16) | (~r1(X!0, Y!16)) | (~((~p2(tptp_fun_X_4(Y!16))) | (~r1(Y!16, tptp_fun_X_4(Y!16))) | p2(tptp_fun_Y_5(Y!16)) | (~r1(tptp_fun_X_4(Y!16), tptp_fun_Y_5(Y!16)))))) <=> (p2(Y!16) | (~r1(X!0, Y!16)) | (~((~r1(Y!16, tptp_fun_X_4(Y!16))) | (~r1(tptp_fun_X_4(Y!16), tptp_fun_Y_5(Y!16))) | p2(tptp_fun_Y_5(Y!16)) | (~p2(tptp_fun_X_4(Y!16))))))),
% 0.81/0.76 inference(rewrite,[status(thm)],[])).
% 0.81/0.76 tff(310,plain,
% 0.81/0.76 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!16) | (~r1(X!0, Y!16)) | (~((~p2(tptp_fun_X_4(Y!16))) | (~r1(Y!16, tptp_fun_X_4(Y!16))) | p2(tptp_fun_Y_5(Y!16)) | (~r1(tptp_fun_X_4(Y!16), tptp_fun_Y_5(Y!16))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!16) | (~r1(X!0, Y!16)) | (~((~r1(Y!16, tptp_fun_X_4(Y!16))) | (~r1(tptp_fun_X_4(Y!16), tptp_fun_Y_5(Y!16))) | p2(tptp_fun_Y_5(Y!16)) | (~p2(tptp_fun_X_4(Y!16)))))))),
% 0.81/0.76 inference(monotonicity,[status(thm)],[309])).
% 0.81/0.76 tff(311,plain,
% 0.81/0.76 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!16) | (~r1(X!0, Y!16)) | (~((~p2(tptp_fun_X_4(Y!16))) | (~r1(Y!16, tptp_fun_X_4(Y!16))) | p2(tptp_fun_Y_5(Y!16)) | (~r1(tptp_fun_X_4(Y!16), tptp_fun_Y_5(Y!16))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!16) | (~r1(X!0, Y!16)) | (~((~r1(Y!16, tptp_fun_X_4(Y!16))) | (~r1(tptp_fun_X_4(Y!16), tptp_fun_Y_5(Y!16))) | p2(tptp_fun_Y_5(Y!16)) | (~p2(tptp_fun_X_4(Y!16))))))),
% 0.81/0.76 inference(transitivity,[status(thm)],[310, 308])).
% 0.81/0.76 tff(312,plain,
% 0.81/0.76 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!16) | (~r1(X!0, Y!16)) | (~((~p2(tptp_fun_X_4(Y!16))) | (~r1(Y!16, tptp_fun_X_4(Y!16))) | p2(tptp_fun_Y_5(Y!16)) | (~r1(tptp_fun_X_4(Y!16), tptp_fun_Y_5(Y!16))))))),
% 0.81/0.76 inference(quant_inst,[status(thm)],[])).
% 0.81/0.76 tff(313,plain,
% 0.81/0.76 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!16) | (~r1(X!0, Y!16)) | (~((~r1(Y!16, tptp_fun_X_4(Y!16))) | (~r1(tptp_fun_X_4(Y!16), tptp_fun_Y_5(Y!16))) | p2(tptp_fun_Y_5(Y!16)) | (~p2(tptp_fun_X_4(Y!16)))))),
% 0.81/0.77 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.81/0.77 tff(314,plain,
% 0.81/0.77 ($false),
% 0.81/0.77 inference(unit_resolution,[status(thm)],[313, 307, 306, 304, 302])).
% 0.81/0.77 % SZS output end Proof
%------------------------------------------------------------------------------