TSTP Solution File: LCL674+1.005 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL674+1.005 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 04:57:45 EDT 2022
% Result : Theorem 0.18s 0.40s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL674+1.005 : 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 : n010.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 23:48:43 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.18/0.40 % SZS status Theorem
% 0.18/0.40 % SZS output start Proof
% 0.18/0.40 tff(r1_type, type, (
% 0.18/0.40 r1: ( $i * $i ) > $o)).
% 0.18/0.40 tff(tptp_fun_X_7_type, type, (
% 0.18/0.40 tptp_fun_X_7: $i > $i)).
% 0.18/0.40 tff(tptp_fun_X_9_type, type, (
% 0.18/0.40 tptp_fun_X_9: $i > $i)).
% 0.18/0.40 tff(tptp_fun_X_0_type, type, (
% 0.18/0.40 tptp_fun_X_0: $i)).
% 0.18/0.40 tff(p3_type, type, (
% 0.18/0.40 p3: $i > $o)).
% 0.18/0.40 tff(p102_type, type, (
% 0.18/0.40 p102: $i > $o)).
% 0.18/0.40 tff(tptp_fun_X_8_type, type, (
% 0.18/0.40 tptp_fun_X_8: $i > $i)).
% 0.18/0.40 tff(p103_type, type, (
% 0.18/0.40 p103: $i > $o)).
% 0.18/0.40 tff(p101_type, type, (
% 0.18/0.40 p101: $i > $o)).
% 0.18/0.40 tff(p1_type, type, (
% 0.18/0.40 p1: $i > $o)).
% 0.18/0.40 tff(p100_type, type, (
% 0.18/0.40 p100: $i > $o)).
% 0.18/0.40 tff(p2_type, type, (
% 0.18/0.40 p2: $i > $o)).
% 0.18/0.40 tff(p4_type, type, (
% 0.18/0.40 p4: $i > $o)).
% 0.18/0.40 tff(p104_type, type, (
% 0.18/0.40 p104: $i > $o)).
% 0.18/0.40 tff(p5_type, type, (
% 0.18/0.40 p5: $i > $o)).
% 0.18/0.40 tff(p105_type, type, (
% 0.18/0.40 p105: $i > $o)).
% 0.18/0.40 tff(p6_type, type, (
% 0.18/0.40 p6: $i > $o)).
% 0.18/0.40 tff(p106_type, type, (
% 0.18/0.40 p106: $i > $o)).
% 0.18/0.40 tff(tptp_fun_X_10_type, type, (
% 0.18/0.40 tptp_fun_X_10: $i > $i)).
% 0.18/0.40 tff(tptp_fun_X_6_type, type, (
% 0.18/0.40 tptp_fun_X_6: $i > $i)).
% 0.18/0.40 tff(tptp_fun_X_5_type, type, (
% 0.18/0.40 tptp_fun_X_5: $i > $i)).
% 0.18/0.40 tff(tptp_fun_X_4_type, type, (
% 0.18/0.40 tptp_fun_X_4: $i > $i)).
% 0.18/0.40 tff(tptp_fun_X_3_type, type, (
% 0.18/0.40 tptp_fun_X_3: $i > $i)).
% 0.18/0.40 tff(tptp_fun_X_2_type, type, (
% 0.18/0.40 tptp_fun_X_2: $i > $i)).
% 0.18/0.40 tff(tptp_fun_X_1_type, type, (
% 0.18/0.40 tptp_fun_X_1: $i > $i)).
% 0.18/0.40 tff(1,assumption,(~r1(X!0, X!0)), introduced(assumption)).
% 0.18/0.40 tff(2,plain,
% 0.18/0.40 (^[X: $i] : refl(r1(X, X) <=> r1(X, X))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(3,plain,
% 0.18/0.40 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 0.18/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.18/0.40 tff(4,plain,
% 0.18/0.40 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(5,axiom,(![X: $i] : r1(X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity')).
% 0.18/0.40 tff(6,plain,
% 0.18/0.40 (![X: $i] : r1(X, X)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.18/0.40 tff(7,plain,(
% 0.18/0.40 ![X: $i] : r1(X, X)),
% 0.18/0.40 inference(skolemize,[status(sab)],[6])).
% 0.18/0.40 tff(8,plain,
% 0.18/0.40 (![X: $i] : r1(X, X)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.18/0.40 tff(9,plain,
% 0.18/0.40 ((~![X: $i] : r1(X, X)) | r1(X!0, X!0)),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(10,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.18/0.40 tff(11,plain,(r1(X!0, X!0)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.40 tff(12,plain,
% 0.18/0.40 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (~((~(p105(Y) | (~p104(Y)) | (~(p106(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | (~r1(Y, tptp_fun_X_1(Y))) | p6(tptp_fun_X_1(Y)) | p106(tptp_fun_X_1(Y)) | (~p105(tptp_fun_X_1(Y))) | (~p6(tptp_fun_X_2(Y))) | (~p105(tptp_fun_X_2(Y))))))) | (~(p104(Y) | (~p103(Y)) | (~(p105(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p5(tptp_fun_X_3(Y)) | p105(tptp_fun_X_4(Y)) | (~p104(tptp_fun_X_3(Y))) | (~p5(tptp_fun_X_4(Y))) | (~p104(tptp_fun_X_4(Y))))))) | (~(p103(Y) | (~p102(Y)) | (~(p4(tptp_fun_X_5(Y)) | p104(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))) | p104(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_5(Y))) | (~p4(tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_6(Y))))))) | (~(p102(Y) | (~p101(Y)) | (~(p103(tptp_fun_X_8(Y)) | p103(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)) | (~p102(tptp_fun_X_7(Y))) | (~p3(tptp_fun_X_8(Y))) | (~p102(tptp_fun_X_8(Y))))))) | (~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p2(tptp_fun_X_9(Y)) | p102(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_10(Y))) | p102(tptp_fun_X_10(Y)) | (~p101(tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_10(Y))) | (~p101(tptp_fun_X_10(Y))))))) | (~((~p105(Y)) | (~((~(p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X))))) | (~((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X))))))))) | (~((~p104(Y)) | (~((~(p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X))))) | (~((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X))))))))) | (~((~p103(Y)) | (~((~(p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X))))) | (~((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X))))))))) | (~((~p102(Y)) | (~((~(p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X))))) | (~((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X))))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))) | (~(p105(Y) | (~p106(Y)))) | (~(p104(Y) | (~p105(Y)))) | (~(p103(Y) | (~p104(Y)))) | (~(p102(Y) | (~p103(Y)))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y))))))) <=> ((~r1(X!0, Y)) | (~((~(p105(Y) | (~p104(Y)) | (~(p106(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | (~r1(Y, tptp_fun_X_1(Y))) | p6(tptp_fun_X_1(Y)) | p106(tptp_fun_X_1(Y)) | (~p105(tptp_fun_X_1(Y))) | (~p6(tptp_fun_X_2(Y))) | (~p105(tptp_fun_X_2(Y))))))) | (~(p104(Y) | (~p103(Y)) | (~(p105(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p5(tptp_fun_X_3(Y)) | p105(tptp_fun_X_4(Y)) | (~p104(tptp_fun_X_3(Y))) | (~p5(tptp_fun_X_4(Y))) | (~p104(tptp_fun_X_4(Y))))))) | (~(p103(Y) | (~p102(Y)) | (~(p4(tptp_fun_X_5(Y)) | p104(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))) | p104(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_5(Y))) | (~p4(tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_6(Y))))))) | (~(p102(Y) | (~p101(Y)) | (~(p103(tptp_fun_X_8(Y)) | p103(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)) | (~p102(tptp_fun_X_7(Y))) | (~p3(tptp_fun_X_8(Y))) | (~p102(tptp_fun_X_8(Y))))))) | (~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p2(tptp_fun_X_9(Y)) | p102(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_10(Y))) | p102(tptp_fun_X_10(Y)) | (~p101(tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_10(Y))) | (~p101(tptp_fun_X_10(Y))))))) | (~(p105(Y) | (~p106(Y)))) | (~(p104(Y) | (~p105(Y)))) | (~(p103(Y) | (~p104(Y)))) | (~(p102(Y) | (~p103(Y)))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y)))) | (~((~p105(Y)) | (~((~(p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X))))) | (~((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X))))))))) | (~((~p104(Y)) | (~((~(p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X))))) | (~((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X))))))))) | (~((~p103(Y)) | (~((~(p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X))))) | (~((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X))))))))) | (~((~p102(Y)) | (~((~(p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X))))) | (~((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X))))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))))))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(13,plain,
% 0.18/0.40 (![Y: $i] : ((~r1(X!0, Y)) | (~((~(p105(Y) | (~p104(Y)) | (~(p106(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | (~r1(Y, tptp_fun_X_1(Y))) | p6(tptp_fun_X_1(Y)) | p106(tptp_fun_X_1(Y)) | (~p105(tptp_fun_X_1(Y))) | (~p6(tptp_fun_X_2(Y))) | (~p105(tptp_fun_X_2(Y))))))) | (~(p104(Y) | (~p103(Y)) | (~(p105(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p5(tptp_fun_X_3(Y)) | p105(tptp_fun_X_4(Y)) | (~p104(tptp_fun_X_3(Y))) | (~p5(tptp_fun_X_4(Y))) | (~p104(tptp_fun_X_4(Y))))))) | (~(p103(Y) | (~p102(Y)) | (~(p4(tptp_fun_X_5(Y)) | p104(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))) | p104(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_5(Y))) | (~p4(tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_6(Y))))))) | (~(p102(Y) | (~p101(Y)) | (~(p103(tptp_fun_X_8(Y)) | p103(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)) | (~p102(tptp_fun_X_7(Y))) | (~p3(tptp_fun_X_8(Y))) | (~p102(tptp_fun_X_8(Y))))))) | (~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p2(tptp_fun_X_9(Y)) | p102(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_10(Y))) | p102(tptp_fun_X_10(Y)) | (~p101(tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_10(Y))) | (~p101(tptp_fun_X_10(Y))))))) | (~((~p105(Y)) | (~((~(p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X))))) | (~((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X))))))))) | (~((~p104(Y)) | (~((~(p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X))))) | (~((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X))))))))) | (~((~p103(Y)) | (~((~(p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X))))) | (~((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X))))))))) | (~((~p102(Y)) | (~((~(p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X))))) | (~((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X))))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))) | (~(p105(Y) | (~p106(Y)))) | (~(p104(Y) | (~p105(Y)))) | (~(p103(Y) | (~p104(Y)))) | (~(p102(Y) | (~p103(Y)))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~(p105(Y) | (~p104(Y)) | (~(p106(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | (~r1(Y, tptp_fun_X_1(Y))) | p6(tptp_fun_X_1(Y)) | p106(tptp_fun_X_1(Y)) | (~p105(tptp_fun_X_1(Y))) | (~p6(tptp_fun_X_2(Y))) | (~p105(tptp_fun_X_2(Y))))))) | (~(p104(Y) | (~p103(Y)) | (~(p105(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p5(tptp_fun_X_3(Y)) | p105(tptp_fun_X_4(Y)) | (~p104(tptp_fun_X_3(Y))) | (~p5(tptp_fun_X_4(Y))) | (~p104(tptp_fun_X_4(Y))))))) | (~(p103(Y) | (~p102(Y)) | (~(p4(tptp_fun_X_5(Y)) | p104(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))) | p104(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_5(Y))) | (~p4(tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_6(Y))))))) | (~(p102(Y) | (~p101(Y)) | (~(p103(tptp_fun_X_8(Y)) | p103(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)) | (~p102(tptp_fun_X_7(Y))) | (~p3(tptp_fun_X_8(Y))) | (~p102(tptp_fun_X_8(Y))))))) | (~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p2(tptp_fun_X_9(Y)) | p102(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_10(Y))) | p102(tptp_fun_X_10(Y)) | (~p101(tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_10(Y))) | (~p101(tptp_fun_X_10(Y))))))) | (~(p105(Y) | (~p106(Y)))) | (~(p104(Y) | (~p105(Y)))) | (~(p103(Y) | (~p104(Y)))) | (~(p102(Y) | (~p103(Y)))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y)))) | (~((~p105(Y)) | (~((~(p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X))))) | (~((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X))))))))) | (~((~p104(Y)) | (~((~(p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X))))) | (~((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X))))))))) | (~((~p103(Y)) | (~((~(p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X))))) | (~((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X))))))))) | (~((~p102(Y)) | (~((~(p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X))))) | (~((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X))))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[12])).
% 0.18/0.40 tff(14,plain,
% 0.18/0.40 (^[Y: $i] : refl(((~r1(X!0, Y)) | (~((~(p105(Y) | (~p104(Y)) | (~(p106(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | (~r1(Y, tptp_fun_X_1(Y))) | p6(tptp_fun_X_1(Y)) | p106(tptp_fun_X_1(Y)) | (~p105(tptp_fun_X_1(Y))) | (~p6(tptp_fun_X_2(Y))) | (~p105(tptp_fun_X_2(Y))))))) | (~(p104(Y) | (~p103(Y)) | (~(p105(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p5(tptp_fun_X_3(Y)) | p105(tptp_fun_X_4(Y)) | (~p104(tptp_fun_X_3(Y))) | (~p5(tptp_fun_X_4(Y))) | (~p104(tptp_fun_X_4(Y))))))) | (~(p103(Y) | (~p102(Y)) | (~(p4(tptp_fun_X_5(Y)) | p104(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))) | p104(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_5(Y))) | (~p4(tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_6(Y))))))) | (~(p102(Y) | (~p101(Y)) | (~(p103(tptp_fun_X_8(Y)) | p103(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)) | (~p102(tptp_fun_X_7(Y))) | (~p3(tptp_fun_X_8(Y))) | (~p102(tptp_fun_X_8(Y))))))) | (~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p2(tptp_fun_X_9(Y)) | p102(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_10(Y))) | p102(tptp_fun_X_10(Y)) | (~p101(tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_10(Y))) | (~p101(tptp_fun_X_10(Y))))))) | (~((~p105(Y)) | (~((~(p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X))))) | (~((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X))))))))) | (~((~p104(Y)) | (~((~(p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X))))) | (~((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X))))))))) | (~((~p103(Y)) | (~((~(p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X))))) | (~((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X))))))))) | (~((~p102(Y)) | (~((~(p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X))))) | (~((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X))))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))) | (~(p105(Y) | (~p106(Y)))) | (~(p104(Y) | (~p105(Y)))) | (~(p103(Y) | (~p104(Y)))) | (~(p102(Y) | (~p103(Y)))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y))))))) <=> ((~r1(X!0, Y)) | (~((~(p105(Y) | (~p104(Y)) | (~(p106(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | (~r1(Y, tptp_fun_X_1(Y))) | p6(tptp_fun_X_1(Y)) | p106(tptp_fun_X_1(Y)) | (~p105(tptp_fun_X_1(Y))) | (~p6(tptp_fun_X_2(Y))) | (~p105(tptp_fun_X_2(Y))))))) | (~(p104(Y) | (~p103(Y)) | (~(p105(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p5(tptp_fun_X_3(Y)) | p105(tptp_fun_X_4(Y)) | (~p104(tptp_fun_X_3(Y))) | (~p5(tptp_fun_X_4(Y))) | (~p104(tptp_fun_X_4(Y))))))) | (~(p103(Y) | (~p102(Y)) | (~(p4(tptp_fun_X_5(Y)) | p104(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))) | p104(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_5(Y))) | (~p4(tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_6(Y))))))) | (~(p102(Y) | (~p101(Y)) | (~(p103(tptp_fun_X_8(Y)) | p103(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)) | (~p102(tptp_fun_X_7(Y))) | (~p3(tptp_fun_X_8(Y))) | (~p102(tptp_fun_X_8(Y))))))) | (~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p2(tptp_fun_X_9(Y)) | p102(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_10(Y))) | p102(tptp_fun_X_10(Y)) | (~p101(tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_10(Y))) | (~p101(tptp_fun_X_10(Y))))))) | (~((~p105(Y)) | (~((~(p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X))))) | (~((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X))))))))) | (~((~p104(Y)) | (~((~(p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X))))) | (~((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X))))))))) | (~((~p103(Y)) | (~((~(p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X))))) | (~((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X))))))))) | (~((~p102(Y)) | (~((~(p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X))))) | (~((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X))))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))) | (~(p105(Y) | (~p106(Y)))) | (~(p104(Y) | (~p105(Y)))) | (~(p103(Y) | (~p104(Y)))) | (~(p102(Y) | (~p103(Y)))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y))))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(15,plain,
% 0.18/0.40 (![Y: $i] : ((~r1(X!0, Y)) | (~((~(p105(Y) | (~p104(Y)) | (~(p106(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | (~r1(Y, tptp_fun_X_1(Y))) | p6(tptp_fun_X_1(Y)) | p106(tptp_fun_X_1(Y)) | (~p105(tptp_fun_X_1(Y))) | (~p6(tptp_fun_X_2(Y))) | (~p105(tptp_fun_X_2(Y))))))) | (~(p104(Y) | (~p103(Y)) | (~(p105(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p5(tptp_fun_X_3(Y)) | p105(tptp_fun_X_4(Y)) | (~p104(tptp_fun_X_3(Y))) | (~p5(tptp_fun_X_4(Y))) | (~p104(tptp_fun_X_4(Y))))))) | (~(p103(Y) | (~p102(Y)) | (~(p4(tptp_fun_X_5(Y)) | p104(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))) | p104(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_5(Y))) | (~p4(tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_6(Y))))))) | (~(p102(Y) | (~p101(Y)) | (~(p103(tptp_fun_X_8(Y)) | p103(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)) | (~p102(tptp_fun_X_7(Y))) | (~p3(tptp_fun_X_8(Y))) | (~p102(tptp_fun_X_8(Y))))))) | (~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p2(tptp_fun_X_9(Y)) | p102(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_10(Y))) | p102(tptp_fun_X_10(Y)) | (~p101(tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_10(Y))) | (~p101(tptp_fun_X_10(Y))))))) | (~((~p105(Y)) | (~((~(p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X))))) | (~((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X))))))))) | (~((~p104(Y)) | (~((~(p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X))))) | (~((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X))))))))) | (~((~p103(Y)) | (~((~(p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X))))) | (~((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X))))))))) | (~((~p102(Y)) | (~((~(p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X))))) | (~((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X))))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))) | (~(p105(Y) | (~p106(Y)))) | (~(p104(Y) | (~p105(Y)))) | (~(p103(Y) | (~p104(Y)))) | (~(p102(Y) | (~p103(Y)))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~(p105(Y) | (~p104(Y)) | (~(p106(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | (~r1(Y, tptp_fun_X_1(Y))) | p6(tptp_fun_X_1(Y)) | p106(tptp_fun_X_1(Y)) | (~p105(tptp_fun_X_1(Y))) | (~p6(tptp_fun_X_2(Y))) | (~p105(tptp_fun_X_2(Y))))))) | (~(p104(Y) | (~p103(Y)) | (~(p105(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p5(tptp_fun_X_3(Y)) | p105(tptp_fun_X_4(Y)) | (~p104(tptp_fun_X_3(Y))) | (~p5(tptp_fun_X_4(Y))) | (~p104(tptp_fun_X_4(Y))))))) | (~(p103(Y) | (~p102(Y)) | (~(p4(tptp_fun_X_5(Y)) | p104(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))) | p104(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_5(Y))) | (~p4(tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_6(Y))))))) | (~(p102(Y) | (~p101(Y)) | (~(p103(tptp_fun_X_8(Y)) | p103(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)) | (~p102(tptp_fun_X_7(Y))) | (~p3(tptp_fun_X_8(Y))) | (~p102(tptp_fun_X_8(Y))))))) | (~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p2(tptp_fun_X_9(Y)) | p102(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_10(Y))) | p102(tptp_fun_X_10(Y)) | (~p101(tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_10(Y))) | (~p101(tptp_fun_X_10(Y))))))) | (~((~p105(Y)) | (~((~(p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X))))) | (~((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X))))))))) | (~((~p104(Y)) | (~((~(p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X))))) | (~((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X))))))))) | (~((~p103(Y)) | (~((~(p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X))))) | (~((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X))))))))) | (~((~p102(Y)) | (~((~(p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X))))) | (~((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X))))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))) | (~(p105(Y) | (~p106(Y)))) | (~(p104(Y) | (~p105(Y)))) | (~(p103(Y) | (~p104(Y)))) | (~(p102(Y) | (~p103(Y)))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y)))))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[14])).
% 0.18/0.41 tff(16,plain,
% 0.18/0.41 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (~((~(p105(Y) | (~p104(Y)) | (~(p106(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | (~r1(Y, tptp_fun_X_1(Y))) | p6(tptp_fun_X_1(Y)) | p106(tptp_fun_X_1(Y)) | (~p105(tptp_fun_X_1(Y))) | (~p6(tptp_fun_X_2(Y))) | (~p105(tptp_fun_X_2(Y))))))) | (~(p104(Y) | (~p103(Y)) | (~(p105(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p5(tptp_fun_X_3(Y)) | p105(tptp_fun_X_4(Y)) | (~p104(tptp_fun_X_3(Y))) | (~p5(tptp_fun_X_4(Y))) | (~p104(tptp_fun_X_4(Y))))))) | (~(p103(Y) | (~p102(Y)) | (~(p4(tptp_fun_X_5(Y)) | p104(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))) | p104(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_5(Y))) | (~p4(tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_6(Y))))))) | (~(p102(Y) | (~p101(Y)) | (~(p103(tptp_fun_X_8(Y)) | p103(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)) | (~p102(tptp_fun_X_7(Y))) | (~p3(tptp_fun_X_8(Y))) | (~p102(tptp_fun_X_8(Y))))))) | (~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p2(tptp_fun_X_9(Y)) | p102(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_10(Y))) | p102(tptp_fun_X_10(Y)) | (~p101(tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_10(Y))) | (~p101(tptp_fun_X_10(Y))))))) | (~((~p105(Y)) | (~((~(p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X))))) | (~((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X))))))))) | (~((~p104(Y)) | (~((~(p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X))))) | (~((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X))))))))) | (~((~p103(Y)) | (~((~(p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X))))) | (~((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X))))))))) | (~((~p102(Y)) | (~((~(p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X))))) | (~((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X))))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))) | (~(p105(Y) | (~p106(Y)))) | (~(p104(Y) | (~p105(Y)))) | (~(p103(Y) | (~p104(Y)))) | (~(p102(Y) | (~p103(Y)))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y))))))) <=> ((~r1(X!0, Y)) | (~((~(p105(Y) | (~p104(Y)) | (~(p106(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | (~r1(Y, tptp_fun_X_1(Y))) | p6(tptp_fun_X_1(Y)) | p106(tptp_fun_X_1(Y)) | (~p105(tptp_fun_X_1(Y))) | (~p6(tptp_fun_X_2(Y))) | (~p105(tptp_fun_X_2(Y))))))) | (~(p104(Y) | (~p103(Y)) | (~(p105(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p5(tptp_fun_X_3(Y)) | p105(tptp_fun_X_4(Y)) | (~p104(tptp_fun_X_3(Y))) | (~p5(tptp_fun_X_4(Y))) | (~p104(tptp_fun_X_4(Y))))))) | (~(p103(Y) | (~p102(Y)) | (~(p4(tptp_fun_X_5(Y)) | p104(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))) | p104(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_5(Y))) | (~p4(tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_6(Y))))))) | (~(p102(Y) | (~p101(Y)) | (~(p103(tptp_fun_X_8(Y)) | p103(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)) | (~p102(tptp_fun_X_7(Y))) | (~p3(tptp_fun_X_8(Y))) | (~p102(tptp_fun_X_8(Y))))))) | (~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p2(tptp_fun_X_9(Y)) | p102(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_10(Y))) | p102(tptp_fun_X_10(Y)) | (~p101(tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_10(Y))) | (~p101(tptp_fun_X_10(Y))))))) | (~((~p105(Y)) | (~((~(p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X))))) | (~((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X))))))))) | (~((~p104(Y)) | (~((~(p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X))))) | (~((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X))))))))) | (~((~p103(Y)) | (~((~(p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X))))) | (~((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X))))))))) | (~((~p102(Y)) | (~((~(p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X))))) | (~((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X))))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))) | (~(p105(Y) | (~p106(Y)))) | (~(p104(Y) | (~p105(Y)))) | (~(p103(Y) | (~p104(Y)))) | (~(p102(Y) | (~p103(Y)))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y))))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(17,plain,
% 0.18/0.41 (![Y: $i] : ((~r1(X!0, Y)) | (~((~(p105(Y) | (~p104(Y)) | (~(p106(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | (~r1(Y, tptp_fun_X_1(Y))) | p6(tptp_fun_X_1(Y)) | p106(tptp_fun_X_1(Y)) | (~p105(tptp_fun_X_1(Y))) | (~p6(tptp_fun_X_2(Y))) | (~p105(tptp_fun_X_2(Y))))))) | (~(p104(Y) | (~p103(Y)) | (~(p105(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p5(tptp_fun_X_3(Y)) | p105(tptp_fun_X_4(Y)) | (~p104(tptp_fun_X_3(Y))) | (~p5(tptp_fun_X_4(Y))) | (~p104(tptp_fun_X_4(Y))))))) | (~(p103(Y) | (~p102(Y)) | (~(p4(tptp_fun_X_5(Y)) | p104(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))) | p104(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_5(Y))) | (~p4(tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_6(Y))))))) | (~(p102(Y) | (~p101(Y)) | (~(p103(tptp_fun_X_8(Y)) | p103(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)) | (~p102(tptp_fun_X_7(Y))) | (~p3(tptp_fun_X_8(Y))) | (~p102(tptp_fun_X_8(Y))))))) | (~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p2(tptp_fun_X_9(Y)) | p102(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_10(Y))) | p102(tptp_fun_X_10(Y)) | (~p101(tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_10(Y))) | (~p101(tptp_fun_X_10(Y))))))) | (~((~p105(Y)) | (~((~(p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X))))) | (~((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X))))))))) | (~((~p104(Y)) | (~((~(p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X))))) | (~((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X))))))))) | (~((~p103(Y)) | (~((~(p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X))))) | (~((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X))))))))) | (~((~p102(Y)) | (~((~(p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X))))) | (~((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X))))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))) | (~(p105(Y) | (~p106(Y)))) | (~(p104(Y) | (~p105(Y)))) | (~(p103(Y) | (~p104(Y)))) | (~(p102(Y) | (~p103(Y)))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~(p105(Y) | (~p104(Y)) | (~(p106(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | (~r1(Y, tptp_fun_X_1(Y))) | p6(tptp_fun_X_1(Y)) | p106(tptp_fun_X_1(Y)) | (~p105(tptp_fun_X_1(Y))) | (~p6(tptp_fun_X_2(Y))) | (~p105(tptp_fun_X_2(Y))))))) | (~(p104(Y) | (~p103(Y)) | (~(p105(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p5(tptp_fun_X_3(Y)) | p105(tptp_fun_X_4(Y)) | (~p104(tptp_fun_X_3(Y))) | (~p5(tptp_fun_X_4(Y))) | (~p104(tptp_fun_X_4(Y))))))) | (~(p103(Y) | (~p102(Y)) | (~(p4(tptp_fun_X_5(Y)) | p104(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))) | p104(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_5(Y))) | (~p4(tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_6(Y))))))) | (~(p102(Y) | (~p101(Y)) | (~(p103(tptp_fun_X_8(Y)) | p103(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)) | (~p102(tptp_fun_X_7(Y))) | (~p3(tptp_fun_X_8(Y))) | (~p102(tptp_fun_X_8(Y))))))) | (~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p2(tptp_fun_X_9(Y)) | p102(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_10(Y))) | p102(tptp_fun_X_10(Y)) | (~p101(tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_10(Y))) | (~p101(tptp_fun_X_10(Y))))))) | (~((~p105(Y)) | (~((~(p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X))))) | (~((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X))))))))) | (~((~p104(Y)) | (~((~(p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X))))) | (~((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X))))))))) | (~((~p103(Y)) | (~((~(p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X))))) | (~((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X))))))))) | (~((~p102(Y)) | (~((~(p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X))))) | (~((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X))))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))) | (~(p105(Y) | (~p106(Y)))) | (~(p104(Y) | (~p105(Y)))) | (~(p103(Y) | (~p104(Y)))) | (~(p102(Y) | (~p103(Y)))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y)))))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[16])).
% 0.18/0.41 tff(18,plain,
% 0.18/0.41 (![Y: $i] : ((~r1(X!0, Y)) | (~((~(p105(Y) | (~p104(Y)) | (~(p106(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | (~r1(Y, tptp_fun_X_1(Y))) | p6(tptp_fun_X_1(Y)) | p106(tptp_fun_X_1(Y)) | (~p105(tptp_fun_X_1(Y))) | (~p6(tptp_fun_X_2(Y))) | (~p105(tptp_fun_X_2(Y))))))) | (~(p104(Y) | (~p103(Y)) | (~(p105(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p5(tptp_fun_X_3(Y)) | p105(tptp_fun_X_4(Y)) | (~p104(tptp_fun_X_3(Y))) | (~p5(tptp_fun_X_4(Y))) | (~p104(tptp_fun_X_4(Y))))))) | (~(p103(Y) | (~p102(Y)) | (~(p4(tptp_fun_X_5(Y)) | p104(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))) | p104(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_5(Y))) | (~p4(tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_6(Y))))))) | (~(p102(Y) | (~p101(Y)) | (~(p103(tptp_fun_X_8(Y)) | p103(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)) | (~p102(tptp_fun_X_7(Y))) | (~p3(tptp_fun_X_8(Y))) | (~p102(tptp_fun_X_8(Y))))))) | (~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p2(tptp_fun_X_9(Y)) | p102(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_10(Y))) | p102(tptp_fun_X_10(Y)) | (~p101(tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_10(Y))) | (~p101(tptp_fun_X_10(Y))))))) | (~((~p105(Y)) | (~((~(p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X))))) | (~((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X))))))))) | (~((~p104(Y)) | (~((~(p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X))))) | (~((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X))))))))) | (~((~p103(Y)) | (~((~(p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X))))) | (~((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X))))))))) | (~((~p102(Y)) | (~((~(p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X))))) | (~((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X))))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))) | (~(p105(Y) | (~p106(Y)))) | (~(p104(Y) | (~p105(Y)))) | (~(p103(Y) | (~p104(Y)))) | (~(p102(Y) | (~p103(Y)))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~(p105(Y) | (~p104(Y)) | (~(p106(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | (~r1(Y, tptp_fun_X_1(Y))) | p6(tptp_fun_X_1(Y)) | p106(tptp_fun_X_1(Y)) | (~p105(tptp_fun_X_1(Y))) | (~p6(tptp_fun_X_2(Y))) | (~p105(tptp_fun_X_2(Y))))))) | (~(p104(Y) | (~p103(Y)) | (~(p105(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p5(tptp_fun_X_3(Y)) | p105(tptp_fun_X_4(Y)) | (~p104(tptp_fun_X_3(Y))) | (~p5(tptp_fun_X_4(Y))) | (~p104(tptp_fun_X_4(Y))))))) | (~(p103(Y) | (~p102(Y)) | (~(p4(tptp_fun_X_5(Y)) | p104(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))) | p104(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_5(Y))) | (~p4(tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_6(Y))))))) | (~(p102(Y) | (~p101(Y)) | (~(p103(tptp_fun_X_8(Y)) | p103(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)) | (~p102(tptp_fun_X_7(Y))) | (~p3(tptp_fun_X_8(Y))) | (~p102(tptp_fun_X_8(Y))))))) | (~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p2(tptp_fun_X_9(Y)) | p102(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_10(Y))) | p102(tptp_fun_X_10(Y)) | (~p101(tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_10(Y))) | (~p101(tptp_fun_X_10(Y))))))) | (~((~p105(Y)) | (~((~(p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X))))) | (~((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X))))))))) | (~((~p104(Y)) | (~((~(p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X))))) | (~((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X))))))))) | (~((~p103(Y)) | (~((~(p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X))))) | (~((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X))))))))) | (~((~p102(Y)) | (~((~(p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X))))) | (~((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X))))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))) | (~(p105(Y) | (~p106(Y)))) | (~(p104(Y) | (~p105(Y)))) | (~(p103(Y) | (~p104(Y)))) | (~(p102(Y) | (~p103(Y)))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y)))))))),
% 0.18/0.41 inference(transitivity,[status(thm)],[17, 15])).
% 0.18/0.41 tff(19,plain,
% 0.18/0.41 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (((~((~p105(Y)) & p104(Y))) | ((~((~r1(Y, tptp_fun_X_1(Y))) | (~((~p6(tptp_fun_X_1(Y))) & (~p106(tptp_fun_X_1(Y))) & p105(tptp_fun_X_1(Y)))))) & (~((~r1(Y, tptp_fun_X_2(Y))) | (~(p6(tptp_fun_X_2(Y)) & (~p106(tptp_fun_X_2(Y))) & p105(tptp_fun_X_2(Y)))))))) & ((~((~p104(Y)) & p103(Y))) | ((~((~r1(Y, tptp_fun_X_3(Y))) | (~((~p5(tptp_fun_X_3(Y))) & (~p105(tptp_fun_X_3(Y))) & p104(tptp_fun_X_3(Y)))))) & (~((~r1(Y, tptp_fun_X_4(Y))) | (~(p5(tptp_fun_X_4(Y)) & (~p105(tptp_fun_X_4(Y))) & p104(tptp_fun_X_4(Y)))))))) & ((~((~p103(Y)) & p102(Y))) | ((~((~r1(Y, tptp_fun_X_5(Y))) | (~((~p4(tptp_fun_X_5(Y))) & (~p104(tptp_fun_X_5(Y))) & p103(tptp_fun_X_5(Y)))))) & (~((~r1(Y, tptp_fun_X_6(Y))) | (~(p4(tptp_fun_X_6(Y)) & (~p104(tptp_fun_X_6(Y))) & p103(tptp_fun_X_6(Y)))))))) & ((~((~p102(Y)) & p101(Y))) | ((~((~r1(Y, tptp_fun_X_7(Y))) | (~((~p3(tptp_fun_X_7(Y))) & (~p103(tptp_fun_X_7(Y))) & p102(tptp_fun_X_7(Y)))))) & (~((~r1(Y, tptp_fun_X_8(Y))) | (~(p3(tptp_fun_X_8(Y)) & (~p103(tptp_fun_X_8(Y))) & p102(tptp_fun_X_8(Y)))))))) & ((~((~p101(Y)) & p100(Y))) | ((~((~r1(Y, tptp_fun_X_9(Y))) | (~((~p2(tptp_fun_X_9(Y))) & (~p102(tptp_fun_X_9(Y))) & p101(tptp_fun_X_9(Y)))))) & (~((~r1(Y, tptp_fun_X_10(Y))) | (~(p2(tptp_fun_X_10(Y)) & (~p102(tptp_fun_X_10(Y))) & p101(tptp_fun_X_10(Y)))))))) & ((~p105(Y)) | ((p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X)))) & ((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X)))))) & ((~p104(Y)) | ((p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X)))) & ((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X)))))) & ((~p103(Y)) | ((p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X)))) & ((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X)))))) & ((~p102(Y)) | ((p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X)))) & ((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X)))))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p105(Y) | (~p106(Y))) & (p104(Y) | (~p105(Y))) & (p103(Y) | (~p104(Y))) & (p102(Y) | (~p103(Y))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) <=> ((~r1(X!0, Y)) | (~((~(p105(Y) | (~p104(Y)) | (~(p106(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | (~r1(Y, tptp_fun_X_1(Y))) | p6(tptp_fun_X_1(Y)) | p106(tptp_fun_X_1(Y)) | (~p105(tptp_fun_X_1(Y))) | (~p6(tptp_fun_X_2(Y))) | (~p105(tptp_fun_X_2(Y))))))) | (~(p104(Y) | (~p103(Y)) | (~(p105(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p5(tptp_fun_X_3(Y)) | p105(tptp_fun_X_4(Y)) | (~p104(tptp_fun_X_3(Y))) | (~p5(tptp_fun_X_4(Y))) | (~p104(tptp_fun_X_4(Y))))))) | (~(p103(Y) | (~p102(Y)) | (~(p4(tptp_fun_X_5(Y)) | p104(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))) | p104(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_5(Y))) | (~p4(tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_6(Y))))))) | (~(p102(Y) | (~p101(Y)) | (~(p103(tptp_fun_X_8(Y)) | p103(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)) | (~p102(tptp_fun_X_7(Y))) | (~p3(tptp_fun_X_8(Y))) | (~p102(tptp_fun_X_8(Y))))))) | (~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p2(tptp_fun_X_9(Y)) | p102(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_10(Y))) | p102(tptp_fun_X_10(Y)) | (~p101(tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_10(Y))) | (~p101(tptp_fun_X_10(Y))))))) | (~((~p105(Y)) | (~((~(p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X))))) | (~((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X))))))))) | (~((~p104(Y)) | (~((~(p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X))))) | (~((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X))))))))) | (~((~p103(Y)) | (~((~(p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X))))) | (~((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X))))))))) | (~((~p102(Y)) | (~((~(p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X))))) | (~((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X))))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))) | (~(p105(Y) | (~p106(Y)))) | (~(p104(Y) | (~p105(Y)))) | (~(p103(Y) | (~p104(Y)))) | (~(p102(Y) | (~p103(Y)))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y))))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(20,plain,
% 0.18/0.41 (![Y: $i] : ((~r1(X!0, Y)) | (((~((~p105(Y)) & p104(Y))) | ((~((~r1(Y, tptp_fun_X_1(Y))) | (~((~p6(tptp_fun_X_1(Y))) & (~p106(tptp_fun_X_1(Y))) & p105(tptp_fun_X_1(Y)))))) & (~((~r1(Y, tptp_fun_X_2(Y))) | (~(p6(tptp_fun_X_2(Y)) & (~p106(tptp_fun_X_2(Y))) & p105(tptp_fun_X_2(Y)))))))) & ((~((~p104(Y)) & p103(Y))) | ((~((~r1(Y, tptp_fun_X_3(Y))) | (~((~p5(tptp_fun_X_3(Y))) & (~p105(tptp_fun_X_3(Y))) & p104(tptp_fun_X_3(Y)))))) & (~((~r1(Y, tptp_fun_X_4(Y))) | (~(p5(tptp_fun_X_4(Y)) & (~p105(tptp_fun_X_4(Y))) & p104(tptp_fun_X_4(Y)))))))) & ((~((~p103(Y)) & p102(Y))) | ((~((~r1(Y, tptp_fun_X_5(Y))) | (~((~p4(tptp_fun_X_5(Y))) & (~p104(tptp_fun_X_5(Y))) & p103(tptp_fun_X_5(Y)))))) & (~((~r1(Y, tptp_fun_X_6(Y))) | (~(p4(tptp_fun_X_6(Y)) & (~p104(tptp_fun_X_6(Y))) & p103(tptp_fun_X_6(Y)))))))) & ((~((~p102(Y)) & p101(Y))) | ((~((~r1(Y, tptp_fun_X_7(Y))) | (~((~p3(tptp_fun_X_7(Y))) & (~p103(tptp_fun_X_7(Y))) & p102(tptp_fun_X_7(Y)))))) & (~((~r1(Y, tptp_fun_X_8(Y))) | (~(p3(tptp_fun_X_8(Y)) & (~p103(tptp_fun_X_8(Y))) & p102(tptp_fun_X_8(Y)))))))) & ((~((~p101(Y)) & p100(Y))) | ((~((~r1(Y, tptp_fun_X_9(Y))) | (~((~p2(tptp_fun_X_9(Y))) & (~p102(tptp_fun_X_9(Y))) & p101(tptp_fun_X_9(Y)))))) & (~((~r1(Y, tptp_fun_X_10(Y))) | (~(p2(tptp_fun_X_10(Y)) & (~p102(tptp_fun_X_10(Y))) & p101(tptp_fun_X_10(Y)))))))) & ((~p105(Y)) | ((p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X)))) & ((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X)))))) & ((~p104(Y)) | ((p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X)))) & ((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X)))))) & ((~p103(Y)) | ((p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X)))) & ((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X)))))) & ((~p102(Y)) | ((p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X)))) & ((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X)))))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p105(Y) | (~p106(Y))) & (p104(Y) | (~p105(Y))) & (p103(Y) | (~p104(Y))) & (p102(Y) | (~p103(Y))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~(p105(Y) | (~p104(Y)) | (~(p106(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | (~r1(Y, tptp_fun_X_1(Y))) | p6(tptp_fun_X_1(Y)) | p106(tptp_fun_X_1(Y)) | (~p105(tptp_fun_X_1(Y))) | (~p6(tptp_fun_X_2(Y))) | (~p105(tptp_fun_X_2(Y))))))) | (~(p104(Y) | (~p103(Y)) | (~(p105(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p5(tptp_fun_X_3(Y)) | p105(tptp_fun_X_4(Y)) | (~p104(tptp_fun_X_3(Y))) | (~p5(tptp_fun_X_4(Y))) | (~p104(tptp_fun_X_4(Y))))))) | (~(p103(Y) | (~p102(Y)) | (~(p4(tptp_fun_X_5(Y)) | p104(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))) | p104(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_5(Y))) | (~p4(tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_6(Y))))))) | (~(p102(Y) | (~p101(Y)) | (~(p103(tptp_fun_X_8(Y)) | p103(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)) | (~p102(tptp_fun_X_7(Y))) | (~p3(tptp_fun_X_8(Y))) | (~p102(tptp_fun_X_8(Y))))))) | (~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p2(tptp_fun_X_9(Y)) | p102(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_10(Y))) | p102(tptp_fun_X_10(Y)) | (~p101(tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_10(Y))) | (~p101(tptp_fun_X_10(Y))))))) | (~((~p105(Y)) | (~((~(p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X))))) | (~((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X))))))))) | (~((~p104(Y)) | (~((~(p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X))))) | (~((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X))))))))) | (~((~p103(Y)) | (~((~(p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X))))) | (~((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X))))))))) | (~((~p102(Y)) | (~((~(p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X))))) | (~((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X))))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))) | (~(p105(Y) | (~p106(Y)))) | (~(p104(Y) | (~p105(Y)))) | (~(p103(Y) | (~p104(Y)))) | (~(p102(Y) | (~p103(Y)))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y)))))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[19])).
% 0.18/0.42 tff(21,plain,
% 0.18/0.42 ((![Y: $i] : (p3(Y) | (~r1(X!0, Y))) & (![Y: $i] : ((~r1(X!0, Y)) | (((~((~p105(Y)) & p104(Y))) | ((~((~r1(Y, tptp_fun_X_1(Y))) | (~((~p6(tptp_fun_X_1(Y))) & (~p106(tptp_fun_X_1(Y))) & p105(tptp_fun_X_1(Y)))))) & (~((~r1(Y, tptp_fun_X_2(Y))) | (~(p6(tptp_fun_X_2(Y)) & (~p106(tptp_fun_X_2(Y))) & p105(tptp_fun_X_2(Y)))))))) & ((~((~p104(Y)) & p103(Y))) | ((~((~r1(Y, tptp_fun_X_3(Y))) | (~((~p5(tptp_fun_X_3(Y))) & (~p105(tptp_fun_X_3(Y))) & p104(tptp_fun_X_3(Y)))))) & (~((~r1(Y, tptp_fun_X_4(Y))) | (~(p5(tptp_fun_X_4(Y)) & (~p105(tptp_fun_X_4(Y))) & p104(tptp_fun_X_4(Y)))))))) & ((~((~p103(Y)) & p102(Y))) | ((~((~r1(Y, tptp_fun_X_5(Y))) | (~((~p4(tptp_fun_X_5(Y))) & (~p104(tptp_fun_X_5(Y))) & p103(tptp_fun_X_5(Y)))))) & (~((~r1(Y, tptp_fun_X_6(Y))) | (~(p4(tptp_fun_X_6(Y)) & (~p104(tptp_fun_X_6(Y))) & p103(tptp_fun_X_6(Y)))))))) & ((~((~p102(Y)) & p101(Y))) | ((~((~r1(Y, tptp_fun_X_7(Y))) | (~((~p3(tptp_fun_X_7(Y))) & (~p103(tptp_fun_X_7(Y))) & p102(tptp_fun_X_7(Y)))))) & (~((~r1(Y, tptp_fun_X_8(Y))) | (~(p3(tptp_fun_X_8(Y)) & (~p103(tptp_fun_X_8(Y))) & p102(tptp_fun_X_8(Y)))))))) & ((~((~p101(Y)) & p100(Y))) | ((~((~r1(Y, tptp_fun_X_9(Y))) | (~((~p2(tptp_fun_X_9(Y))) & (~p102(tptp_fun_X_9(Y))) & p101(tptp_fun_X_9(Y)))))) & (~((~r1(Y, tptp_fun_X_10(Y))) | (~(p2(tptp_fun_X_10(Y)) & (~p102(tptp_fun_X_10(Y))) & p101(tptp_fun_X_10(Y)))))))) & ((~p105(Y)) | ((p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X)))) & ((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X)))))) & ((~p104(Y)) | ((p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X)))) & ((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X)))))) & ((~p103(Y)) | ((p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X)))) & ((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X)))))) & ((~p102(Y)) | ((p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X)))) & ((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X)))))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p105(Y) | (~p106(Y))) & (p104(Y) | (~p105(Y))) & (p103(Y) | (~p104(Y))) & (p102(Y) | (~p103(Y))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X!0)) & p100(X!0))) <=> (![Y: $i] : (p3(Y) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | (((~((~p105(Y)) & p104(Y))) | ((~((~r1(Y, tptp_fun_X_1(Y))) | (~((~p6(tptp_fun_X_1(Y))) & (~p106(tptp_fun_X_1(Y))) & p105(tptp_fun_X_1(Y)))))) & (~((~r1(Y, tptp_fun_X_2(Y))) | (~(p6(tptp_fun_X_2(Y)) & (~p106(tptp_fun_X_2(Y))) & p105(tptp_fun_X_2(Y)))))))) & ((~((~p104(Y)) & p103(Y))) | ((~((~r1(Y, tptp_fun_X_3(Y))) | (~((~p5(tptp_fun_X_3(Y))) & (~p105(tptp_fun_X_3(Y))) & p104(tptp_fun_X_3(Y)))))) & (~((~r1(Y, tptp_fun_X_4(Y))) | (~(p5(tptp_fun_X_4(Y)) & (~p105(tptp_fun_X_4(Y))) & p104(tptp_fun_X_4(Y)))))))) & ((~((~p103(Y)) & p102(Y))) | ((~((~r1(Y, tptp_fun_X_5(Y))) | (~((~p4(tptp_fun_X_5(Y))) & (~p104(tptp_fun_X_5(Y))) & p103(tptp_fun_X_5(Y)))))) & (~((~r1(Y, tptp_fun_X_6(Y))) | (~(p4(tptp_fun_X_6(Y)) & (~p104(tptp_fun_X_6(Y))) & p103(tptp_fun_X_6(Y)))))))) & ((~((~p102(Y)) & p101(Y))) | ((~((~r1(Y, tptp_fun_X_7(Y))) | (~((~p3(tptp_fun_X_7(Y))) & (~p103(tptp_fun_X_7(Y))) & p102(tptp_fun_X_7(Y)))))) & (~((~r1(Y, tptp_fun_X_8(Y))) | (~(p3(tptp_fun_X_8(Y)) & (~p103(tptp_fun_X_8(Y))) & p102(tptp_fun_X_8(Y)))))))) & ((~((~p101(Y)) & p100(Y))) | ((~((~r1(Y, tptp_fun_X_9(Y))) | (~((~p2(tptp_fun_X_9(Y))) & (~p102(tptp_fun_X_9(Y))) & p101(tptp_fun_X_9(Y)))))) & (~((~r1(Y, tptp_fun_X_10(Y))) | (~(p2(tptp_fun_X_10(Y)) & (~p102(tptp_fun_X_10(Y))) & p101(tptp_fun_X_10(Y)))))))) & ((~p105(Y)) | ((p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X)))) & ((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X)))))) & ((~p104(Y)) | ((p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X)))) & ((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X)))))) & ((~p103(Y)) | ((p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X)))) & ((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X)))))) & ((~p102(Y)) | ((p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X)))) & ((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X)))))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p105(Y) | (~p106(Y))) & (p104(Y) | (~p105(Y))) & (p103(Y) | (~p104(Y))) & (p102(Y) | (~p103(Y))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X!0)) & p100(X!0))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(22,plain,
% 0.18/0.42 ((![Y: $i] : ((~r1(X!0, Y)) | ((((~((~r1(Y, tptp_fun_X_1(Y))) | (~((~p6(tptp_fun_X_1(Y))) & (~p106(tptp_fun_X_1(Y))) & p105(tptp_fun_X_1(Y)))))) & (~((~r1(Y, tptp_fun_X_2(Y))) | (~(p6(tptp_fun_X_2(Y)) & (~p106(tptp_fun_X_2(Y))) & p105(tptp_fun_X_2(Y))))))) | (~((~p105(Y)) & p104(Y)))) & (((~((~r1(Y, tptp_fun_X_3(Y))) | (~((~p5(tptp_fun_X_3(Y))) & (~p105(tptp_fun_X_3(Y))) & p104(tptp_fun_X_3(Y)))))) & (~((~r1(Y, tptp_fun_X_4(Y))) | (~(p5(tptp_fun_X_4(Y)) & (~p105(tptp_fun_X_4(Y))) & p104(tptp_fun_X_4(Y))))))) | (~((~p104(Y)) & p103(Y)))) & (((~((~r1(Y, tptp_fun_X_5(Y))) | (~((~p4(tptp_fun_X_5(Y))) & (~p104(tptp_fun_X_5(Y))) & p103(tptp_fun_X_5(Y)))))) & (~((~r1(Y, tptp_fun_X_6(Y))) | (~(p4(tptp_fun_X_6(Y)) & (~p104(tptp_fun_X_6(Y))) & p103(tptp_fun_X_6(Y))))))) | (~((~p103(Y)) & p102(Y)))) & (((~((~r1(Y, tptp_fun_X_7(Y))) | (~((~p3(tptp_fun_X_7(Y))) & (~p103(tptp_fun_X_7(Y))) & p102(tptp_fun_X_7(Y)))))) & (~((~r1(Y, tptp_fun_X_8(Y))) | (~(p3(tptp_fun_X_8(Y)) & (~p103(tptp_fun_X_8(Y))) & p102(tptp_fun_X_8(Y))))))) | (~((~p102(Y)) & p101(Y)))) & (((~((~r1(Y, tptp_fun_X_9(Y))) | (~((~p2(tptp_fun_X_9(Y))) & (~p102(tptp_fun_X_9(Y))) & p101(tptp_fun_X_9(Y)))))) & (~((~r1(Y, tptp_fun_X_10(Y))) | (~(p2(tptp_fun_X_10(Y)) & (~p102(tptp_fun_X_10(Y))) & p101(tptp_fun_X_10(Y))))))) | (~((~p101(Y)) & p100(Y)))) & ((~p105(Y)) | ((p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X)))) & ((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X)))))) & ((~p104(Y)) | ((p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X)))) & ((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X)))))) & ((~p103(Y)) | ((p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X)))) & ((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X)))))) & ((~p102(Y)) | ((p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X)))) & ((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X)))))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p105(Y) | (~p106(Y))) & (p104(Y) | (~p105(Y))) & (p103(Y) | (~p104(Y))) & (p102(Y) | (~p103(Y))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X!0)) & p100(X!0)) <=> (![Y: $i] : ((~r1(X!0, Y)) | (((~((~p105(Y)) & p104(Y))) | ((~((~r1(Y, tptp_fun_X_1(Y))) | (~((~p6(tptp_fun_X_1(Y))) & (~p106(tptp_fun_X_1(Y))) & p105(tptp_fun_X_1(Y)))))) & (~((~r1(Y, tptp_fun_X_2(Y))) | (~(p6(tptp_fun_X_2(Y)) & (~p106(tptp_fun_X_2(Y))) & p105(tptp_fun_X_2(Y)))))))) & ((~((~p104(Y)) & p103(Y))) | ((~((~r1(Y, tptp_fun_X_3(Y))) | (~((~p5(tptp_fun_X_3(Y))) & (~p105(tptp_fun_X_3(Y))) & p104(tptp_fun_X_3(Y)))))) & (~((~r1(Y, tptp_fun_X_4(Y))) | (~(p5(tptp_fun_X_4(Y)) & (~p105(tptp_fun_X_4(Y))) & p104(tptp_fun_X_4(Y)))))))) & ((~((~p103(Y)) & p102(Y))) | ((~((~r1(Y, tptp_fun_X_5(Y))) | (~((~p4(tptp_fun_X_5(Y))) & (~p104(tptp_fun_X_5(Y))) & p103(tptp_fun_X_5(Y)))))) & (~((~r1(Y, tptp_fun_X_6(Y))) | (~(p4(tptp_fun_X_6(Y)) & (~p104(tptp_fun_X_6(Y))) & p103(tptp_fun_X_6(Y)))))))) & ((~((~p102(Y)) & p101(Y))) | ((~((~r1(Y, tptp_fun_X_7(Y))) | (~((~p3(tptp_fun_X_7(Y))) & (~p103(tptp_fun_X_7(Y))) & p102(tptp_fun_X_7(Y)))))) & (~((~r1(Y, tptp_fun_X_8(Y))) | (~(p3(tptp_fun_X_8(Y)) & (~p103(tptp_fun_X_8(Y))) & p102(tptp_fun_X_8(Y)))))))) & ((~((~p101(Y)) & p100(Y))) | ((~((~r1(Y, tptp_fun_X_9(Y))) | (~((~p2(tptp_fun_X_9(Y))) & (~p102(tptp_fun_X_9(Y))) & p101(tptp_fun_X_9(Y)))))) & (~((~r1(Y, tptp_fun_X_10(Y))) | (~(p2(tptp_fun_X_10(Y)) & (~p102(tptp_fun_X_10(Y))) & p101(tptp_fun_X_10(Y)))))))) & ((~p105(Y)) | ((p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X)))) & ((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X)))))) & ((~p104(Y)) | ((p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X)))) & ((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X)))))) & ((~p103(Y)) | ((p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X)))) & ((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X)))))) & ((~p102(Y)) | ((p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X)))) & ((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X)))))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p105(Y) | (~p106(Y))) & (p104(Y) | (~p105(Y))) & (p103(Y) | (~p104(Y))) & (p102(Y) | (~p103(Y))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X!0)) & p100(X!0))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(23,plain,
% 0.18/0.42 ((![Y: $i] : (p3(Y) | (~r1(X!0, Y))) & (![Y: $i] : ((~r1(X!0, Y)) | ((((~((~r1(Y, tptp_fun_X_1(Y))) | (~((~p6(tptp_fun_X_1(Y))) & (~p106(tptp_fun_X_1(Y))) & p105(tptp_fun_X_1(Y)))))) & (~((~r1(Y, tptp_fun_X_2(Y))) | (~(p6(tptp_fun_X_2(Y)) & (~p106(tptp_fun_X_2(Y))) & p105(tptp_fun_X_2(Y))))))) | (~((~p105(Y)) & p104(Y)))) & (((~((~r1(Y, tptp_fun_X_3(Y))) | (~((~p5(tptp_fun_X_3(Y))) & (~p105(tptp_fun_X_3(Y))) & p104(tptp_fun_X_3(Y)))))) & (~((~r1(Y, tptp_fun_X_4(Y))) | (~(p5(tptp_fun_X_4(Y)) & (~p105(tptp_fun_X_4(Y))) & p104(tptp_fun_X_4(Y))))))) | (~((~p104(Y)) & p103(Y)))) & (((~((~r1(Y, tptp_fun_X_5(Y))) | (~((~p4(tptp_fun_X_5(Y))) & (~p104(tptp_fun_X_5(Y))) & p103(tptp_fun_X_5(Y)))))) & (~((~r1(Y, tptp_fun_X_6(Y))) | (~(p4(tptp_fun_X_6(Y)) & (~p104(tptp_fun_X_6(Y))) & p103(tptp_fun_X_6(Y))))))) | (~((~p103(Y)) & p102(Y)))) & (((~((~r1(Y, tptp_fun_X_7(Y))) | (~((~p3(tptp_fun_X_7(Y))) & (~p103(tptp_fun_X_7(Y))) & p102(tptp_fun_X_7(Y)))))) & (~((~r1(Y, tptp_fun_X_8(Y))) | (~(p3(tptp_fun_X_8(Y)) & (~p103(tptp_fun_X_8(Y))) & p102(tptp_fun_X_8(Y))))))) | (~((~p102(Y)) & p101(Y)))) & (((~((~r1(Y, tptp_fun_X_9(Y))) | (~((~p2(tptp_fun_X_9(Y))) & (~p102(tptp_fun_X_9(Y))) & p101(tptp_fun_X_9(Y)))))) & (~((~r1(Y, tptp_fun_X_10(Y))) | (~(p2(tptp_fun_X_10(Y)) & (~p102(tptp_fun_X_10(Y))) & p101(tptp_fun_X_10(Y))))))) | (~((~p101(Y)) & p100(Y)))) & ((~p105(Y)) | ((p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X)))) & ((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X)))))) & ((~p104(Y)) | ((p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X)))) & ((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X)))))) & ((~p103(Y)) | ((p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X)))) & ((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X)))))) & ((~p102(Y)) | ((p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X)))) & ((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X)))))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p105(Y) | (~p106(Y))) & (p104(Y) | (~p105(Y))) & (p103(Y) | (~p104(Y))) & (p102(Y) | (~p103(Y))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X!0)) & p100(X!0))) <=> (![Y: $i] : (p3(Y) | (~r1(X!0, Y))) & (![Y: $i] : ((~r1(X!0, Y)) | (((~((~p105(Y)) & p104(Y))) | ((~((~r1(Y, tptp_fun_X_1(Y))) | (~((~p6(tptp_fun_X_1(Y))) & (~p106(tptp_fun_X_1(Y))) & p105(tptp_fun_X_1(Y)))))) & (~((~r1(Y, tptp_fun_X_2(Y))) | (~(p6(tptp_fun_X_2(Y)) & (~p106(tptp_fun_X_2(Y))) & p105(tptp_fun_X_2(Y)))))))) & ((~((~p104(Y)) & p103(Y))) | ((~((~r1(Y, tptp_fun_X_3(Y))) | (~((~p5(tptp_fun_X_3(Y))) & (~p105(tptp_fun_X_3(Y))) & p104(tptp_fun_X_3(Y)))))) & (~((~r1(Y, tptp_fun_X_4(Y))) | (~(p5(tptp_fun_X_4(Y)) & (~p105(tptp_fun_X_4(Y))) & p104(tptp_fun_X_4(Y)))))))) & ((~((~p103(Y)) & p102(Y))) | ((~((~r1(Y, tptp_fun_X_5(Y))) | (~((~p4(tptp_fun_X_5(Y))) & (~p104(tptp_fun_X_5(Y))) & p103(tptp_fun_X_5(Y)))))) & (~((~r1(Y, tptp_fun_X_6(Y))) | (~(p4(tptp_fun_X_6(Y)) & (~p104(tptp_fun_X_6(Y))) & p103(tptp_fun_X_6(Y)))))))) & ((~((~p102(Y)) & p101(Y))) | ((~((~r1(Y, tptp_fun_X_7(Y))) | (~((~p3(tptp_fun_X_7(Y))) & (~p103(tptp_fun_X_7(Y))) & p102(tptp_fun_X_7(Y)))))) & (~((~r1(Y, tptp_fun_X_8(Y))) | (~(p3(tptp_fun_X_8(Y)) & (~p103(tptp_fun_X_8(Y))) & p102(tptp_fun_X_8(Y)))))))) & ((~((~p101(Y)) & p100(Y))) | ((~((~r1(Y, tptp_fun_X_9(Y))) | (~((~p2(tptp_fun_X_9(Y))) & (~p102(tptp_fun_X_9(Y))) & p101(tptp_fun_X_9(Y)))))) & (~((~r1(Y, tptp_fun_X_10(Y))) | (~(p2(tptp_fun_X_10(Y)) & (~p102(tptp_fun_X_10(Y))) & p101(tptp_fun_X_10(Y)))))))) & ((~p105(Y)) | ((p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X)))) & ((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X)))))) & ((~p104(Y)) | ((p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X)))) & ((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X)))))) & ((~p103(Y)) | ((p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X)))) & ((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X)))))) & ((~p102(Y)) | ((p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X)))) & ((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X)))))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p105(Y) | (~p106(Y))) & (p104(Y) | (~p105(Y))) & (p103(Y) | (~p104(Y))) & (p102(Y) | (~p103(Y))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X!0)) & p100(X!0)))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[22])).
% 0.18/0.42 tff(24,plain,
% 0.18/0.42 ((![Y: $i] : (p3(Y) | (~r1(X!0, Y))) & (![Y: $i] : ((~r1(X!0, Y)) | ((((~((~r1(Y, tptp_fun_X_1(Y))) | (~((~p6(tptp_fun_X_1(Y))) & (~p106(tptp_fun_X_1(Y))) & p105(tptp_fun_X_1(Y)))))) & (~((~r1(Y, tptp_fun_X_2(Y))) | (~(p6(tptp_fun_X_2(Y)) & (~p106(tptp_fun_X_2(Y))) & p105(tptp_fun_X_2(Y))))))) | (~((~p105(Y)) & p104(Y)))) & (((~((~r1(Y, tptp_fun_X_3(Y))) | (~((~p5(tptp_fun_X_3(Y))) & (~p105(tptp_fun_X_3(Y))) & p104(tptp_fun_X_3(Y)))))) & (~((~r1(Y, tptp_fun_X_4(Y))) | (~(p5(tptp_fun_X_4(Y)) & (~p105(tptp_fun_X_4(Y))) & p104(tptp_fun_X_4(Y))))))) | (~((~p104(Y)) & p103(Y)))) & (((~((~r1(Y, tptp_fun_X_5(Y))) | (~((~p4(tptp_fun_X_5(Y))) & (~p104(tptp_fun_X_5(Y))) & p103(tptp_fun_X_5(Y)))))) & (~((~r1(Y, tptp_fun_X_6(Y))) | (~(p4(tptp_fun_X_6(Y)) & (~p104(tptp_fun_X_6(Y))) & p103(tptp_fun_X_6(Y))))))) | (~((~p103(Y)) & p102(Y)))) & (((~((~r1(Y, tptp_fun_X_7(Y))) | (~((~p3(tptp_fun_X_7(Y))) & (~p103(tptp_fun_X_7(Y))) & p102(tptp_fun_X_7(Y)))))) & (~((~r1(Y, tptp_fun_X_8(Y))) | (~(p3(tptp_fun_X_8(Y)) & (~p103(tptp_fun_X_8(Y))) & p102(tptp_fun_X_8(Y))))))) | (~((~p102(Y)) & p101(Y)))) & (((~((~r1(Y, tptp_fun_X_9(Y))) | (~((~p2(tptp_fun_X_9(Y))) & (~p102(tptp_fun_X_9(Y))) & p101(tptp_fun_X_9(Y)))))) & (~((~r1(Y, tptp_fun_X_10(Y))) | (~(p2(tptp_fun_X_10(Y)) & (~p102(tptp_fun_X_10(Y))) & p101(tptp_fun_X_10(Y))))))) | (~((~p101(Y)) & p100(Y)))) & ((~p105(Y)) | ((p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X)))) & ((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X)))))) & ((~p104(Y)) | ((p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X)))) & ((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X)))))) & ((~p103(Y)) | ((p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X)))) & ((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X)))))) & ((~p102(Y)) | ((p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X)))) & ((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X)))))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p105(Y) | (~p106(Y))) & (p104(Y) | (~p105(Y))) & (p103(Y) | (~p104(Y))) & (p102(Y) | (~p103(Y))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X!0)) & p100(X!0))) <=> (![Y: $i] : (p3(Y) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | (((~((~p105(Y)) & p104(Y))) | ((~((~r1(Y, tptp_fun_X_1(Y))) | (~((~p6(tptp_fun_X_1(Y))) & (~p106(tptp_fun_X_1(Y))) & p105(tptp_fun_X_1(Y)))))) & (~((~r1(Y, tptp_fun_X_2(Y))) | (~(p6(tptp_fun_X_2(Y)) & (~p106(tptp_fun_X_2(Y))) & p105(tptp_fun_X_2(Y)))))))) & ((~((~p104(Y)) & p103(Y))) | ((~((~r1(Y, tptp_fun_X_3(Y))) | (~((~p5(tptp_fun_X_3(Y))) & (~p105(tptp_fun_X_3(Y))) & p104(tptp_fun_X_3(Y)))))) & (~((~r1(Y, tptp_fun_X_4(Y))) | (~(p5(tptp_fun_X_4(Y)) & (~p105(tptp_fun_X_4(Y))) & p104(tptp_fun_X_4(Y)))))))) & ((~((~p103(Y)) & p102(Y))) | ((~((~r1(Y, tptp_fun_X_5(Y))) | (~((~p4(tptp_fun_X_5(Y))) & (~p104(tptp_fun_X_5(Y))) & p103(tptp_fun_X_5(Y)))))) & (~((~r1(Y, tptp_fun_X_6(Y))) | (~(p4(tptp_fun_X_6(Y)) & (~p104(tptp_fun_X_6(Y))) & p103(tptp_fun_X_6(Y)))))))) & ((~((~p102(Y)) & p101(Y))) | ((~((~r1(Y, tptp_fun_X_7(Y))) | (~((~p3(tptp_fun_X_7(Y))) & (~p103(tptp_fun_X_7(Y))) & p102(tptp_fun_X_7(Y)))))) & (~((~r1(Y, tptp_fun_X_8(Y))) | (~(p3(tptp_fun_X_8(Y)) & (~p103(tptp_fun_X_8(Y))) & p102(tptp_fun_X_8(Y)))))))) & ((~((~p101(Y)) & p100(Y))) | ((~((~r1(Y, tptp_fun_X_9(Y))) | (~((~p2(tptp_fun_X_9(Y))) & (~p102(tptp_fun_X_9(Y))) & p101(tptp_fun_X_9(Y)))))) & (~((~r1(Y, tptp_fun_X_10(Y))) | (~(p2(tptp_fun_X_10(Y)) & (~p102(tptp_fun_X_10(Y))) & p101(tptp_fun_X_10(Y)))))))) & ((~p105(Y)) | ((p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X)))) & ((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X)))))) & ((~p104(Y)) | ((p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X)))) & ((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X)))))) & ((~p103(Y)) | ((p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X)))) & ((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X)))))) & ((~p102(Y)) | ((p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X)))) & ((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X)))))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p105(Y) | (~p106(Y))) & (p104(Y) | (~p105(Y))) & (p103(Y) | (~p104(Y))) & (p102(Y) | (~p103(Y))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X!0)) & p100(X!0))),
% 0.18/0.42 inference(transitivity,[status(thm)],[23, 21])).
% 0.18/0.42 tff(25,plain,
% 0.18/0.42 (?[X: $i] : (~((~![Y: $i] : (p3(Y) | (~r1(X, Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | ((((~![X: $i] : ((~r1(Y, X)) | (~((~p6(X)) & (~p106(X)) & p105(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p6(X) & (~p106(X)) & p105(X)))))) | (~((~p105(Y)) & p104(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p5(X)) & (~p105(X)) & p104(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p5(X) & (~p105(X)) & p104(X)))))) | (~((~p104(Y)) & p103(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p4(X)) & (~p104(X)) & p103(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p4(X) & (~p104(X)) & p103(X)))))) | (~((~p103(Y)) & p102(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p3(X)) & (~p103(X)) & p102(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p3(X) & (~p103(X)) & p102(X)))))) | (~((~p102(Y)) & p101(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p2(X)) & (~p102(X)) & p101(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p2(X) & (~p102(X)) & p101(X)))))) | (~((~p101(Y)) & p100(Y)))) & ((~p105(Y)) | ((p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X)))) & ((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X)))))) & ((~p104(Y)) | ((p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X)))) & ((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X)))))) & ((~p103(Y)) | ((p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X)))) & ((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X)))))) & ((~p102(Y)) | ((p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X)))) & ((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X)))))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p105(Y) | (~p106(Y))) & (p104(Y) | (~p105(Y))) & (p103(Y) | (~p104(Y))) & (p102(Y) | (~p103(Y))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X)) & p100(X))))) <=> ?[X: $i] : (~((~![Y: $i] : (p3(Y) | (~r1(X, Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | ((((~![X: $i] : ((~r1(Y, X)) | (~((~p6(X)) & (~p106(X)) & p105(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p6(X) & (~p106(X)) & p105(X)))))) | (~((~p105(Y)) & p104(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p5(X)) & (~p105(X)) & p104(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p5(X) & (~p105(X)) & p104(X)))))) | (~((~p104(Y)) & p103(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p4(X)) & (~p104(X)) & p103(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p4(X) & (~p104(X)) & p103(X)))))) | (~((~p103(Y)) & p102(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p3(X)) & (~p103(X)) & p102(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p3(X) & (~p103(X)) & p102(X)))))) | (~((~p102(Y)) & p101(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p2(X)) & (~p102(X)) & p101(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p2(X) & (~p102(X)) & p101(X)))))) | (~((~p101(Y)) & p100(Y)))) & ((~p105(Y)) | ((p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X)))) & ((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X)))))) & ((~p104(Y)) | ((p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X)))) & ((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X)))))) & ((~p103(Y)) | ((p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X)))) & ((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X)))))) & ((~p102(Y)) | ((p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X)))) & ((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X)))))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p105(Y) | (~p106(Y))) & (p104(Y) | (~p105(Y))) & (p103(Y) | (~p104(Y))) & (p102(Y) | (~p103(Y))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X)) & p100(X)))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(26,plain,
% 0.18/0.43 ((~(~?[X: $i] : (~((~![Y: $i] : (p3(Y) | (~r1(X, Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | ((((~![X: $i] : ((~r1(Y, X)) | (~((~p6(X)) & (~p106(X)) & p105(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p6(X) & (~p106(X)) & p105(X)))))) | (~((~p105(Y)) & p104(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p5(X)) & (~p105(X)) & p104(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p5(X) & (~p105(X)) & p104(X)))))) | (~((~p104(Y)) & p103(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p4(X)) & (~p104(X)) & p103(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p4(X) & (~p104(X)) & p103(X)))))) | (~((~p103(Y)) & p102(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p3(X)) & (~p103(X)) & p102(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p3(X) & (~p103(X)) & p102(X)))))) | (~((~p102(Y)) & p101(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p2(X)) & (~p102(X)) & p101(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p2(X) & (~p102(X)) & p101(X)))))) | (~((~p101(Y)) & p100(Y)))) & ((~p105(Y)) | ((p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X)))) & ((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X)))))) & ((~p104(Y)) | ((p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X)))) & ((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X)))))) & ((~p103(Y)) | ((p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X)))) & ((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X)))))) & ((~p102(Y)) | ((p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X)))) & ((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X)))))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p105(Y) | (~p106(Y))) & (p104(Y) | (~p105(Y))) & (p103(Y) | (~p104(Y))) & (p102(Y) | (~p103(Y))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X)) & p100(X))))))) <=> ?[X: $i] : (~((~![Y: $i] : (p3(Y) | (~r1(X, Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | ((((~![X: $i] : ((~r1(Y, X)) | (~((~p6(X)) & (~p106(X)) & p105(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p6(X) & (~p106(X)) & p105(X)))))) | (~((~p105(Y)) & p104(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p5(X)) & (~p105(X)) & p104(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p5(X) & (~p105(X)) & p104(X)))))) | (~((~p104(Y)) & p103(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p4(X)) & (~p104(X)) & p103(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p4(X) & (~p104(X)) & p103(X)))))) | (~((~p103(Y)) & p102(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p3(X)) & (~p103(X)) & p102(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p3(X) & (~p103(X)) & p102(X)))))) | (~((~p102(Y)) & p101(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p2(X)) & (~p102(X)) & p101(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p2(X) & (~p102(X)) & p101(X)))))) | (~((~p101(Y)) & p100(Y)))) & ((~p105(Y)) | ((p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X)))) & ((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X)))))) & ((~p104(Y)) | ((p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X)))) & ((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X)))))) & ((~p103(Y)) | ((p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X)))) & ((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X)))))) & ((~p102(Y)) | ((p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X)))) & ((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X)))))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p105(Y) | (~p106(Y))) & (p104(Y) | (~p105(Y))) & (p103(Y) | (~p104(Y))) & (p102(Y) | (~p103(Y))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X)) & p100(X)))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(27,plain,
% 0.18/0.43 ((~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~((![Y: $i] : ((~r1(X, Y)) | (((((((((((((((((((~![X: $i] : ((~r1(Y, X)) | (~(((~p6(X)) & (~p106(X))) & p105(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~((p6(X) & (~p106(X))) & p105(X)))))) | (~((~p105(Y)) & p104(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~(((~p5(X)) & (~p105(X))) & p104(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~((p5(X) & (~p105(X))) & p104(X)))))) | (~((~p104(Y)) & p103(Y))))) & (((~![X: $i] : ((~r1(Y, X)) | (~(((~p4(X)) & (~p104(X))) & p103(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~((p4(X) & (~p104(X))) & p103(X)))))) | (~((~p103(Y)) & p102(Y))))) & (((~![X: $i] : ((~r1(Y, X)) | (~(((~p3(X)) & (~p103(X))) & p102(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~((p3(X) & (~p103(X))) & p102(X)))))) | (~((~p102(Y)) & p101(Y))))) & (((~![X: $i] : ((~r1(Y, X)) | (~(((~p2(X)) & (~p102(X))) & p101(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~((p2(X) & (~p102(X))) & p101(X)))))) | (~((~p101(Y)) & p100(Y))))) & (((![X: $i] : (((~r1(Y, X)) | (~p6(X))) | (~p105(X))) | p6(Y)) & (![X: $i] : (((~r1(Y, X)) | p6(X)) | (~p105(X))) | (~p6(Y)))) | (~p105(Y)))) & (((![X: $i] : (((~r1(Y, X)) | (~p5(X))) | (~p104(X))) | p5(Y)) & (![X: $i] : (((~r1(Y, X)) | p5(X)) | (~p104(X))) | (~p5(Y)))) | (~p104(Y)))) & (((![X: $i] : (((~r1(Y, X)) | (~p4(X))) | (~p103(X))) | p4(Y)) & (![X: $i] : (((~r1(Y, X)) | p4(X)) | (~p103(X))) | (~p4(Y)))) | (~p103(Y)))) & (((![X: $i] : (((~r1(Y, X)) | (~p3(X))) | (~p102(X))) | p3(Y)) & (![X: $i] : (((~r1(Y, X)) | p3(X)) | (~p102(X))) | (~p3(Y)))) | (~p102(Y)))) & (((![X: $i] : (((~r1(Y, X)) | (~p2(X))) | (~p101(X))) | p2(Y)) & (![X: $i] : (((~r1(Y, X)) | p2(X)) | (~p101(X))) | (~p2(Y)))) | (~p101(Y)))) & (((![X: $i] : (((~r1(Y, X)) | (~p1(X))) | (~p100(X))) | p1(Y)) & (![X: $i] : (((~r1(Y, X)) | p1(X)) | (~p100(X))) | (~p1(Y)))) | (~p100(Y)))) & (p105(Y) | (~p106(Y)))) & (p104(Y) | (~p105(Y)))) & (p103(Y) | (~p104(Y)))) & (p102(Y) | (~p103(Y)))) & (p101(Y) | (~p102(Y)))) & (p100(Y) | (~p101(Y))))) & (~p101(X))) & p100(X)))))) <=> (~?[X: $i] : (~((~![Y: $i] : (p3(Y) | (~r1(X, Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | ((((~![X: $i] : ((~r1(Y, X)) | (~((~p6(X)) & (~p106(X)) & p105(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p6(X) & (~p106(X)) & p105(X)))))) | (~((~p105(Y)) & p104(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p5(X)) & (~p105(X)) & p104(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p5(X) & (~p105(X)) & p104(X)))))) | (~((~p104(Y)) & p103(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p4(X)) & (~p104(X)) & p103(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p4(X) & (~p104(X)) & p103(X)))))) | (~((~p103(Y)) & p102(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p3(X)) & (~p103(X)) & p102(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p3(X) & (~p103(X)) & p102(X)))))) | (~((~p102(Y)) & p101(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p2(X)) & (~p102(X)) & p101(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p2(X) & (~p102(X)) & p101(X)))))) | (~((~p101(Y)) & p100(Y)))) & ((~p105(Y)) | ((p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X)))) & ((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X)))))) & ((~p104(Y)) | ((p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X)))) & ((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X)))))) & ((~p103(Y)) | ((p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X)))) & ((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X)))))) & ((~p102(Y)) | ((p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X)))) & ((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X)))))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p105(Y) | (~p106(Y))) & (p104(Y) | (~p105(Y))) & (p103(Y) | (~p104(Y))) & (p102(Y) | (~p103(Y))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X)) & p100(X))))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(28,plain,
% 0.18/0.43 ((~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~((![Y: $i] : ((~r1(X, Y)) | (((((((((((((((((((~![X: $i] : ((~r1(Y, X)) | (~(((~p6(X)) & (~p106(X))) & p105(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~((p6(X) & (~p106(X))) & p105(X)))))) | (~((~p105(Y)) & p104(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~(((~p5(X)) & (~p105(X))) & p104(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~((p5(X) & (~p105(X))) & p104(X)))))) | (~((~p104(Y)) & p103(Y))))) & (((~![X: $i] : ((~r1(Y, X)) | (~(((~p4(X)) & (~p104(X))) & p103(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~((p4(X) & (~p104(X))) & p103(X)))))) | (~((~p103(Y)) & p102(Y))))) & (((~![X: $i] : ((~r1(Y, X)) | (~(((~p3(X)) & (~p103(X))) & p102(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~((p3(X) & (~p103(X))) & p102(X)))))) | (~((~p102(Y)) & p101(Y))))) & (((~![X: $i] : ((~r1(Y, X)) | (~(((~p2(X)) & (~p102(X))) & p101(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~((p2(X) & (~p102(X))) & p101(X)))))) | (~((~p101(Y)) & p100(Y))))) & (((![X: $i] : (((~r1(Y, X)) | (~p6(X))) | (~p105(X))) | p6(Y)) & (![X: $i] : (((~r1(Y, X)) | p6(X)) | (~p105(X))) | (~p6(Y)))) | (~p105(Y)))) & (((![X: $i] : (((~r1(Y, X)) | (~p5(X))) | (~p104(X))) | p5(Y)) & (![X: $i] : (((~r1(Y, X)) | p5(X)) | (~p104(X))) | (~p5(Y)))) | (~p104(Y)))) & (((![X: $i] : (((~r1(Y, X)) | (~p4(X))) | (~p103(X))) | p4(Y)) & (![X: $i] : (((~r1(Y, X)) | p4(X)) | (~p103(X))) | (~p4(Y)))) | (~p103(Y)))) & (((![X: $i] : (((~r1(Y, X)) | (~p3(X))) | (~p102(X))) | p3(Y)) & (![X: $i] : (((~r1(Y, X)) | p3(X)) | (~p102(X))) | (~p3(Y)))) | (~p102(Y)))) & (((![X: $i] : (((~r1(Y, X)) | (~p2(X))) | (~p101(X))) | p2(Y)) & (![X: $i] : (((~r1(Y, X)) | p2(X)) | (~p101(X))) | (~p2(Y)))) | (~p101(Y)))) & (((![X: $i] : (((~r1(Y, X)) | (~p1(X))) | (~p100(X))) | p1(Y)) & (![X: $i] : (((~r1(Y, X)) | p1(X)) | (~p100(X))) | (~p1(Y)))) | (~p100(Y)))) & (p105(Y) | (~p106(Y)))) & (p104(Y) | (~p105(Y)))) & (p103(Y) | (~p104(Y)))) & (p102(Y) | (~p103(Y)))) & (p101(Y) | (~p102(Y)))) & (p100(Y) | (~p101(Y))))) & (~p101(X))) & p100(X))))))) <=> (~(~?[X: $i] : (~((~![Y: $i] : (p3(Y) | (~r1(X, Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | ((((~![X: $i] : ((~r1(Y, X)) | (~((~p6(X)) & (~p106(X)) & p105(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p6(X) & (~p106(X)) & p105(X)))))) | (~((~p105(Y)) & p104(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p5(X)) & (~p105(X)) & p104(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p5(X) & (~p105(X)) & p104(X)))))) | (~((~p104(Y)) & p103(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p4(X)) & (~p104(X)) & p103(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p4(X) & (~p104(X)) & p103(X)))))) | (~((~p103(Y)) & p102(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p3(X)) & (~p103(X)) & p102(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p3(X) & (~p103(X)) & p102(X)))))) | (~((~p102(Y)) & p101(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p2(X)) & (~p102(X)) & p101(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p2(X) & (~p102(X)) & p101(X)))))) | (~((~p101(Y)) & p100(Y)))) & ((~p105(Y)) | ((p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X)))) & ((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X)))))) & ((~p104(Y)) | ((p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X)))) & ((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X)))))) & ((~p103(Y)) | ((p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X)))) & ((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X)))))) & ((~p102(Y)) | ((p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X)))) & ((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X)))))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p105(Y) | (~p106(Y))) & (p104(Y) | (~p105(Y))) & (p103(Y) | (~p104(Y))) & (p102(Y) | (~p103(Y))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X)) & p100(X)))))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[27])).
% 0.18/0.43 tff(29,plain,
% 0.18/0.43 ((~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~((![Y: $i] : ((~r1(X, Y)) | (((((((((((((((((((~![X: $i] : ((~r1(Y, X)) | (~(((~p6(X)) & (~p106(X))) & p105(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~((p6(X) & (~p106(X))) & p105(X)))))) | (~((~p105(Y)) & p104(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~(((~p5(X)) & (~p105(X))) & p104(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~((p5(X) & (~p105(X))) & p104(X)))))) | (~((~p104(Y)) & p103(Y))))) & (((~![X: $i] : ((~r1(Y, X)) | (~(((~p4(X)) & (~p104(X))) & p103(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~((p4(X) & (~p104(X))) & p103(X)))))) | (~((~p103(Y)) & p102(Y))))) & (((~![X: $i] : ((~r1(Y, X)) | (~(((~p3(X)) & (~p103(X))) & p102(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~((p3(X) & (~p103(X))) & p102(X)))))) | (~((~p102(Y)) & p101(Y))))) & (((~![X: $i] : ((~r1(Y, X)) | (~(((~p2(X)) & (~p102(X))) & p101(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~((p2(X) & (~p102(X))) & p101(X)))))) | (~((~p101(Y)) & p100(Y))))) & (((![X: $i] : (((~r1(Y, X)) | (~p6(X))) | (~p105(X))) | p6(Y)) & (![X: $i] : (((~r1(Y, X)) | p6(X)) | (~p105(X))) | (~p6(Y)))) | (~p105(Y)))) & (((![X: $i] : (((~r1(Y, X)) | (~p5(X))) | (~p104(X))) | p5(Y)) & (![X: $i] : (((~r1(Y, X)) | p5(X)) | (~p104(X))) | (~p5(Y)))) | (~p104(Y)))) & (((![X: $i] : (((~r1(Y, X)) | (~p4(X))) | (~p103(X))) | p4(Y)) & (![X: $i] : (((~r1(Y, X)) | p4(X)) | (~p103(X))) | (~p4(Y)))) | (~p103(Y)))) & (((![X: $i] : (((~r1(Y, X)) | (~p3(X))) | (~p102(X))) | p3(Y)) & (![X: $i] : (((~r1(Y, X)) | p3(X)) | (~p102(X))) | (~p3(Y)))) | (~p102(Y)))) & (((![X: $i] : (((~r1(Y, X)) | (~p2(X))) | (~p101(X))) | p2(Y)) & (![X: $i] : (((~r1(Y, X)) | p2(X)) | (~p101(X))) | (~p2(Y)))) | (~p101(Y)))) & (((![X: $i] : (((~r1(Y, X)) | (~p1(X))) | (~p100(X))) | p1(Y)) & (![X: $i] : (((~r1(Y, X)) | p1(X)) | (~p100(X))) | (~p1(Y)))) | (~p100(Y)))) & (p105(Y) | (~p106(Y)))) & (p104(Y) | (~p105(Y)))) & (p103(Y) | (~p104(Y)))) & (p102(Y) | (~p103(Y)))) & (p101(Y) | (~p102(Y)))) & (p100(Y) | (~p101(Y))))) & (~p101(X))) & p100(X))))))) <=> ?[X: $i] : (~((~![Y: $i] : (p3(Y) | (~r1(X, Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | ((((~![X: $i] : ((~r1(Y, X)) | (~((~p6(X)) & (~p106(X)) & p105(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p6(X) & (~p106(X)) & p105(X)))))) | (~((~p105(Y)) & p104(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p5(X)) & (~p105(X)) & p104(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p5(X) & (~p105(X)) & p104(X)))))) | (~((~p104(Y)) & p103(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p4(X)) & (~p104(X)) & p103(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p4(X) & (~p104(X)) & p103(X)))))) | (~((~p103(Y)) & p102(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p3(X)) & (~p103(X)) & p102(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p3(X) & (~p103(X)) & p102(X)))))) | (~((~p102(Y)) & p101(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p2(X)) & (~p102(X)) & p101(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p2(X) & (~p102(X)) & p101(X)))))) | (~((~p101(Y)) & p100(Y)))) & ((~p105(Y)) | ((p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X)))) & ((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X)))))) & ((~p104(Y)) | ((p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X)))) & ((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X)))))) & ((~p103(Y)) | ((p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X)))) & ((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X)))))) & ((~p102(Y)) | ((p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X)))) & ((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X)))))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p105(Y) | (~p106(Y))) & (p104(Y) | (~p105(Y))) & (p103(Y) | (~p104(Y))) & (p102(Y) | (~p103(Y))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X)) & p100(X)))))),
% 0.18/0.44 inference(transitivity,[status(thm)],[28, 26])).
% 0.18/0.44 tff(30,axiom,(~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~((![Y: $i] : ((~r1(X, Y)) | (((((((((((((((((((~![X: $i] : ((~r1(Y, X)) | (~(((~p6(X)) & (~p106(X))) & p105(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~((p6(X) & (~p106(X))) & p105(X)))))) | (~((~p105(Y)) & p104(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~(((~p5(X)) & (~p105(X))) & p104(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~((p5(X) & (~p105(X))) & p104(X)))))) | (~((~p104(Y)) & p103(Y))))) & (((~![X: $i] : ((~r1(Y, X)) | (~(((~p4(X)) & (~p104(X))) & p103(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~((p4(X) & (~p104(X))) & p103(X)))))) | (~((~p103(Y)) & p102(Y))))) & (((~![X: $i] : ((~r1(Y, X)) | (~(((~p3(X)) & (~p103(X))) & p102(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~((p3(X) & (~p103(X))) & p102(X)))))) | (~((~p102(Y)) & p101(Y))))) & (((~![X: $i] : ((~r1(Y, X)) | (~(((~p2(X)) & (~p102(X))) & p101(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~((p2(X) & (~p102(X))) & p101(X)))))) | (~((~p101(Y)) & p100(Y))))) & (((![X: $i] : (((~r1(Y, X)) | (~p6(X))) | (~p105(X))) | p6(Y)) & (![X: $i] : (((~r1(Y, X)) | p6(X)) | (~p105(X))) | (~p6(Y)))) | (~p105(Y)))) & (((![X: $i] : (((~r1(Y, X)) | (~p5(X))) | (~p104(X))) | p5(Y)) & (![X: $i] : (((~r1(Y, X)) | p5(X)) | (~p104(X))) | (~p5(Y)))) | (~p104(Y)))) & (((![X: $i] : (((~r1(Y, X)) | (~p4(X))) | (~p103(X))) | p4(Y)) & (![X: $i] : (((~r1(Y, X)) | p4(X)) | (~p103(X))) | (~p4(Y)))) | (~p103(Y)))) & (((![X: $i] : (((~r1(Y, X)) | (~p3(X))) | (~p102(X))) | p3(Y)) & (![X: $i] : (((~r1(Y, X)) | p3(X)) | (~p102(X))) | (~p3(Y)))) | (~p102(Y)))) & (((![X: $i] : (((~r1(Y, X)) | (~p2(X))) | (~p101(X))) | p2(Y)) & (![X: $i] : (((~r1(Y, X)) | p2(X)) | (~p101(X))) | (~p2(Y)))) | (~p101(Y)))) & (((![X: $i] : (((~r1(Y, X)) | (~p1(X))) | (~p100(X))) | p1(Y)) & (![X: $i] : (((~r1(Y, X)) | p1(X)) | (~p100(X))) | (~p1(Y)))) | (~p100(Y)))) & (p105(Y) | (~p106(Y)))) & (p104(Y) | (~p105(Y)))) & (p103(Y) | (~p104(Y)))) & (p102(Y) | (~p103(Y)))) & (p101(Y) | (~p102(Y)))) & (p100(Y) | (~p101(Y))))) & (~p101(X))) & p100(X))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','main')).
% 0.18/0.44 tff(31,plain,
% 0.18/0.44 (?[X: $i] : (~((~![Y: $i] : (p3(Y) | (~r1(X, Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | ((((~![X: $i] : ((~r1(Y, X)) | (~((~p6(X)) & (~p106(X)) & p105(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p6(X) & (~p106(X)) & p105(X)))))) | (~((~p105(Y)) & p104(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p5(X)) & (~p105(X)) & p104(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p5(X) & (~p105(X)) & p104(X)))))) | (~((~p104(Y)) & p103(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p4(X)) & (~p104(X)) & p103(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p4(X) & (~p104(X)) & p103(X)))))) | (~((~p103(Y)) & p102(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p3(X)) & (~p103(X)) & p102(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p3(X) & (~p103(X)) & p102(X)))))) | (~((~p102(Y)) & p101(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p2(X)) & (~p102(X)) & p101(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p2(X) & (~p102(X)) & p101(X)))))) | (~((~p101(Y)) & p100(Y)))) & ((~p105(Y)) | ((p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X)))) & ((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X)))))) & ((~p104(Y)) | ((p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X)))) & ((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X)))))) & ((~p103(Y)) | ((p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X)))) & ((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X)))))) & ((~p102(Y)) | ((p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X)))) & ((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X)))))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p105(Y) | (~p106(Y))) & (p104(Y) | (~p105(Y))) & (p103(Y) | (~p104(Y))) & (p102(Y) | (~p103(Y))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X)) & p100(X)))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.18/0.44 tff(32,plain,
% 0.18/0.44 (?[X: $i] : (~((~![Y: $i] : (p3(Y) | (~r1(X, Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | ((((~![X: $i] : ((~r1(Y, X)) | (~((~p6(X)) & (~p106(X)) & p105(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p6(X) & (~p106(X)) & p105(X)))))) | (~((~p105(Y)) & p104(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p5(X)) & (~p105(X)) & p104(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p5(X) & (~p105(X)) & p104(X)))))) | (~((~p104(Y)) & p103(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p4(X)) & (~p104(X)) & p103(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p4(X) & (~p104(X)) & p103(X)))))) | (~((~p103(Y)) & p102(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p3(X)) & (~p103(X)) & p102(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p3(X) & (~p103(X)) & p102(X)))))) | (~((~p102(Y)) & p101(Y)))) & (((~![X: $i] : ((~r1(Y, X)) | (~((~p2(X)) & (~p102(X)) & p101(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p2(X) & (~p102(X)) & p101(X)))))) | (~((~p101(Y)) & p100(Y)))) & ((~p105(Y)) | ((p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X)))) & ((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X)))))) & ((~p104(Y)) | ((p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X)))) & ((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X)))))) & ((~p103(Y)) | ((p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X)))) & ((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X)))))) & ((~p102(Y)) | ((p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X)))) & ((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X)))))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p105(Y) | (~p106(Y))) & (p104(Y) | (~p105(Y))) & (p103(Y) | (~p104(Y))) & (p102(Y) | (~p103(Y))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X)) & p100(X)))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[31, 25])).
% 0.18/0.44 tff(33,plain,
% 0.18/0.44 (![Y: $i] : (p3(Y) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | (((~((~p105(Y)) & p104(Y))) | ((~((~r1(Y, tptp_fun_X_1(Y))) | (~((~p6(tptp_fun_X_1(Y))) & (~p106(tptp_fun_X_1(Y))) & p105(tptp_fun_X_1(Y)))))) & (~((~r1(Y, tptp_fun_X_2(Y))) | (~(p6(tptp_fun_X_2(Y)) & (~p106(tptp_fun_X_2(Y))) & p105(tptp_fun_X_2(Y)))))))) & ((~((~p104(Y)) & p103(Y))) | ((~((~r1(Y, tptp_fun_X_3(Y))) | (~((~p5(tptp_fun_X_3(Y))) & (~p105(tptp_fun_X_3(Y))) & p104(tptp_fun_X_3(Y)))))) & (~((~r1(Y, tptp_fun_X_4(Y))) | (~(p5(tptp_fun_X_4(Y)) & (~p105(tptp_fun_X_4(Y))) & p104(tptp_fun_X_4(Y)))))))) & ((~((~p103(Y)) & p102(Y))) | ((~((~r1(Y, tptp_fun_X_5(Y))) | (~((~p4(tptp_fun_X_5(Y))) & (~p104(tptp_fun_X_5(Y))) & p103(tptp_fun_X_5(Y)))))) & (~((~r1(Y, tptp_fun_X_6(Y))) | (~(p4(tptp_fun_X_6(Y)) & (~p104(tptp_fun_X_6(Y))) & p103(tptp_fun_X_6(Y)))))))) & ((~((~p102(Y)) & p101(Y))) | ((~((~r1(Y, tptp_fun_X_7(Y))) | (~((~p3(tptp_fun_X_7(Y))) & (~p103(tptp_fun_X_7(Y))) & p102(tptp_fun_X_7(Y)))))) & (~((~r1(Y, tptp_fun_X_8(Y))) | (~(p3(tptp_fun_X_8(Y)) & (~p103(tptp_fun_X_8(Y))) & p102(tptp_fun_X_8(Y)))))))) & ((~((~p101(Y)) & p100(Y))) | ((~((~r1(Y, tptp_fun_X_9(Y))) | (~((~p2(tptp_fun_X_9(Y))) & (~p102(tptp_fun_X_9(Y))) & p101(tptp_fun_X_9(Y)))))) & (~((~r1(Y, tptp_fun_X_10(Y))) | (~(p2(tptp_fun_X_10(Y)) & (~p102(tptp_fun_X_10(Y))) & p101(tptp_fun_X_10(Y)))))))) & ((~p105(Y)) | ((p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X)))) & ((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X)))))) & ((~p104(Y)) | ((p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X)))) & ((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X)))))) & ((~p103(Y)) | ((p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X)))) & ((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X)))))) & ((~p102(Y)) | ((p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X)))) & ((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X)))))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p105(Y) | (~p106(Y))) & (p104(Y) | (~p105(Y))) & (p103(Y) | (~p104(Y))) & (p102(Y) | (~p103(Y))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X!0)) & p100(X!0)),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[32, 24])).
% 0.18/0.44 tff(34,plain,
% 0.18/0.44 (![Y: $i] : ((~r1(X!0, Y)) | (((~((~p105(Y)) & p104(Y))) | ((~((~r1(Y, tptp_fun_X_1(Y))) | (~((~p6(tptp_fun_X_1(Y))) & (~p106(tptp_fun_X_1(Y))) & p105(tptp_fun_X_1(Y)))))) & (~((~r1(Y, tptp_fun_X_2(Y))) | (~(p6(tptp_fun_X_2(Y)) & (~p106(tptp_fun_X_2(Y))) & p105(tptp_fun_X_2(Y)))))))) & ((~((~p104(Y)) & p103(Y))) | ((~((~r1(Y, tptp_fun_X_3(Y))) | (~((~p5(tptp_fun_X_3(Y))) & (~p105(tptp_fun_X_3(Y))) & p104(tptp_fun_X_3(Y)))))) & (~((~r1(Y, tptp_fun_X_4(Y))) | (~(p5(tptp_fun_X_4(Y)) & (~p105(tptp_fun_X_4(Y))) & p104(tptp_fun_X_4(Y)))))))) & ((~((~p103(Y)) & p102(Y))) | ((~((~r1(Y, tptp_fun_X_5(Y))) | (~((~p4(tptp_fun_X_5(Y))) & (~p104(tptp_fun_X_5(Y))) & p103(tptp_fun_X_5(Y)))))) & (~((~r1(Y, tptp_fun_X_6(Y))) | (~(p4(tptp_fun_X_6(Y)) & (~p104(tptp_fun_X_6(Y))) & p103(tptp_fun_X_6(Y)))))))) & ((~((~p102(Y)) & p101(Y))) | ((~((~r1(Y, tptp_fun_X_7(Y))) | (~((~p3(tptp_fun_X_7(Y))) & (~p103(tptp_fun_X_7(Y))) & p102(tptp_fun_X_7(Y)))))) & (~((~r1(Y, tptp_fun_X_8(Y))) | (~(p3(tptp_fun_X_8(Y)) & (~p103(tptp_fun_X_8(Y))) & p102(tptp_fun_X_8(Y)))))))) & ((~((~p101(Y)) & p100(Y))) | ((~((~r1(Y, tptp_fun_X_9(Y))) | (~((~p2(tptp_fun_X_9(Y))) & (~p102(tptp_fun_X_9(Y))) & p101(tptp_fun_X_9(Y)))))) & (~((~r1(Y, tptp_fun_X_10(Y))) | (~(p2(tptp_fun_X_10(Y)) & (~p102(tptp_fun_X_10(Y))) & p101(tptp_fun_X_10(Y)))))))) & ((~p105(Y)) | ((p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X)))) & ((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X)))))) & ((~p104(Y)) | ((p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X)))) & ((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X)))))) & ((~p103(Y)) | ((p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X)))) & ((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X)))))) & ((~p102(Y)) | ((p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X)))) & ((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X)))))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p105(Y) | (~p106(Y))) & (p104(Y) | (~p105(Y))) & (p103(Y) | (~p104(Y))) & (p102(Y) | (~p103(Y))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y)))))),
% 0.18/0.44 inference(and_elim,[status(thm)],[33])).
% 0.18/0.44 tff(35,plain,
% 0.18/0.44 (![Y: $i] : ((~r1(X!0, Y)) | (~((~(p105(Y) | (~p104(Y)) | (~(p106(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | (~r1(Y, tptp_fun_X_1(Y))) | p6(tptp_fun_X_1(Y)) | p106(tptp_fun_X_1(Y)) | (~p105(tptp_fun_X_1(Y))) | (~p6(tptp_fun_X_2(Y))) | (~p105(tptp_fun_X_2(Y))))))) | (~(p104(Y) | (~p103(Y)) | (~(p105(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p5(tptp_fun_X_3(Y)) | p105(tptp_fun_X_4(Y)) | (~p104(tptp_fun_X_3(Y))) | (~p5(tptp_fun_X_4(Y))) | (~p104(tptp_fun_X_4(Y))))))) | (~(p103(Y) | (~p102(Y)) | (~(p4(tptp_fun_X_5(Y)) | p104(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))) | p104(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_5(Y))) | (~p4(tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_6(Y))))))) | (~(p102(Y) | (~p101(Y)) | (~(p103(tptp_fun_X_8(Y)) | p103(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)) | (~p102(tptp_fun_X_7(Y))) | (~p3(tptp_fun_X_8(Y))) | (~p102(tptp_fun_X_8(Y))))))) | (~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p2(tptp_fun_X_9(Y)) | p102(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_10(Y))) | p102(tptp_fun_X_10(Y)) | (~p101(tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_10(Y))) | (~p101(tptp_fun_X_10(Y))))))) | (~((~p105(Y)) | (~((~(p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X))))) | (~((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X))))))))) | (~((~p104(Y)) | (~((~(p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X))))) | (~((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X))))))))) | (~((~p103(Y)) | (~((~(p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X))))) | (~((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X))))))))) | (~((~p102(Y)) | (~((~(p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X))))) | (~((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X))))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))) | (~(p105(Y) | (~p106(Y)))) | (~(p104(Y) | (~p105(Y)))) | (~(p103(Y) | (~p104(Y)))) | (~(p102(Y) | (~p103(Y)))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y)))))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[34, 20])).
% 0.18/0.44 tff(36,plain,
% 0.18/0.44 (![Y: $i] : ((~r1(X!0, Y)) | (~((~(p105(Y) | (~p104(Y)) | (~(p106(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | (~r1(Y, tptp_fun_X_1(Y))) | p6(tptp_fun_X_1(Y)) | p106(tptp_fun_X_1(Y)) | (~p105(tptp_fun_X_1(Y))) | (~p6(tptp_fun_X_2(Y))) | (~p105(tptp_fun_X_2(Y))))))) | (~(p104(Y) | (~p103(Y)) | (~(p105(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p5(tptp_fun_X_3(Y)) | p105(tptp_fun_X_4(Y)) | (~p104(tptp_fun_X_3(Y))) | (~p5(tptp_fun_X_4(Y))) | (~p104(tptp_fun_X_4(Y))))))) | (~(p103(Y) | (~p102(Y)) | (~(p4(tptp_fun_X_5(Y)) | p104(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))) | p104(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_5(Y))) | (~p4(tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_6(Y))))))) | (~(p102(Y) | (~p101(Y)) | (~(p103(tptp_fun_X_8(Y)) | p103(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)) | (~p102(tptp_fun_X_7(Y))) | (~p3(tptp_fun_X_8(Y))) | (~p102(tptp_fun_X_8(Y))))))) | (~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p2(tptp_fun_X_9(Y)) | p102(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_10(Y))) | p102(tptp_fun_X_10(Y)) | (~p101(tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_10(Y))) | (~p101(tptp_fun_X_10(Y))))))) | (~((~p105(Y)) | (~((~(p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X))))) | (~((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X))))))))) | (~((~p104(Y)) | (~((~(p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X))))) | (~((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X))))))))) | (~((~p103(Y)) | (~((~(p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X))))) | (~((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X))))))))) | (~((~p102(Y)) | (~((~(p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X))))) | (~((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X))))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))) | (~(p105(Y) | (~p106(Y)))) | (~(p104(Y) | (~p105(Y)))) | (~(p103(Y) | (~p104(Y)))) | (~(p102(Y) | (~p103(Y)))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y)))))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[35, 18])).
% 0.18/0.44 tff(37,plain,
% 0.18/0.44 (![Y: $i] : ((~r1(X!0, Y)) | (~((~(p105(Y) | (~p104(Y)) | (~(p106(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | (~r1(Y, tptp_fun_X_1(Y))) | p6(tptp_fun_X_1(Y)) | p106(tptp_fun_X_1(Y)) | (~p105(tptp_fun_X_1(Y))) | (~p6(tptp_fun_X_2(Y))) | (~p105(tptp_fun_X_2(Y))))))) | (~(p104(Y) | (~p103(Y)) | (~(p105(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p5(tptp_fun_X_3(Y)) | p105(tptp_fun_X_4(Y)) | (~p104(tptp_fun_X_3(Y))) | (~p5(tptp_fun_X_4(Y))) | (~p104(tptp_fun_X_4(Y))))))) | (~(p103(Y) | (~p102(Y)) | (~(p4(tptp_fun_X_5(Y)) | p104(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))) | p104(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_5(Y))) | (~p4(tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_6(Y))))))) | (~(p102(Y) | (~p101(Y)) | (~(p103(tptp_fun_X_8(Y)) | p103(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)) | (~p102(tptp_fun_X_7(Y))) | (~p3(tptp_fun_X_8(Y))) | (~p102(tptp_fun_X_8(Y))))))) | (~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p2(tptp_fun_X_9(Y)) | p102(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_10(Y))) | p102(tptp_fun_X_10(Y)) | (~p101(tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_10(Y))) | (~p101(tptp_fun_X_10(Y))))))) | (~(p105(Y) | (~p106(Y)))) | (~(p104(Y) | (~p105(Y)))) | (~(p103(Y) | (~p104(Y)))) | (~(p102(Y) | (~p103(Y)))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y)))) | (~((~p105(Y)) | (~((~(p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X))))) | (~((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X))))))))) | (~((~p104(Y)) | (~((~(p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X))))) | (~((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X))))))))) | (~((~p103(Y)) | (~((~(p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X))))) | (~((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X))))))))) | (~((~p102(Y)) | (~((~(p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X))))) | (~((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X))))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[36, 13])).
% 0.18/0.44 tff(38,plain,
% 0.18/0.44 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~(p105(Y) | (~p104(Y)) | (~(p106(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | (~r1(Y, tptp_fun_X_1(Y))) | p6(tptp_fun_X_1(Y)) | p106(tptp_fun_X_1(Y)) | (~p105(tptp_fun_X_1(Y))) | (~p6(tptp_fun_X_2(Y))) | (~p105(tptp_fun_X_2(Y))))))) | (~(p104(Y) | (~p103(Y)) | (~(p105(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p5(tptp_fun_X_3(Y)) | p105(tptp_fun_X_4(Y)) | (~p104(tptp_fun_X_3(Y))) | (~p5(tptp_fun_X_4(Y))) | (~p104(tptp_fun_X_4(Y))))))) | (~(p103(Y) | (~p102(Y)) | (~(p4(tptp_fun_X_5(Y)) | p104(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))) | p104(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_5(Y))) | (~p4(tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_6(Y))))))) | (~(p102(Y) | (~p101(Y)) | (~(p103(tptp_fun_X_8(Y)) | p103(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)) | (~p102(tptp_fun_X_7(Y))) | (~p3(tptp_fun_X_8(Y))) | (~p102(tptp_fun_X_8(Y))))))) | 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X))))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))))))) | ((~r1(X!0, X!0)) | (~((~(p105(X!0) | (~p106(X!0)))) | (~(p102(X!0) | (~p101(X!0)) | (~(p103(tptp_fun_X_8(X!0)) | p103(tptp_fun_X_7(X!0)) | (~r1(X!0, tptp_fun_X_8(X!0))) | (~r1(X!0, tptp_fun_X_7(X!0))) | p3(tptp_fun_X_7(X!0)) | (~p102(tptp_fun_X_7(X!0))) | (~p3(tptp_fun_X_8(X!0))) | (~p102(tptp_fun_X_8(X!0))))))) | (~(p105(X!0) | (~p104(X!0)) | (~(p106(tptp_fun_X_2(X!0)) | (~r1(X!0, tptp_fun_X_2(X!0))) | (~r1(X!0, tptp_fun_X_1(X!0))) | p6(tptp_fun_X_1(X!0)) | p106(tptp_fun_X_1(X!0)) | (~p105(tptp_fun_X_1(X!0))) | (~p6(tptp_fun_X_2(X!0))) | (~p105(tptp_fun_X_2(X!0))))))) | (~(p104(X!0) | (~p105(X!0)))) | (~(p103(X!0) | (~p104(X!0)))) | (~(p102(X!0) | (~p103(X!0)))) | (~(p101(X!0) | (~p102(X!0)))) | (~(p100(X!0) | (~p101(X!0)))) | (~((~p105(X!0)) | (~((~(p6(X!0) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(X!0, X))))) | (~((~p6(X!0)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(X!0, X))))))))) | (~((~p104(X!0)) | (~((~(p5(X!0) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(X!0, X))))) | (~((~p5(X!0)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(X!0, X))))))))) | (~((~p103(X!0)) | (~((~(p4(X!0) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(X!0, X))))) | (~((~p4(X!0)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(X!0, X))))))))) | (~((~p102(X!0)) | (~((~(p3(X!0) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(X!0, X))))) | (~((~p3(X!0)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(X!0, X))))))))) | (~((~p101(X!0)) | (~((~(p2(X!0) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(X!0, X))))) | (~((~p2(X!0)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(X!0, X))))))))) | (~(p104(X!0) | (~p103(X!0)) | (~((~p104(tptp_fun_X_4(X!0))) | p105(tptp_fun_X_4(X!0)) | (~p104(tptp_fun_X_3(X!0))) | (~p5(tptp_fun_X_4(X!0))) | p105(tptp_fun_X_3(X!0)) | p5(tptp_fun_X_3(X!0)) | (~r1(X!0, tptp_fun_X_4(X!0))) | (~r1(X!0, tptp_fun_X_3(X!0))))))) | (~(p103(X!0) | (~p102(X!0)) | (~((~p4(tptp_fun_X_6(X!0))) | (~p103(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_5(X!0))) | p4(tptp_fun_X_5(X!0)) | p104(tptp_fun_X_5(X!0)) | (~p103(tptp_fun_X_5(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0))) | p104(tptp_fun_X_6(X!0)))))) | (~(p101(X!0) | (~p100(X!0)) | (~((~p101(tptp_fun_X_9(X!0))) | (~p2(tptp_fun_X_10(X!0))) | (~p101(tptp_fun_X_10(X!0))) | p102(tptp_fun_X_10(X!0)) | p2(tptp_fun_X_9(X!0)) | p102(tptp_fun_X_9(X!0)) | (~r1(X!0, tptp_fun_X_10(X!0))) | (~r1(X!0, tptp_fun_X_9(X!0))))))) | (~((~p100(X!0)) | (~((~(p1(X!0) | ![X: $i] : ((~r1(X!0, X)) | (~p100(X)) | (~p1(X))))) | (~((~p1(X!0)) | ![X: $i] : ((~r1(X!0, X)) | (~p100(X)) | p1(X)))))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~(p105(Y) | (~p104(Y)) | (~(p106(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | (~r1(Y, tptp_fun_X_1(Y))) | p6(tptp_fun_X_1(Y)) | p106(tptp_fun_X_1(Y)) | (~p105(tptp_fun_X_1(Y))) | (~p6(tptp_fun_X_2(Y))) | (~p105(tptp_fun_X_2(Y))))))) | (~(p104(Y) | (~p103(Y)) | (~(p105(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p5(tptp_fun_X_3(Y)) | p105(tptp_fun_X_4(Y)) | (~p104(tptp_fun_X_3(Y))) | (~p5(tptp_fun_X_4(Y))) | (~p104(tptp_fun_X_4(Y))))))) | (~(p103(Y) | (~p102(Y)) | (~(p4(tptp_fun_X_5(Y)) | p104(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))) | p104(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_5(Y))) | (~p4(tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_6(Y))))))) | (~(p102(Y) | (~p101(Y)) | (~(p103(tptp_fun_X_8(Y)) | p103(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)) | (~p102(tptp_fun_X_7(Y))) | (~p3(tptp_fun_X_8(Y))) | (~p102(tptp_fun_X_8(Y))))))) | (~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p2(tptp_fun_X_9(Y)) | p102(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_10(Y))) | p102(tptp_fun_X_10(Y)) | (~p101(tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_10(Y))) | (~p101(tptp_fun_X_10(Y))))))) | (~(p105(Y) | (~p106(Y)))) | (~(p104(Y) | (~p105(Y)))) | (~(p103(Y) | (~p104(Y)))) | (~(p102(Y) | (~p103(Y)))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y)))) | (~((~p105(Y)) | (~((~(p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X))))) | (~((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X))))))))) | (~((~p104(Y)) | (~((~(p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X))))) | (~((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X))))))))) | (~((~p103(Y)) | (~((~(p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X))))) | (~((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X))))))))) | (~((~p102(Y)) | (~((~(p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X))))) | (~((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X))))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))))))) | (~r1(X!0, X!0)) | (~((~(p105(X!0) | (~p106(X!0)))) | (~(p102(X!0) | (~p101(X!0)) | (~(p103(tptp_fun_X_8(X!0)) | p103(tptp_fun_X_7(X!0)) | (~r1(X!0, tptp_fun_X_8(X!0))) | (~r1(X!0, tptp_fun_X_7(X!0))) | p3(tptp_fun_X_7(X!0)) | (~p102(tptp_fun_X_7(X!0))) | (~p3(tptp_fun_X_8(X!0))) | (~p102(tptp_fun_X_8(X!0))))))) | (~(p105(X!0) | (~p104(X!0)) | (~(p106(tptp_fun_X_2(X!0)) | (~r1(X!0, tptp_fun_X_2(X!0))) | (~r1(X!0, tptp_fun_X_1(X!0))) | p6(tptp_fun_X_1(X!0)) | p106(tptp_fun_X_1(X!0)) | (~p105(tptp_fun_X_1(X!0))) | (~p6(tptp_fun_X_2(X!0))) | (~p105(tptp_fun_X_2(X!0))))))) | (~(p104(X!0) | (~p105(X!0)))) | (~(p103(X!0) | (~p104(X!0)))) | (~(p102(X!0) | (~p103(X!0)))) | (~(p101(X!0) | (~p102(X!0)))) | (~(p100(X!0) | (~p101(X!0)))) | (~((~p105(X!0)) | (~((~(p6(X!0) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(X!0, X))))) | (~((~p6(X!0)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(X!0, X))))))))) | (~((~p104(X!0)) | (~((~(p5(X!0) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(X!0, X))))) | (~((~p5(X!0)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(X!0, X))))))))) | (~((~p103(X!0)) | (~((~(p4(X!0) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(X!0, X))))) | (~((~p4(X!0)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(X!0, X))))))))) | (~((~p102(X!0)) | (~((~(p3(X!0) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(X!0, X))))) | (~((~p3(X!0)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(X!0, X))))))))) | (~((~p101(X!0)) | (~((~(p2(X!0) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(X!0, X))))) | (~((~p2(X!0)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(X!0, X))))))))) | (~(p104(X!0) | (~p103(X!0)) | (~((~p104(tptp_fun_X_4(X!0))) | p105(tptp_fun_X_4(X!0)) | (~p104(tptp_fun_X_3(X!0))) | (~p5(tptp_fun_X_4(X!0))) | p105(tptp_fun_X_3(X!0)) | p5(tptp_fun_X_3(X!0)) | (~r1(X!0, tptp_fun_X_4(X!0))) | (~r1(X!0, tptp_fun_X_3(X!0))))))) | (~(p103(X!0) | (~p102(X!0)) | (~((~p4(tptp_fun_X_6(X!0))) | (~p103(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_5(X!0))) | p4(tptp_fun_X_5(X!0)) | p104(tptp_fun_X_5(X!0)) | (~p103(tptp_fun_X_5(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0))) | p104(tptp_fun_X_6(X!0)))))) | (~(p101(X!0) | (~p100(X!0)) | (~((~p101(tptp_fun_X_9(X!0))) | (~p2(tptp_fun_X_10(X!0))) | (~p101(tptp_fun_X_10(X!0))) | p102(tptp_fun_X_10(X!0)) | p2(tptp_fun_X_9(X!0)) | p102(tptp_fun_X_9(X!0)) | (~r1(X!0, tptp_fun_X_10(X!0))) | (~r1(X!0, tptp_fun_X_9(X!0))))))) | (~((~p100(X!0)) | (~((~(p1(X!0) | ![X: $i] : ((~r1(X!0, X)) | (~p100(X)) | (~p1(X))))) | (~((~p1(X!0)) | ![X: $i] : ((~r1(X!0, X)) | (~p100(X)) | p1(X)))))))))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(39,plain,
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(~p102(tptp_fun_X_7(X!0))) | (~p3(tptp_fun_X_8(X!0))) | (~p102(tptp_fun_X_8(X!0))))))) | (~(p101(X!0) | (~p100(X!0)) | (~((~r1(X!0, tptp_fun_X_9(X!0))) | p2(tptp_fun_X_9(X!0)) | p102(tptp_fun_X_9(X!0)) | (~r1(X!0, tptp_fun_X_10(X!0))) | p102(tptp_fun_X_10(X!0)) | (~p101(tptp_fun_X_9(X!0))) | (~p2(tptp_fun_X_10(X!0))) | (~p101(tptp_fun_X_10(X!0))))))) | (~(p105(X!0) | (~p106(X!0)))) | (~(p104(X!0) | (~p105(X!0)))) | (~(p103(X!0) | (~p104(X!0)))) | (~(p102(X!0) | (~p103(X!0)))) | (~(p101(X!0) | (~p102(X!0)))) | (~(p100(X!0) | (~p101(X!0)))) | (~((~p105(X!0)) | (~((~(p6(X!0) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(X!0, X))))) | (~((~p6(X!0)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(X!0, X))))))))) | (~((~p104(X!0)) | (~((~(p5(X!0) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(X!0, X))))) | (~((~p5(X!0)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(X!0, X))))))))) | (~((~p103(X!0)) | (~((~(p4(X!0) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(X!0, X))))) | (~((~p4(X!0)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(X!0, X))))))))) | (~((~p102(X!0)) | (~((~(p3(X!0) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(X!0, X))))) | (~((~p3(X!0)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(X!0, X))))))))) | (~((~p101(X!0)) | (~((~(p2(X!0) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(X!0, X))))) | (~((~p2(X!0)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(X!0, X))))))))) | (~((~p100(X!0)) | (~((~(p1(X!0) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(X!0, X))))) | (~((~p1(X!0)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(X!0, X)))))))))))) <=> ((~r1(X!0, X!0)) | (~((~(p105(X!0) | (~p106(X!0)))) | (~(p102(X!0) | (~p101(X!0)) | (~(p103(tptp_fun_X_8(X!0)) | p103(tptp_fun_X_7(X!0)) | (~r1(X!0, tptp_fun_X_8(X!0))) | (~r1(X!0, tptp_fun_X_7(X!0))) | p3(tptp_fun_X_7(X!0)) | (~p102(tptp_fun_X_7(X!0))) | (~p3(tptp_fun_X_8(X!0))) | (~p102(tptp_fun_X_8(X!0))))))) | (~(p105(X!0) | (~p104(X!0)) | (~(p106(tptp_fun_X_2(X!0)) | (~r1(X!0, tptp_fun_X_2(X!0))) | (~r1(X!0, tptp_fun_X_1(X!0))) | p6(tptp_fun_X_1(X!0)) | p106(tptp_fun_X_1(X!0)) | (~p105(tptp_fun_X_1(X!0))) | (~p6(tptp_fun_X_2(X!0))) | (~p105(tptp_fun_X_2(X!0))))))) | (~(p104(X!0) | (~p105(X!0)))) | (~(p103(X!0) | (~p104(X!0)))) | (~(p102(X!0) | (~p103(X!0)))) | (~(p101(X!0) | (~p102(X!0)))) | (~(p100(X!0) | (~p101(X!0)))) | (~((~p105(X!0)) | (~((~(p6(X!0) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(X!0, X))))) | (~((~p6(X!0)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(X!0, X))))))))) | (~((~p104(X!0)) | (~((~(p5(X!0) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(X!0, X))))) | (~((~p5(X!0)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(X!0, X))))))))) | (~((~p103(X!0)) | (~((~(p4(X!0) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(X!0, X))))) | (~((~p4(X!0)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(X!0, X))))))))) | (~((~p102(X!0)) | (~((~(p3(X!0) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(X!0, X))))) | (~((~p3(X!0)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(X!0, X))))))))) | (~((~p101(X!0)) | (~((~(p2(X!0) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(X!0, X))))) | (~((~p2(X!0)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(X!0, X))))))))) | (~(p104(X!0) | (~p103(X!0)) | (~((~p104(tptp_fun_X_4(X!0))) | p105(tptp_fun_X_4(X!0)) | (~p104(tptp_fun_X_3(X!0))) | (~p5(tptp_fun_X_4(X!0))) | p105(tptp_fun_X_3(X!0)) | p5(tptp_fun_X_3(X!0)) | (~r1(X!0, tptp_fun_X_4(X!0))) | (~r1(X!0, tptp_fun_X_3(X!0))))))) | (~(p103(X!0) | (~p102(X!0)) | (~((~p4(tptp_fun_X_6(X!0))) | (~p103(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_5(X!0))) | p4(tptp_fun_X_5(X!0)) | p104(tptp_fun_X_5(X!0)) | (~p103(tptp_fun_X_5(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0))) | p104(tptp_fun_X_6(X!0)))))) | (~(p101(X!0) | (~p100(X!0)) | (~((~p101(tptp_fun_X_9(X!0))) | (~p2(tptp_fun_X_10(X!0))) | (~p101(tptp_fun_X_10(X!0))) | p102(tptp_fun_X_10(X!0)) | p2(tptp_fun_X_9(X!0)) | p102(tptp_fun_X_9(X!0)) | (~r1(X!0, tptp_fun_X_10(X!0))) | (~r1(X!0, tptp_fun_X_9(X!0))))))) | (~((~p100(X!0)) | (~((~(p1(X!0) | ![X: $i] : ((~r1(X!0, X)) | (~p100(X)) | (~p1(X))))) | (~((~p1(X!0)) | ![X: $i] : ((~r1(X!0, X)) | (~p100(X)) | p1(X)))))))))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(40,plain,
% 0.18/0.45 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~(p105(Y) | (~p104(Y)) | (~(p106(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | (~r1(Y, tptp_fun_X_1(Y))) | p6(tptp_fun_X_1(Y)) | p106(tptp_fun_X_1(Y)) | (~p105(tptp_fun_X_1(Y))) | (~p6(tptp_fun_X_2(Y))) | (~p105(tptp_fun_X_2(Y))))))) | (~(p104(Y) | (~p103(Y)) | (~(p105(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p5(tptp_fun_X_3(Y)) | p105(tptp_fun_X_4(Y)) | (~p104(tptp_fun_X_3(Y))) | (~p5(tptp_fun_X_4(Y))) | (~p104(tptp_fun_X_4(Y))))))) | (~(p103(Y) | (~p102(Y)) | (~(p4(tptp_fun_X_5(Y)) | p104(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))) | p104(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_5(Y))) | (~p4(tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_6(Y))))))) | (~(p102(Y) | (~p101(Y)) | (~(p103(tptp_fun_X_8(Y)) | p103(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)) | (~p102(tptp_fun_X_7(Y))) | (~p3(tptp_fun_X_8(Y))) | (~p102(tptp_fun_X_8(Y))))))) | (~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p2(tptp_fun_X_9(Y)) | p102(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_10(Y))) | p102(tptp_fun_X_10(Y)) | (~p101(tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_10(Y))) | (~p101(tptp_fun_X_10(Y))))))) | (~(p105(Y) | (~p106(Y)))) | (~(p104(Y) | (~p105(Y)))) | (~(p103(Y) | (~p104(Y)))) | (~(p102(Y) | (~p103(Y)))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y)))) | (~((~p105(Y)) | (~((~(p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X))))) | (~((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X))))))))) | (~((~p104(Y)) | (~((~(p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X))))) | (~((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X))))))))) | (~((~p103(Y)) | (~((~(p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X))))) | (~((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X))))))))) | (~((~p102(Y)) | (~((~(p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X))))) | (~((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X))))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))))))) | ((~r1(X!0, X!0)) | (~((~(p105(X!0) | (~p104(X!0)) | (~(p106(tptp_fun_X_2(X!0)) | (~r1(X!0, tptp_fun_X_2(X!0))) | (~r1(X!0, tptp_fun_X_1(X!0))) | p6(tptp_fun_X_1(X!0)) | p106(tptp_fun_X_1(X!0)) | (~p105(tptp_fun_X_1(X!0))) | (~p6(tptp_fun_X_2(X!0))) | (~p105(tptp_fun_X_2(X!0))))))) | (~(p104(X!0) | (~p103(X!0)) | (~(p105(tptp_fun_X_3(X!0)) | (~r1(X!0, tptp_fun_X_4(X!0))) | (~r1(X!0, tptp_fun_X_3(X!0))) | p5(tptp_fun_X_3(X!0)) | p105(tptp_fun_X_4(X!0)) | (~p104(tptp_fun_X_3(X!0))) | (~p5(tptp_fun_X_4(X!0))) | (~p104(tptp_fun_X_4(X!0))))))) | (~(p103(X!0) | (~p102(X!0)) | (~(p4(tptp_fun_X_5(X!0)) | p104(tptp_fun_X_5(X!0)) | (~r1(X!0, tptp_fun_X_5(X!0))) | p104(tptp_fun_X_6(X!0)) | (~r1(X!0, tptp_fun_X_6(X!0))) | (~p103(tptp_fun_X_5(X!0))) | (~p4(tptp_fun_X_6(X!0))) | (~p103(tptp_fun_X_6(X!0))))))) | (~(p102(X!0) | (~p101(X!0)) | (~(p103(tptp_fun_X_8(X!0)) | p103(tptp_fun_X_7(X!0)) | (~r1(X!0, tptp_fun_X_8(X!0))) | (~r1(X!0, tptp_fun_X_7(X!0))) | p3(tptp_fun_X_7(X!0)) | (~p102(tptp_fun_X_7(X!0))) | (~p3(tptp_fun_X_8(X!0))) | (~p102(tptp_fun_X_8(X!0))))))) | (~(p101(X!0) | (~p100(X!0)) | (~((~r1(X!0, tptp_fun_X_9(X!0))) | p2(tptp_fun_X_9(X!0)) | p102(tptp_fun_X_9(X!0)) | (~r1(X!0, tptp_fun_X_10(X!0))) | p102(tptp_fun_X_10(X!0)) | (~p101(tptp_fun_X_9(X!0))) | (~p2(tptp_fun_X_10(X!0))) | (~p101(tptp_fun_X_10(X!0))))))) | (~(p105(X!0) | (~p106(X!0)))) | (~(p104(X!0) | (~p105(X!0)))) | (~(p103(X!0) | (~p104(X!0)))) | (~(p102(X!0) | (~p103(X!0)))) | (~(p101(X!0) | (~p102(X!0)))) | (~(p100(X!0) | (~p101(X!0)))) | (~((~p105(X!0)) | (~((~(p6(X!0) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(X!0, X))))) | (~((~p6(X!0)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(X!0, X))))))))) | (~((~p104(X!0)) | (~((~(p5(X!0) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(X!0, X))))) | (~((~p5(X!0)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(X!0, X))))))))) | (~((~p103(X!0)) | (~((~(p4(X!0) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(X!0, X))))) | (~((~p4(X!0)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(X!0, X))))))))) | (~((~p102(X!0)) | (~((~(p3(X!0) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(X!0, X))))) | (~((~p3(X!0)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(X!0, X))))))))) | (~((~p101(X!0)) | (~((~(p2(X!0) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(X!0, X))))) | (~((~p2(X!0)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(X!0, X))))))))) | (~((~p100(X!0)) | (~((~(p1(X!0) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(X!0, X))))) | (~((~p1(X!0)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(X!0, X))))))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~(p105(Y) | (~p104(Y)) | (~(p106(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | (~r1(Y, tptp_fun_X_1(Y))) | p6(tptp_fun_X_1(Y)) | p106(tptp_fun_X_1(Y)) | (~p105(tptp_fun_X_1(Y))) | (~p6(tptp_fun_X_2(Y))) | (~p105(tptp_fun_X_2(Y))))))) | (~(p104(Y) | (~p103(Y)) | (~(p105(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p5(tptp_fun_X_3(Y)) | p105(tptp_fun_X_4(Y)) | (~p104(tptp_fun_X_3(Y))) | (~p5(tptp_fun_X_4(Y))) | (~p104(tptp_fun_X_4(Y))))))) | (~(p103(Y) | (~p102(Y)) | (~(p4(tptp_fun_X_5(Y)) | p104(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))) | p104(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_5(Y))) | (~p4(tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_6(Y))))))) | (~(p102(Y) | (~p101(Y)) | (~(p103(tptp_fun_X_8(Y)) | p103(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)) | (~p102(tptp_fun_X_7(Y))) | (~p3(tptp_fun_X_8(Y))) | (~p102(tptp_fun_X_8(Y))))))) | (~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p2(tptp_fun_X_9(Y)) | p102(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_10(Y))) | p102(tptp_fun_X_10(Y)) | (~p101(tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_10(Y))) | (~p101(tptp_fun_X_10(Y))))))) | (~(p105(Y) | (~p106(Y)))) | (~(p104(Y) | (~p105(Y)))) | (~(p103(Y) | (~p104(Y)))) | (~(p102(Y) | (~p103(Y)))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y)))) | (~((~p105(Y)) | (~((~(p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X))))) | (~((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X))))))))) | (~((~p104(Y)) | (~((~(p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X))))) | (~((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X))))))))) | (~((~p103(Y)) | (~((~(p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X))))) | (~((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X))))))))) | (~((~p102(Y)) | (~((~(p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X))))) | (~((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X))))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))))))) | ((~r1(X!0, X!0)) | (~((~(p105(X!0) | (~p106(X!0)))) | (~(p102(X!0) | (~p101(X!0)) | (~(p103(tptp_fun_X_8(X!0)) | p103(tptp_fun_X_7(X!0)) | (~r1(X!0, tptp_fun_X_8(X!0))) | (~r1(X!0, tptp_fun_X_7(X!0))) | p3(tptp_fun_X_7(X!0)) | (~p102(tptp_fun_X_7(X!0))) | (~p3(tptp_fun_X_8(X!0))) | (~p102(tptp_fun_X_8(X!0))))))) | (~(p105(X!0) | (~p104(X!0)) | (~(p106(tptp_fun_X_2(X!0)) | (~r1(X!0, tptp_fun_X_2(X!0))) | (~r1(X!0, tptp_fun_X_1(X!0))) | p6(tptp_fun_X_1(X!0)) | p106(tptp_fun_X_1(X!0)) | (~p105(tptp_fun_X_1(X!0))) | (~p6(tptp_fun_X_2(X!0))) | (~p105(tptp_fun_X_2(X!0))))))) | (~(p104(X!0) | (~p105(X!0)))) | (~(p103(X!0) | (~p104(X!0)))) | (~(p102(X!0) | (~p103(X!0)))) | (~(p101(X!0) | (~p102(X!0)))) | (~(p100(X!0) | (~p101(X!0)))) | (~((~p105(X!0)) | (~((~(p6(X!0) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(X!0, X))))) | (~((~p6(X!0)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(X!0, X))))))))) | (~((~p104(X!0)) | (~((~(p5(X!0) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(X!0, X))))) | (~((~p5(X!0)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(X!0, X))))))))) | (~((~p103(X!0)) | (~((~(p4(X!0) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(X!0, X))))) | (~((~p4(X!0)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(X!0, X))))))))) | (~((~p102(X!0)) | (~((~(p3(X!0) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(X!0, X))))) | (~((~p3(X!0)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(X!0, X))))))))) | (~((~p101(X!0)) | (~((~(p2(X!0) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(X!0, X))))) | (~((~p2(X!0)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(X!0, X))))))))) | (~(p104(X!0) | (~p103(X!0)) | (~((~p104(tptp_fun_X_4(X!0))) | p105(tptp_fun_X_4(X!0)) | (~p104(tptp_fun_X_3(X!0))) | (~p5(tptp_fun_X_4(X!0))) | p105(tptp_fun_X_3(X!0)) | p5(tptp_fun_X_3(X!0)) | (~r1(X!0, tptp_fun_X_4(X!0))) | (~r1(X!0, tptp_fun_X_3(X!0))))))) | (~(p103(X!0) | (~p102(X!0)) | (~((~p4(tptp_fun_X_6(X!0))) | (~p103(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_5(X!0))) | p4(tptp_fun_X_5(X!0)) | p104(tptp_fun_X_5(X!0)) | (~p103(tptp_fun_X_5(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0))) | p104(tptp_fun_X_6(X!0)))))) | (~(p101(X!0) | (~p100(X!0)) | (~((~p101(tptp_fun_X_9(X!0))) | (~p2(tptp_fun_X_10(X!0))) | (~p101(tptp_fun_X_10(X!0))) | p102(tptp_fun_X_10(X!0)) | p2(tptp_fun_X_9(X!0)) | p102(tptp_fun_X_9(X!0)) | (~r1(X!0, tptp_fun_X_10(X!0))) | (~r1(X!0, tptp_fun_X_9(X!0))))))) | (~((~p100(X!0)) | (~((~(p1(X!0) | ![X: $i] : ((~r1(X!0, X)) | (~p100(X)) | (~p1(X))))) | (~((~p1(X!0)) | ![X: $i] : ((~r1(X!0, X)) | (~p100(X)) | p1(X))))))))))))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[39])).
% 0.18/0.46 tff(41,plain,
% 0.18/0.46 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~(p105(Y) | (~p104(Y)) | (~(p106(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | (~r1(Y, tptp_fun_X_1(Y))) | p6(tptp_fun_X_1(Y)) | p106(tptp_fun_X_1(Y)) | (~p105(tptp_fun_X_1(Y))) | (~p6(tptp_fun_X_2(Y))) | (~p105(tptp_fun_X_2(Y))))))) | (~(p104(Y) | (~p103(Y)) | (~(p105(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p5(tptp_fun_X_3(Y)) | p105(tptp_fun_X_4(Y)) | (~p104(tptp_fun_X_3(Y))) | (~p5(tptp_fun_X_4(Y))) | (~p104(tptp_fun_X_4(Y))))))) | (~(p103(Y) | (~p102(Y)) | (~(p4(tptp_fun_X_5(Y)) | p104(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))) | p104(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_5(Y))) | (~p4(tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_6(Y))))))) | (~(p102(Y) | (~p101(Y)) | (~(p103(tptp_fun_X_8(Y)) | p103(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)) | (~p102(tptp_fun_X_7(Y))) | (~p3(tptp_fun_X_8(Y))) | (~p102(tptp_fun_X_8(Y))))))) | (~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p2(tptp_fun_X_9(Y)) | p102(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_10(Y))) | p102(tptp_fun_X_10(Y)) | (~p101(tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_10(Y))) | (~p101(tptp_fun_X_10(Y))))))) | (~(p105(Y) | (~p106(Y)))) | (~(p104(Y) | (~p105(Y)))) | (~(p103(Y) | (~p104(Y)))) | (~(p102(Y) | (~p103(Y)))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y)))) | (~((~p105(Y)) | (~((~(p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X))))) | (~((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X))))))))) | (~((~p104(Y)) | (~((~(p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X))))) | (~((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X))))))))) | (~((~p103(Y)) | (~((~(p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X))))) | (~((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X))))))))) | (~((~p102(Y)) | (~((~(p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X))))) | (~((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X))))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))))))) | ((~r1(X!0, X!0)) | (~((~(p105(X!0) | (~p104(X!0)) | (~(p106(tptp_fun_X_2(X!0)) | (~r1(X!0, tptp_fun_X_2(X!0))) | (~r1(X!0, tptp_fun_X_1(X!0))) | p6(tptp_fun_X_1(X!0)) | p106(tptp_fun_X_1(X!0)) | (~p105(tptp_fun_X_1(X!0))) | (~p6(tptp_fun_X_2(X!0))) | (~p105(tptp_fun_X_2(X!0))))))) | (~(p104(X!0) | (~p103(X!0)) | (~(p105(tptp_fun_X_3(X!0)) | (~r1(X!0, tptp_fun_X_4(X!0))) | (~r1(X!0, tptp_fun_X_3(X!0))) | p5(tptp_fun_X_3(X!0)) | p105(tptp_fun_X_4(X!0)) | (~p104(tptp_fun_X_3(X!0))) | (~p5(tptp_fun_X_4(X!0))) | (~p104(tptp_fun_X_4(X!0))))))) | (~(p103(X!0) | (~p102(X!0)) | (~(p4(tptp_fun_X_5(X!0)) | p104(tptp_fun_X_5(X!0)) | (~r1(X!0, tptp_fun_X_5(X!0))) | p104(tptp_fun_X_6(X!0)) | (~r1(X!0, tptp_fun_X_6(X!0))) | (~p103(tptp_fun_X_5(X!0))) | (~p4(tptp_fun_X_6(X!0))) | (~p103(tptp_fun_X_6(X!0))))))) | (~(p102(X!0) | (~p101(X!0)) | (~(p103(tptp_fun_X_8(X!0)) | p103(tptp_fun_X_7(X!0)) | (~r1(X!0, tptp_fun_X_8(X!0))) | (~r1(X!0, tptp_fun_X_7(X!0))) | p3(tptp_fun_X_7(X!0)) | (~p102(tptp_fun_X_7(X!0))) | (~p3(tptp_fun_X_8(X!0))) | (~p102(tptp_fun_X_8(X!0))))))) | (~(p101(X!0) | (~p100(X!0)) | (~((~r1(X!0, tptp_fun_X_9(X!0))) | p2(tptp_fun_X_9(X!0)) | p102(tptp_fun_X_9(X!0)) | (~r1(X!0, tptp_fun_X_10(X!0))) | p102(tptp_fun_X_10(X!0)) | (~p101(tptp_fun_X_9(X!0))) | (~p2(tptp_fun_X_10(X!0))) | (~p101(tptp_fun_X_10(X!0))))))) | (~(p105(X!0) | (~p106(X!0)))) | (~(p104(X!0) | (~p105(X!0)))) | (~(p103(X!0) | (~p104(X!0)))) | (~(p102(X!0) | (~p103(X!0)))) | (~(p101(X!0) | (~p102(X!0)))) | (~(p100(X!0) | (~p101(X!0)))) | (~((~p105(X!0)) | (~((~(p6(X!0) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(X!0, X))))) | (~((~p6(X!0)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(X!0, X))))))))) | (~((~p104(X!0)) | (~((~(p5(X!0) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(X!0, X))))) | (~((~p5(X!0)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(X!0, X))))))))) | (~((~p103(X!0)) | (~((~(p4(X!0) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(X!0, X))))) | (~((~p4(X!0)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(X!0, X))))))))) | (~((~p102(X!0)) | (~((~(p3(X!0) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(X!0, X))))) | (~((~p3(X!0)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(X!0, X))))))))) | (~((~p101(X!0)) | (~((~(p2(X!0) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(X!0, X))))) | (~((~p2(X!0)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(X!0, X))))))))) | (~((~p100(X!0)) | (~((~(p1(X!0) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(X!0, X))))) | (~((~p1(X!0)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(X!0, X))))))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~(p105(Y) | (~p104(Y)) | (~(p106(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | (~r1(Y, tptp_fun_X_1(Y))) | p6(tptp_fun_X_1(Y)) | p106(tptp_fun_X_1(Y)) | (~p105(tptp_fun_X_1(Y))) | (~p6(tptp_fun_X_2(Y))) | (~p105(tptp_fun_X_2(Y))))))) | (~(p104(Y) | (~p103(Y)) | (~(p105(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p5(tptp_fun_X_3(Y)) | p105(tptp_fun_X_4(Y)) | (~p104(tptp_fun_X_3(Y))) | (~p5(tptp_fun_X_4(Y))) | (~p104(tptp_fun_X_4(Y))))))) | (~(p103(Y) | (~p102(Y)) | (~(p4(tptp_fun_X_5(Y)) | p104(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))) | p104(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_5(Y))) | (~p4(tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_6(Y))))))) | (~(p102(Y) | (~p101(Y)) | (~(p103(tptp_fun_X_8(Y)) | p103(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)) | (~p102(tptp_fun_X_7(Y))) | (~p3(tptp_fun_X_8(Y))) | (~p102(tptp_fun_X_8(Y))))))) | (~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p2(tptp_fun_X_9(Y)) | p102(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_10(Y))) | p102(tptp_fun_X_10(Y)) | (~p101(tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_10(Y))) | (~p101(tptp_fun_X_10(Y))))))) | (~(p105(Y) | (~p106(Y)))) | (~(p104(Y) | (~p105(Y)))) | (~(p103(Y) | (~p104(Y)))) | (~(p102(Y) | (~p103(Y)))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y)))) | (~((~p105(Y)) | (~((~(p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X))))) | (~((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X))))))))) | (~((~p104(Y)) | (~((~(p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X))))) | (~((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X))))))))) | (~((~p103(Y)) | (~((~(p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X))))) | (~((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X))))))))) | (~((~p102(Y)) | (~((~(p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X))))) | (~((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X))))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))))))) | (~r1(X!0, X!0)) | (~((~(p105(X!0) | (~p106(X!0)))) | (~(p102(X!0) | (~p101(X!0)) | (~(p103(tptp_fun_X_8(X!0)) | p103(tptp_fun_X_7(X!0)) | (~r1(X!0, tptp_fun_X_8(X!0))) | (~r1(X!0, tptp_fun_X_7(X!0))) | p3(tptp_fun_X_7(X!0)) | (~p102(tptp_fun_X_7(X!0))) | (~p3(tptp_fun_X_8(X!0))) | (~p102(tptp_fun_X_8(X!0))))))) | (~(p105(X!0) | (~p104(X!0)) | (~(p106(tptp_fun_X_2(X!0)) | (~r1(X!0, tptp_fun_X_2(X!0))) | (~r1(X!0, tptp_fun_X_1(X!0))) | p6(tptp_fun_X_1(X!0)) | p106(tptp_fun_X_1(X!0)) | (~p105(tptp_fun_X_1(X!0))) | (~p6(tptp_fun_X_2(X!0))) | (~p105(tptp_fun_X_2(X!0))))))) | (~(p104(X!0) | (~p105(X!0)))) | (~(p103(X!0) | (~p104(X!0)))) | (~(p102(X!0) | (~p103(X!0)))) | (~(p101(X!0) | (~p102(X!0)))) | (~(p100(X!0) | (~p101(X!0)))) | (~((~p105(X!0)) | (~((~(p6(X!0) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(X!0, X))))) | (~((~p6(X!0)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(X!0, X))))))))) | (~((~p104(X!0)) | (~((~(p5(X!0) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(X!0, X))))) | (~((~p5(X!0)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(X!0, X))))))))) | (~((~p103(X!0)) | (~((~(p4(X!0) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(X!0, X))))) | (~((~p4(X!0)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(X!0, X))))))))) | (~((~p102(X!0)) | (~((~(p3(X!0) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(X!0, X))))) | (~((~p3(X!0)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(X!0, X))))))))) | (~((~p101(X!0)) | (~((~(p2(X!0) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(X!0, X))))) | (~((~p2(X!0)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(X!0, X))))))))) | (~(p104(X!0) | (~p103(X!0)) | (~((~p104(tptp_fun_X_4(X!0))) | p105(tptp_fun_X_4(X!0)) | (~p104(tptp_fun_X_3(X!0))) | (~p5(tptp_fun_X_4(X!0))) | p105(tptp_fun_X_3(X!0)) | p5(tptp_fun_X_3(X!0)) | (~r1(X!0, tptp_fun_X_4(X!0))) | (~r1(X!0, tptp_fun_X_3(X!0))))))) | (~(p103(X!0) | (~p102(X!0)) | (~((~p4(tptp_fun_X_6(X!0))) | (~p103(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_5(X!0))) | p4(tptp_fun_X_5(X!0)) | p104(tptp_fun_X_5(X!0)) | (~p103(tptp_fun_X_5(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0))) | p104(tptp_fun_X_6(X!0)))))) | (~(p101(X!0) | (~p100(X!0)) | (~((~p101(tptp_fun_X_9(X!0))) | (~p2(tptp_fun_X_10(X!0))) | (~p101(tptp_fun_X_10(X!0))) | p102(tptp_fun_X_10(X!0)) | p2(tptp_fun_X_9(X!0)) | p102(tptp_fun_X_9(X!0)) | (~r1(X!0, tptp_fun_X_10(X!0))) | (~r1(X!0, tptp_fun_X_9(X!0))))))) | (~((~p100(X!0)) | (~((~(p1(X!0) | ![X: $i] : ((~r1(X!0, X)) | (~p100(X)) | (~p1(X))))) | (~((~p1(X!0)) | ![X: $i] : ((~r1(X!0, X)) | (~p100(X)) | p1(X)))))))))))),
% 0.18/0.46 inference(transitivity,[status(thm)],[40, 38])).
% 0.18/0.46 tff(42,plain,
% 0.18/0.46 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~(p105(Y) | (~p104(Y)) | (~(p106(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | (~r1(Y, tptp_fun_X_1(Y))) | p6(tptp_fun_X_1(Y)) | p106(tptp_fun_X_1(Y)) | (~p105(tptp_fun_X_1(Y))) | (~p6(tptp_fun_X_2(Y))) | (~p105(tptp_fun_X_2(Y))))))) | (~(p104(Y) | (~p103(Y)) | (~(p105(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p5(tptp_fun_X_3(Y)) | p105(tptp_fun_X_4(Y)) | (~p104(tptp_fun_X_3(Y))) | (~p5(tptp_fun_X_4(Y))) | (~p104(tptp_fun_X_4(Y))))))) | (~(p103(Y) | (~p102(Y)) | (~(p4(tptp_fun_X_5(Y)) | p104(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))) | p104(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_5(Y))) | (~p4(tptp_fun_X_6(Y))) | (~p103(tptp_fun_X_6(Y))))))) | (~(p102(Y) | (~p101(Y)) | (~(p103(tptp_fun_X_8(Y)) | p103(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)) | (~p102(tptp_fun_X_7(Y))) | (~p3(tptp_fun_X_8(Y))) | (~p102(tptp_fun_X_8(Y))))))) | (~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p2(tptp_fun_X_9(Y)) | p102(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_10(Y))) | p102(tptp_fun_X_10(Y)) | (~p101(tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_10(Y))) | (~p101(tptp_fun_X_10(Y))))))) | (~(p105(Y) | (~p106(Y)))) | (~(p104(Y) | (~p105(Y)))) | (~(p103(Y) | (~p104(Y)))) | (~(p102(Y) | (~p103(Y)))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y)))) | (~((~p105(Y)) | (~((~(p6(Y) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(Y, X))))) | (~((~p6(Y)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(Y, X))))))))) | (~((~p104(Y)) | (~((~(p5(Y) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(Y, X))))) | (~((~p5(Y)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(Y, X))))))))) | (~((~p103(Y)) | (~((~(p4(Y) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(Y, X))))) | (~((~p4(Y)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(Y, X))))))))) | (~((~p102(Y)) | (~((~(p3(Y) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(Y, X))))) | (~((~p3(Y)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(Y, X))))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))))))) | ((~r1(X!0, X!0)) | (~((~(p105(X!0) | (~p104(X!0)) | (~(p106(tptp_fun_X_2(X!0)) | (~r1(X!0, tptp_fun_X_2(X!0))) | (~r1(X!0, tptp_fun_X_1(X!0))) | p6(tptp_fun_X_1(X!0)) | p106(tptp_fun_X_1(X!0)) | (~p105(tptp_fun_X_1(X!0))) | (~p6(tptp_fun_X_2(X!0))) | (~p105(tptp_fun_X_2(X!0))))))) | (~(p104(X!0) | (~p103(X!0)) | (~(p105(tptp_fun_X_3(X!0)) | (~r1(X!0, tptp_fun_X_4(X!0))) | (~r1(X!0, tptp_fun_X_3(X!0))) | p5(tptp_fun_X_3(X!0)) | p105(tptp_fun_X_4(X!0)) | (~p104(tptp_fun_X_3(X!0))) | (~p5(tptp_fun_X_4(X!0))) | (~p104(tptp_fun_X_4(X!0))))))) | (~(p103(X!0) | (~p102(X!0)) | (~(p4(tptp_fun_X_5(X!0)) | p104(tptp_fun_X_5(X!0)) | (~r1(X!0, tptp_fun_X_5(X!0))) | p104(tptp_fun_X_6(X!0)) | (~r1(X!0, tptp_fun_X_6(X!0))) | (~p103(tptp_fun_X_5(X!0))) | (~p4(tptp_fun_X_6(X!0))) | (~p103(tptp_fun_X_6(X!0))))))) | (~(p102(X!0) | (~p101(X!0)) | (~(p103(tptp_fun_X_8(X!0)) | p103(tptp_fun_X_7(X!0)) | (~r1(X!0, tptp_fun_X_8(X!0))) | (~r1(X!0, tptp_fun_X_7(X!0))) | p3(tptp_fun_X_7(X!0)) | (~p102(tptp_fun_X_7(X!0))) | (~p3(tptp_fun_X_8(X!0))) | (~p102(tptp_fun_X_8(X!0))))))) | (~(p101(X!0) | (~p100(X!0)) | (~((~r1(X!0, tptp_fun_X_9(X!0))) | p2(tptp_fun_X_9(X!0)) | p102(tptp_fun_X_9(X!0)) | (~r1(X!0, tptp_fun_X_10(X!0))) | p102(tptp_fun_X_10(X!0)) | (~p101(tptp_fun_X_9(X!0))) | (~p2(tptp_fun_X_10(X!0))) | (~p101(tptp_fun_X_10(X!0))))))) | (~(p105(X!0) | (~p106(X!0)))) | (~(p104(X!0) | (~p105(X!0)))) | (~(p103(X!0) | (~p104(X!0)))) | (~(p102(X!0) | (~p103(X!0)))) | (~(p101(X!0) | (~p102(X!0)))) | (~(p100(X!0) | (~p101(X!0)))) | (~((~p105(X!0)) | (~((~(p6(X!0) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(X!0, X))))) | (~((~p6(X!0)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(X!0, X))))))))) | (~((~p104(X!0)) | (~((~(p5(X!0) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(X!0, X))))) | (~((~p5(X!0)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(X!0, X))))))))) | (~((~p103(X!0)) | (~((~(p4(X!0) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(X!0, X))))) | (~((~p4(X!0)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(X!0, X))))))))) | (~((~p102(X!0)) | (~((~(p3(X!0) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(X!0, X))))) | (~((~p3(X!0)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(X!0, X))))))))) | (~((~p101(X!0)) | (~((~(p2(X!0) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(X!0, X))))) | (~((~p2(X!0)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(X!0, X))))))))) | (~((~p100(X!0)) | (~((~(p1(X!0) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(X!0, X))))) | (~((~p1(X!0)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(X!0, X))))))))))))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(43,plain,
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% 0.18/0.47 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.18/0.47 tff(44,plain,
% 0.18/0.47 ((~r1(X!0, X!0)) | (~((~(p105(X!0) | (~p106(X!0)))) | (~(p102(X!0) | (~p101(X!0)) | (~(p103(tptp_fun_X_8(X!0)) | p103(tptp_fun_X_7(X!0)) | (~r1(X!0, tptp_fun_X_8(X!0))) | (~r1(X!0, tptp_fun_X_7(X!0))) | p3(tptp_fun_X_7(X!0)) | (~p102(tptp_fun_X_7(X!0))) | (~p3(tptp_fun_X_8(X!0))) | (~p102(tptp_fun_X_8(X!0))))))) | (~(p105(X!0) | (~p104(X!0)) | (~(p106(tptp_fun_X_2(X!0)) | (~r1(X!0, tptp_fun_X_2(X!0))) | (~r1(X!0, tptp_fun_X_1(X!0))) | p6(tptp_fun_X_1(X!0)) | p106(tptp_fun_X_1(X!0)) | (~p105(tptp_fun_X_1(X!0))) | (~p6(tptp_fun_X_2(X!0))) | (~p105(tptp_fun_X_2(X!0))))))) | (~(p104(X!0) | (~p105(X!0)))) | (~(p103(X!0) | (~p104(X!0)))) | (~(p102(X!0) | (~p103(X!0)))) | (~(p101(X!0) | (~p102(X!0)))) | (~(p100(X!0) | (~p101(X!0)))) | (~((~p105(X!0)) | (~((~(p6(X!0) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(X!0, X))))) | (~((~p6(X!0)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(X!0, X))))))))) | (~((~p104(X!0)) | (~((~(p5(X!0) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(X!0, X))))) | (~((~p5(X!0)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(X!0, X))))))))) | (~((~p103(X!0)) | (~((~(p4(X!0) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(X!0, X))))) | (~((~p4(X!0)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(X!0, X))))))))) | (~((~p102(X!0)) | (~((~(p3(X!0) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(X!0, X))))) | (~((~p3(X!0)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(X!0, X))))))))) | (~((~p101(X!0)) | (~((~(p2(X!0) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(X!0, X))))) | (~((~p2(X!0)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(X!0, X))))))))) | (~(p104(X!0) | (~p103(X!0)) | (~((~p104(tptp_fun_X_4(X!0))) | p105(tptp_fun_X_4(X!0)) | (~p104(tptp_fun_X_3(X!0))) | (~p5(tptp_fun_X_4(X!0))) | p105(tptp_fun_X_3(X!0)) | p5(tptp_fun_X_3(X!0)) | (~r1(X!0, tptp_fun_X_4(X!0))) | (~r1(X!0, tptp_fun_X_3(X!0))))))) | (~(p103(X!0) | (~p102(X!0)) | (~((~p4(tptp_fun_X_6(X!0))) | (~p103(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_5(X!0))) | p4(tptp_fun_X_5(X!0)) | p104(tptp_fun_X_5(X!0)) | (~p103(tptp_fun_X_5(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0))) | p104(tptp_fun_X_6(X!0)))))) | (~(p101(X!0) | (~p100(X!0)) | (~((~p101(tptp_fun_X_9(X!0))) | (~p2(tptp_fun_X_10(X!0))) | (~p101(tptp_fun_X_10(X!0))) | p102(tptp_fun_X_10(X!0)) | p2(tptp_fun_X_9(X!0)) | p102(tptp_fun_X_9(X!0)) | (~r1(X!0, tptp_fun_X_10(X!0))) | (~r1(X!0, tptp_fun_X_9(X!0))))))) | (~((~p100(X!0)) | (~((~(p1(X!0) | ![X: $i] : ((~r1(X!0, X)) | (~p100(X)) | (~p1(X))))) | (~((~p1(X!0)) | ![X: $i] : ((~r1(X!0, X)) | (~p100(X)) | p1(X))))))))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[43, 37])).
% 0.18/0.47 tff(45,plain,
% 0.18/0.47 (~((~(p105(X!0) | (~p106(X!0)))) | (~(p102(X!0) | (~p101(X!0)) | (~(p103(tptp_fun_X_8(X!0)) | p103(tptp_fun_X_7(X!0)) | (~r1(X!0, tptp_fun_X_8(X!0))) | (~r1(X!0, tptp_fun_X_7(X!0))) | p3(tptp_fun_X_7(X!0)) | (~p102(tptp_fun_X_7(X!0))) | (~p3(tptp_fun_X_8(X!0))) | (~p102(tptp_fun_X_8(X!0))))))) | (~(p105(X!0) | (~p104(X!0)) | (~(p106(tptp_fun_X_2(X!0)) | (~r1(X!0, tptp_fun_X_2(X!0))) | (~r1(X!0, tptp_fun_X_1(X!0))) | p6(tptp_fun_X_1(X!0)) | p106(tptp_fun_X_1(X!0)) | (~p105(tptp_fun_X_1(X!0))) | (~p6(tptp_fun_X_2(X!0))) | (~p105(tptp_fun_X_2(X!0))))))) | (~(p104(X!0) | (~p105(X!0)))) | (~(p103(X!0) | (~p104(X!0)))) | (~(p102(X!0) | (~p103(X!0)))) | (~(p101(X!0) | (~p102(X!0)))) | (~(p100(X!0) | (~p101(X!0)))) | (~((~p105(X!0)) | (~((~(p6(X!0) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(X!0, X))))) | (~((~p6(X!0)) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(X!0, X))))))))) | (~((~p104(X!0)) | (~((~(p5(X!0) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(X!0, X))))) | (~((~p5(X!0)) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(X!0, X))))))))) | (~((~p103(X!0)) | (~((~(p4(X!0) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(X!0, X))))) | (~((~p4(X!0)) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(X!0, X))))))))) | (~((~p102(X!0)) | (~((~(p3(X!0) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(X!0, X))))) | (~((~p3(X!0)) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(X!0, X))))))))) | (~((~p101(X!0)) | (~((~(p2(X!0) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(X!0, X))))) | (~((~p2(X!0)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(X!0, X))))))))) | (~(p104(X!0) | (~p103(X!0)) | (~((~p104(tptp_fun_X_4(X!0))) | p105(tptp_fun_X_4(X!0)) | (~p104(tptp_fun_X_3(X!0))) | (~p5(tptp_fun_X_4(X!0))) | p105(tptp_fun_X_3(X!0)) | p5(tptp_fun_X_3(X!0)) | (~r1(X!0, tptp_fun_X_4(X!0))) | (~r1(X!0, tptp_fun_X_3(X!0))))))) | (~(p103(X!0) | (~p102(X!0)) | (~((~p4(tptp_fun_X_6(X!0))) | (~p103(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_5(X!0))) | p4(tptp_fun_X_5(X!0)) | p104(tptp_fun_X_5(X!0)) | (~p103(tptp_fun_X_5(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0))) | p104(tptp_fun_X_6(X!0)))))) | (~(p101(X!0) | (~p100(X!0)) | (~((~p101(tptp_fun_X_9(X!0))) | (~p2(tptp_fun_X_10(X!0))) | (~p101(tptp_fun_X_10(X!0))) | p102(tptp_fun_X_10(X!0)) | p2(tptp_fun_X_9(X!0)) | p102(tptp_fun_X_9(X!0)) | (~r1(X!0, tptp_fun_X_10(X!0))) | (~r1(X!0, tptp_fun_X_9(X!0))))))) | (~((~p100(X!0)) | (~((~(p1(X!0) | ![X: $i] : ((~r1(X!0, X)) | (~p100(X)) | (~p1(X))))) | (~((~p1(X!0)) | ![X: $i] : ((~r1(X!0, X)) | (~p100(X)) | p1(X)))))))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[44, 11])).
% 0.18/0.47 tff(46,plain,
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% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(47,plain,
% 0.18/0.47 (p101(X!0) | (~p100(X!0)) | (~((~p101(tptp_fun_X_9(X!0))) | (~p2(tptp_fun_X_10(X!0))) | (~p101(tptp_fun_X_10(X!0))) | p102(tptp_fun_X_10(X!0)) | p2(tptp_fun_X_9(X!0)) | p102(tptp_fun_X_9(X!0)) | (~r1(X!0, tptp_fun_X_10(X!0))) | (~r1(X!0, tptp_fun_X_9(X!0)))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.18/0.47 tff(48,plain,
% 0.18/0.47 (p100(X!0)),
% 0.18/0.47 inference(and_elim,[status(thm)],[33])).
% 0.18/0.47 tff(49,plain,
% 0.18/0.47 (~p101(X!0)),
% 0.18/0.47 inference(and_elim,[status(thm)],[33])).
% 0.18/0.47 tff(50,plain,
% 0.18/0.47 ((~(p101(X!0) | (~p100(X!0)) | (~((~p101(tptp_fun_X_9(X!0))) | (~p2(tptp_fun_X_10(X!0))) | (~p101(tptp_fun_X_10(X!0))) | p102(tptp_fun_X_10(X!0)) | p2(tptp_fun_X_9(X!0)) | p102(tptp_fun_X_9(X!0)) | (~r1(X!0, tptp_fun_X_10(X!0))) | (~r1(X!0, tptp_fun_X_9(X!0))))))) | p101(X!0) | (~p100(X!0)) | (~((~p101(tptp_fun_X_9(X!0))) | (~p2(tptp_fun_X_10(X!0))) | (~p101(tptp_fun_X_10(X!0))) | p102(tptp_fun_X_10(X!0)) | p2(tptp_fun_X_9(X!0)) | p102(tptp_fun_X_9(X!0)) | (~r1(X!0, tptp_fun_X_10(X!0))) | (~r1(X!0, tptp_fun_X_9(X!0)))))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(51,plain,
% 0.18/0.47 ((~(p101(X!0) | (~p100(X!0)) | (~((~p101(tptp_fun_X_9(X!0))) | (~p2(tptp_fun_X_10(X!0))) | (~p101(tptp_fun_X_10(X!0))) | p102(tptp_fun_X_10(X!0)) | p2(tptp_fun_X_9(X!0)) | p102(tptp_fun_X_9(X!0)) | (~r1(X!0, tptp_fun_X_10(X!0))) | (~r1(X!0, tptp_fun_X_9(X!0))))))) | (~((~p101(tptp_fun_X_9(X!0))) | (~p2(tptp_fun_X_10(X!0))) | (~p101(tptp_fun_X_10(X!0))) | p102(tptp_fun_X_10(X!0)) | p2(tptp_fun_X_9(X!0)) | p102(tptp_fun_X_9(X!0)) | (~r1(X!0, tptp_fun_X_10(X!0))) | (~r1(X!0, tptp_fun_X_9(X!0)))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[50, 49, 48])).
% 0.18/0.47 tff(52,plain,
% 0.18/0.47 (~((~p101(tptp_fun_X_9(X!0))) | (~p2(tptp_fun_X_10(X!0))) | (~p101(tptp_fun_X_10(X!0))) | p102(tptp_fun_X_10(X!0)) | p2(tptp_fun_X_9(X!0)) | p102(tptp_fun_X_9(X!0)) | (~r1(X!0, tptp_fun_X_10(X!0))) | (~r1(X!0, tptp_fun_X_9(X!0))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[51, 47])).
% 0.18/0.47 tff(53,plain,
% 0.18/0.47 (((~p101(tptp_fun_X_9(X!0))) | (~p2(tptp_fun_X_10(X!0))) | (~p101(tptp_fun_X_10(X!0))) | p102(tptp_fun_X_10(X!0)) | p2(tptp_fun_X_9(X!0)) | p102(tptp_fun_X_9(X!0)) | (~r1(X!0, tptp_fun_X_10(X!0))) | (~r1(X!0, tptp_fun_X_9(X!0)))) | r1(X!0, tptp_fun_X_9(X!0))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(54,plain,
% 0.18/0.47 (r1(X!0, tptp_fun_X_9(X!0))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.18/0.47 tff(55,plain,
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(~((~p2(tptp_fun_X_9(X!0))) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(tptp_fun_X_9(X!0), X))))))))) | (~((~p100(tptp_fun_X_9(X!0))) | (~((~(p1(tptp_fun_X_9(X!0)) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(tptp_fun_X_9(X!0), X))))) | (~((~p1(tptp_fun_X_9(X!0))) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(tptp_fun_X_9(X!0), X))))))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~(p105(Y) | (~p104(Y)) | (~(p106(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | (~r1(Y, tptp_fun_X_1(Y))) | p6(tptp_fun_X_1(Y)) | p106(tptp_fun_X_1(Y)) | (~p105(tptp_fun_X_1(Y))) | (~p6(tptp_fun_X_2(Y))) | (~p105(tptp_fun_X_2(Y))))))) | (~(p104(Y) | (~p103(Y)) | (~(p105(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_3(Y))) | p5(tptp_fun_X_3(Y)) | p105(tptp_fun_X_4(Y)) | (~p104(tptp_fun_X_3(Y))) | (~p5(tptp_fun_X_4(Y))) | (~p104(tptp_fun_X_4(Y))))))) | (~(p103(Y) | (~p102(Y)) | (~(p4(tptp_fun_X_5(Y)) | p104(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))) | p104(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))) 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(~(p103(tptp_fun_X_9(X!0)) | (~p104(tptp_fun_X_9(X!0))))) | (~(p102(tptp_fun_X_9(X!0)) | (~p103(tptp_fun_X_9(X!0))))) | (~(p101(tptp_fun_X_9(X!0)) | (~p102(tptp_fun_X_9(X!0))))) | (~(p100(tptp_fun_X_9(X!0)) | (~p101(tptp_fun_X_9(X!0))))) | (~((~p105(tptp_fun_X_9(X!0))) | (~((~(p6(tptp_fun_X_9(X!0)) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(tptp_fun_X_9(X!0), X))))) | (~((~p6(tptp_fun_X_9(X!0))) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(tptp_fun_X_9(X!0), X))))))))) | (~((~p104(tptp_fun_X_9(X!0))) | (~((~(p5(tptp_fun_X_9(X!0)) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(tptp_fun_X_9(X!0), X))))) | (~((~p5(tptp_fun_X_9(X!0))) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(tptp_fun_X_9(X!0), X))))))))) | (~((~p103(tptp_fun_X_9(X!0))) | (~((~(p4(tptp_fun_X_9(X!0)) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(tptp_fun_X_9(X!0), X))))) | (~((~p4(tptp_fun_X_9(X!0))) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(tptp_fun_X_9(X!0), X))))))))) | (~((~p102(tptp_fun_X_9(X!0))) | (~((~(p3(tptp_fun_X_9(X!0)) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(tptp_fun_X_9(X!0), X))))) | (~((~p3(tptp_fun_X_9(X!0))) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(tptp_fun_X_9(X!0), X))))))))) | (~((~p101(tptp_fun_X_9(X!0))) | (~((~(p2(tptp_fun_X_9(X!0)) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(tptp_fun_X_9(X!0), X))))) | (~((~p2(tptp_fun_X_9(X!0))) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(tptp_fun_X_9(X!0), X))))))))) | (~((~p100(tptp_fun_X_9(X!0))) | (~((~(p1(tptp_fun_X_9(X!0)) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(tptp_fun_X_9(X!0), X))))) | (~((~p1(tptp_fun_X_9(X!0))) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(tptp_fun_X_9(X!0), X))))))))))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(56,plain,
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X))))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))))))) | ((~r1(X!0, tptp_fun_X_9(X!0))) | (~((~(p105(tptp_fun_X_9(X!0)) | (~p104(tptp_fun_X_9(X!0))) | (~(p106(tptp_fun_X_2(tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_2(tptp_fun_X_9(X!0)))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_1(tptp_fun_X_9(X!0)))) | p6(tptp_fun_X_1(tptp_fun_X_9(X!0))) | p106(tptp_fun_X_1(tptp_fun_X_9(X!0))) | (~p105(tptp_fun_X_1(tptp_fun_X_9(X!0)))) | (~p6(tptp_fun_X_2(tptp_fun_X_9(X!0)))) | (~p105(tptp_fun_X_2(tptp_fun_X_9(X!0)))))))) | (~(p104(tptp_fun_X_9(X!0)) | (~p103(tptp_fun_X_9(X!0))) | (~(p105(tptp_fun_X_3(tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_4(tptp_fun_X_9(X!0)))) | (~r1(tptp_fun_X_9(X!0), 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((~p6(X)) | (~p105(X)) | (~r1(tptp_fun_X_9(X!0), X))))) | (~((~p6(tptp_fun_X_9(X!0))) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(tptp_fun_X_9(X!0), X))))))))) | (~((~p104(tptp_fun_X_9(X!0))) | (~((~(p5(tptp_fun_X_9(X!0)) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(tptp_fun_X_9(X!0), X))))) | (~((~p5(tptp_fun_X_9(X!0))) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(tptp_fun_X_9(X!0), X))))))))) | (~((~p103(tptp_fun_X_9(X!0))) | (~((~(p4(tptp_fun_X_9(X!0)) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(tptp_fun_X_9(X!0), X))))) | (~((~p4(tptp_fun_X_9(X!0))) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(tptp_fun_X_9(X!0), X))))))))) | (~((~p102(tptp_fun_X_9(X!0))) | (~((~(p3(tptp_fun_X_9(X!0)) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(tptp_fun_X_9(X!0), X))))) | (~((~p3(tptp_fun_X_9(X!0))) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(tptp_fun_X_9(X!0), X))))))))) | (~((~p101(tptp_fun_X_9(X!0))) | (~((~(p2(tptp_fun_X_9(X!0)) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(tptp_fun_X_9(X!0), X))))) | (~((~p2(tptp_fun_X_9(X!0))) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(tptp_fun_X_9(X!0), X))))))))) | (~((~p100(tptp_fun_X_9(X!0))) | (~((~(p1(tptp_fun_X_9(X!0)) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(tptp_fun_X_9(X!0), X))))) | (~((~p1(tptp_fun_X_9(X!0))) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(tptp_fun_X_9(X!0), X))))))))))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(57,plain,
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X))))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))))))) | (~r1(X!0, tptp_fun_X_9(X!0))) | (~((~(p105(tptp_fun_X_9(X!0)) | (~p104(tptp_fun_X_9(X!0))) | (~(p106(tptp_fun_X_2(tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_2(tptp_fun_X_9(X!0)))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_1(tptp_fun_X_9(X!0)))) | p6(tptp_fun_X_1(tptp_fun_X_9(X!0))) | p106(tptp_fun_X_1(tptp_fun_X_9(X!0))) | (~p105(tptp_fun_X_1(tptp_fun_X_9(X!0)))) | (~p6(tptp_fun_X_2(tptp_fun_X_9(X!0)))) | (~p105(tptp_fun_X_2(tptp_fun_X_9(X!0)))))))) | (~(p104(tptp_fun_X_9(X!0)) | (~p103(tptp_fun_X_9(X!0))) | (~(p105(tptp_fun_X_3(tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_4(tptp_fun_X_9(X!0)))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_3(tptp_fun_X_9(X!0)))) | p5(tptp_fun_X_3(tptp_fun_X_9(X!0))) | p105(tptp_fun_X_4(tptp_fun_X_9(X!0))) | (~p104(tptp_fun_X_3(tptp_fun_X_9(X!0)))) | (~p5(tptp_fun_X_4(tptp_fun_X_9(X!0)))) | (~p104(tptp_fun_X_4(tptp_fun_X_9(X!0)))))))) | (~(p103(tptp_fun_X_9(X!0)) | (~p102(tptp_fun_X_9(X!0))) | (~(p4(tptp_fun_X_5(tptp_fun_X_9(X!0))) | p104(tptp_fun_X_5(tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_5(tptp_fun_X_9(X!0)))) | p104(tptp_fun_X_6(tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_6(tptp_fun_X_9(X!0)))) | (~p103(tptp_fun_X_5(tptp_fun_X_9(X!0)))) | (~p4(tptp_fun_X_6(tptp_fun_X_9(X!0)))) | (~p103(tptp_fun_X_6(tptp_fun_X_9(X!0)))))))) | (~(p102(tptp_fun_X_9(X!0)) | (~p101(tptp_fun_X_9(X!0))) | (~(p103(tptp_fun_X_8(tptp_fun_X_9(X!0))) | p103(tptp_fun_X_7(tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_8(tptp_fun_X_9(X!0)))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_7(tptp_fun_X_9(X!0)))) | p3(tptp_fun_X_7(tptp_fun_X_9(X!0))) | (~p102(tptp_fun_X_7(tptp_fun_X_9(X!0)))) | (~p3(tptp_fun_X_8(tptp_fun_X_9(X!0)))) | (~p102(tptp_fun_X_8(tptp_fun_X_9(X!0)))))))) | (~(p101(tptp_fun_X_9(X!0)) | (~p100(tptp_fun_X_9(X!0))) | (~((~r1(tptp_fun_X_9(X!0), tptp_fun_X_9(tptp_fun_X_9(X!0)))) | p2(tptp_fun_X_9(tptp_fun_X_9(X!0))) | p102(tptp_fun_X_9(tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_10(tptp_fun_X_9(X!0)))) | p102(tptp_fun_X_10(tptp_fun_X_9(X!0))) | (~p101(tptp_fun_X_9(tptp_fun_X_9(X!0)))) | (~p2(tptp_fun_X_10(tptp_fun_X_9(X!0)))) | (~p101(tptp_fun_X_10(tptp_fun_X_9(X!0)))))))) | (~(p105(tptp_fun_X_9(X!0)) | (~p106(tptp_fun_X_9(X!0))))) | (~(p104(tptp_fun_X_9(X!0)) | (~p105(tptp_fun_X_9(X!0))))) | (~(p103(tptp_fun_X_9(X!0)) | (~p104(tptp_fun_X_9(X!0))))) | (~(p102(tptp_fun_X_9(X!0)) | (~p103(tptp_fun_X_9(X!0))))) | (~(p101(tptp_fun_X_9(X!0)) | (~p102(tptp_fun_X_9(X!0))))) | (~(p100(tptp_fun_X_9(X!0)) | (~p101(tptp_fun_X_9(X!0))))) | (~((~p105(tptp_fun_X_9(X!0))) | (~((~(p6(tptp_fun_X_9(X!0)) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(tptp_fun_X_9(X!0), X))))) | (~((~p6(tptp_fun_X_9(X!0))) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(tptp_fun_X_9(X!0), X))))))))) | (~((~p104(tptp_fun_X_9(X!0))) | (~((~(p5(tptp_fun_X_9(X!0)) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(tptp_fun_X_9(X!0), X))))) | (~((~p5(tptp_fun_X_9(X!0))) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(tptp_fun_X_9(X!0), X))))))))) | (~((~p103(tptp_fun_X_9(X!0))) | (~((~(p4(tptp_fun_X_9(X!0)) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(tptp_fun_X_9(X!0), X))))) | (~((~p4(tptp_fun_X_9(X!0))) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(tptp_fun_X_9(X!0), X))))))))) | (~((~p102(tptp_fun_X_9(X!0))) | (~((~(p3(tptp_fun_X_9(X!0)) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(tptp_fun_X_9(X!0), X))))) | (~((~p3(tptp_fun_X_9(X!0))) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(tptp_fun_X_9(X!0), X))))))))) | (~((~p101(tptp_fun_X_9(X!0))) | (~((~(p2(tptp_fun_X_9(X!0)) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(tptp_fun_X_9(X!0), X))))) | (~((~p2(tptp_fun_X_9(X!0))) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(tptp_fun_X_9(X!0), X))))))))) | (~((~p100(tptp_fun_X_9(X!0))) | (~((~(p1(tptp_fun_X_9(X!0)) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(tptp_fun_X_9(X!0), X))))) | (~((~p1(tptp_fun_X_9(X!0))) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(tptp_fun_X_9(X!0), X)))))))))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.18/0.48 tff(58,plain,
% 0.18/0.48 (~((~(p105(tptp_fun_X_9(X!0)) | (~p104(tptp_fun_X_9(X!0))) | (~(p106(tptp_fun_X_2(tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_2(tptp_fun_X_9(X!0)))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_1(tptp_fun_X_9(X!0)))) | p6(tptp_fun_X_1(tptp_fun_X_9(X!0))) | p106(tptp_fun_X_1(tptp_fun_X_9(X!0))) | (~p105(tptp_fun_X_1(tptp_fun_X_9(X!0)))) | (~p6(tptp_fun_X_2(tptp_fun_X_9(X!0)))) | (~p105(tptp_fun_X_2(tptp_fun_X_9(X!0)))))))) | (~(p104(tptp_fun_X_9(X!0)) | (~p103(tptp_fun_X_9(X!0))) | (~(p105(tptp_fun_X_3(tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_4(tptp_fun_X_9(X!0)))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_3(tptp_fun_X_9(X!0)))) | p5(tptp_fun_X_3(tptp_fun_X_9(X!0))) | p105(tptp_fun_X_4(tptp_fun_X_9(X!0))) | (~p104(tptp_fun_X_3(tptp_fun_X_9(X!0)))) | (~p5(tptp_fun_X_4(tptp_fun_X_9(X!0)))) | (~p104(tptp_fun_X_4(tptp_fun_X_9(X!0)))))))) | (~(p103(tptp_fun_X_9(X!0)) | (~p102(tptp_fun_X_9(X!0))) | (~(p4(tptp_fun_X_5(tptp_fun_X_9(X!0))) | p104(tptp_fun_X_5(tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_5(tptp_fun_X_9(X!0)))) | p104(tptp_fun_X_6(tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_6(tptp_fun_X_9(X!0)))) | (~p103(tptp_fun_X_5(tptp_fun_X_9(X!0)))) | (~p4(tptp_fun_X_6(tptp_fun_X_9(X!0)))) | (~p103(tptp_fun_X_6(tptp_fun_X_9(X!0)))))))) | (~(p102(tptp_fun_X_9(X!0)) | (~p101(tptp_fun_X_9(X!0))) | (~(p103(tptp_fun_X_8(tptp_fun_X_9(X!0))) | p103(tptp_fun_X_7(tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_8(tptp_fun_X_9(X!0)))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_7(tptp_fun_X_9(X!0)))) | p3(tptp_fun_X_7(tptp_fun_X_9(X!0))) | (~p102(tptp_fun_X_7(tptp_fun_X_9(X!0)))) | (~p3(tptp_fun_X_8(tptp_fun_X_9(X!0)))) | (~p102(tptp_fun_X_8(tptp_fun_X_9(X!0)))))))) | (~(p101(tptp_fun_X_9(X!0)) | (~p100(tptp_fun_X_9(X!0))) | (~((~r1(tptp_fun_X_9(X!0), tptp_fun_X_9(tptp_fun_X_9(X!0)))) | p2(tptp_fun_X_9(tptp_fun_X_9(X!0))) | p102(tptp_fun_X_9(tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_10(tptp_fun_X_9(X!0)))) | p102(tptp_fun_X_10(tptp_fun_X_9(X!0))) | (~p101(tptp_fun_X_9(tptp_fun_X_9(X!0)))) | (~p2(tptp_fun_X_10(tptp_fun_X_9(X!0)))) | (~p101(tptp_fun_X_10(tptp_fun_X_9(X!0)))))))) | (~(p105(tptp_fun_X_9(X!0)) | (~p106(tptp_fun_X_9(X!0))))) | (~(p104(tptp_fun_X_9(X!0)) | (~p105(tptp_fun_X_9(X!0))))) | (~(p103(tptp_fun_X_9(X!0)) | (~p104(tptp_fun_X_9(X!0))))) | (~(p102(tptp_fun_X_9(X!0)) | (~p103(tptp_fun_X_9(X!0))))) | (~(p101(tptp_fun_X_9(X!0)) | (~p102(tptp_fun_X_9(X!0))))) | (~(p100(tptp_fun_X_9(X!0)) | (~p101(tptp_fun_X_9(X!0))))) | (~((~p105(tptp_fun_X_9(X!0))) | (~((~(p6(tptp_fun_X_9(X!0)) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(tptp_fun_X_9(X!0), X))))) | (~((~p6(tptp_fun_X_9(X!0))) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(tptp_fun_X_9(X!0), X))))))))) | (~((~p104(tptp_fun_X_9(X!0))) | (~((~(p5(tptp_fun_X_9(X!0)) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(tptp_fun_X_9(X!0), X))))) | (~((~p5(tptp_fun_X_9(X!0))) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(tptp_fun_X_9(X!0), X))))))))) | (~((~p103(tptp_fun_X_9(X!0))) | (~((~(p4(tptp_fun_X_9(X!0)) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(tptp_fun_X_9(X!0), X))))) | (~((~p4(tptp_fun_X_9(X!0))) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(tptp_fun_X_9(X!0), X))))))))) | (~((~p102(tptp_fun_X_9(X!0))) | (~((~(p3(tptp_fun_X_9(X!0)) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(tptp_fun_X_9(X!0), X))))) | (~((~p3(tptp_fun_X_9(X!0))) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(tptp_fun_X_9(X!0), X))))))))) | (~((~p101(tptp_fun_X_9(X!0))) | (~((~(p2(tptp_fun_X_9(X!0)) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(tptp_fun_X_9(X!0), X))))) | (~((~p2(tptp_fun_X_9(X!0))) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(tptp_fun_X_9(X!0), X))))))))) | (~((~p100(tptp_fun_X_9(X!0))) | (~((~(p1(tptp_fun_X_9(X!0)) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(tptp_fun_X_9(X!0), X))))) | (~((~p1(tptp_fun_X_9(X!0))) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(tptp_fun_X_9(X!0), X))))))))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[57, 37, 54])).
% 0.18/0.48 tff(59,plain,
% 0.18/0.48 (((~(p105(tptp_fun_X_9(X!0)) | (~p104(tptp_fun_X_9(X!0))) | (~(p106(tptp_fun_X_2(tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_2(tptp_fun_X_9(X!0)))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_1(tptp_fun_X_9(X!0)))) | p6(tptp_fun_X_1(tptp_fun_X_9(X!0))) | p106(tptp_fun_X_1(tptp_fun_X_9(X!0))) | (~p105(tptp_fun_X_1(tptp_fun_X_9(X!0)))) | (~p6(tptp_fun_X_2(tptp_fun_X_9(X!0)))) | (~p105(tptp_fun_X_2(tptp_fun_X_9(X!0)))))))) | (~(p104(tptp_fun_X_9(X!0)) | (~p103(tptp_fun_X_9(X!0))) | (~(p105(tptp_fun_X_3(tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_4(tptp_fun_X_9(X!0)))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_3(tptp_fun_X_9(X!0)))) | p5(tptp_fun_X_3(tptp_fun_X_9(X!0))) | p105(tptp_fun_X_4(tptp_fun_X_9(X!0))) | (~p104(tptp_fun_X_3(tptp_fun_X_9(X!0)))) | (~p5(tptp_fun_X_4(tptp_fun_X_9(X!0)))) | (~p104(tptp_fun_X_4(tptp_fun_X_9(X!0)))))))) | (~(p103(tptp_fun_X_9(X!0)) | (~p102(tptp_fun_X_9(X!0))) | (~(p4(tptp_fun_X_5(tptp_fun_X_9(X!0))) | p104(tptp_fun_X_5(tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_5(tptp_fun_X_9(X!0)))) | p104(tptp_fun_X_6(tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_6(tptp_fun_X_9(X!0)))) | (~p103(tptp_fun_X_5(tptp_fun_X_9(X!0)))) | (~p4(tptp_fun_X_6(tptp_fun_X_9(X!0)))) | (~p103(tptp_fun_X_6(tptp_fun_X_9(X!0)))))))) | (~(p102(tptp_fun_X_9(X!0)) | (~p101(tptp_fun_X_9(X!0))) | (~(p103(tptp_fun_X_8(tptp_fun_X_9(X!0))) | p103(tptp_fun_X_7(tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_8(tptp_fun_X_9(X!0)))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_7(tptp_fun_X_9(X!0)))) | p3(tptp_fun_X_7(tptp_fun_X_9(X!0))) | (~p102(tptp_fun_X_7(tptp_fun_X_9(X!0)))) | (~p3(tptp_fun_X_8(tptp_fun_X_9(X!0)))) | (~p102(tptp_fun_X_8(tptp_fun_X_9(X!0)))))))) | (~(p101(tptp_fun_X_9(X!0)) | (~p100(tptp_fun_X_9(X!0))) | (~((~r1(tptp_fun_X_9(X!0), tptp_fun_X_9(tptp_fun_X_9(X!0)))) | p2(tptp_fun_X_9(tptp_fun_X_9(X!0))) | p102(tptp_fun_X_9(tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_10(tptp_fun_X_9(X!0)))) | p102(tptp_fun_X_10(tptp_fun_X_9(X!0))) | (~p101(tptp_fun_X_9(tptp_fun_X_9(X!0)))) | (~p2(tptp_fun_X_10(tptp_fun_X_9(X!0)))) | (~p101(tptp_fun_X_10(tptp_fun_X_9(X!0)))))))) | (~(p105(tptp_fun_X_9(X!0)) | (~p106(tptp_fun_X_9(X!0))))) | (~(p104(tptp_fun_X_9(X!0)) | (~p105(tptp_fun_X_9(X!0))))) | (~(p103(tptp_fun_X_9(X!0)) | (~p104(tptp_fun_X_9(X!0))))) | (~(p102(tptp_fun_X_9(X!0)) | (~p103(tptp_fun_X_9(X!0))))) | (~(p101(tptp_fun_X_9(X!0)) | (~p102(tptp_fun_X_9(X!0))))) | (~(p100(tptp_fun_X_9(X!0)) | (~p101(tptp_fun_X_9(X!0))))) | (~((~p105(tptp_fun_X_9(X!0))) | (~((~(p6(tptp_fun_X_9(X!0)) | ![X: $i] : ((~p6(X)) | (~p105(X)) | (~r1(tptp_fun_X_9(X!0), X))))) | (~((~p6(tptp_fun_X_9(X!0))) | ![X: $i] : (p6(X) | (~p105(X)) | (~r1(tptp_fun_X_9(X!0), X))))))))) | (~((~p104(tptp_fun_X_9(X!0))) | (~((~(p5(tptp_fun_X_9(X!0)) | ![X: $i] : ((~p5(X)) | (~p104(X)) | (~r1(tptp_fun_X_9(X!0), X))))) | (~((~p5(tptp_fun_X_9(X!0))) | ![X: $i] : (p5(X) | (~p104(X)) | (~r1(tptp_fun_X_9(X!0), X))))))))) | (~((~p103(tptp_fun_X_9(X!0))) | (~((~(p4(tptp_fun_X_9(X!0)) | ![X: $i] : ((~p4(X)) | (~p103(X)) | (~r1(tptp_fun_X_9(X!0), X))))) | (~((~p4(tptp_fun_X_9(X!0))) | ![X: $i] : (p4(X) | (~p103(X)) | (~r1(tptp_fun_X_9(X!0), X))))))))) | (~((~p102(tptp_fun_X_9(X!0))) | (~((~(p3(tptp_fun_X_9(X!0)) | ![X: $i] : ((~p3(X)) | (~p102(X)) | (~r1(tptp_fun_X_9(X!0), X))))) | (~((~p3(tptp_fun_X_9(X!0))) | ![X: $i] : (p3(X) | (~p102(X)) | (~r1(tptp_fun_X_9(X!0), X))))))))) | (~((~p101(tptp_fun_X_9(X!0))) | (~((~(p2(tptp_fun_X_9(X!0)) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(tptp_fun_X_9(X!0), X))))) | (~((~p2(tptp_fun_X_9(X!0))) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(tptp_fun_X_9(X!0), X))))))))) | (~((~p100(tptp_fun_X_9(X!0))) | (~((~(p1(tptp_fun_X_9(X!0)) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(tptp_fun_X_9(X!0), X))))) | (~((~p1(tptp_fun_X_9(X!0))) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(tptp_fun_X_9(X!0), X)))))))))) | (p102(tptp_fun_X_9(X!0)) | (~p101(tptp_fun_X_9(X!0))) | (~(p103(tptp_fun_X_8(tptp_fun_X_9(X!0))) | p103(tptp_fun_X_7(tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_8(tptp_fun_X_9(X!0)))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_7(tptp_fun_X_9(X!0)))) | p3(tptp_fun_X_7(tptp_fun_X_9(X!0))) | (~p102(tptp_fun_X_7(tptp_fun_X_9(X!0)))) | (~p3(tptp_fun_X_8(tptp_fun_X_9(X!0)))) | (~p102(tptp_fun_X_8(tptp_fun_X_9(X!0)))))))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(60,plain,
% 0.18/0.48 (p102(tptp_fun_X_9(X!0)) | (~p101(tptp_fun_X_9(X!0))) | (~(p103(tptp_fun_X_8(tptp_fun_X_9(X!0))) | p103(tptp_fun_X_7(tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_8(tptp_fun_X_9(X!0)))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_7(tptp_fun_X_9(X!0)))) | p3(tptp_fun_X_7(tptp_fun_X_9(X!0))) | (~p102(tptp_fun_X_7(tptp_fun_X_9(X!0)))) | (~p3(tptp_fun_X_8(tptp_fun_X_9(X!0)))) | (~p102(tptp_fun_X_8(tptp_fun_X_9(X!0))))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.18/0.48 tff(61,plain,
% 0.18/0.48 (((~p101(tptp_fun_X_9(X!0))) | (~p2(tptp_fun_X_10(X!0))) | (~p101(tptp_fun_X_10(X!0))) | p102(tptp_fun_X_10(X!0)) | p2(tptp_fun_X_9(X!0)) | p102(tptp_fun_X_9(X!0)) | (~r1(X!0, tptp_fun_X_10(X!0))) | (~r1(X!0, tptp_fun_X_9(X!0)))) | (~p102(tptp_fun_X_9(X!0)))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(62,plain,
% 0.18/0.48 (~p102(tptp_fun_X_9(X!0))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[61, 52])).
% 0.18/0.48 tff(63,plain,
% 0.18/0.48 (((~p101(tptp_fun_X_9(X!0))) | (~p2(tptp_fun_X_10(X!0))) | (~p101(tptp_fun_X_10(X!0))) | p102(tptp_fun_X_10(X!0)) | p2(tptp_fun_X_9(X!0)) | p102(tptp_fun_X_9(X!0)) | (~r1(X!0, tptp_fun_X_10(X!0))) | (~r1(X!0, tptp_fun_X_9(X!0)))) | p101(tptp_fun_X_9(X!0))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(64,plain,
% 0.18/0.48 (p101(tptp_fun_X_9(X!0))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[63, 52])).
% 0.18/0.48 tff(65,plain,
% 0.18/0.48 ((~(p102(tptp_fun_X_9(X!0)) | (~p101(tptp_fun_X_9(X!0))) | (~(p103(tptp_fun_X_8(tptp_fun_X_9(X!0))) | p103(tptp_fun_X_7(tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_8(tptp_fun_X_9(X!0)))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_7(tptp_fun_X_9(X!0)))) | p3(tptp_fun_X_7(tptp_fun_X_9(X!0))) | (~p102(tptp_fun_X_7(tptp_fun_X_9(X!0)))) | (~p3(tptp_fun_X_8(tptp_fun_X_9(X!0)))) | (~p102(tptp_fun_X_8(tptp_fun_X_9(X!0)))))))) | p102(tptp_fun_X_9(X!0)) | (~p101(tptp_fun_X_9(X!0))) | (~(p103(tptp_fun_X_8(tptp_fun_X_9(X!0))) | p103(tptp_fun_X_7(tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_8(tptp_fun_X_9(X!0)))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_7(tptp_fun_X_9(X!0)))) | p3(tptp_fun_X_7(tptp_fun_X_9(X!0))) | (~p102(tptp_fun_X_7(tptp_fun_X_9(X!0)))) | (~p3(tptp_fun_X_8(tptp_fun_X_9(X!0)))) | (~p102(tptp_fun_X_8(tptp_fun_X_9(X!0))))))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(66,plain,
% 0.18/0.48 ((~(p102(tptp_fun_X_9(X!0)) | (~p101(tptp_fun_X_9(X!0))) | (~(p103(tptp_fun_X_8(tptp_fun_X_9(X!0))) | p103(tptp_fun_X_7(tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_8(tptp_fun_X_9(X!0)))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_7(tptp_fun_X_9(X!0)))) | p3(tptp_fun_X_7(tptp_fun_X_9(X!0))) | (~p102(tptp_fun_X_7(tptp_fun_X_9(X!0)))) | (~p3(tptp_fun_X_8(tptp_fun_X_9(X!0)))) | (~p102(tptp_fun_X_8(tptp_fun_X_9(X!0)))))))) | (~(p103(tptp_fun_X_8(tptp_fun_X_9(X!0))) | p103(tptp_fun_X_7(tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_8(tptp_fun_X_9(X!0)))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_7(tptp_fun_X_9(X!0)))) | p3(tptp_fun_X_7(tptp_fun_X_9(X!0))) | (~p102(tptp_fun_X_7(tptp_fun_X_9(X!0)))) | (~p3(tptp_fun_X_8(tptp_fun_X_9(X!0)))) | (~p102(tptp_fun_X_8(tptp_fun_X_9(X!0))))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[65, 64, 62])).
% 0.18/0.48 tff(67,plain,
% 0.18/0.48 (~(p103(tptp_fun_X_8(tptp_fun_X_9(X!0))) | p103(tptp_fun_X_7(tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_8(tptp_fun_X_9(X!0)))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_7(tptp_fun_X_9(X!0)))) | p3(tptp_fun_X_7(tptp_fun_X_9(X!0))) | (~p102(tptp_fun_X_7(tptp_fun_X_9(X!0)))) | (~p3(tptp_fun_X_8(tptp_fun_X_9(X!0)))) | (~p102(tptp_fun_X_8(tptp_fun_X_9(X!0)))))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[66, 60])).
% 0.18/0.49 tff(68,plain,
% 0.18/0.49 ((p103(tptp_fun_X_8(tptp_fun_X_9(X!0))) | p103(tptp_fun_X_7(tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_8(tptp_fun_X_9(X!0)))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_7(tptp_fun_X_9(X!0)))) | p3(tptp_fun_X_7(tptp_fun_X_9(X!0))) | (~p102(tptp_fun_X_7(tptp_fun_X_9(X!0)))) | (~p3(tptp_fun_X_8(tptp_fun_X_9(X!0)))) | (~p102(tptp_fun_X_8(tptp_fun_X_9(X!0))))) | (~p3(tptp_fun_X_7(tptp_fun_X_9(X!0))))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(69,plain,
% 0.18/0.49 (~p3(tptp_fun_X_7(tptp_fun_X_9(X!0)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.18/0.49 tff(70,plain,
% 0.18/0.49 (^[Y: $i] : refl((p3(Y) | (~r1(X!0, Y))) <=> (p3(Y) | (~r1(X!0, Y))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(71,plain,
% 0.18/0.49 (![Y: $i] : (p3(Y) | (~r1(X!0, Y))) <=> ![Y: $i] : (p3(Y) | (~r1(X!0, Y)))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[70])).
% 0.18/0.49 tff(72,plain,
% 0.18/0.49 (![Y: $i] : (p3(Y) | (~r1(X!0, Y)))),
% 0.18/0.49 inference(and_elim,[status(thm)],[33])).
% 0.18/0.49 tff(73,plain,
% 0.18/0.49 (![Y: $i] : (p3(Y) | (~r1(X!0, Y)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.18/0.49 tff(74,plain,
% 0.18/0.49 (((~![Y: $i] : (p3(Y) | (~r1(X!0, Y)))) | (p3(tptp_fun_X_7(tptp_fun_X_9(X!0))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_9(X!0)))))) <=> ((~![Y: $i] : (p3(Y) | (~r1(X!0, Y)))) | p3(tptp_fun_X_7(tptp_fun_X_9(X!0))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_9(X!0)))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(75,plain,
% 0.18/0.49 ((~![Y: $i] : (p3(Y) | (~r1(X!0, Y)))) | (p3(tptp_fun_X_7(tptp_fun_X_9(X!0))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_9(X!0)))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(76,plain,
% 0.18/0.49 ((~![Y: $i] : (p3(Y) | (~r1(X!0, Y)))) | p3(tptp_fun_X_7(tptp_fun_X_9(X!0))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_9(X!0))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.18/0.49 tff(77,plain,
% 0.18/0.49 (~r1(X!0, tptp_fun_X_7(tptp_fun_X_9(X!0)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[76, 73, 69])).
% 0.18/0.49 tff(78,plain,
% 0.18/0.49 ((p103(tptp_fun_X_8(tptp_fun_X_9(X!0))) | p103(tptp_fun_X_7(tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_8(tptp_fun_X_9(X!0)))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_7(tptp_fun_X_9(X!0)))) | p3(tptp_fun_X_7(tptp_fun_X_9(X!0))) | (~p102(tptp_fun_X_7(tptp_fun_X_9(X!0)))) | (~p3(tptp_fun_X_8(tptp_fun_X_9(X!0)))) | (~p102(tptp_fun_X_8(tptp_fun_X_9(X!0))))) | r1(tptp_fun_X_9(X!0), tptp_fun_X_7(tptp_fun_X_9(X!0)))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(79,plain,
% 0.18/0.49 (r1(tptp_fun_X_9(X!0), tptp_fun_X_7(tptp_fun_X_9(X!0)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[78, 67])).
% 0.18/0.49 tff(80,plain,
% 0.18/0.49 (![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(81,plain,
% 0.18/0.49 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((r1(X, Y) & r1(Y, Z)) <=> (~((~r1(Y, Z)) | (~r1(X, Y))))), ((~(r1(X, Y) & r1(Y, Z))) <=> (~(~((~r1(Y, Z)) | (~r1(X, Y))))))), rewrite((~(~((~r1(Y, Z)) | (~r1(X, Y))))) <=> ((~r1(Y, Z)) | (~r1(X, Y)))), ((~(r1(X, Y) & r1(Y, Z))) <=> ((~r1(Y, Z)) | (~r1(X, Y))))), (((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)) <=> (((~r1(Y, Z)) | (~r1(X, Y))) | r1(X, Z)))), rewrite((((~r1(Y, Z)) | (~r1(X, Y))) | r1(X, Z)) <=> (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))), (((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)) <=> (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(82,plain,
% 0.18/0.49 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[81])).
% 0.18/0.49 tff(83,plain,
% 0.18/0.49 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(84,plain,
% 0.18/0.49 (^[X: $i, Y: $i, Z: $i] : rewrite(((r1(X, Y) & r1(Y, Z)) => r1(X, Z)) <=> ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(85,plain,
% 0.18/0.49 (![X: $i, Y: $i, Z: $i] : ((r1(X, Y) & r1(Y, Z)) => r1(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[84])).
% 0.18/0.49 tff(86,axiom,(![X: $i, Y: $i, Z: $i] : ((r1(X, Y) & r1(Y, Z)) => r1(X, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','transitivity')).
% 0.18/0.49 tff(87,plain,
% 0.18/0.49 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.18/0.49 tff(88,plain,
% 0.18/0.49 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.18/0.49 tff(89,plain,(
% 0.18/0.49 ![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 0.18/0.49 inference(skolemize,[status(sab)],[88])).
% 0.18/0.49 tff(90,plain,
% 0.18/0.49 (![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.18/0.49 tff(91,plain,
% 0.18/0.49 (![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[90, 80])).
% 0.18/0.49 tff(92,plain,
% 0.18/0.49 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_7(tptp_fun_X_9(X!0)))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_9(X!0))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_7(tptp_fun_X_9(X!0)))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_9(X!0))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(93,plain,
% 0.18/0.49 ((r1(X!0, tptp_fun_X_7(tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_7(tptp_fun_X_9(X!0)))) | (~r1(X!0, tptp_fun_X_9(X!0)))) <=> ((~r1(X!0, tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_7(tptp_fun_X_9(X!0)))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_9(X!0))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(94,plain,
% 0.18/0.49 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_7(tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_7(tptp_fun_X_9(X!0)))) | (~r1(X!0, tptp_fun_X_9(X!0))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_7(tptp_fun_X_9(X!0)))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_9(X!0)))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[93])).
% 0.18/0.49 tff(95,plain,
% 0.18/0.49 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_7(tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_7(tptp_fun_X_9(X!0)))) | (~r1(X!0, tptp_fun_X_9(X!0))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_7(tptp_fun_X_9(X!0)))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_9(X!0))))),
% 0.18/0.49 inference(transitivity,[status(thm)],[94, 92])).
% 0.18/0.49 tff(96,plain,
% 0.18/0.49 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_7(tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_7(tptp_fun_X_9(X!0)))) | (~r1(X!0, tptp_fun_X_9(X!0))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(97,plain,
% 0.18/0.49 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, tptp_fun_X_9(X!0))) | (~r1(tptp_fun_X_9(X!0), tptp_fun_X_7(tptp_fun_X_9(X!0)))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_9(X!0)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.18/0.49 tff(98,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[97, 91, 54, 79, 77])).
% 0.18/0.49 % SZS output end Proof
%------------------------------------------------------------------------------