TSTP Solution File: LCL668+1.001 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL668+1.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 04:57:39 EDT 2022
% Result : Theorem 7.87s 5.23s
% Output : Proof 7.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL668+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 23:39:27 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 7.87/5.23 % SZS status Theorem
% 7.87/5.23 % SZS output start Proof
% 7.87/5.23 tff(p5_type, type, (
% 7.87/5.23 p5: $i > $o)).
% 7.87/5.23 tff(tptp_fun_Y_11_type, type, (
% 7.87/5.23 tptp_fun_Y_11: $i > $i)).
% 7.87/5.23 tff(tptp_fun_X_10_type, type, (
% 7.87/5.23 tptp_fun_X_10: $i > $i)).
% 7.87/5.23 tff(tptp_fun_Y_9_type, type, (
% 7.87/5.23 tptp_fun_Y_9: $i > $i)).
% 7.87/5.23 tff(tptp_fun_X_3_type, type, (
% 7.87/5.23 tptp_fun_X_3: $i)).
% 7.87/5.23 tff(p1_type, type, (
% 7.87/5.23 p1: $i > $o)).
% 7.87/5.23 tff(r1_type, type, (
% 7.87/5.23 r1: ( $i * $i ) > $o)).
% 7.87/5.23 tff(p2_type, type, (
% 7.87/5.23 p2: $i > $o)).
% 7.87/5.23 tff(p3_type, type, (
% 7.87/5.23 p3: $i > $o)).
% 7.87/5.23 tff(p4_type, type, (
% 7.87/5.23 p4: $i > $o)).
% 7.87/5.23 tff(tptp_fun_Y_2_type, type, (
% 7.87/5.23 tptp_fun_Y_2: $i)).
% 7.87/5.23 tff(p6_type, type, (
% 7.87/5.23 p6: $i > $o)).
% 7.87/5.23 tff(tptp_fun_X_8_type, type, (
% 7.87/5.23 tptp_fun_X_8: $i > $i)).
% 7.87/5.23 tff(tptp_fun_X_0_type, type, (
% 7.87/5.23 tptp_fun_X_0: $i)).
% 7.87/5.23 tff(tptp_fun_X_17_type, type, (
% 7.87/5.23 tptp_fun_X_17: $i)).
% 7.87/5.23 tff(tptp_fun_Y_16_type, type, (
% 7.87/5.23 tptp_fun_Y_16: $i)).
% 7.87/5.23 tff(tptp_fun_X_15_type, type, (
% 7.87/5.23 tptp_fun_X_15: $i)).
% 7.87/5.23 tff(tptp_fun_Y_14_type, type, (
% 7.87/5.23 tptp_fun_Y_14: $i)).
% 7.87/5.23 tff(tptp_fun_X_13_type, type, (
% 7.87/5.23 tptp_fun_X_13: $i)).
% 7.87/5.23 tff(tptp_fun_Y_12_type, type, (
% 7.87/5.23 tptp_fun_Y_12: $i)).
% 7.87/5.23 tff(tptp_fun_X_7_type, type, (
% 7.87/5.23 tptp_fun_X_7: $i)).
% 7.87/5.23 tff(p8_type, type, (
% 7.87/5.23 p8: $i > $o)).
% 7.87/5.23 tff(p10_type, type, (
% 7.87/5.23 p10: $i > $o)).
% 7.87/5.23 tff(p12_type, type, (
% 7.87/5.23 p12: $i > $o)).
% 7.87/5.23 tff(tptp_fun_Y_6_type, type, (
% 7.87/5.23 tptp_fun_Y_6: $i)).
% 7.87/5.23 tff(tptp_fun_X_5_type, type, (
% 7.87/5.23 tptp_fun_X_5: $i)).
% 7.87/5.23 tff(tptp_fun_Y_4_type, type, (
% 7.87/5.23 tptp_fun_Y_4: $i)).
% 7.87/5.23 tff(p7_type, type, (
% 7.87/5.23 p7: $i > $o)).
% 7.87/5.23 tff(tptp_fun_Y_1_type, type, (
% 7.87/5.23 tptp_fun_Y_1: $i)).
% 7.87/5.23 tff(1,plain,
% 7.87/5.23 (^[X: $i] : refl(r1(X, X) <=> r1(X, X))),
% 7.87/5.23 inference(bind,[status(th)],[])).
% 7.87/5.23 tff(2,plain,
% 7.87/5.23 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 7.87/5.23 inference(quant_intro,[status(thm)],[1])).
% 7.87/5.23 tff(3,plain,
% 7.87/5.23 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 7.87/5.23 inference(rewrite,[status(thm)],[])).
% 7.87/5.23 tff(4,axiom,(![X: $i] : r1(X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity')).
% 7.87/5.23 tff(5,plain,
% 7.87/5.23 (![X: $i] : r1(X, X)),
% 7.87/5.23 inference(modus_ponens,[status(thm)],[4, 3])).
% 7.87/5.23 tff(6,plain,(
% 7.87/5.23 ![X: $i] : r1(X, X)),
% 7.87/5.23 inference(skolemize,[status(sab)],[5])).
% 7.87/5.23 tff(7,plain,
% 7.87/5.23 (![X: $i] : r1(X, X)),
% 7.87/5.23 inference(modus_ponens,[status(thm)],[6, 2])).
% 7.87/5.23 tff(8,plain,
% 7.87/5.23 ((~![X: $i] : r1(X, X)) | r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))),
% 7.87/5.23 inference(quant_inst,[status(thm)],[])).
% 7.87/5.23 tff(9,plain,
% 7.87/5.23 (r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))),
% 7.87/5.23 inference(unit_resolution,[status(thm)],[8, 7])).
% 7.87/5.23 tff(10,plain,
% 7.87/5.23 (^[Y: $i] : refl(((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))))))))))))) <=> ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))))))))))))))),
% 7.87/5.23 inference(bind,[status(th)],[])).
% 7.87/5.23 tff(11,plain,
% 7.87/5.23 (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))))))),
% 7.87/5.23 inference(quant_intro,[status(thm)],[10])).
% 7.87/5.23 tff(12,plain,
% 7.87/5.23 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))))))))))))) <=> ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))))))))))))))),
% 7.87/5.23 inference(bind,[status(th)],[])).
% 7.87/5.23 tff(13,plain,
% 7.87/5.23 (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))))))),
% 7.87/5.23 inference(quant_intro,[status(thm)],[12])).
% 7.87/5.23 tff(14,plain,
% 7.87/5.23 (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))))))),
% 7.87/5.23 inference(transitivity,[status(thm)],[13, 11])).
% 7.87/5.23 tff(15,plain,
% 7.87/5.23 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X)))))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X)))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))))))))) <=> ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))))))))))))))),
% 7.87/5.23 inference(bind,[status(th)],[])).
% 7.87/5.23 tff(16,plain,
% 7.87/5.23 (![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X)))))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X)))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))))))),
% 7.87/5.23 inference(quant_intro,[status(thm)],[15])).
% 7.87/5.23 tff(17,plain,
% 7.87/5.23 (((~((~r1(X!0, Y!1)) | p7(Y!1))) & (r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & r1(Y!4, X!5) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X)))))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X)))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))))))))) & (r1(X!0, Y!12) & r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))) <=> ((~((~r1(X!0, Y!1)) | p7(Y!1))) & r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & r1(Y!4, X!5) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X)))))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X)))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))))))))) & r1(X!0, Y!12) & r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))),
% 7.87/5.24 inference(rewrite,[status(thm)],[])).
% 7.87/5.24 tff(18,plain,
% 7.87/5.24 ((r1(X!0, Y!12) & (r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))) <=> (r1(X!0, Y!12) & r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))),
% 7.87/5.24 inference(rewrite,[status(thm)],[])).
% 7.87/5.24 tff(19,plain,
% 7.87/5.24 ((r1(Y!12, X!13) & (r1(X!13, Y!14) & r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))) <=> (r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))),
% 7.87/5.24 inference(rewrite,[status(thm)],[])).
% 7.87/5.24 tff(20,plain,
% 7.87/5.24 ((r1(X!13, Y!14) & (r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))) <=> (r1(X!13, Y!14) & r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))),
% 7.87/5.24 inference(rewrite,[status(thm)],[])).
% 7.87/5.24 tff(21,plain,
% 7.87/5.24 ((r1(Y!14, X!15) & (r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))) <=> (r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))),
% 7.87/5.24 inference(rewrite,[status(thm)],[])).
% 7.87/5.24 tff(22,plain,
% 7.87/5.24 (((~(~r1(X!15, Y!16))) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17))))) <=> (r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))),
% 7.87/5.24 inference(rewrite,[status(thm)],[])).
% 7.87/5.24 tff(23,plain,
% 7.87/5.24 ((~(~r1(Y!14, X!15))) <=> r1(Y!14, X!15)),
% 7.87/5.24 inference(rewrite,[status(thm)],[])).
% 7.87/5.24 tff(24,plain,
% 7.87/5.24 (((~(~r1(Y!14, X!15))) & ((~(~r1(X!15, Y!16))) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))) <=> (r1(Y!14, X!15) & (r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17))))))),
% 7.87/5.24 inference(monotonicity,[status(thm)],[23, 22])).
% 7.87/5.24 tff(25,plain,
% 7.87/5.24 (((~(~r1(Y!14, X!15))) & ((~(~r1(X!15, Y!16))) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))) <=> (r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))),
% 7.87/5.24 inference(transitivity,[status(thm)],[24, 21])).
% 7.87/5.24 tff(26,plain,
% 7.87/5.24 ((~(~r1(X!13, Y!14))) <=> r1(X!13, Y!14)),
% 7.87/5.24 inference(rewrite,[status(thm)],[])).
% 7.87/5.24 tff(27,plain,
% 7.87/5.24 (((~(~r1(X!13, Y!14))) & ((~(~r1(Y!14, X!15))) & ((~(~r1(X!15, Y!16))) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17))))))) <=> (r1(X!13, Y!14) & (r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17))))))),
% 7.87/5.24 inference(monotonicity,[status(thm)],[26, 25])).
% 7.87/5.24 tff(28,plain,
% 7.87/5.24 (((~(~r1(X!13, Y!14))) & ((~(~r1(Y!14, X!15))) & ((~(~r1(X!15, Y!16))) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17))))))) <=> (r1(X!13, Y!14) & r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))),
% 7.87/5.24 inference(transitivity,[status(thm)],[27, 20])).
% 7.87/5.24 tff(29,plain,
% 7.87/5.24 ((~(~r1(Y!12, X!13))) <=> r1(Y!12, X!13)),
% 7.87/5.24 inference(rewrite,[status(thm)],[])).
% 7.87/5.24 tff(30,plain,
% 7.87/5.24 (((~(~r1(Y!12, X!13))) & ((~(~r1(X!13, Y!14))) & ((~(~r1(Y!14, X!15))) & ((~(~r1(X!15, Y!16))) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))))) <=> (r1(Y!12, X!13) & (r1(X!13, Y!14) & r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17))))))),
% 7.87/5.24 inference(monotonicity,[status(thm)],[29, 28])).
% 7.87/5.24 tff(31,plain,
% 7.87/5.24 (((~(~r1(Y!12, X!13))) & ((~(~r1(X!13, Y!14))) & ((~(~r1(Y!14, X!15))) & ((~(~r1(X!15, Y!16))) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))))) <=> (r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))),
% 7.87/5.24 inference(transitivity,[status(thm)],[30, 19])).
% 7.87/5.24 tff(32,plain,
% 7.87/5.24 ((~(~r1(X!0, Y!12))) <=> r1(X!0, Y!12)),
% 7.87/5.24 inference(rewrite,[status(thm)],[])).
% 7.87/5.24 tff(33,plain,
% 7.87/5.24 (((~(~r1(X!0, Y!12))) & ((~(~r1(Y!12, X!13))) & ((~(~r1(X!13, Y!14))) & ((~(~r1(Y!14, X!15))) & ((~(~r1(X!15, Y!16))) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17))))))))) <=> (r1(X!0, Y!12) & (r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17))))))),
% 7.87/5.24 inference(monotonicity,[status(thm)],[32, 31])).
% 7.87/5.24 tff(34,plain,
% 7.87/5.24 (((~(~r1(X!0, Y!12))) & ((~(~r1(Y!12, X!13))) & ((~(~r1(X!13, Y!14))) & ((~(~r1(Y!14, X!15))) & ((~(~r1(X!15, Y!16))) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17))))))))) <=> (r1(X!0, Y!12) & r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))),
% 7.87/5.24 inference(transitivity,[status(thm)],[33, 18])).
% 7.87/5.24 tff(35,plain,
% 7.87/5.24 ((r1(X!0, Y!2) & (r1(Y!2, X!3) & r1(X!3, Y!4) & r1(Y!4, X!5) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))))) <=> (r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & r1(Y!4, X!5) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))))),
% 7.87/5.24 inference(rewrite,[status(thm)],[])).
% 7.87/5.24 tff(36,plain,
% 7.87/5.24 ((r1(Y!2, X!3) & (r1(X!3, Y!4) & r1(Y!4, X!5) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))))) <=> (r1(Y!2, X!3) & r1(X!3, Y!4) & r1(Y!4, X!5) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))))),
% 7.87/5.24 inference(rewrite,[status(thm)],[])).
% 7.87/5.24 tff(37,plain,
% 7.87/5.24 ((r1(X!3, Y!4) & (r1(Y!4, X!5) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))))) <=> (r1(X!3, Y!4) & r1(Y!4, X!5) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))))),
% 7.87/5.24 inference(rewrite,[status(thm)],[])).
% 7.87/5.24 tff(38,plain,
% 7.87/5.24 ((r1(Y!4, X!5) & (r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))))) <=> (r1(Y!4, X!5) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))))),
% 7.87/5.24 inference(rewrite,[status(thm)],[])).
% 7.87/5.24 tff(39,plain,
% 7.87/5.24 (((~(~r1(X!5, Y!6))) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7)))))) <=> (r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))))),
% 7.87/5.24 inference(rewrite,[status(thm)],[])).
% 7.87/5.24 tff(40,plain,
% 7.87/5.24 ((~(~r1(Y!4, X!5))) <=> r1(Y!4, X!5)),
% 7.87/5.24 inference(rewrite,[status(thm)],[])).
% 7.87/5.24 tff(41,plain,
% 7.87/5.24 (((~(~r1(Y!4, X!5))) & ((~(~r1(X!5, Y!6))) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))))) <=> (r1(Y!4, X!5) & (r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7)))))))),
% 7.87/5.24 inference(monotonicity,[status(thm)],[40, 39])).
% 7.87/5.24 tff(42,plain,
% 7.87/5.24 (((~(~r1(Y!4, X!5))) & ((~(~r1(X!5, Y!6))) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))))) <=> (r1(Y!4, X!5) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))))),
% 7.87/5.24 inference(transitivity,[status(thm)],[41, 38])).
% 7.87/5.24 tff(43,plain,
% 7.87/5.24 ((~(~r1(X!3, Y!4))) <=> r1(X!3, Y!4)),
% 7.87/5.24 inference(rewrite,[status(thm)],[])).
% 7.87/5.24 tff(44,plain,
% 7.87/5.24 (((~(~r1(X!3, Y!4))) & ((~(~r1(Y!4, X!5))) & ((~(~r1(X!5, Y!6))) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7)))))))) <=> (r1(X!3, Y!4) & (r1(Y!4, X!5) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7)))))))),
% 7.87/5.24 inference(monotonicity,[status(thm)],[43, 42])).
% 7.87/5.24 tff(45,plain,
% 7.87/5.24 (((~(~r1(X!3, Y!4))) & ((~(~r1(Y!4, X!5))) & ((~(~r1(X!5, Y!6))) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7)))))))) <=> (r1(X!3, Y!4) & r1(Y!4, X!5) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))))),
% 7.87/5.24 inference(transitivity,[status(thm)],[44, 37])).
% 7.87/5.24 tff(46,plain,
% 7.87/5.24 ((~(~r1(Y!2, X!3))) <=> r1(Y!2, X!3)),
% 7.87/5.24 inference(rewrite,[status(thm)],[])).
% 7.87/5.24 tff(47,plain,
% 7.87/5.24 (((~(~r1(Y!2, X!3))) & ((~(~r1(X!3, Y!4))) & ((~(~r1(Y!4, X!5))) & ((~(~r1(X!5, Y!6))) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))))))) <=> (r1(Y!2, X!3) & (r1(X!3, Y!4) & r1(Y!4, X!5) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7)))))))),
% 7.87/5.24 inference(monotonicity,[status(thm)],[46, 45])).
% 7.87/5.24 tff(48,plain,
% 7.87/5.24 (((~(~r1(Y!2, X!3))) & ((~(~r1(X!3, Y!4))) & ((~(~r1(Y!4, X!5))) & ((~(~r1(X!5, Y!6))) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))))))) <=> (r1(Y!2, X!3) & r1(X!3, Y!4) & r1(Y!4, X!5) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))))),
% 7.87/5.24 inference(transitivity,[status(thm)],[47, 36])).
% 7.87/5.24 tff(49,plain,
% 7.87/5.24 ((~(~r1(X!0, Y!2))) <=> r1(X!0, Y!2)),
% 7.87/5.24 inference(rewrite,[status(thm)],[])).
% 7.87/5.24 tff(50,plain,
% 7.87/5.24 (((~(~r1(X!0, Y!2))) & ((~(~r1(Y!2, X!3))) & ((~(~r1(X!3, Y!4))) & ((~(~r1(Y!4, X!5))) & ((~(~r1(X!5, Y!6))) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7)))))))))) <=> (r1(X!0, Y!2) & (r1(Y!2, X!3) & r1(X!3, Y!4) & r1(Y!4, X!5) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7)))))))),
% 7.87/5.24 inference(monotonicity,[status(thm)],[49, 48])).
% 7.87/5.24 tff(51,plain,
% 7.87/5.24 (((~(~r1(X!0, Y!2))) & ((~(~r1(Y!2, X!3))) & ((~(~r1(X!3, Y!4))) & ((~(~r1(Y!4, X!5))) & ((~(~r1(X!5, Y!6))) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7)))))))))) <=> (r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & r1(Y!4, X!5) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))))),
% 7.87/5.24 inference(transitivity,[status(thm)],[50, 35])).
% 7.87/5.24 tff(52,plain,
% 7.87/5.24 ((~((~r1(X!0, Y!1)) | p7(Y!1))) <=> (~((~r1(X!0, Y!1)) | p7(Y!1)))),
% 7.87/5.24 inference(rewrite,[status(thm)],[])).
% 7.87/5.24 tff(53,plain,
% 7.87/5.24 (((~((~r1(X!0, Y!1)) | p7(Y!1))) & ((~(~r1(X!0, Y!2))) & ((~(~r1(Y!2, X!3))) & ((~(~r1(X!3, Y!4))) & ((~(~r1(Y!4, X!5))) & ((~(~r1(X!5, Y!6))) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X)))))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X)))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))))))))) & ((~(~r1(X!0, Y!12))) & ((~(~r1(Y!12, X!13))) & ((~(~r1(X!13, Y!14))) & ((~(~r1(Y!14, X!15))) & ((~(~r1(X!15, Y!16))) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))))))) <=> ((~((~r1(X!0, Y!1)) | p7(Y!1))) & (r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & r1(Y!4, X!5) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X)))))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X)))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))))))))) & (r1(X!0, Y!12) & r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17))))))),
% 7.87/5.24 inference(monotonicity,[status(thm)],[52, 51, 34])).
% 7.87/5.24 tff(54,plain,
% 7.87/5.24 (((~((~r1(X!0, Y!1)) | p7(Y!1))) & ((~(~r1(X!0, Y!2))) & ((~(~r1(Y!2, X!3))) & ((~(~r1(X!3, Y!4))) & ((~(~r1(Y!4, X!5))) & ((~(~r1(X!5, Y!6))) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X)))))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X)))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))))))))) & ((~(~r1(X!0, Y!12))) & ((~(~r1(Y!12, X!13))) & ((~(~r1(X!13, Y!14))) & ((~(~r1(Y!14, X!15))) & ((~(~r1(X!15, Y!16))) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))))))) <=> ((~((~r1(X!0, Y!1)) | p7(Y!1))) & r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & r1(Y!4, X!5) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X)))))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X)))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))))))))) & r1(X!0, Y!12) & r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))),
% 7.87/5.24 inference(transitivity,[status(thm)],[53, 17])).
% 7.87/5.24 tff(55,plain,
% 7.87/5.24 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p12(X)) & (~p10(X)) & (~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p6(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X)))))))))))))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p6(X) & p5(X) & p4(X) & p3(X) & p2(X) & p1(X)))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p12(X)) & (~p10(X)) & (~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p6(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X)))))))))))))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p6(X) & p5(X) & p4(X) & p3(X) & p2(X) & p1(X))))))))))),
% 7.87/5.24 inference(rewrite,[status(thm)],[])).
% 7.87/5.24 tff(56,plain,
% 7.87/5.24 ((~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p12(X)) & (~p10(X)) & (~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p6(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X)))))))))))))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p6(X) & p5(X) & p4(X) & p3(X) & p2(X) & p1(X)))))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p12(X)) & (~p10(X)) & (~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p6(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X)))))))))))))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p6(X) & p5(X) & p4(X) & p3(X) & p2(X) & p1(X))))))))))),
% 7.87/5.25 inference(rewrite,[status(thm)],[])).
% 7.87/5.25 tff(57,plain,
% 7.87/5.25 ((~?[X: $i] : (~(((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((((((~p12(X)) & (~p10(X))) & (~p8(X))) & (~p6(X))) & (~p4(X))) & (~p2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | p7(Y))) | (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p5(X)) & (~p1(X))) | (p1(X) & p5(X)))))))))))) | ![X: $i] : ((~r1(Y, X)) | p6(X))) | (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p4(X)) & (~p5(X))) | (p5(X) & p4(X))))))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y))) | (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p3(X)) & (~p4(X))) | (p4(X) & p3(X)))))))))) | ![X: $i] : ((~r1(Y, X)) | p4(X))) | (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p2(X)) & (~p3(X))) | (p3(X) & p2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~![Y: $i] : ((~r1(X, Y)) | (~(~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p1(X)) & (~p2(X))) | (p2(X) & p1(X)))))))))))))))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((((p6(X) & p5(X)) & p4(X)) & p3(X)) & p2(X)) & p1(X))))))))))) <=> (~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p12(X)) & (~p10(X)) & (~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p6(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X)))))))))))))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p6(X) & p5(X) & p4(X) & p3(X) & p2(X) & p1(X)))))))))))),
% 7.87/5.25 inference(rewrite,[status(thm)],[])).
% 7.87/5.25 tff(58,plain,
% 7.87/5.25 ((~(~?[X: $i] : (~(((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((((((~p12(X)) & (~p10(X))) & (~p8(X))) & (~p6(X))) & (~p4(X))) & (~p2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | p7(Y))) | (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p5(X)) & (~p1(X))) | (p1(X) & p5(X)))))))))))) | ![X: $i] : ((~r1(Y, X)) | p6(X))) | (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p4(X)) & (~p5(X))) | (p5(X) & p4(X))))))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y))) | (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p3(X)) & (~p4(X))) | (p4(X) & p3(X)))))))))) | ![X: $i] : ((~r1(Y, X)) | p4(X))) | (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p2(X)) & (~p3(X))) | (p3(X) & p2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~![Y: $i] : ((~r1(X, Y)) | (~(~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p1(X)) & (~p2(X))) | (p2(X) & p1(X)))))))))))))))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((((p6(X) & p5(X)) & p4(X)) & p3(X)) & p2(X)) & p1(X)))))))))))) <=> (~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p12(X)) & (~p10(X)) & (~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p6(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X)))))))))))))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p6(X) & p5(X) & p4(X) & p3(X) & p2(X) & p1(X))))))))))))),
% 7.87/5.25 inference(monotonicity,[status(thm)],[57])).
% 7.87/5.25 tff(59,plain,
% 7.87/5.25 ((~(~?[X: $i] : (~(((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((((((~p12(X)) & (~p10(X))) & (~p8(X))) & (~p6(X))) & (~p4(X))) & (~p2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | p7(Y))) | (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p5(X)) & (~p1(X))) | (p1(X) & p5(X)))))))))))) | ![X: $i] : ((~r1(Y, X)) | p6(X))) | (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p4(X)) & (~p5(X))) | (p5(X) & p4(X))))))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y))) | (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p3(X)) & (~p4(X))) | (p4(X) & p3(X)))))))))) | ![X: $i] : ((~r1(Y, X)) | p4(X))) | (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p2(X)) & (~p3(X))) | (p3(X) & p2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~![Y: $i] : ((~r1(X, Y)) | (~(~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p1(X)) & (~p2(X))) | (p2(X) & p1(X)))))))))))))))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((((p6(X) & p5(X)) & p4(X)) & p3(X)) & p2(X)) & p1(X)))))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p12(X)) & (~p10(X)) & (~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p6(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X)))))))))))))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p6(X) & p5(X) & p4(X) & p3(X) & p2(X) & p1(X))))))))))),
% 7.87/5.25 inference(transitivity,[status(thm)],[58, 56])).
% 7.87/5.25 tff(60,axiom,(~(~?[X: $i] : (~(((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((((((~p12(X)) & (~p10(X))) & (~p8(X))) & (~p6(X))) & (~p4(X))) & (~p2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | p7(Y))) | (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p5(X)) & (~p1(X))) | (p1(X) & p5(X)))))))))))) | ![X: $i] : ((~r1(Y, X)) | p6(X))) | (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p4(X)) & (~p5(X))) | (p5(X) & p4(X))))))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y))) | (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p3(X)) & (~p4(X))) | (p4(X) & p3(X)))))))))) | ![X: $i] : ((~r1(Y, X)) | p4(X))) | (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p2(X)) & (~p3(X))) | (p3(X) & p2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~![Y: $i] : ((~r1(X, Y)) | (~(~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p1(X)) & (~p2(X))) | (p2(X) & p1(X)))))))))))))))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((((p6(X) & p5(X)) & p4(X)) & p3(X)) & p2(X)) & p1(X)))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','main')).
% 7.87/5.25 tff(61,plain,
% 7.87/5.25 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p12(X)) & (~p10(X)) & (~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p6(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X)))))))))))))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p6(X) & p5(X) & p4(X) & p3(X) & p2(X) & p1(X))))))))))),
% 7.87/5.25 inference(modus_ponens,[status(thm)],[60, 59])).
% 7.87/5.25 tff(62,plain,
% 7.87/5.25 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p12(X)) & (~p10(X)) & (~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p6(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X)))))))))))))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p6(X) & p5(X) & p4(X) & p3(X) & p2(X) & p1(X))))))))))),
% 7.87/5.25 inference(modus_ponens,[status(thm)],[61, 55])).
% 7.87/5.25 tff(63,plain,
% 7.87/5.25 ((~((~r1(X!0, Y!1)) | p7(Y!1))) & r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & r1(Y!4, X!5) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X)))))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X)))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))))))))) & r1(X!0, Y!12) & r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17))))),
% 7.87/5.25 inference(modus_ponens,[status(thm)],[62, 54])).
% 7.87/5.25 tff(64,plain,
% 7.87/5.25 (![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X)))))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X)))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X)))))))))))))))))),
% 7.87/5.25 inference(and_elim,[status(thm)],[63])).
% 7.87/5.25 tff(65,plain,
% 7.87/5.25 (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))))))),
% 7.87/5.25 inference(modus_ponens,[status(thm)],[64, 16])).
% 7.87/5.25 tff(66,plain,
% 7.87/5.25 (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))))))),
% 7.87/5.25 inference(modus_ponens,[status(thm)],[65, 14])).
% 7.87/5.25 tff(67,plain,
% 7.87/5.25 (r1(X!0, Y!2)),
% 7.87/5.25 inference(and_elim,[status(thm)],[63])).
% 7.87/5.25 tff(68,plain,
% 7.87/5.25 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))))))) | ((~r1(X!0, Y!2)) | (~((~r1(Y!2, tptp_fun_X_8(Y!2))) | p6(tptp_fun_X_8(Y!2)) | (~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y!2, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))))))) | (~r1(X!0, Y!2)) | (~((~r1(Y!2, tptp_fun_X_8(Y!2))) | p6(tptp_fun_X_8(Y!2)) | (~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y!2, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))))))),
% 7.87/5.26 inference(rewrite,[status(thm)],[])).
% 7.87/5.26 tff(69,plain,
% 7.87/5.26 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))))))) | ((~r1(X!0, Y!2)) | (~((~r1(Y!2, tptp_fun_X_8(Y!2))) | p6(tptp_fun_X_8(Y!2)) | (~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y!2, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))))))),
% 7.87/5.26 inference(quant_inst,[status(thm)],[])).
% 7.87/5.26 tff(70,plain,
% 7.87/5.26 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))))))) | (~r1(X!0, Y!2)) | (~((~r1(Y!2, tptp_fun_X_8(Y!2))) | p6(tptp_fun_X_8(Y!2)) | (~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y!2, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))))))))))))),
% 7.87/5.26 inference(modus_ponens,[status(thm)],[69, 68])).
% 7.87/5.26 tff(71,plain,
% 7.87/5.26 (~((~r1(Y!2, tptp_fun_X_8(Y!2))) | p6(tptp_fun_X_8(Y!2)) | (~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y!2, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))))),
% 7.87/5.26 inference(unit_resolution,[status(thm)],[70, 67, 66])).
% 7.87/5.26 tff(72,plain,
% 7.87/5.26 (((~r1(Y!2, tptp_fun_X_8(Y!2))) | p6(tptp_fun_X_8(Y!2)) | (~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y!2, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))))))))))) | ![X: $i] : ((~r1(Y!2, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))),
% 7.87/5.26 inference(tautology,[status(thm)],[])).
% 7.87/5.26 tff(73,plain,
% 7.87/5.26 (![X: $i] : ((~r1(Y!2, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))),
% 7.87/5.26 inference(unit_resolution,[status(thm)],[72, 71])).
% 7.87/5.26 tff(74,plain,
% 7.87/5.26 (r1(Y!2, X!3)),
% 7.87/5.26 inference(and_elim,[status(thm)],[63])).
% 7.87/5.26 tff(75,plain,
% 7.87/5.26 (((~![X: $i] : ((~r1(Y!2, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))) | ((~r1(Y!2, X!3)) | (~((~r1(X!3, tptp_fun_Y_9(X!3))) | p5(tptp_fun_Y_9(X!3)) | (~![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X!3, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))) <=> ((~![X: $i] : ((~r1(Y!2, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))) | (~r1(Y!2, X!3)) | (~((~r1(X!3, tptp_fun_Y_9(X!3))) | p5(tptp_fun_Y_9(X!3)) | (~![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X!3, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))),
% 7.87/5.26 inference(rewrite,[status(thm)],[])).
% 7.87/5.26 tff(76,plain,
% 7.87/5.26 ((~![X: $i] : ((~r1(Y!2, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))) | ((~r1(Y!2, X!3)) | (~((~r1(X!3, tptp_fun_Y_9(X!3))) | p5(tptp_fun_Y_9(X!3)) | (~![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X!3, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))),
% 7.87/5.26 inference(quant_inst,[status(thm)],[])).
% 7.87/5.26 tff(77,plain,
% 7.87/5.26 ((~![X: $i] : ((~r1(Y!2, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))) | (~r1(Y!2, X!3)) | (~((~r1(X!3, tptp_fun_Y_9(X!3))) | p5(tptp_fun_Y_9(X!3)) | (~![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X!3, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))))))))),
% 7.87/5.26 inference(modus_ponens,[status(thm)],[76, 75])).
% 7.87/5.26 tff(78,plain,
% 7.87/5.26 (~((~r1(X!3, tptp_fun_Y_9(X!3))) | p5(tptp_fun_Y_9(X!3)) | (~![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X!3, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))),
% 7.87/5.26 inference(unit_resolution,[status(thm)],[77, 74, 73])).
% 7.87/5.26 tff(79,plain,
% 7.87/5.26 (((~r1(X!3, tptp_fun_Y_9(X!3))) | p5(tptp_fun_Y_9(X!3)) | (~![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X!3, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))))))) | r1(X!3, tptp_fun_Y_9(X!3))),
% 7.87/5.26 inference(tautology,[status(thm)],[])).
% 7.87/5.26 tff(80,plain,
% 7.87/5.26 (r1(X!3, tptp_fun_Y_9(X!3))),
% 7.87/5.26 inference(unit_resolution,[status(thm)],[79, 78])).
% 7.87/5.26 tff(81,plain,
% 7.87/5.26 (((~r1(Y!2, tptp_fun_X_8(Y!2))) | p6(tptp_fun_X_8(Y!2)) | (~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y!2, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))))))))))) | ![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))),
% 7.87/5.26 inference(tautology,[status(thm)],[])).
% 7.87/5.26 tff(82,plain,
% 7.87/5.26 (![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))),
% 7.87/5.26 inference(unit_resolution,[status(thm)],[81, 71])).
% 7.87/5.26 tff(83,plain,
% 7.87/5.26 (((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | ((~r1(Y!2, X!3)) | ![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) <=> ((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~r1(Y!2, X!3)) | ![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))),
% 7.87/5.26 inference(rewrite,[status(thm)],[])).
% 7.87/5.26 tff(84,plain,
% 7.87/5.26 ((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | ((~r1(Y!2, X!3)) | ![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))),
% 7.87/5.26 inference(quant_inst,[status(thm)],[])).
% 7.87/5.26 tff(85,plain,
% 7.87/5.26 ((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~r1(Y!2, X!3)) | ![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))))),
% 7.87/5.26 inference(modus_ponens,[status(thm)],[84, 83])).
% 7.87/5.26 tff(86,plain,
% 7.87/5.26 (![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))))),
% 7.87/5.26 inference(unit_resolution,[status(thm)],[85, 74, 82])).
% 7.87/5.26 tff(87,plain,
% 7.87/5.26 (((~![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))))) | ((~r1(X!3, tptp_fun_Y_9(X!3))) | ![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))))) <=> ((~![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))))) | (~r1(X!3, tptp_fun_Y_9(X!3))) | ![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))))),
% 7.87/5.26 inference(rewrite,[status(thm)],[])).
% 7.87/5.26 tff(88,plain,
% 7.87/5.26 ((~![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))))) | ((~r1(X!3, tptp_fun_Y_9(X!3))) | ![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))))),
% 7.87/5.26 inference(quant_inst,[status(thm)],[])).
% 7.87/5.26 tff(89,plain,
% 7.87/5.26 ((~![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))))) | (~r1(X!3, tptp_fun_Y_9(X!3))) | ![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))),
% 7.87/5.26 inference(modus_ponens,[status(thm)],[88, 87])).
% 7.87/5.26 tff(90,plain,
% 7.87/5.26 (![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))),
% 7.87/5.26 inference(unit_resolution,[status(thm)],[89, 86, 80])).
% 7.87/5.26 tff(91,plain,
% 7.87/5.26 (((~r1(X!3, tptp_fun_Y_9(X!3))) | p5(tptp_fun_Y_9(X!3)) | (~![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X!3, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))))))) | ![Y: $i] : ((~r1(X!3, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))),
% 7.87/5.27 inference(tautology,[status(thm)],[])).
% 7.87/5.27 tff(92,plain,
% 7.87/5.27 (![Y: $i] : ((~r1(X!3, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))),
% 7.87/5.27 inference(unit_resolution,[status(thm)],[91, 78])).
% 7.87/5.27 tff(93,plain,
% 7.87/5.27 (((~![Y: $i] : ((~r1(X!3, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))) | ((~r1(X!3, tptp_fun_Y_9(X!3))) | (~((~r1(tptp_fun_Y_9(X!3), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p4(tptp_fun_X_10(tptp_fun_Y_9(X!3))) | (~![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))) <=> ((~![Y: $i] : ((~r1(X!3, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))) | (~r1(X!3, tptp_fun_Y_9(X!3))) | (~((~r1(tptp_fun_Y_9(X!3), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p4(tptp_fun_X_10(tptp_fun_Y_9(X!3))) | (~![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))),
% 7.87/5.27 inference(rewrite,[status(thm)],[])).
% 7.87/5.27 tff(94,plain,
% 7.87/5.27 ((~![Y: $i] : ((~r1(X!3, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))) | ((~r1(X!3, tptp_fun_Y_9(X!3))) | (~((~r1(tptp_fun_Y_9(X!3), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p4(tptp_fun_X_10(tptp_fun_Y_9(X!3))) | (~![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))),
% 7.87/5.27 inference(quant_inst,[status(thm)],[])).
% 7.87/5.27 tff(95,plain,
% 7.87/5.27 ((~![Y: $i] : ((~r1(X!3, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))) | (~r1(X!3, tptp_fun_Y_9(X!3))) | (~((~r1(tptp_fun_Y_9(X!3), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p4(tptp_fun_X_10(tptp_fun_Y_9(X!3))) | (~![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))))),
% 7.87/5.27 inference(modus_ponens,[status(thm)],[94, 93])).
% 7.87/5.27 tff(96,plain,
% 7.87/5.27 (~((~r1(tptp_fun_Y_9(X!3), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p4(tptp_fun_X_10(tptp_fun_Y_9(X!3))) | (~![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))),
% 7.87/5.27 inference(unit_resolution,[status(thm)],[95, 80, 92])).
% 7.87/5.27 tff(97,plain,
% 7.87/5.27 (((~r1(tptp_fun_Y_9(X!3), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p4(tptp_fun_X_10(tptp_fun_Y_9(X!3))) | (~![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))) | r1(tptp_fun_Y_9(X!3), tptp_fun_X_10(tptp_fun_Y_9(X!3)))),
% 7.87/5.27 inference(tautology,[status(thm)],[])).
% 7.87/5.27 tff(98,plain,
% 7.87/5.27 (r1(tptp_fun_Y_9(X!3), tptp_fun_X_10(tptp_fun_Y_9(X!3)))),
% 7.87/5.27 inference(unit_resolution,[status(thm)],[97, 96])).
% 7.87/5.27 tff(99,plain,
% 7.87/5.27 (((~![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))) | ((~r1(tptp_fun_Y_9(X!3), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))) | (~r1(tptp_fun_Y_9(X!3), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))),
% 7.87/5.27 inference(rewrite,[status(thm)],[])).
% 7.87/5.27 tff(100,plain,
% 7.87/5.27 ((~![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))) | ((~r1(tptp_fun_Y_9(X!3), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))),
% 7.87/5.27 inference(quant_inst,[status(thm)],[])).
% 7.87/5.27 tff(101,plain,
% 7.87/5.27 ((~![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))) | (~r1(tptp_fun_Y_9(X!3), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))),
% 7.87/5.27 inference(modus_ponens,[status(thm)],[100, 99])).
% 7.87/5.27 tff(102,plain,
% 7.87/5.27 (![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))),
% 7.87/5.27 inference(unit_resolution,[status(thm)],[101, 98, 90])).
% 7.87/5.27 tff(103,plain,
% 7.87/5.27 (((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))),
% 7.87/5.27 inference(rewrite,[status(thm)],[])).
% 7.87/5.27 tff(104,plain,
% 7.87/5.27 ((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))),
% 7.87/5.27 inference(quant_inst,[status(thm)],[])).
% 7.87/5.27 tff(105,plain,
% 7.87/5.27 ((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))),
% 7.87/5.27 inference(modus_ponens,[status(thm)],[104, 103])).
% 7.87/5.27 tff(106,plain,
% 7.87/5.27 (![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))),
% 7.87/5.27 inference(unit_resolution,[status(thm)],[105, 102, 9])).
% 7.87/5.27 tff(107,plain,
% 7.87/5.27 (((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))),
% 7.87/5.27 inference(rewrite,[status(thm)],[])).
% 7.87/5.27 tff(108,plain,
% 7.87/5.27 ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))),
% 7.87/5.27 inference(quant_inst,[status(thm)],[])).
% 7.87/5.27 tff(109,plain,
% 7.87/5.27 ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))),
% 7.87/5.27 inference(modus_ponens,[status(thm)],[108, 107])).
% 7.87/5.27 tff(110,plain,
% 7.87/5.27 (![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))),
% 7.87/5.27 inference(unit_resolution,[status(thm)],[109, 9, 106])).
% 7.87/5.27 tff(111,plain,
% 7.87/5.27 (((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))),
% 7.87/5.27 inference(rewrite,[status(thm)],[])).
% 7.87/5.27 tff(112,plain,
% 7.87/5.27 ((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))),
% 7.87/5.27 inference(quant_inst,[status(thm)],[])).
% 7.87/5.27 tff(113,plain,
% 7.87/5.27 ((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))),
% 7.87/5.27 inference(modus_ponens,[status(thm)],[112, 111])).
% 7.87/5.27 tff(114,plain,
% 7.87/5.27 (![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))),
% 7.87/5.27 inference(unit_resolution,[status(thm)],[113, 9, 110])).
% 7.87/5.27 tff(115,plain,
% 7.87/5.27 (((~r1(tptp_fun_Y_9(X!3), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p4(tptp_fun_X_10(tptp_fun_Y_9(X!3))) | (~![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))) | ![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))),
% 7.87/5.27 inference(tautology,[status(thm)],[])).
% 7.87/5.27 tff(116,plain,
% 7.87/5.27 (![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))),
% 7.87/5.27 inference(unit_resolution,[status(thm)],[115, 96])).
% 7.87/5.27 tff(117,plain,
% 7.87/5.27 (((~![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))) | ((~r1(tptp_fun_Y_9(X!3), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | (~((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))) | (~r1(tptp_fun_Y_9(X!3), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | (~((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))),
% 7.87/5.27 inference(rewrite,[status(thm)],[])).
% 7.87/5.27 tff(118,plain,
% 7.87/5.27 ((~![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))) | ((~r1(tptp_fun_Y_9(X!3), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | (~((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))),
% 7.87/5.27 inference(quant_inst,[status(thm)],[])).
% 7.87/5.27 tff(119,plain,
% 7.87/5.27 ((~![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))) | (~r1(tptp_fun_Y_9(X!3), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | (~((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))),
% 7.87/5.27 inference(modus_ponens,[status(thm)],[118, 117])).
% 7.87/5.27 tff(120,plain,
% 7.87/5.27 (~((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))),
% 7.87/5.27 inference(unit_resolution,[status(thm)],[119, 98, 116])).
% 7.87/5.27 tff(121,plain,
% 7.87/5.27 (((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))) | r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))),
% 7.87/5.27 inference(tautology,[status(thm)],[])).
% 7.87/5.27 tff(122,plain,
% 7.87/5.27 (r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))),
% 7.87/5.27 inference(unit_resolution,[status(thm)],[121, 120])).
% 7.87/5.27 tff(123,plain,
% 7.87/5.27 (((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~((~p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | (~(p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~((~p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | (~(p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))))))),
% 7.87/5.27 inference(rewrite,[status(thm)],[])).
% 7.87/5.27 tff(124,plain,
% 7.87/5.27 (((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~((~p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | (~(p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))))) <=> ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~((~p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | (~(p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))))))),
% 7.87/5.27 inference(rewrite,[status(thm)],[])).
% 7.87/5.27 tff(125,plain,
% 7.87/5.27 (((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~((~p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | (~(p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~((~p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | (~(p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))))))),
% 7.87/5.27 inference(monotonicity,[status(thm)],[124])).
% 7.87/5.27 tff(126,plain,
% 7.87/5.27 (((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~((~p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | (~(p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~((~p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | (~(p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))))))),
% 7.87/5.27 inference(transitivity,[status(thm)],[125, 123])).
% 7.87/5.27 tff(127,plain,
% 7.87/5.27 ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~((~p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | (~(p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))))))),
% 7.87/5.27 inference(quant_inst,[status(thm)],[])).
% 7.87/5.27 tff(128,plain,
% 7.87/5.27 ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~((~p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | (~(p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))))),
% 7.87/5.27 inference(modus_ponens,[status(thm)],[127, 126])).
% 7.87/5.27 tff(129,plain,
% 7.87/5.27 (~((~((~p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | (~(p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))))),
% 7.87/5.27 inference(unit_resolution,[status(thm)],[128, 122, 114])).
% 7.87/5.27 tff(130,plain,
% 7.87/5.27 (((~((~p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | (~(p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | (p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))),
% 7.87/5.27 inference(tautology,[status(thm)],[])).
% 7.87/5.27 tff(131,plain,
% 7.87/5.27 (p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))),
% 7.87/5.27 inference(unit_resolution,[status(thm)],[130, 129])).
% 7.87/5.27 tff(132,plain,
% 7.87/5.27 (((~r1(X!3, tptp_fun_Y_9(X!3))) | p5(tptp_fun_Y_9(X!3)) | (~![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X!3, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))))))) | ![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))),
% 7.87/5.27 inference(tautology,[status(thm)],[])).
% 7.87/5.27 tff(133,plain,
% 7.87/5.27 (![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))),
% 7.87/5.27 inference(unit_resolution,[status(thm)],[132, 78])).
% 7.87/5.27 tff(134,plain,
% 7.87/5.27 (((~![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | ((~r1(X!3, tptp_fun_Y_9(X!3))) | ![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) <=> ((~![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~r1(X!3, tptp_fun_Y_9(X!3))) | ![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))),
% 7.87/5.27 inference(rewrite,[status(thm)],[])).
% 7.87/5.27 tff(135,plain,
% 7.87/5.27 ((~![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | ((~r1(X!3, tptp_fun_Y_9(X!3))) | ![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))),
% 7.87/5.28 inference(quant_inst,[status(thm)],[])).
% 7.87/5.28 tff(136,plain,
% 7.87/5.28 ((~![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~r1(X!3, tptp_fun_Y_9(X!3))) | ![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))))),
% 7.87/5.28 inference(modus_ponens,[status(thm)],[135, 134])).
% 7.87/5.28 tff(137,plain,
% 7.87/5.28 (![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))))),
% 7.87/5.28 inference(unit_resolution,[status(thm)],[136, 80, 133])).
% 7.87/5.28 tff(138,plain,
% 7.87/5.28 (((~![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))))) | ((~r1(tptp_fun_Y_9(X!3), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))))) | (~r1(tptp_fun_Y_9(X!3), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))))),
% 7.87/5.28 inference(rewrite,[status(thm)],[])).
% 7.87/5.28 tff(139,plain,
% 7.87/5.28 ((~![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))))) | ((~r1(tptp_fun_Y_9(X!3), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))))),
% 7.87/5.28 inference(quant_inst,[status(thm)],[])).
% 7.87/5.28 tff(140,plain,
% 7.87/5.28 ((~![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))))) | (~r1(tptp_fun_Y_9(X!3), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))),
% 7.87/5.28 inference(modus_ponens,[status(thm)],[139, 138])).
% 7.87/5.28 tff(141,plain,
% 7.87/5.28 (![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))),
% 7.87/5.28 inference(unit_resolution,[status(thm)],[140, 98, 137])).
% 7.87/5.28 tff(142,plain,
% 7.87/5.28 (((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))),
% 7.87/5.28 inference(rewrite,[status(thm)],[])).
% 7.87/5.28 tff(143,plain,
% 7.87/5.28 ((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))),
% 7.87/5.28 inference(quant_inst,[status(thm)],[])).
% 7.87/5.28 tff(144,plain,
% 7.87/5.28 ((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))),
% 7.87/5.28 inference(modus_ponens,[status(thm)],[143, 142])).
% 7.87/5.28 tff(145,plain,
% 7.87/5.28 (![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))),
% 7.87/5.28 inference(unit_resolution,[status(thm)],[144, 141, 9])).
% 7.87/5.28 tff(146,plain,
% 7.87/5.28 (((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))),
% 7.87/5.28 inference(rewrite,[status(thm)],[])).
% 7.87/5.28 tff(147,plain,
% 7.87/5.28 ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))),
% 7.87/5.28 inference(quant_inst,[status(thm)],[])).
% 7.87/5.28 tff(148,plain,
% 7.87/5.28 ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))),
% 7.87/5.28 inference(modus_ponens,[status(thm)],[147, 146])).
% 7.87/5.28 tff(149,plain,
% 7.87/5.28 (![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))),
% 7.87/5.28 inference(unit_resolution,[status(thm)],[148, 9, 145])).
% 7.87/5.28 tff(150,plain,
% 7.87/5.28 (((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))),
% 7.87/5.28 inference(rewrite,[status(thm)],[])).
% 7.87/5.28 tff(151,plain,
% 7.87/5.28 ((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))),
% 7.87/5.28 inference(quant_inst,[status(thm)],[])).
% 7.87/5.28 tff(152,plain,
% 7.87/5.28 ((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))),
% 7.87/5.28 inference(modus_ponens,[status(thm)],[151, 150])).
% 7.87/5.28 tff(153,plain,
% 7.87/5.28 (![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))),
% 7.87/5.28 inference(unit_resolution,[status(thm)],[152, 9, 149])).
% 7.87/5.28 tff(154,plain,
% 7.87/5.28 (((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~((~p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | (~(p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~((~p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | (~(p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))))))),
% 7.87/5.28 inference(rewrite,[status(thm)],[])).
% 7.87/5.28 tff(155,plain,
% 7.87/5.28 ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~((~p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | (~(p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))))))),
% 7.87/5.28 inference(quant_inst,[status(thm)],[])).
% 7.87/5.28 tff(156,plain,
% 7.87/5.28 ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~((~p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | (~(p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))))),
% 7.87/5.28 inference(modus_ponens,[status(thm)],[155, 154])).
% 7.87/5.28 tff(157,plain,
% 7.87/5.28 (~((~((~p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | (~(p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))))),
% 7.87/5.28 inference(unit_resolution,[status(thm)],[156, 122, 153])).
% 7.87/5.28 tff(158,plain,
% 7.87/5.28 (((~((~p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | (~(p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | ((~p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))),
% 7.87/5.28 inference(tautology,[status(thm)],[])).
% 7.87/5.28 tff(159,plain,
% 7.87/5.28 ((~p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))),
% 7.87/5.28 inference(unit_resolution,[status(thm)],[158, 157])).
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% 7.87/5.28 (((~r1(tptp_fun_Y_9(X!3), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p4(tptp_fun_X_10(tptp_fun_Y_9(X!3))) | (~![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))) | ![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))),
% 7.87/5.28 inference(tautology,[status(thm)],[])).
% 7.87/5.28 tff(161,plain,
% 7.87/5.28 (![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))),
% 7.87/5.28 inference(unit_resolution,[status(thm)],[160, 96])).
% 7.87/5.28 tff(162,plain,
% 7.87/5.28 (((~![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | ((~r1(tptp_fun_Y_9(X!3), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~r1(tptp_fun_Y_9(X!3), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))),
% 7.87/5.28 inference(rewrite,[status(thm)],[])).
% 7.87/5.28 tff(163,plain,
% 7.87/5.28 ((~![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | ((~r1(tptp_fun_Y_9(X!3), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))),
% 7.87/5.28 inference(quant_inst,[status(thm)],[])).
% 7.87/5.28 tff(164,plain,
% 7.87/5.28 ((~![X: $i] : ((~r1(tptp_fun_Y_9(X!3), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~r1(tptp_fun_Y_9(X!3), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))))),
% 7.87/5.28 inference(modus_ponens,[status(thm)],[163, 162])).
% 7.87/5.28 tff(165,plain,
% 7.87/5.28 (![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))))),
% 7.87/5.28 inference(unit_resolution,[status(thm)],[164, 98, 161])).
% 7.87/5.28 tff(166,plain,
% 7.87/5.28 (((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))))),
% 7.87/5.28 inference(rewrite,[status(thm)],[])).
% 7.87/5.28 tff(167,plain,
% 7.87/5.28 ((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))))),
% 7.87/5.28 inference(quant_inst,[status(thm)],[])).
% 7.87/5.28 tff(168,plain,
% 7.87/5.28 ((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))),
% 7.87/5.28 inference(modus_ponens,[status(thm)],[167, 166])).
% 7.87/5.28 tff(169,plain,
% 7.87/5.28 (![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))),
% 7.87/5.28 inference(unit_resolution,[status(thm)],[168, 165, 9])).
% 7.87/5.28 tff(170,plain,
% 7.87/5.28 (((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))),
% 7.87/5.28 inference(rewrite,[status(thm)],[])).
% 7.87/5.28 tff(171,plain,
% 7.87/5.28 ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))),
% 7.87/5.28 inference(quant_inst,[status(thm)],[])).
% 7.87/5.28 tff(172,plain,
% 7.87/5.28 ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))),
% 7.87/5.28 inference(modus_ponens,[status(thm)],[171, 170])).
% 7.87/5.28 tff(173,plain,
% 7.87/5.28 (![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))),
% 7.87/5.28 inference(unit_resolution,[status(thm)],[172, 9, 169])).
% 7.87/5.28 tff(174,plain,
% 7.87/5.28 (((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))),
% 7.87/5.28 inference(rewrite,[status(thm)],[])).
% 7.87/5.28 tff(175,plain,
% 7.87/5.28 ((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))),
% 7.87/5.28 inference(quant_inst,[status(thm)],[])).
% 7.87/5.28 tff(176,plain,
% 7.87/5.28 ((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))),
% 7.87/5.28 inference(modus_ponens,[status(thm)],[175, 174])).
% 7.87/5.28 tff(177,plain,
% 7.87/5.28 (![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))),
% 7.87/5.28 inference(unit_resolution,[status(thm)],[176, 9, 173])).
% 7.87/5.28 tff(178,plain,
% 7.87/5.28 (((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~(p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))) | (~((~p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~(p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))) | (~((~p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))))))),
% 7.87/5.28 inference(rewrite,[status(thm)],[])).
% 7.87/5.28 tff(179,plain,
% 7.87/5.28 (((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~((~p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | (~(p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))))) <=> ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~(p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))) | (~((~p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))))))),
% 7.87/5.28 inference(rewrite,[status(thm)],[])).
% 7.87/5.28 tff(180,plain,
% 7.87/5.28 (((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~((~p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | (~(p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~(p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))) | (~((~p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))))))))),
% 7.87/5.28 inference(monotonicity,[status(thm)],[179])).
% 7.87/5.28 tff(181,plain,
% 7.87/5.28 (((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~((~p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | (~(p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~(p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))) | (~((~p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))))))),
% 7.87/5.28 inference(transitivity,[status(thm)],[180, 178])).
% 7.87/5.28 tff(182,plain,
% 7.87/5.28 ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~((~p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | (~(p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))))))),
% 7.87/5.28 inference(quant_inst,[status(thm)],[])).
% 7.87/5.28 tff(183,plain,
% 7.87/5.28 ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~(p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))) | (~((~p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))))))),
% 7.87/5.28 inference(modus_ponens,[status(thm)],[182, 181])).
% 7.87/5.28 tff(184,plain,
% 7.87/5.28 (~((~(p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))) | (~((~p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))))),
% 7.87/5.28 inference(unit_resolution,[status(thm)],[183, 122, 177])).
% 7.87/5.28 tff(185,plain,
% 7.87/5.28 (((~(p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))) | (~((~p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))))) | (p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))),
% 7.87/5.28 inference(tautology,[status(thm)],[])).
% 7.87/5.28 tff(186,plain,
% 7.87/5.28 (p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))),
% 7.87/5.28 inference(unit_resolution,[status(thm)],[185, 184])).
% 7.87/5.28 tff(187,plain,
% 7.87/5.28 (((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))) | (~p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))),
% 7.87/5.28 inference(tautology,[status(thm)],[])).
% 7.87/5.28 tff(188,plain,
% 7.87/5.28 (~p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))),
% 7.87/5.28 inference(unit_resolution,[status(thm)],[187, 120])).
% 7.87/5.28 tff(189,plain,
% 7.87/5.28 ((~(p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))) | p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))),
% 7.87/5.28 inference(tautology,[status(thm)],[])).
% 7.87/5.28 tff(190,plain,
% 7.87/5.28 ((~(p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))) | p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))),
% 7.87/5.28 inference(unit_resolution,[status(thm)],[189, 188])).
% 7.87/5.28 tff(191,plain,
% 7.87/5.28 (p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))),
% 7.87/5.28 inference(unit_resolution,[status(thm)],[190, 186])).
% 7.87/5.28 tff(192,plain,
% 7.87/5.28 ((~((~p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | (~p4(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))),
% 7.87/5.28 inference(tautology,[status(thm)],[])).
% 7.87/5.28 tff(193,plain,
% 7.87/5.28 (~p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))),
% 7.87/5.28 inference(unit_resolution,[status(thm)],[192, 191, 159])).
% 7.87/5.28 tff(194,plain,
% 7.87/5.28 (((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))),
% 7.87/5.28 inference(tautology,[status(thm)],[])).
% 7.87/5.28 tff(195,plain,
% 7.87/5.28 (![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))),
% 7.87/5.28 inference(unit_resolution,[status(thm)],[194, 120])).
% 7.87/5.28 tff(196,plain,
% 7.87/5.28 (((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))),
% 7.87/5.28 inference(rewrite,[status(thm)],[])).
% 7.87/5.28 tff(197,plain,
% 7.87/5.28 ((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))),
% 7.87/5.28 inference(quant_inst,[status(thm)],[])).
% 7.87/5.28 tff(198,plain,
% 7.87/5.28 ((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))),
% 7.87/5.28 inference(modus_ponens,[status(thm)],[197, 196])).
% 7.87/5.28 tff(199,plain,
% 7.87/5.28 (![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))),
% 7.87/5.28 inference(unit_resolution,[status(thm)],[198, 195, 9])).
% 7.87/5.28 tff(200,plain,
% 7.87/5.28 (((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))),
% 7.87/5.28 inference(rewrite,[status(thm)],[])).
% 7.87/5.28 tff(201,plain,
% 7.87/5.28 ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))),
% 7.87/5.28 inference(quant_inst,[status(thm)],[])).
% 7.87/5.28 tff(202,plain,
% 7.87/5.28 ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))),
% 7.87/5.28 inference(modus_ponens,[status(thm)],[201, 200])).
% 7.87/5.28 tff(203,plain,
% 7.87/5.28 (![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))),
% 7.87/5.28 inference(unit_resolution,[status(thm)],[202, 9, 199])).
% 7.87/5.28 tff(204,plain,
% 7.87/5.28 (((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))),
% 7.87/5.28 inference(rewrite,[status(thm)],[])).
% 7.87/5.28 tff(205,plain,
% 7.87/5.28 ((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))),
% 7.87/5.28 inference(quant_inst,[status(thm)],[])).
% 7.87/5.28 tff(206,plain,
% 7.87/5.28 ((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))),
% 7.87/5.28 inference(modus_ponens,[status(thm)],[205, 204])).
% 7.87/5.28 tff(207,plain,
% 7.87/5.28 (![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))),
% 7.87/5.28 inference(unit_resolution,[status(thm)],[206, 9, 203])).
% 7.87/5.28 tff(208,plain,
% 7.87/5.28 (((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~(p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~(p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))))))),
% 7.87/5.29 inference(rewrite,[status(thm)],[])).
% 7.87/5.29 tff(209,plain,
% 7.87/5.29 (((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~((~p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | (~(p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))))) <=> ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~(p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))))))),
% 7.87/5.29 inference(rewrite,[status(thm)],[])).
% 7.87/5.29 tff(210,plain,
% 7.87/5.29 (((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~((~p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | (~(p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~(p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))))))))),
% 7.87/5.29 inference(monotonicity,[status(thm)],[209])).
% 7.87/5.29 tff(211,plain,
% 7.87/5.29 (((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~((~p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | (~(p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~(p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))))))),
% 7.87/5.29 inference(transitivity,[status(thm)],[210, 208])).
% 7.87/5.29 tff(212,plain,
% 7.87/5.29 ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~((~p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | (~(p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))))))),
% 7.87/5.29 inference(quant_inst,[status(thm)],[])).
% 7.87/5.29 tff(213,plain,
% 7.87/5.29 ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~(p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))))))),
% 7.87/5.29 inference(modus_ponens,[status(thm)],[212, 211])).
% 7.87/5.29 tff(214,plain,
% 7.87/5.29 (~((~(p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))))),
% 7.87/5.29 inference(unit_resolution,[status(thm)],[213, 122, 207])).
% 7.87/5.29 tff(215,plain,
% 7.87/5.29 (((~(p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))))) | ((~p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))),
% 7.87/5.29 inference(tautology,[status(thm)],[])).
% 7.87/5.29 tff(216,plain,
% 7.87/5.29 ((~p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))),
% 7.87/5.29 inference(unit_resolution,[status(thm)],[215, 214])).
% 7.87/5.29 tff(217,plain,
% 7.87/5.29 (((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))),
% 7.87/5.29 inference(tautology,[status(thm)],[])).
% 7.87/5.29 tff(218,plain,
% 7.87/5.29 (![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))),
% 7.87/5.29 inference(unit_resolution,[status(thm)],[217, 120])).
% 7.87/5.29 tff(219,plain,
% 7.87/5.29 (((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))),
% 7.87/5.29 inference(rewrite,[status(thm)],[])).
% 7.87/5.29 tff(220,plain,
% 7.87/5.29 ((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))),
% 7.87/5.29 inference(quant_inst,[status(thm)],[])).
% 7.87/5.29 tff(221,plain,
% 7.87/5.29 ((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))))),
% 7.87/5.29 inference(modus_ponens,[status(thm)],[220, 219])).
% 7.87/5.29 tff(222,plain,
% 7.87/5.29 (![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))))),
% 7.87/5.29 inference(unit_resolution,[status(thm)],[221, 218, 9])).
% 7.87/5.29 tff(223,plain,
% 7.87/5.29 (((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))))),
% 7.87/5.29 inference(rewrite,[status(thm)],[])).
% 7.87/5.29 tff(224,plain,
% 7.87/5.29 ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))))),
% 7.87/5.29 inference(quant_inst,[status(thm)],[])).
% 7.87/5.29 tff(225,plain,
% 7.87/5.29 ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))),
% 7.87/5.29 inference(modus_ponens,[status(thm)],[224, 223])).
% 7.87/5.29 tff(226,plain,
% 7.87/5.29 (![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))),
% 7.87/5.29 inference(unit_resolution,[status(thm)],[225, 9, 222])).
% 7.87/5.29 tff(227,plain,
% 7.87/5.29 (((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))),
% 7.87/5.29 inference(rewrite,[status(thm)],[])).
% 7.87/5.29 tff(228,plain,
% 7.87/5.29 ((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))),
% 7.87/5.29 inference(quant_inst,[status(thm)],[])).
% 7.87/5.29 tff(229,plain,
% 7.87/5.29 ((~![Y: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | ![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))),
% 7.87/5.29 inference(modus_ponens,[status(thm)],[228, 227])).
% 7.87/5.29 tff(230,plain,
% 7.87/5.29 (![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))),
% 7.87/5.29 inference(unit_resolution,[status(thm)],[229, 9, 226])).
% 7.87/5.29 tff(231,plain,
% 7.87/5.29 (((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~(p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~(p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))))))),
% 7.87/5.29 inference(rewrite,[status(thm)],[])).
% 7.87/5.29 tff(232,plain,
% 7.87/5.29 (((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~((~p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | (~(p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))))) <=> ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~(p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))))))),
% 7.87/5.29 inference(rewrite,[status(thm)],[])).
% 7.87/5.29 tff(233,plain,
% 7.87/5.29 (((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~((~p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | (~(p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~(p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))))))))),
% 7.87/5.29 inference(monotonicity,[status(thm)],[232])).
% 7.87/5.29 tff(234,plain,
% 7.87/5.29 (((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~((~p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | (~(p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~(p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))))))),
% 7.87/5.29 inference(transitivity,[status(thm)],[233, 231])).
% 7.87/5.29 tff(235,plain,
% 7.87/5.29 ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))) | ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~((~p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | (~(p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))))))),
% 7.87/5.29 inference(quant_inst,[status(thm)],[])).
% 7.87/5.29 tff(236,plain,
% 7.87/5.29 ((~![X: $i] : ((~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_9(X!3)), tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~((~(p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))))))),
% 7.87/5.29 inference(modus_ponens,[status(thm)],[235, 234])).
% 7.87/5.29 tff(237,plain,
% 7.87/5.29 (~((~(p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))))),
% 7.87/5.29 inference(unit_resolution,[status(thm)],[236, 122, 230])).
% 7.87/5.29 tff(238,plain,
% 7.87/5.29 (((~(p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))))) | (p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))),
% 7.87/5.29 inference(tautology,[status(thm)],[])).
% 7.87/5.29 tff(239,plain,
% 7.87/5.29 (p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))),
% 7.87/5.29 inference(unit_resolution,[status(thm)],[238, 237])).
% 7.87/5.29 tff(240,plain,
% 7.87/5.29 ((~(p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))) | p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))),
% 7.87/5.29 inference(tautology,[status(thm)],[])).
% 7.87/5.29 tff(241,plain,
% 7.87/5.29 ((~(p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p3(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))) | p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))),
% 7.87/5.29 inference(unit_resolution,[status(thm)],[240, 188])).
% 7.87/5.29 tff(242,plain,
% 7.87/5.29 (p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))),
% 7.87/5.29 inference(unit_resolution,[status(thm)],[241, 239])).
% 7.87/5.29 tff(243,plain,
% 7.87/5.29 ((~((~p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))))) | (~p2(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))) | (~p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))),
% 7.87/5.29 inference(tautology,[status(thm)],[])).
% 7.87/5.29 tff(244,plain,
% 7.87/5.29 (~p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))),
% 7.87/5.29 inference(unit_resolution,[status(thm)],[243, 242, 216])).
% 7.87/5.29 tff(245,plain,
% 7.87/5.29 ((~(p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))))) | p1(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3)))) | p5(tptp_fun_Y_11(tptp_fun_X_10(tptp_fun_Y_9(X!3))))),
% 7.87/5.29 inference(tautology,[status(thm)],[])).
% 7.87/5.29 tff(246,plain,
% 7.87/5.29 ($false),
% 7.87/5.29 inference(unit_resolution,[status(thm)],[245, 244, 193, 131])).
% 7.87/5.29 % SZS output end Proof
%------------------------------------------------------------------------------