TSTP Solution File: LCL636+1.001 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL636+1.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 04:56:50 EDT 2022
% Result : Theorem 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LCL636+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Sep 1 22:43:10 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.41 % SZS status Theorem
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 tff(p2_type, type, (
% 0.21/0.41 p2: $i > $o)).
% 0.21/0.41 tff(tptp_fun_Y_3_type, type, (
% 0.21/0.41 tptp_fun_Y_3: $i)).
% 0.21/0.41 tff(p101_type, type, (
% 0.21/0.41 p101: $i > $o)).
% 0.21/0.41 tff(tptp_fun_Y_4_type, type, (
% 0.21/0.41 tptp_fun_Y_4: $i)).
% 0.21/0.41 tff(p102_type, type, (
% 0.21/0.41 p102: $i > $o)).
% 0.21/0.41 tff(r1_type, type, (
% 0.21/0.41 r1: ( $i * $i ) > $o)).
% 0.21/0.41 tff(tptp_fun_X_0_type, type, (
% 0.21/0.41 tptp_fun_X_0: $i)).
% 0.21/0.41 tff(p100_type, type, (
% 0.21/0.41 p100: $i > $o)).
% 0.21/0.41 tff(p1_type, type, (
% 0.21/0.41 p1: $i > $o)).
% 0.21/0.41 tff(tptp_fun_X_2_type, type, (
% 0.21/0.41 tptp_fun_X_2: $i > $i)).
% 0.21/0.41 tff(tptp_fun_X_1_type, type, (
% 0.21/0.41 tptp_fun_X_1: $i > $i)).
% 0.21/0.41 tff(1,plain,
% 0.21/0.41 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) & (![Y: $i] : ((~r1(X!0, Y)) | (((~((~p101(Y)) & p100(Y))) | ((~((~r1(Y, tptp_fun_X_1(Y))) | (~((~p2(tptp_fun_X_1(Y))) & (~p102(tptp_fun_X_1(Y))) & p101(tptp_fun_X_1(Y)))))) & (~((~r1(Y, tptp_fun_X_2(Y))) | (~(p2(tptp_fun_X_2(Y)) & (~p102(tptp_fun_X_2(Y))) & p101(tptp_fun_X_2(Y)))))))) & ((~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)) | ((![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))) | p1(Y)) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & ((~((~p101(X!0)) & p100(X!0))) | ((~((~r1(X!0, Y!3)) | (~((~p2(Y!3)) & (~p102(Y!3)) & p101(Y!3))))) & (~((~r1(X!0, Y!4)) | (~(p2(Y!4) & (~p102(Y!4)) & p101(Y!4))))))) & ((~p101(X!0)) | ((p2(X!0) | ![Y: $i] : ((~p2(Y)) | (~p101(Y)) | (~r1(X!0, Y)))) & ((~p2(X!0)) | ![Y: $i] : (p2(Y) | (~p101(Y)) | (~r1(X!0, Y)))))) & ((~p100(X!0)) | ((![Y: $i] : ((~p100(Y)) | (~p1(Y)) | (~r1(X!0, Y))) | p1(X!0)) & ((~p1(X!0)) | ![Y: $i] : ((~p100(Y)) | p1(Y) | (~r1(X!0, Y)))))) & (p101(X!0) | (~p102(X!0))) & (p100(X!0) | (~p101(X!0))) & (~p101(X!0)) & p100(X!0))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | (((~((~p101(Y)) & p100(Y))) | ((~((~r1(Y, tptp_fun_X_1(Y))) | (~((~p2(tptp_fun_X_1(Y))) & (~p102(tptp_fun_X_1(Y))) & p101(tptp_fun_X_1(Y)))))) & (~((~r1(Y, tptp_fun_X_2(Y))) | (~(p2(tptp_fun_X_2(Y)) & (~p102(tptp_fun_X_2(Y))) & p101(tptp_fun_X_2(Y)))))))) & ((~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)) | ((![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))) | p1(Y)) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & ((~((~p101(X!0)) & p100(X!0))) | ((~((~r1(X!0, Y!3)) | (~((~p2(Y!3)) & (~p102(Y!3)) & p101(Y!3))))) & (~((~r1(X!0, Y!4)) | (~(p2(Y!4) & (~p102(Y!4)) & p101(Y!4))))))) & ((~p101(X!0)) | ((p2(X!0) | ![Y: $i] : ((~p2(Y)) | (~p101(Y)) | (~r1(X!0, Y)))) & ((~p2(X!0)) | ![Y: $i] : (p2(Y) | (~p101(Y)) | (~r1(X!0, Y)))))) & ((~p100(X!0)) | ((![Y: $i] : ((~p100(Y)) | (~p1(Y)) | (~r1(X!0, Y))) | p1(X!0)) & ((~p1(X!0)) | ![Y: $i] : ((~p100(Y)) | p1(Y) | (~r1(X!0, Y)))))) & (p101(X!0) | (~p102(X!0))) & (p100(X!0) | (~p101(X!0))) & (~p101(X!0)) & p100(X!0))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(2,plain,
% 0.21/0.41 ((![Y: $i] : ((~r1(X!0, Y)) | ((((~((~r1(Y, tptp_fun_X_1(Y))) | (~((~p2(tptp_fun_X_1(Y))) & (~p102(tptp_fun_X_1(Y))) & p101(tptp_fun_X_1(Y)))))) & (~((~r1(Y, tptp_fun_X_2(Y))) | (~(p2(tptp_fun_X_2(Y)) & (~p102(tptp_fun_X_2(Y))) & p101(tptp_fun_X_2(Y))))))) | (~((~p101(Y)) & p100(Y)))) & ((~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)) | ((![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))) | p1(Y)) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & ((~((~p101(X!0)) & p100(X!0))) | ((~((~r1(X!0, Y!3)) | (~((~p2(Y!3)) & (~p102(Y!3)) & p101(Y!3))))) & (~((~r1(X!0, Y!4)) | (~(p2(Y!4) & (~p102(Y!4)) & p101(Y!4))))))) & ((~p101(X!0)) | ((p2(X!0) | ![Y: $i] : ((~p2(Y)) | (~p101(Y)) | (~r1(X!0, Y)))) & ((~p2(X!0)) | ![Y: $i] : (p2(Y) | (~p101(Y)) | (~r1(X!0, Y)))))) & ((~p100(X!0)) | ((![Y: $i] : ((~p100(Y)) | (~p1(Y)) | (~r1(X!0, Y))) | p1(X!0)) & ((~p1(X!0)) | ![Y: $i] : ((~p100(Y)) | p1(Y) | (~r1(X!0, Y)))))) & (p101(X!0) | (~p102(X!0))) & (p100(X!0) | (~p101(X!0))) & (~p101(X!0)) & p100(X!0)) <=> (![Y: $i] : ((~r1(X!0, Y)) | (((~((~p101(Y)) & p100(Y))) | ((~((~r1(Y, tptp_fun_X_1(Y))) | (~((~p2(tptp_fun_X_1(Y))) & (~p102(tptp_fun_X_1(Y))) & p101(tptp_fun_X_1(Y)))))) & (~((~r1(Y, tptp_fun_X_2(Y))) | (~(p2(tptp_fun_X_2(Y)) & (~p102(tptp_fun_X_2(Y))) & p101(tptp_fun_X_2(Y)))))))) & ((~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)) | ((![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))) | p1(Y)) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & ((~((~p101(X!0)) & p100(X!0))) | ((~((~r1(X!0, Y!3)) | (~((~p2(Y!3)) & (~p102(Y!3)) & p101(Y!3))))) & (~((~r1(X!0, Y!4)) | (~(p2(Y!4) & (~p102(Y!4)) & p101(Y!4))))))) & ((~p101(X!0)) | ((p2(X!0) | ![Y: $i] : ((~p2(Y)) | (~p101(Y)) | (~r1(X!0, Y)))) & ((~p2(X!0)) | ![Y: $i] : (p2(Y) | (~p101(Y)) | (~r1(X!0, Y)))))) & ((~p100(X!0)) | ((![Y: $i] : ((~p100(Y)) | (~p1(Y)) | (~r1(X!0, Y))) | p1(X!0)) & ((~p1(X!0)) | ![Y: $i] : ((~p100(Y)) | p1(Y) | (~r1(X!0, Y)))))) & (p101(X!0) | (~p102(X!0))) & (p100(X!0) | (~p101(X!0))) & (~p101(X!0)) & p100(X!0))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(3,plain,
% 0.21/0.41 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) & (![Y: $i] : ((~r1(X!0, Y)) | ((((~((~r1(Y, tptp_fun_X_1(Y))) | (~((~p2(tptp_fun_X_1(Y))) & (~p102(tptp_fun_X_1(Y))) & p101(tptp_fun_X_1(Y)))))) & (~((~r1(Y, tptp_fun_X_2(Y))) | (~(p2(tptp_fun_X_2(Y)) & (~p102(tptp_fun_X_2(Y))) & p101(tptp_fun_X_2(Y))))))) | (~((~p101(Y)) & p100(Y)))) & ((~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)) | ((![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))) | p1(Y)) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & ((~((~p101(X!0)) & p100(X!0))) | ((~((~r1(X!0, Y!3)) | (~((~p2(Y!3)) & (~p102(Y!3)) & p101(Y!3))))) & (~((~r1(X!0, Y!4)) | (~(p2(Y!4) & (~p102(Y!4)) & p101(Y!4))))))) & ((~p101(X!0)) | ((p2(X!0) | ![Y: $i] : ((~p2(Y)) | (~p101(Y)) | (~r1(X!0, Y)))) & ((~p2(X!0)) | ![Y: $i] : (p2(Y) | (~p101(Y)) | (~r1(X!0, Y)))))) & ((~p100(X!0)) | ((![Y: $i] : ((~p100(Y)) | (~p1(Y)) | (~r1(X!0, Y))) | p1(X!0)) & ((~p1(X!0)) | ![Y: $i] : ((~p100(Y)) | p1(Y) | (~r1(X!0, Y)))))) & (p101(X!0) | (~p102(X!0))) & (p100(X!0) | (~p101(X!0))) & (~p101(X!0)) & p100(X!0))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) & (![Y: $i] : ((~r1(X!0, Y)) | (((~((~p101(Y)) & p100(Y))) | ((~((~r1(Y, tptp_fun_X_1(Y))) | (~((~p2(tptp_fun_X_1(Y))) & (~p102(tptp_fun_X_1(Y))) & p101(tptp_fun_X_1(Y)))))) & (~((~r1(Y, tptp_fun_X_2(Y))) | (~(p2(tptp_fun_X_2(Y)) & (~p102(tptp_fun_X_2(Y))) & p101(tptp_fun_X_2(Y)))))))) & ((~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)) | ((![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))) | p1(Y)) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & ((~((~p101(X!0)) & p100(X!0))) | ((~((~r1(X!0, Y!3)) | (~((~p2(Y!3)) & (~p102(Y!3)) & p101(Y!3))))) & (~((~r1(X!0, Y!4)) | (~(p2(Y!4) & (~p102(Y!4)) & p101(Y!4))))))) & ((~p101(X!0)) | ((p2(X!0) | ![Y: $i] : ((~p2(Y)) | (~p101(Y)) | (~r1(X!0, Y)))) & ((~p2(X!0)) | ![Y: $i] : (p2(Y) | (~p101(Y)) | (~r1(X!0, Y)))))) & ((~p100(X!0)) | ((![Y: $i] : ((~p100(Y)) | (~p1(Y)) | (~r1(X!0, Y))) | p1(X!0)) & ((~p1(X!0)) | ![Y: $i] : ((~p100(Y)) | p1(Y) | (~r1(X!0, Y)))))) & (p101(X!0) | (~p102(X!0))) & (p100(X!0) | (~p101(X!0))) & (~p101(X!0)) & p100(X!0)))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[2])).
% 0.21/0.41 tff(4,plain,
% 0.21/0.41 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) & (![Y: $i] : ((~r1(X!0, Y)) | ((((~((~r1(Y, tptp_fun_X_1(Y))) | (~((~p2(tptp_fun_X_1(Y))) & (~p102(tptp_fun_X_1(Y))) & p101(tptp_fun_X_1(Y)))))) & (~((~r1(Y, tptp_fun_X_2(Y))) | (~(p2(tptp_fun_X_2(Y)) & (~p102(tptp_fun_X_2(Y))) & p101(tptp_fun_X_2(Y))))))) | (~((~p101(Y)) & p100(Y)))) & ((~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)) | ((![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))) | p1(Y)) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & ((~((~p101(X!0)) & p100(X!0))) | ((~((~r1(X!0, Y!3)) | (~((~p2(Y!3)) & (~p102(Y!3)) & p101(Y!3))))) & (~((~r1(X!0, Y!4)) | (~(p2(Y!4) & (~p102(Y!4)) & p101(Y!4))))))) & ((~p101(X!0)) | ((p2(X!0) | ![Y: $i] : ((~p2(Y)) | (~p101(Y)) | (~r1(X!0, Y)))) & ((~p2(X!0)) | ![Y: $i] : (p2(Y) | (~p101(Y)) | (~r1(X!0, Y)))))) & ((~p100(X!0)) | ((![Y: $i] : ((~p100(Y)) | (~p1(Y)) | (~r1(X!0, Y))) | p1(X!0)) & ((~p1(X!0)) | ![Y: $i] : ((~p100(Y)) | p1(Y) | (~r1(X!0, Y)))))) & (p101(X!0) | (~p102(X!0))) & (p100(X!0) | (~p101(X!0))) & (~p101(X!0)) & p100(X!0))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | (((~((~p101(Y)) & p100(Y))) | ((~((~r1(Y, tptp_fun_X_1(Y))) | (~((~p2(tptp_fun_X_1(Y))) & (~p102(tptp_fun_X_1(Y))) & p101(tptp_fun_X_1(Y)))))) & (~((~r1(Y, tptp_fun_X_2(Y))) | (~(p2(tptp_fun_X_2(Y)) & (~p102(tptp_fun_X_2(Y))) & p101(tptp_fun_X_2(Y)))))))) & ((~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)) | ((![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))) | p1(Y)) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & ((~((~p101(X!0)) & p100(X!0))) | ((~((~r1(X!0, Y!3)) | (~((~p2(Y!3)) & (~p102(Y!3)) & p101(Y!3))))) & (~((~r1(X!0, Y!4)) | (~(p2(Y!4) & (~p102(Y!4)) & p101(Y!4))))))) & ((~p101(X!0)) | ((p2(X!0) | ![Y: $i] : ((~p2(Y)) | (~p101(Y)) | (~r1(X!0, Y)))) & ((~p2(X!0)) | ![Y: $i] : (p2(Y) | (~p101(Y)) | (~r1(X!0, Y)))))) & ((~p100(X!0)) | ((![Y: $i] : ((~p100(Y)) | (~p1(Y)) | (~r1(X!0, Y))) | p1(X!0)) & ((~p1(X!0)) | ![Y: $i] : ((~p100(Y)) | p1(Y) | (~r1(X!0, Y)))))) & (p101(X!0) | (~p102(X!0))) & (p100(X!0) | (~p101(X!0))) & (~p101(X!0)) & p100(X!0))),
% 0.21/0.41 inference(transitivity,[status(thm)],[3, 1])).
% 0.21/0.41 tff(5,plain,
% 0.21/0.41 (?[X: $i] : (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) | (~(![Y: $i] : ((~r1(X, 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)))) & ((~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)) | ((![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))) | p1(Y)) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & ((~((~p101(X)) & p100(X))) | ((~![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) & (~p102(Y)) & p101(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & (~p102(Y)) & p101(Y))))))) & ((~p101(X)) | ((p2(X) | ![Y: $i] : ((~p2(Y)) | (~p101(Y)) | (~r1(X, Y)))) & ((~p2(X)) | ![Y: $i] : (p2(Y) | (~p101(Y)) | (~r1(X, Y)))))) & ((~p100(X)) | ((![Y: $i] : ((~p100(Y)) | (~p1(Y)) | (~r1(X, Y))) | p1(X)) & ((~p1(X)) | ![Y: $i] : ((~p100(Y)) | p1(Y) | (~r1(X, Y)))))) & (p101(X) | (~p102(X))) & (p100(X) | (~p101(X))) & (~p101(X)) & p100(X))))) <=> ?[X: $i] : (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) | (~(![Y: $i] : ((~r1(X, 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)))) & ((~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)) | ((![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))) | p1(Y)) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & ((~((~p101(X)) & p100(X))) | ((~![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) & (~p102(Y)) & p101(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & (~p102(Y)) & p101(Y))))))) & ((~p101(X)) | ((p2(X) | ![Y: $i] : ((~p2(Y)) | (~p101(Y)) | (~r1(X, Y)))) & ((~p2(X)) | ![Y: $i] : (p2(Y) | (~p101(Y)) | (~r1(X, Y)))))) & ((~p100(X)) | ((![Y: $i] : ((~p100(Y)) | (~p1(Y)) | (~r1(X, Y))) | p1(X)) & ((~p1(X)) | ![Y: $i] : ((~p100(Y)) | p1(Y) | (~r1(X, Y)))))) & (p101(X) | (~p102(X))) & (p100(X) | (~p101(X))) & (~p101(X)) & p100(X)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(6,plain,
% 0.21/0.42 ((~(~?[X: $i] : (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) | (~(![Y: $i] : ((~r1(X, 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)))) & ((~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)) | ((![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))) | p1(Y)) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & ((~((~p101(X)) & p100(X))) | ((~![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) & (~p102(Y)) & p101(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & (~p102(Y)) & p101(Y))))))) & ((~p101(X)) | ((p2(X) | ![Y: $i] : ((~p2(Y)) | (~p101(Y)) | (~r1(X, Y)))) & ((~p2(X)) | ![Y: $i] : (p2(Y) | (~p101(Y)) | (~r1(X, Y)))))) & ((~p100(X)) | ((![Y: $i] : ((~p100(Y)) | (~p1(Y)) | (~r1(X, Y))) | p1(X)) & ((~p1(X)) | ![Y: $i] : ((~p100(Y)) | p1(Y) | (~r1(X, Y)))))) & (p101(X) | (~p102(X))) & (p100(X) | (~p101(X))) & (~p101(X)) & p100(X))))))) <=> ?[X: $i] : (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) | (~(![Y: $i] : ((~r1(X, 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)))) & ((~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)) | ((![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))) | p1(Y)) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & ((~((~p101(X)) & p100(X))) | ((~![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) & (~p102(Y)) & p101(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & (~p102(Y)) & p101(Y))))))) & ((~p101(X)) | ((p2(X) | ![Y: $i] : ((~p2(Y)) | (~p101(Y)) | (~r1(X, Y)))) & ((~p2(X)) | ![Y: $i] : (p2(Y) | (~p101(Y)) | (~r1(X, Y)))))) & ((~p100(X)) | ((![Y: $i] : ((~p100(Y)) | (~p1(Y)) | (~r1(X, Y))) | p1(X)) & ((~p1(X)) | ![Y: $i] : ((~p100(Y)) | p1(Y) | (~r1(X, Y)))))) & (p101(X) | (~p102(X))) & (p100(X) | (~p101(X))) & (~p101(X)) & p100(X)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(7,plain,
% 0.21/0.42 ((~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~(((((((![Y: $i] : ((~r1(X, 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)) | (~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)))) & (p101(Y) | (~p102(Y)))) & (p100(Y) | (~p101(Y))))) & (((~![Y: $i] : ((~r1(X, Y)) | (~(((~p2(Y)) & (~p102(Y))) & p101(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p102(Y))) & p101(Y)))))) | (~((~p101(X)) & p100(X))))) & (((![Y: $i] : (((~r1(X, Y)) | (~p2(Y))) | (~p101(Y))) | p2(X)) & (![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~p101(Y))) | (~p2(X)))) | (~p101(X)))) & (((![Y: $i] : (((~r1(X, Y)) | (~p1(Y))) | (~p100(Y))) | p1(X)) & (![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~p100(Y))) | (~p1(X)))) | (~p100(X)))) & (p101(X) | (~p102(X)))) & (p100(X) | (~p101(X)))) & (~p101(X))) & p100(X)))))) <=> (~?[X: $i] : (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) | (~(![Y: $i] : ((~r1(X, 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)))) & ((~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)) | ((![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))) | p1(Y)) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & ((~((~p101(X)) & p100(X))) | ((~![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) & (~p102(Y)) & p101(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & (~p102(Y)) & p101(Y))))))) & ((~p101(X)) | ((p2(X) | ![Y: $i] : ((~p2(Y)) | (~p101(Y)) | (~r1(X, Y)))) & ((~p2(X)) | ![Y: $i] : (p2(Y) | (~p101(Y)) | (~r1(X, Y)))))) & ((~p100(X)) | ((![Y: $i] : ((~p100(Y)) | (~p1(Y)) | (~r1(X, Y))) | p1(X)) & ((~p1(X)) | ![Y: $i] : ((~p100(Y)) | p1(Y) | (~r1(X, Y)))))) & (p101(X) | (~p102(X))) & (p100(X) | (~p101(X))) & (~p101(X)) & p100(X))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(8,plain,
% 0.21/0.42 ((~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~(((((((![Y: $i] : ((~r1(X, 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)) | (~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)))) & (p101(Y) | (~p102(Y)))) & (p100(Y) | (~p101(Y))))) & (((~![Y: $i] : ((~r1(X, Y)) | (~(((~p2(Y)) & (~p102(Y))) & p101(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p102(Y))) & p101(Y)))))) | (~((~p101(X)) & p100(X))))) & (((![Y: $i] : (((~r1(X, Y)) | (~p2(Y))) | (~p101(Y))) | p2(X)) & (![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~p101(Y))) | (~p2(X)))) | (~p101(X)))) & (((![Y: $i] : (((~r1(X, Y)) | (~p1(Y))) | (~p100(Y))) | p1(X)) & (![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~p100(Y))) | (~p1(X)))) | (~p100(X)))) & (p101(X) | (~p102(X)))) & (p100(X) | (~p101(X)))) & (~p101(X))) & p100(X))))))) <=> (~(~?[X: $i] : (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) | (~(![Y: $i] : ((~r1(X, 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)))) & ((~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)) | ((![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))) | p1(Y)) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & ((~((~p101(X)) & p100(X))) | ((~![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) & (~p102(Y)) & p101(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & (~p102(Y)) & p101(Y))))))) & ((~p101(X)) | ((p2(X) | ![Y: $i] : ((~p2(Y)) | (~p101(Y)) | (~r1(X, Y)))) & ((~p2(X)) | ![Y: $i] : (p2(Y) | (~p101(Y)) | (~r1(X, Y)))))) & ((~p100(X)) | ((![Y: $i] : ((~p100(Y)) | (~p1(Y)) | (~r1(X, Y))) | p1(X)) & ((~p1(X)) | ![Y: $i] : ((~p100(Y)) | p1(Y) | (~r1(X, Y)))))) & (p101(X) | (~p102(X))) & (p100(X) | (~p101(X))) & (~p101(X)) & p100(X)))))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[7])).
% 0.21/0.42 tff(9,plain,
% 0.21/0.42 ((~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~(((((((![Y: $i] : ((~r1(X, 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)) | (~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)))) & (p101(Y) | (~p102(Y)))) & (p100(Y) | (~p101(Y))))) & (((~![Y: $i] : ((~r1(X, Y)) | (~(((~p2(Y)) & (~p102(Y))) & p101(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p102(Y))) & p101(Y)))))) | (~((~p101(X)) & p100(X))))) & (((![Y: $i] : (((~r1(X, Y)) | (~p2(Y))) | (~p101(Y))) | p2(X)) & (![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~p101(Y))) | (~p2(X)))) | (~p101(X)))) & (((![Y: $i] : (((~r1(X, Y)) | (~p1(Y))) | (~p100(Y))) | p1(X)) & (![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~p100(Y))) | (~p1(X)))) | (~p100(X)))) & (p101(X) | (~p102(X)))) & (p100(X) | (~p101(X)))) & (~p101(X))) & p100(X))))))) <=> ?[X: $i] : (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) | (~(![Y: $i] : ((~r1(X, 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)))) & ((~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)) | ((![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))) | p1(Y)) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & ((~((~p101(X)) & p100(X))) | ((~![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) & (~p102(Y)) & p101(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & (~p102(Y)) & p101(Y))))))) & ((~p101(X)) | ((p2(X) | ![Y: $i] : ((~p2(Y)) | (~p101(Y)) | (~r1(X, Y)))) & ((~p2(X)) | ![Y: $i] : (p2(Y) | (~p101(Y)) | (~r1(X, Y)))))) & ((~p100(X)) | ((![Y: $i] : ((~p100(Y)) | (~p1(Y)) | (~r1(X, Y))) | p1(X)) & ((~p1(X)) | ![Y: $i] : ((~p100(Y)) | p1(Y) | (~r1(X, Y)))))) & (p101(X) | (~p102(X))) & (p100(X) | (~p101(X))) & (~p101(X)) & p100(X)))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[8, 6])).
% 0.21/0.42 tff(10,axiom,(~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~(((((((![Y: $i] : ((~r1(X, 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)) | (~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)))) & (p101(Y) | (~p102(Y)))) & (p100(Y) | (~p101(Y))))) & (((~![Y: $i] : ((~r1(X, Y)) | (~(((~p2(Y)) & (~p102(Y))) & p101(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | (~((p2(Y) & (~p102(Y))) & p101(Y)))))) | (~((~p101(X)) & p100(X))))) & (((![Y: $i] : (((~r1(X, Y)) | (~p2(Y))) | (~p101(Y))) | p2(X)) & (![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~p101(Y))) | (~p2(X)))) | (~p101(X)))) & (((![Y: $i] : (((~r1(X, Y)) | (~p1(Y))) | (~p100(Y))) | p1(X)) & (![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~p100(Y))) | (~p1(X)))) | (~p100(X)))) & (p101(X) | (~p102(X)))) & (p100(X) | (~p101(X)))) & (~p101(X))) & p100(X))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','main')).
% 0.21/0.42 tff(11,plain,
% 0.21/0.42 (?[X: $i] : (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) | (~(![Y: $i] : ((~r1(X, 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)))) & ((~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)) | ((![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))) | p1(Y)) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & ((~((~p101(X)) & p100(X))) | ((~![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) & (~p102(Y)) & p101(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & (~p102(Y)) & p101(Y))))))) & ((~p101(X)) | ((p2(X) | ![Y: $i] : ((~p2(Y)) | (~p101(Y)) | (~r1(X, Y)))) & ((~p2(X)) | ![Y: $i] : (p2(Y) | (~p101(Y)) | (~r1(X, Y)))))) & ((~p100(X)) | ((![Y: $i] : ((~p100(Y)) | (~p1(Y)) | (~r1(X, Y))) | p1(X)) & ((~p1(X)) | ![Y: $i] : ((~p100(Y)) | p1(Y) | (~r1(X, Y)))))) & (p101(X) | (~p102(X))) & (p100(X) | (~p101(X))) & (~p101(X)) & p100(X)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.21/0.42 tff(12,plain,
% 0.21/0.42 (?[X: $i] : (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) | (~(![Y: $i] : ((~r1(X, 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)))) & ((~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)) | ((![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))) | p1(Y)) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & ((~((~p101(X)) & p100(X))) | ((~![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) & (~p102(Y)) & p101(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & (~p102(Y)) & p101(Y))))))) & ((~p101(X)) | ((p2(X) | ![Y: $i] : ((~p2(Y)) | (~p101(Y)) | (~r1(X, Y)))) & ((~p2(X)) | ![Y: $i] : (p2(Y) | (~p101(Y)) | (~r1(X, Y)))))) & ((~p100(X)) | ((![Y: $i] : ((~p100(Y)) | (~p1(Y)) | (~r1(X, Y))) | p1(X)) & ((~p1(X)) | ![Y: $i] : ((~p100(Y)) | p1(Y) | (~r1(X, Y)))))) & (p101(X) | (~p102(X))) & (p100(X) | (~p101(X))) & (~p101(X)) & p100(X)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[11, 5])).
% 0.21/0.42 tff(13,plain,
% 0.21/0.42 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | (((~((~p101(Y)) & p100(Y))) | ((~((~r1(Y, tptp_fun_X_1(Y))) | (~((~p2(tptp_fun_X_1(Y))) & (~p102(tptp_fun_X_1(Y))) & p101(tptp_fun_X_1(Y)))))) & (~((~r1(Y, tptp_fun_X_2(Y))) | (~(p2(tptp_fun_X_2(Y)) & (~p102(tptp_fun_X_2(Y))) & p101(tptp_fun_X_2(Y)))))))) & ((~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)) | ((![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))) | p1(Y)) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & ((~((~p101(X!0)) & p100(X!0))) | ((~((~r1(X!0, Y!3)) | (~((~p2(Y!3)) & (~p102(Y!3)) & p101(Y!3))))) & (~((~r1(X!0, Y!4)) | (~(p2(Y!4) & (~p102(Y!4)) & p101(Y!4))))))) & ((~p101(X!0)) | ((p2(X!0) | ![Y: $i] : ((~p2(Y)) | (~p101(Y)) | (~r1(X!0, Y)))) & ((~p2(X!0)) | ![Y: $i] : (p2(Y) | (~p101(Y)) | (~r1(X!0, Y)))))) & ((~p100(X!0)) | ((![Y: $i] : ((~p100(Y)) | (~p1(Y)) | (~r1(X!0, Y))) | p1(X!0)) & ((~p1(X!0)) | ![Y: $i] : ((~p100(Y)) | p1(Y) | (~r1(X!0, Y)))))) & (p101(X!0) | (~p102(X!0))) & (p100(X!0) | (~p101(X!0))) & (~p101(X!0)) & p100(X!0)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[12, 4])).
% 0.21/0.42 tff(14,plain,
% 0.21/0.42 (~p101(X!0)),
% 0.21/0.42 inference(and_elim,[status(thm)],[13])).
% 0.21/0.42 tff(15,plain,
% 0.21/0.42 (p100(X!0)),
% 0.21/0.42 inference(and_elim,[status(thm)],[13])).
% 0.21/0.42 tff(16,plain,
% 0.21/0.42 (((p101(X!0) | (~p100(X!0))) | (~((~r1(X!0, Y!3)) | p2(Y!3) | p102(Y!3) | (~r1(X!0, Y!4)) | p102(Y!4) | (~p101(Y!3)) | (~p2(Y!4)) | (~p101(Y!4))))) <=> ((~p100(X!0)) | p101(X!0) | (~((~r1(X!0, Y!3)) | p2(Y!3) | p102(Y!3) | (~r1(X!0, Y!4)) | p102(Y!4) | (~p101(Y!3)) | (~p2(Y!4)) | (~p101(Y!4)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(17,plain,
% 0.21/0.42 (((~((~r1(X!0, Y!3)) | p2(Y!3) | p102(Y!3) | (~p101(Y!3)))) & (~((~r1(X!0, Y!4)) | p102(Y!4) | (~p2(Y!4)) | (~p101(Y!4))))) <=> (~((~r1(X!0, Y!3)) | p2(Y!3) | p102(Y!3) | (~r1(X!0, Y!4)) | p102(Y!4) | (~p101(Y!3)) | (~p2(Y!4)) | (~p101(Y!4))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(18,plain,
% 0.21/0.42 ((~((~r1(X!0, Y!4)) | (~(p2(Y!4) & (~p102(Y!4)) & p101(Y!4))))) <=> (~((~r1(X!0, Y!4)) | p102(Y!4) | (~p2(Y!4)) | (~p101(Y!4))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(19,plain,
% 0.21/0.42 ((~((~r1(X!0, Y!3)) | (~((~p2(Y!3)) & (~p102(Y!3)) & p101(Y!3))))) <=> (~((~r1(X!0, Y!3)) | p2(Y!3) | p102(Y!3) | (~p101(Y!3))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(20,plain,
% 0.21/0.42 (((~((~r1(X!0, Y!3)) | (~((~p2(Y!3)) & (~p102(Y!3)) & p101(Y!3))))) & (~((~r1(X!0, Y!4)) | (~(p2(Y!4) & (~p102(Y!4)) & p101(Y!4)))))) <=> ((~((~r1(X!0, Y!3)) | p2(Y!3) | p102(Y!3) | (~p101(Y!3)))) & (~((~r1(X!0, Y!4)) | p102(Y!4) | (~p2(Y!4)) | (~p101(Y!4)))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[19, 18])).
% 0.21/0.42 tff(21,plain,
% 0.21/0.42 (((~((~r1(X!0, Y!3)) | (~((~p2(Y!3)) & (~p102(Y!3)) & p101(Y!3))))) & (~((~r1(X!0, Y!4)) | (~(p2(Y!4) & (~p102(Y!4)) & p101(Y!4)))))) <=> (~((~r1(X!0, Y!3)) | p2(Y!3) | p102(Y!3) | (~r1(X!0, Y!4)) | p102(Y!4) | (~p101(Y!3)) | (~p2(Y!4)) | (~p101(Y!4))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[20, 17])).
% 0.21/0.42 tff(22,plain,
% 0.21/0.42 ((~(~(p101(X!0) | (~p100(X!0))))) <=> (p101(X!0) | (~p100(X!0)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(23,plain,
% 0.21/0.43 (((~p101(X!0)) & p100(X!0)) <=> (~(p101(X!0) | (~p100(X!0))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(24,plain,
% 0.21/0.43 ((~((~p101(X!0)) & p100(X!0))) <=> (~(~(p101(X!0) | (~p100(X!0)))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[23])).
% 0.21/0.43 tff(25,plain,
% 0.21/0.43 ((~((~p101(X!0)) & p100(X!0))) <=> (p101(X!0) | (~p100(X!0)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[24, 22])).
% 0.21/0.43 tff(26,plain,
% 0.21/0.43 (((~((~p101(X!0)) & p100(X!0))) | ((~((~r1(X!0, Y!3)) | (~((~p2(Y!3)) & (~p102(Y!3)) & p101(Y!3))))) & (~((~r1(X!0, Y!4)) | (~(p2(Y!4) & (~p102(Y!4)) & p101(Y!4))))))) <=> ((p101(X!0) | (~p100(X!0))) | (~((~r1(X!0, Y!3)) | p2(Y!3) | p102(Y!3) | (~r1(X!0, Y!4)) | p102(Y!4) | (~p101(Y!3)) | (~p2(Y!4)) | (~p101(Y!4)))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[25, 21])).
% 0.21/0.43 tff(27,plain,
% 0.21/0.43 (((~((~p101(X!0)) & p100(X!0))) | ((~((~r1(X!0, Y!3)) | (~((~p2(Y!3)) & (~p102(Y!3)) & p101(Y!3))))) & (~((~r1(X!0, Y!4)) | (~(p2(Y!4) & (~p102(Y!4)) & p101(Y!4))))))) <=> ((~p100(X!0)) | p101(X!0) | (~((~r1(X!0, Y!3)) | p2(Y!3) | p102(Y!3) | (~r1(X!0, Y!4)) | p102(Y!4) | (~p101(Y!3)) | (~p2(Y!4)) | (~p101(Y!4)))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[26, 16])).
% 0.21/0.43 tff(28,plain,
% 0.21/0.43 ((~((~p101(X!0)) & p100(X!0))) | ((~((~r1(X!0, Y!3)) | (~((~p2(Y!3)) & (~p102(Y!3)) & p101(Y!3))))) & (~((~r1(X!0, Y!4)) | (~(p2(Y!4) & (~p102(Y!4)) & p101(Y!4))))))),
% 0.21/0.43 inference(and_elim,[status(thm)],[13])).
% 0.21/0.43 tff(29,plain,
% 0.21/0.43 ((~p100(X!0)) | p101(X!0) | (~((~r1(X!0, Y!3)) | p2(Y!3) | p102(Y!3) | (~r1(X!0, Y!4)) | p102(Y!4) | (~p101(Y!3)) | (~p2(Y!4)) | (~p101(Y!4))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.43 tff(30,plain,
% 0.21/0.43 (~((~r1(X!0, Y!3)) | p2(Y!3) | p102(Y!3) | (~r1(X!0, Y!4)) | p102(Y!4) | (~p101(Y!3)) | (~p2(Y!4)) | (~p101(Y!4)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[29, 15, 14])).
% 0.21/0.43 tff(31,plain,
% 0.21/0.43 (((~r1(X!0, Y!3)) | p2(Y!3) | p102(Y!3) | (~r1(X!0, Y!4)) | p102(Y!4) | (~p101(Y!3)) | (~p2(Y!4)) | (~p101(Y!4))) | (~p2(Y!3))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(32,plain,
% 0.21/0.43 (~p2(Y!3)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.21/0.43 tff(33,plain,
% 0.21/0.43 (((~r1(X!0, Y!3)) | p2(Y!3) | p102(Y!3) | (~r1(X!0, Y!4)) | p102(Y!4) | (~p101(Y!3)) | (~p2(Y!4)) | (~p101(Y!4))) | r1(X!0, Y!3)),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(34,plain,
% 0.21/0.43 (r1(X!0, Y!3)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[33, 30])).
% 0.21/0.43 tff(35,plain,
% 0.21/0.43 (^[Y: $i] : refl((p2(Y) | (~r1(X!0, Y))) <=> (p2(Y) | (~r1(X!0, Y))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(36,plain,
% 0.21/0.43 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[35])).
% 0.21/0.43 tff(37,plain,
% 0.21/0.43 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)))),
% 0.21/0.43 inference(and_elim,[status(thm)],[13])).
% 0.21/0.43 tff(38,plain,
% 0.21/0.43 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.21/0.43 tff(39,plain,
% 0.21/0.43 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)))) | (p2(Y!3) | (~r1(X!0, Y!3)))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)))) | p2(Y!3) | (~r1(X!0, Y!3)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(40,plain,
% 0.21/0.43 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)))) | (p2(Y!3) | (~r1(X!0, Y!3)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(41,plain,
% 0.21/0.43 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)))) | p2(Y!3) | (~r1(X!0, Y!3))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.21/0.43 tff(42,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[41, 38, 34, 32])).
% 0.21/0.43 % SZS output end Proof
%------------------------------------------------------------------------------