TSTP Solution File: LCL676+1.001 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL676+1.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 04:57:47 EDT 2022
% Result : Theorem 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LCL676+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n024.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Sep 2 00:01:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 % SZS output start Proof
% 0.19/0.44 tff(p3_type, type, (
% 0.19/0.44 p3: $i > $o)).
% 0.19/0.44 tff(tptp_fun_X_8_type, type, (
% 0.19/0.44 tptp_fun_X_8: $i > $i)).
% 0.19/0.44 tff(tptp_fun_X_4_type, type, (
% 0.19/0.44 tptp_fun_X_4: $i)).
% 0.19/0.44 tff(r1_type, type, (
% 0.19/0.44 r1: ( $i * $i ) > $o)).
% 0.19/0.44 tff(tptp_fun_X_0_type, type, (
% 0.19/0.44 tptp_fun_X_0: $i)).
% 0.19/0.44 tff(tptp_fun_Y_3_type, type, (
% 0.19/0.44 tptp_fun_Y_3: $i)).
% 0.19/0.44 tff(p1_type, type, (
% 0.19/0.44 p1: $i > $o)).
% 0.19/0.44 tff(p2_type, type, (
% 0.19/0.44 p2: $i > $o)).
% 0.19/0.44 tff(tptp_fun_Y_7_type, type, (
% 0.19/0.44 tptp_fun_Y_7: $i > $i)).
% 0.19/0.44 tff(tptp_fun_X_6_type, type, (
% 0.19/0.44 tptp_fun_X_6: $i > $i)).
% 0.19/0.44 tff(tptp_fun_Y_5_type, type, (
% 0.19/0.44 tptp_fun_Y_5: $i)).
% 0.19/0.44 tff(tptp_fun_X_19_type, type, (
% 0.19/0.44 tptp_fun_X_19: $i > $i)).
% 0.19/0.44 tff(tptp_fun_Y_23_type, type, (
% 0.19/0.44 tptp_fun_Y_23: $i > $i)).
% 0.19/0.44 tff(tptp_fun_X_22_type, type, (
% 0.19/0.44 tptp_fun_X_22: $i > $i)).
% 0.19/0.44 tff(tptp_fun_X_21_type, type, (
% 0.19/0.44 tptp_fun_X_21: $i > $i)).
% 0.19/0.44 tff(tptp_fun_Y_20_type, type, (
% 0.19/0.44 tptp_fun_Y_20: $i > $i)).
% 0.19/0.44 tff(tptp_fun_Y_16_type, type, (
% 0.19/0.44 tptp_fun_Y_16: $i)).
% 0.19/0.44 tff(tptp_fun_X_13_type, type, (
% 0.19/0.44 tptp_fun_X_13: $i > $i)).
% 0.19/0.44 tff(tptp_fun_Y_12_type, type, (
% 0.19/0.44 tptp_fun_Y_12: $i > $i)).
% 0.19/0.44 tff(tptp_fun_Y_18_type, type, (
% 0.19/0.44 tptp_fun_Y_18: $i)).
% 0.19/0.44 tff(tptp_fun_X_17_type, type, (
% 0.19/0.44 tptp_fun_X_17: $i)).
% 0.19/0.44 tff(tptp_fun_X_15_type, type, (
% 0.19/0.44 tptp_fun_X_15: $i)).
% 0.19/0.44 tff(tptp_fun_Y_14_type, type, (
% 0.19/0.44 tptp_fun_Y_14: $i)).
% 0.19/0.44 tff(tptp_fun_Y_11_type, type, (
% 0.19/0.44 tptp_fun_Y_11: $i)).
% 0.19/0.44 tff(p4_type, type, (
% 0.19/0.44 p4: $i > $o)).
% 0.19/0.44 tff(tptp_fun_Y_10_type, type, (
% 0.19/0.44 tptp_fun_Y_10: $i > $i)).
% 0.19/0.44 tff(tptp_fun_X_9_type, type, (
% 0.19/0.44 tptp_fun_X_9: $i > $i)).
% 0.19/0.44 tff(tptp_fun_Y_2_type, type, (
% 0.19/0.44 tptp_fun_Y_2: $i)).
% 0.19/0.44 tff(tptp_fun_Y_1_type, type, (
% 0.19/0.44 tptp_fun_Y_1: $i)).
% 0.19/0.44 tff(1,plain,
% 0.19/0.44 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_19(Y))) | p2(tptp_fun_X_19(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_19(Y), Y))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_19(Y))) | p2(tptp_fun_X_19(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(2,plain,
% 0.19/0.44 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_19(Y))) | p2(tptp_fun_X_19(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_19(Y), Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_19(Y))) | p2(tptp_fun_X_19(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.44 tff(3,plain,
% 0.19/0.44 (^[Y: $i] : refl((p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_19(Y))) | p2(tptp_fun_X_19(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_19(Y), Y))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_19(Y))) | p2(tptp_fun_X_19(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_19(Y), Y))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(4,plain,
% 0.19/0.44 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_19(Y))) | p2(tptp_fun_X_19(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_19(Y), Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_19(Y))) | p2(tptp_fun_X_19(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_19(Y), Y)))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.44 tff(5,plain,
% 0.19/0.44 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_19(Y))) | p2(tptp_fun_X_19(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_19(Y), Y))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_19(Y))) | p2(tptp_fun_X_19(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_19(Y), Y))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(6,plain,
% 0.19/0.44 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_19(Y))) | p2(tptp_fun_X_19(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_19(Y), Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_19(Y))) | p2(tptp_fun_X_19(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_19(Y), Y)))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[5])).
% 0.19/0.45 tff(7,plain,
% 0.19/0.45 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_19(Y))) | p2(tptp_fun_X_19(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_19(Y), Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_19(Y))) | p2(tptp_fun_X_19(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_19(Y), Y)))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[6, 4])).
% 0.19/0.45 tff(8,plain,
% 0.19/0.45 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_19(Y)) & (~p2(tptp_fun_X_19(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_19(Y), Y))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_19(Y))) | p2(tptp_fun_X_19(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_19(Y), Y))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(9,plain,
% 0.19/0.45 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_19(Y)) & (~p2(tptp_fun_X_19(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_19(Y), Y))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_19(Y))) | p2(tptp_fun_X_19(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_19(Y), Y)))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[8])).
% 0.19/0.45 tff(10,plain,
% 0.19/0.45 (((~((~r1(X!0, Y!1)) | p4(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & ((r1(X!0, Y!3) & r1(Y!3, X!4) & ![Y: $i] : ((~p3(Y)) | (~r1(X!4, Y))) & (~p1(Y!3))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) & ![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p4(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p4(tptp_fun_Y_10(Y)))))) & (((((r1(X!0, Y!11) & (~p2(Y!11)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!11, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_12(X)) & p2(tptp_fun_Y_12(X)) & (~((~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))) | p2(tptp_fun_X_13(X)))))))) & (p2(X!0) | (r1(X!0, Y!14) & p2(Y!14) & (~((~r1(Y!14, X!15)) | p2(X!15)))))) | (r1(X!0, Y!16) & ((r1(Y!16, X!17) & r1(X!17, Y!18) & (~p2(Y!18)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!18, X))) & ![X: $i] : (p2(X) | (~r1(Y!16, X)) | (r1(X, tptp_fun_Y_12(X)) & p2(tptp_fun_Y_12(X)) & (~((~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))) | p2(tptp_fun_X_13(X))))))) | ((~p2(Y!16)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!16, X))))) & ![X: $i] : ((~r1(Y!16, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | (r1(Y, tptp_fun_X_19(Y)) & (~p2(tptp_fun_X_19(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_19(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & r1(X, tptp_fun_Y_20(X)) & r1(tptp_fun_Y_20(X), tptp_fun_X_21(X)) & (~p2(tptp_fun_X_21(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(X), Y))))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_19(Y)) & (~p2(tptp_fun_X_19(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_19(Y), Y)))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_22(Y)) & p1(tptp_fun_X_22(Y)) & (~((~r1(tptp_fun_X_22(Y), tptp_fun_Y_23(Y))) | p1(tptp_fun_Y_23(Y))))))) <=> ((~((~r1(X!0, Y!1)) | p4(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & ((r1(X!0, Y!3) & r1(Y!3, X!4) & ![Y: $i] : ((~p3(Y)) | (~r1(X!4, Y))) & (~p1(Y!3))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) & ![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p4(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p4(tptp_fun_Y_10(Y)))))) & ((((r1(X!0, Y!11) & (~p2(Y!11)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!11, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_12(X)) & p2(tptp_fun_Y_12(X)) & (~((~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))) | p2(tptp_fun_X_13(X)))))))) & (p2(X!0) | (r1(X!0, Y!14) & p2(Y!14) & (~((~r1(Y!14, X!15)) | p2(X!15)))))) | (r1(X!0, Y!16) & ((r1(Y!16, X!17) & r1(X!17, Y!18) & (~p2(Y!18)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!18, X))) & ![X: $i] : (p2(X) | (~r1(Y!16, X)) | (r1(X, tptp_fun_Y_12(X)) & p2(tptp_fun_Y_12(X)) & (~((~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))) | p2(tptp_fun_X_13(X))))))) | ((~p2(Y!16)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!16, X))))) & ![X: $i] : ((~r1(Y!16, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | (r1(Y, tptp_fun_X_19(Y)) & (~p2(tptp_fun_X_19(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_19(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & r1(X, tptp_fun_Y_20(X)) & r1(tptp_fun_Y_20(X), tptp_fun_X_21(X)) & (~p2(tptp_fun_X_21(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(X), Y))))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_19(Y)) & (~p2(tptp_fun_X_19(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_19(Y), Y))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_22(Y)) & p1(tptp_fun_X_22(Y)) & (~((~r1(tptp_fun_X_22(Y), tptp_fun_Y_23(Y))) | p1(tptp_fun_Y_23(Y)))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(11,plain,
% 0.19/0.45 (^[Y: $i] : trans(monotonicity(rewrite(((~(~r1(Y, tptp_fun_X_22(Y)))) & (~(~p1(tptp_fun_X_22(Y)))) & (~((~r1(tptp_fun_X_22(Y), tptp_fun_Y_23(Y))) | p1(tptp_fun_Y_23(Y))))) <=> (r1(Y, tptp_fun_X_22(Y)) & p1(tptp_fun_X_22(Y)) & (~((~r1(tptp_fun_X_22(Y), tptp_fun_Y_23(Y))) | p1(tptp_fun_Y_23(Y)))))), (((~r1(X!0, Y)) | p1(Y) | ((~(~r1(Y, tptp_fun_X_22(Y)))) & (~(~p1(tptp_fun_X_22(Y)))) & (~((~r1(tptp_fun_X_22(Y), tptp_fun_Y_23(Y))) | p1(tptp_fun_Y_23(Y)))))) <=> ((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_22(Y)) & p1(tptp_fun_X_22(Y)) & (~((~r1(tptp_fun_X_22(Y), tptp_fun_Y_23(Y))) | p1(tptp_fun_Y_23(Y)))))))), rewrite(((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_22(Y)) & p1(tptp_fun_X_22(Y)) & (~((~r1(tptp_fun_X_22(Y), tptp_fun_Y_23(Y))) | p1(tptp_fun_Y_23(Y)))))) <=> (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_22(Y)) & p1(tptp_fun_X_22(Y)) & (~((~r1(tptp_fun_X_22(Y), tptp_fun_Y_23(Y))) | p1(tptp_fun_Y_23(Y))))))), (((~r1(X!0, Y)) | p1(Y) | ((~(~r1(Y, tptp_fun_X_22(Y)))) & (~(~p1(tptp_fun_X_22(Y)))) & (~((~r1(tptp_fun_X_22(Y), tptp_fun_Y_23(Y))) | p1(tptp_fun_Y_23(Y)))))) <=> (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_22(Y)) & p1(tptp_fun_X_22(Y)) & (~((~r1(tptp_fun_X_22(Y), tptp_fun_Y_23(Y))) | p1(tptp_fun_Y_23(Y))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(12,plain,
% 0.19/0.45 (![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | ((~(~r1(Y, tptp_fun_X_22(Y)))) & (~(~p1(tptp_fun_X_22(Y)))) & (~((~r1(tptp_fun_X_22(Y), tptp_fun_Y_23(Y))) | p1(tptp_fun_Y_23(Y)))))) <=> ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_22(Y)) & p1(tptp_fun_X_22(Y)) & (~((~r1(tptp_fun_X_22(Y), tptp_fun_Y_23(Y))) | p1(tptp_fun_Y_23(Y))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.45 tff(13,plain,
% 0.19/0.45 (((((((~(~r1(X!0, Y!11))) & (~p2(Y!11)) & ![X: $i] : ((~r1(Y!11, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | ((~(~r1(X, tptp_fun_Y_12(X)))) & (~(~p2(tptp_fun_Y_12(X)))) & (~((~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))) | p2(tptp_fun_X_13(X)))))))) & (p2(X!0) | ((~(~r1(X!0, Y!14))) & (~(~p2(Y!14))) & (~((~r1(Y!14, X!15)) | p2(X!15)))))) | ((~(~r1(X!0, Y!16))) & ((((~(~r1(Y!16, X!17))) & ((~(~r1(X!17, Y!18))) & (~p2(Y!18)) & ![X: $i] : ((~r1(Y!18, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!16, X)) | p2(X) | ((~(~r1(X, tptp_fun_Y_12(X)))) & (~(~p2(tptp_fun_Y_12(X)))) & (~((~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))) | p2(tptp_fun_X_13(X))))))) | ((~p2(Y!16)) & ![X: $i] : ((~r1(Y!16, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!16, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_6(Y)))) & (~(~p2(tptp_fun_X_6(Y)))) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | ((~(~r1(Y, tptp_fun_X_19(Y)))) & (~p2(tptp_fun_X_19(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_19(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) & (p2(Y) | ((~(~r1(Y, tptp_fun_X_6(Y)))) & (~(~p2(tptp_fun_X_6(Y)))) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) | ((![Y: $i] : ((~r1(X, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_6(Y)))) & (~(~p2(tptp_fun_X_6(Y)))) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & ((~(~r1(X, tptp_fun_Y_20(X)))) & ((~(~r1(tptp_fun_Y_20(X), tptp_fun_X_21(X)))) & (~p2(tptp_fun_X_21(X))) & ![Y: $i] : ((~r1(tptp_fun_X_21(X), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_19(Y)))) & (~p2(tptp_fun_X_19(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_19(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) <=> (((((r1(X!0, Y!11) & (~p2(Y!11)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!11, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_12(X)) & p2(tptp_fun_Y_12(X)) & (~((~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))) | p2(tptp_fun_X_13(X)))))))) & (p2(X!0) | (r1(X!0, Y!14) & p2(Y!14) & (~((~r1(Y!14, X!15)) | p2(X!15)))))) | (r1(X!0, Y!16) & ((r1(Y!16, X!17) & r1(X!17, Y!18) & (~p2(Y!18)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!18, X))) & ![X: $i] : (p2(X) | (~r1(Y!16, X)) | (r1(X, tptp_fun_Y_12(X)) & p2(tptp_fun_Y_12(X)) & (~((~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))) | p2(tptp_fun_X_13(X))))))) | ((~p2(Y!16)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!16, X))))) & ![X: $i] : ((~r1(Y!16, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | (r1(Y, tptp_fun_X_19(Y)) & (~p2(tptp_fun_X_19(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_19(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & r1(X, tptp_fun_Y_20(X)) & r1(tptp_fun_Y_20(X), tptp_fun_X_21(X)) & (~p2(tptp_fun_X_21(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(X), Y))))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_19(Y)) & (~p2(tptp_fun_X_19(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_19(Y), Y))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(14,plain,
% 0.19/0.45 (^[Y: $i] : trans(monotonicity(rewrite(((~(~r1(Y, tptp_fun_X_9(Y)))) & (~(~p4(tptp_fun_X_9(Y)))) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p4(tptp_fun_Y_10(Y))))) <=> (r1(Y, tptp_fun_X_9(Y)) & p4(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p4(tptp_fun_Y_10(Y)))))), (((~r1(X!0, Y)) | p4(Y) | ((~(~r1(Y, tptp_fun_X_9(Y)))) & (~(~p4(tptp_fun_X_9(Y)))) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p4(tptp_fun_Y_10(Y)))))) <=> ((~r1(X!0, Y)) | p4(Y) | (r1(Y, tptp_fun_X_9(Y)) & p4(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p4(tptp_fun_Y_10(Y)))))))), rewrite(((~r1(X!0, Y)) | p4(Y) | (r1(Y, tptp_fun_X_9(Y)) & p4(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p4(tptp_fun_Y_10(Y)))))) <=> (p4(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p4(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p4(tptp_fun_Y_10(Y))))))), (((~r1(X!0, Y)) | p4(Y) | ((~(~r1(Y, tptp_fun_X_9(Y)))) & (~(~p4(tptp_fun_X_9(Y)))) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p4(tptp_fun_Y_10(Y)))))) <=> (p4(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p4(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p4(tptp_fun_Y_10(Y))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(15,plain,
% 0.19/0.45 (![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | ((~(~r1(Y, tptp_fun_X_9(Y)))) & (~(~p4(tptp_fun_X_9(Y)))) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p4(tptp_fun_Y_10(Y)))))) <=> ![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p4(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p4(tptp_fun_Y_10(Y))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.45 tff(16,plain,
% 0.19/0.45 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(17,plain,
% 0.19/0.45 (((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_6(Y)))) & (~(~p2(tptp_fun_X_6(Y)))) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) <=> ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(18,plain,
% 0.19/0.45 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_6(Y)))) & (~(~p2(tptp_fun_X_6(Y)))) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[17])).
% 0.19/0.45 tff(19,plain,
% 0.19/0.45 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_6(Y)))) & (~(~p2(tptp_fun_X_6(Y)))) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[18, 16])).
% 0.19/0.46 tff(20,plain,
% 0.19/0.46 (((r1(X!0, Y!3) & r1(Y!3, X!4) & ![Y: $i] : ((~p3(Y)) | (~r1(X!4, Y))) & (~p1(Y!3))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) <=> ((r1(X!0, Y!3) & r1(Y!3, X!4) & ![Y: $i] : ((~p3(Y)) | (~r1(X!4, Y))) & (~p1(Y!3))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(21,plain,
% 0.19/0.46 ((r1(X!0, Y!3) & (r1(Y!3, X!4) & ![Y: $i] : ((~p3(Y)) | (~r1(X!4, Y)))) & (~p1(Y!3))) <=> (r1(X!0, Y!3) & r1(Y!3, X!4) & ![Y: $i] : ((~p3(Y)) | (~r1(X!4, Y))) & (~p1(Y!3)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(22,plain,
% 0.19/0.46 (((~(~r1(Y!3, X!4))) & ![Y: $i] : ((~r1(X!4, Y)) | (~p3(Y)))) <=> (r1(Y!3, X!4) & ![Y: $i] : ((~p3(Y)) | (~r1(X!4, Y))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(23,plain,
% 0.19/0.46 ((~(~r1(X!0, Y!3))) <=> r1(X!0, Y!3)),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(24,plain,
% 0.19/0.46 (((~(~r1(X!0, Y!3))) & ((~(~r1(Y!3, X!4))) & ![Y: $i] : ((~r1(X!4, Y)) | (~p3(Y)))) & (~p1(Y!3))) <=> (r1(X!0, Y!3) & (r1(Y!3, X!4) & ![Y: $i] : ((~p3(Y)) | (~r1(X!4, Y)))) & (~p1(Y!3)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[23, 22])).
% 0.19/0.46 tff(25,plain,
% 0.19/0.46 (((~(~r1(X!0, Y!3))) & ((~(~r1(Y!3, X!4))) & ![Y: $i] : ((~r1(X!4, Y)) | (~p3(Y)))) & (~p1(Y!3))) <=> (r1(X!0, Y!3) & r1(Y!3, X!4) & ![Y: $i] : ((~p3(Y)) | (~r1(X!4, Y))) & (~p1(Y!3)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[24, 21])).
% 0.19/0.46 tff(26,plain,
% 0.19/0.46 ((((~(~r1(X!0, Y!3))) & ((~(~r1(Y!3, X!4))) & ![Y: $i] : ((~r1(X!4, Y)) | (~p3(Y)))) & (~p1(Y!3))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_6(Y)))) & (~(~p2(tptp_fun_X_6(Y)))) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) <=> ((r1(X!0, Y!3) & r1(Y!3, X!4) & ![Y: $i] : ((~p3(Y)) | (~r1(X!4, Y))) & (~p1(Y!3))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[25, 17])).
% 0.19/0.46 tff(27,plain,
% 0.19/0.46 ((((~(~r1(X!0, Y!3))) & ((~(~r1(Y!3, X!4))) & ![Y: $i] : ((~r1(X!4, Y)) | (~p3(Y)))) & (~p1(Y!3))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_6(Y)))) & (~(~p2(tptp_fun_X_6(Y)))) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) <=> ((r1(X!0, Y!3) & r1(Y!3, X!4) & ![Y: $i] : ((~p3(Y)) | (~r1(X!4, Y))) & (~p1(Y!3))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[26, 20])).
% 0.19/0.46 tff(28,plain,
% 0.19/0.46 ((~((~r1(X!0, Y!2)) | p1(Y!2))) <=> (~((~r1(X!0, Y!2)) | p1(Y!2)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(29,plain,
% 0.19/0.46 ((~((~r1(X!0, Y!1)) | p4(Y!1))) <=> (~((~r1(X!0, Y!1)) | p4(Y!1)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(30,plain,
% 0.19/0.46 (((~((~r1(X!0, Y!1)) | p4(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & (((~(~r1(X!0, Y!3))) & ((~(~r1(Y!3, X!4))) & ![Y: $i] : ((~r1(X!4, Y)) | (~p3(Y)))) & (~p1(Y!3))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_6(Y)))) & (~(~p2(tptp_fun_X_6(Y)))) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_6(Y)))) & (~(~p2(tptp_fun_X_6(Y)))) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | ((~(~r1(Y, tptp_fun_X_9(Y)))) & (~(~p4(tptp_fun_X_9(Y)))) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p4(tptp_fun_Y_10(Y)))))) & ((((((~(~r1(X!0, Y!11))) & (~p2(Y!11)) & ![X: $i] : ((~r1(Y!11, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | ((~(~r1(X, tptp_fun_Y_12(X)))) & (~(~p2(tptp_fun_Y_12(X)))) & (~((~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))) | p2(tptp_fun_X_13(X)))))))) & (p2(X!0) | ((~(~r1(X!0, Y!14))) & (~(~p2(Y!14))) & (~((~r1(Y!14, X!15)) | p2(X!15)))))) | ((~(~r1(X!0, Y!16))) & ((((~(~r1(Y!16, X!17))) & ((~(~r1(X!17, Y!18))) & (~p2(Y!18)) & ![X: $i] : ((~r1(Y!18, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!16, X)) | p2(X) | ((~(~r1(X, tptp_fun_Y_12(X)))) & (~(~p2(tptp_fun_Y_12(X)))) & (~((~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))) | p2(tptp_fun_X_13(X))))))) | ((~p2(Y!16)) & ![X: $i] : ((~r1(Y!16, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!16, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_6(Y)))) & (~(~p2(tptp_fun_X_6(Y)))) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | ((~(~r1(Y, tptp_fun_X_19(Y)))) & (~p2(tptp_fun_X_19(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_19(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) & (p2(Y) | ((~(~r1(Y, tptp_fun_X_6(Y)))) & (~(~p2(tptp_fun_X_6(Y)))) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) | ((![Y: $i] : ((~r1(X, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_6(Y)))) & (~(~p2(tptp_fun_X_6(Y)))) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & ((~(~r1(X, tptp_fun_Y_20(X)))) & ((~(~r1(tptp_fun_Y_20(X), tptp_fun_X_21(X)))) & (~p2(tptp_fun_X_21(X))) & ![Y: $i] : ((~r1(tptp_fun_X_21(X), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_19(Y)))) & (~p2(tptp_fun_X_19(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_19(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | ((~(~r1(Y, tptp_fun_X_22(Y)))) & (~(~p1(tptp_fun_X_22(Y)))) & (~((~r1(tptp_fun_X_22(Y), tptp_fun_Y_23(Y))) | p1(tptp_fun_Y_23(Y))))))) <=> ((~((~r1(X!0, Y!1)) | p4(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & ((r1(X!0, Y!3) & r1(Y!3, X!4) & ![Y: $i] : ((~p3(Y)) | (~r1(X!4, Y))) & (~p1(Y!3))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) & ![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p4(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p4(tptp_fun_Y_10(Y)))))) & (((((r1(X!0, Y!11) & (~p2(Y!11)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!11, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_12(X)) & p2(tptp_fun_Y_12(X)) & (~((~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))) | p2(tptp_fun_X_13(X)))))))) & (p2(X!0) | (r1(X!0, Y!14) & p2(Y!14) & (~((~r1(Y!14, X!15)) | p2(X!15)))))) | (r1(X!0, Y!16) & ((r1(Y!16, X!17) & r1(X!17, Y!18) & (~p2(Y!18)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!18, X))) & ![X: $i] : (p2(X) | (~r1(Y!16, X)) | (r1(X, tptp_fun_Y_12(X)) & p2(tptp_fun_Y_12(X)) & (~((~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))) | p2(tptp_fun_X_13(X))))))) | ((~p2(Y!16)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!16, X))))) & ![X: $i] : ((~r1(Y!16, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | (r1(Y, tptp_fun_X_19(Y)) & (~p2(tptp_fun_X_19(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_19(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & r1(X, tptp_fun_Y_20(X)) & r1(tptp_fun_Y_20(X), tptp_fun_X_21(X)) & (~p2(tptp_fun_X_21(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(X), Y))))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_19(Y)) & (~p2(tptp_fun_X_19(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_19(Y), Y)))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_22(Y)) & p1(tptp_fun_X_22(Y)) & (~((~r1(tptp_fun_X_22(Y), tptp_fun_Y_23(Y))) | p1(tptp_fun_Y_23(Y)))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[29, 28, 27, 19, 15, 13, 12])).
% 0.19/0.46 tff(31,plain,
% 0.19/0.46 (((~((~r1(X!0, Y!1)) | p4(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & (((~(~r1(X!0, Y!3))) & ((~(~r1(Y!3, X!4))) & ![Y: $i] : ((~r1(X!4, Y)) | (~p3(Y)))) & (~p1(Y!3))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_6(Y)))) & (~(~p2(tptp_fun_X_6(Y)))) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_6(Y)))) & (~(~p2(tptp_fun_X_6(Y)))) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | ((~(~r1(Y, tptp_fun_X_9(Y)))) & (~(~p4(tptp_fun_X_9(Y)))) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p4(tptp_fun_Y_10(Y)))))) & ((((((~(~r1(X!0, Y!11))) & (~p2(Y!11)) & ![X: $i] : ((~r1(Y!11, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | ((~(~r1(X, tptp_fun_Y_12(X)))) & (~(~p2(tptp_fun_Y_12(X)))) & (~((~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))) | p2(tptp_fun_X_13(X)))))))) & (p2(X!0) | ((~(~r1(X!0, Y!14))) & (~(~p2(Y!14))) & (~((~r1(Y!14, X!15)) | p2(X!15)))))) | ((~(~r1(X!0, Y!16))) & ((((~(~r1(Y!16, X!17))) & ((~(~r1(X!17, Y!18))) & (~p2(Y!18)) & ![X: $i] : ((~r1(Y!18, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!16, X)) | p2(X) | ((~(~r1(X, tptp_fun_Y_12(X)))) & (~(~p2(tptp_fun_Y_12(X)))) & (~((~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))) | p2(tptp_fun_X_13(X))))))) | ((~p2(Y!16)) & ![X: $i] : ((~r1(Y!16, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!16, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_6(Y)))) & (~(~p2(tptp_fun_X_6(Y)))) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | ((~(~r1(Y, tptp_fun_X_19(Y)))) & (~p2(tptp_fun_X_19(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_19(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) & (p2(Y) | ((~(~r1(Y, tptp_fun_X_6(Y)))) & (~(~p2(tptp_fun_X_6(Y)))) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) | ((![Y: $i] : ((~r1(X, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_6(Y)))) & (~(~p2(tptp_fun_X_6(Y)))) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & ((~(~r1(X, tptp_fun_Y_20(X)))) & ((~(~r1(tptp_fun_Y_20(X), tptp_fun_X_21(X)))) & (~p2(tptp_fun_X_21(X))) & ![Y: $i] : ((~r1(tptp_fun_X_21(X), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_19(Y)))) & (~p2(tptp_fun_X_19(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_19(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | ((~(~r1(Y, tptp_fun_X_22(Y)))) & (~(~p1(tptp_fun_X_22(Y)))) & (~((~r1(tptp_fun_X_22(Y), tptp_fun_Y_23(Y))) | p1(tptp_fun_Y_23(Y))))))) <=> ((~((~r1(X!0, Y!1)) | p4(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & ((r1(X!0, Y!3) & r1(Y!3, X!4) & ![Y: $i] : ((~p3(Y)) | (~r1(X!4, Y))) & (~p1(Y!3))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) & ![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p4(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p4(tptp_fun_Y_10(Y)))))) & ((((r1(X!0, Y!11) & (~p2(Y!11)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!11, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_12(X)) & p2(tptp_fun_Y_12(X)) & (~((~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))) | p2(tptp_fun_X_13(X)))))))) & (p2(X!0) | (r1(X!0, Y!14) & p2(Y!14) & (~((~r1(Y!14, X!15)) | p2(X!15)))))) | (r1(X!0, Y!16) & ((r1(Y!16, X!17) & r1(X!17, Y!18) & (~p2(Y!18)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!18, X))) & ![X: $i] : (p2(X) | (~r1(Y!16, X)) | (r1(X, tptp_fun_Y_12(X)) & p2(tptp_fun_Y_12(X)) & (~((~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))) | p2(tptp_fun_X_13(X))))))) | ((~p2(Y!16)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!16, X))))) & ![X: $i] : ((~r1(Y!16, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | (r1(Y, tptp_fun_X_19(Y)) & (~p2(tptp_fun_X_19(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_19(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & r1(X, tptp_fun_Y_20(X)) & r1(tptp_fun_Y_20(X), tptp_fun_X_21(X)) & (~p2(tptp_fun_X_21(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(X), Y))))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_19(Y)) & (~p2(tptp_fun_X_19(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_19(Y), Y))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_22(Y)) & p1(tptp_fun_X_22(Y)) & (~((~r1(tptp_fun_X_22(Y), tptp_fun_Y_23(Y))) | p1(tptp_fun_Y_23(Y)))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[30, 10])).
% 0.19/0.47 tff(32,plain,
% 0.19/0.47 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p3(Y))))) | p1(Y)) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)))))) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p4(X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p3(Y))))) | p1(Y)) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)))))) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p4(X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(33,plain,
% 0.19/0.47 ((~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p3(Y))))) | p1(Y)) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)))))) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p4(X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p3(Y))))) | p1(Y)) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)))))) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p4(X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(34,plain,
% 0.19/0.47 ((~?[X: $i] : (~(((((((![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p3(Y)))))) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p4(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))) | (~p4(X))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)))))) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))) | (~((((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | (~((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) & ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) <=> (~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p3(Y))))) | p1(Y)) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)))))) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p4(X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(35,plain,
% 0.19/0.47 ((~(~?[X: $i] : (~(((((((![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p3(Y)))))) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p4(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))) | (~p4(X))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)))))) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))) | (~((((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | (~((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) & ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))))))))) <=> (~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p3(Y))))) | p1(Y)) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)))))) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p4(X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[34])).
% 0.19/0.47 tff(36,plain,
% 0.19/0.47 ((~(~?[X: $i] : (~(((((((![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p3(Y)))))) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p4(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))) | (~p4(X))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)))))) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))) | (~((((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | (~((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) & ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p3(Y))))) | p1(Y)) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)))))) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p4(X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[35, 33])).
% 0.19/0.48 tff(37,axiom,(~(~?[X: $i] : (~(((((((![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p3(Y)))))) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p4(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))) | (~p4(X))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)))))) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))) | (~((((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | (~((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) & ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','main')).
% 0.19/0.48 tff(38,plain,
% 0.19/0.48 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p3(Y))))) | p1(Y)) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)))))) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p4(X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.48 tff(39,plain,
% 0.19/0.48 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p3(Y))))) | p1(Y)) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)))))) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p4(X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[38, 32])).
% 0.19/0.48 tff(40,plain,
% 0.19/0.48 ((~((~r1(X!0, Y!1)) | p4(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & ((r1(X!0, Y!3) & r1(Y!3, X!4) & ![Y: $i] : ((~p3(Y)) | (~r1(X!4, Y))) & (~p1(Y!3))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) & ![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p4(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p4(tptp_fun_Y_10(Y)))))) & ((((r1(X!0, Y!11) & (~p2(Y!11)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!11, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_12(X)) & p2(tptp_fun_Y_12(X)) & (~((~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))) | p2(tptp_fun_X_13(X)))))))) & (p2(X!0) | (r1(X!0, Y!14) & p2(Y!14) & (~((~r1(Y!14, X!15)) | p2(X!15)))))) | (r1(X!0, Y!16) & ((r1(Y!16, X!17) & r1(X!17, Y!18) & (~p2(Y!18)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!18, X))) & ![X: $i] : (p2(X) | (~r1(Y!16, X)) | (r1(X, tptp_fun_Y_12(X)) & p2(tptp_fun_Y_12(X)) & (~((~r1(tptp_fun_Y_12(X), tptp_fun_X_13(X))) | p2(tptp_fun_X_13(X))))))) | ((~p2(Y!16)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!16, X))))) & ![X: $i] : ((~r1(Y!16, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | (r1(Y, tptp_fun_X_19(Y)) & (~p2(tptp_fun_X_19(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_19(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & r1(X, tptp_fun_Y_20(X)) & r1(tptp_fun_Y_20(X), tptp_fun_X_21(X)) & (~p2(tptp_fun_X_21(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(X), Y))))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_19(Y)) & (~p2(tptp_fun_X_19(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_19(Y), Y))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_22(Y)) & p1(tptp_fun_X_22(Y)) & (~((~r1(tptp_fun_X_22(Y), tptp_fun_Y_23(Y))) | p1(tptp_fun_Y_23(Y))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[39, 31])).
% 0.19/0.48 tff(41,plain,
% 0.19/0.48 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_19(Y)) & (~p2(tptp_fun_X_19(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_19(Y), Y)))))),
% 0.19/0.48 inference(and_elim,[status(thm)],[40])).
% 0.19/0.48 tff(42,plain,
% 0.19/0.48 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_19(Y))) | p2(tptp_fun_X_19(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_19(Y), Y)))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[41, 9])).
% 0.19/0.48 tff(43,plain,
% 0.19/0.48 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_19(Y))) | p2(tptp_fun_X_19(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_19(Y), Y)))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[42, 7])).
% 0.19/0.48 tff(44,plain,
% 0.19/0.48 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_19(Y))) | p2(tptp_fun_X_19(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[43, 2])).
% 0.19/0.48 tff(45,assumption,(~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))), introduced(assumption)).
% 0.19/0.48 tff(46,plain,
% 0.19/0.48 (((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | (~p2(Y!5))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(47,plain,
% 0.19/0.48 (~p2(Y!5)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.19/0.48 tff(48,plain,
% 0.19/0.48 (((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | r1(X!0, Y!5)),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(49,plain,
% 0.19/0.48 (r1(X!0, Y!5)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[48, 45])).
% 0.19/0.48 tff(50,plain,
% 0.19/0.48 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_19(Y))) | p2(tptp_fun_X_19(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | (p2(Y!5) | (~r1(X!0, Y!5)) | (~((~r1(Y!5, tptp_fun_X_19(Y!5))) | p2(tptp_fun_X_19(Y!5)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_19(Y))) | p2(tptp_fun_X_19(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | p2(Y!5) | (~r1(X!0, Y!5)) | (~((~r1(Y!5, tptp_fun_X_19(Y!5))) | p2(tptp_fun_X_19(Y!5)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(51,plain,
% 0.19/0.48 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_19(Y))) | p2(tptp_fun_X_19(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | (p2(Y!5) | (~r1(X!0, Y!5)) | (~((~r1(Y!5, tptp_fun_X_19(Y!5))) | p2(tptp_fun_X_19(Y!5)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(52,plain,
% 0.19/0.48 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_19(Y))) | p2(tptp_fun_X_19(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | p2(Y!5) | (~r1(X!0, Y!5)) | (~((~r1(Y!5, tptp_fun_X_19(Y!5))) | p2(tptp_fun_X_19(Y!5)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.19/0.48 tff(53,plain,
% 0.19/0.48 (~((~r1(Y!5, tptp_fun_X_19(Y!5))) | p2(tptp_fun_X_19(Y!5)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[52, 49, 47, 44])).
% 0.19/0.48 tff(54,plain,
% 0.19/0.48 (((~r1(Y!5, tptp_fun_X_19(Y!5))) | p2(tptp_fun_X_19(Y!5)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | r1(Y!5, tptp_fun_X_19(Y!5))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(55,plain,
% 0.19/0.48 (r1(Y!5, tptp_fun_X_19(Y!5))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.19/0.48 tff(56,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(57,plain,
% 0.19/0.48 (^[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)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(58,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[57])).
% 0.19/0.48 tff(59,plain,
% 0.19/0.48 (![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))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(60,plain,
% 0.19/0.48 (^[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)))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(61,plain,
% 0.19/0.48 (![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))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[60])).
% 0.19/0.48 tff(62,axiom,(![X: $i, Y: $i, Z: $i] : ((r1(X, Y) & r1(Y, Z)) => r1(X, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','transitivity')).
% 0.19/0.48 tff(63,plain,
% 0.19/0.48 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.48 tff(64,plain,
% 0.19/0.48 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.19/0.48 tff(65,plain,(
% 0.19/0.48 ![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 0.19/0.48 inference(skolemize,[status(sab)],[64])).
% 0.19/0.48 tff(66,plain,
% 0.19/0.48 (![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.19/0.48 tff(67,plain,
% 0.19/0.48 (![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[66, 56])).
% 0.19/0.48 tff(68,plain,
% 0.19/0.48 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, Y!5)) | (~r1(Y!5, tptp_fun_X_19(Y!5))) | r1(X!0, tptp_fun_X_19(Y!5)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!5)) | (~r1(Y!5, tptp_fun_X_19(Y!5))) | r1(X!0, tptp_fun_X_19(Y!5)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(69,plain,
% 0.19/0.48 ((r1(X!0, tptp_fun_X_19(Y!5)) | (~r1(Y!5, tptp_fun_X_19(Y!5))) | (~r1(X!0, Y!5))) <=> ((~r1(X!0, Y!5)) | (~r1(Y!5, tptp_fun_X_19(Y!5))) | r1(X!0, tptp_fun_X_19(Y!5)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(70,plain,
% 0.19/0.48 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_19(Y!5)) | (~r1(Y!5, tptp_fun_X_19(Y!5))) | (~r1(X!0, Y!5)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, Y!5)) | (~r1(Y!5, tptp_fun_X_19(Y!5))) | r1(X!0, tptp_fun_X_19(Y!5))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[69])).
% 0.19/0.48 tff(71,plain,
% 0.19/0.48 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_19(Y!5)) | (~r1(Y!5, tptp_fun_X_19(Y!5))) | (~r1(X!0, Y!5)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!5)) | (~r1(Y!5, tptp_fun_X_19(Y!5))) | r1(X!0, tptp_fun_X_19(Y!5)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[70, 68])).
% 0.19/0.48 tff(72,plain,
% 0.19/0.48 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_19(Y!5)) | (~r1(Y!5, tptp_fun_X_19(Y!5))) | (~r1(X!0, Y!5)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(73,plain,
% 0.19/0.48 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!5)) | (~r1(Y!5, tptp_fun_X_19(Y!5))) | r1(X!0, tptp_fun_X_19(Y!5))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.19/0.48 tff(74,plain,
% 0.19/0.48 (r1(X!0, tptp_fun_X_19(Y!5))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[73, 67, 49, 55])).
% 0.19/0.48 tff(75,plain,
% 0.19/0.48 (((~r1(Y!5, tptp_fun_X_19(Y!5))) | p2(tptp_fun_X_19(Y!5)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | (~p2(tptp_fun_X_19(Y!5)))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(76,plain,
% 0.19/0.48 (~p2(tptp_fun_X_19(Y!5))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[75, 53])).
% 0.19/0.48 tff(77,plain,
% 0.19/0.48 (((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(78,plain,
% 0.19/0.48 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[77, 45])).
% 0.19/0.48 tff(79,plain,
% 0.19/0.48 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (p2(tptp_fun_X_19(Y!5)) | (~r1(X!0, tptp_fun_X_19(Y!5))) | (~((~r1(tptp_fun_X_19(Y!5), tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | (~p2(tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | (~r1(tptp_fun_X_6(tptp_fun_X_19(Y!5)), tptp_fun_Y_7(tptp_fun_X_19(Y!5)))) | p2(tptp_fun_Y_7(tptp_fun_X_19(Y!5))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | p2(tptp_fun_X_19(Y!5)) | (~r1(X!0, tptp_fun_X_19(Y!5))) | (~((~r1(tptp_fun_X_19(Y!5), tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | (~p2(tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | (~r1(tptp_fun_X_6(tptp_fun_X_19(Y!5)), tptp_fun_Y_7(tptp_fun_X_19(Y!5)))) | p2(tptp_fun_Y_7(tptp_fun_X_19(Y!5))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(80,plain,
% 0.19/0.48 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (p2(tptp_fun_X_19(Y!5)) | (~r1(X!0, tptp_fun_X_19(Y!5))) | (~((~r1(tptp_fun_X_19(Y!5), tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | (~p2(tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | (~r1(tptp_fun_X_6(tptp_fun_X_19(Y!5)), tptp_fun_Y_7(tptp_fun_X_19(Y!5)))) | p2(tptp_fun_Y_7(tptp_fun_X_19(Y!5))))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(81,plain,
% 0.19/0.49 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | p2(tptp_fun_X_19(Y!5)) | (~r1(X!0, tptp_fun_X_19(Y!5))) | (~((~r1(tptp_fun_X_19(Y!5), tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | (~p2(tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | (~r1(tptp_fun_X_6(tptp_fun_X_19(Y!5)), tptp_fun_Y_7(tptp_fun_X_19(Y!5)))) | p2(tptp_fun_Y_7(tptp_fun_X_19(Y!5)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.19/0.49 tff(82,plain,
% 0.19/0.49 ((~r1(X!0, tptp_fun_X_19(Y!5))) | (~((~r1(tptp_fun_X_19(Y!5), tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | (~p2(tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | (~r1(tptp_fun_X_6(tptp_fun_X_19(Y!5)), tptp_fun_Y_7(tptp_fun_X_19(Y!5)))) | p2(tptp_fun_Y_7(tptp_fun_X_19(Y!5)))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[81, 78, 76])).
% 0.19/0.49 tff(83,plain,
% 0.19/0.49 (~((~r1(tptp_fun_X_19(Y!5), tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | (~p2(tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | (~r1(tptp_fun_X_6(tptp_fun_X_19(Y!5)), tptp_fun_Y_7(tptp_fun_X_19(Y!5)))) | p2(tptp_fun_Y_7(tptp_fun_X_19(Y!5))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[82, 74])).
% 0.19/0.49 tff(84,plain,
% 0.19/0.49 (((~r1(tptp_fun_X_19(Y!5), tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | (~p2(tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | (~r1(tptp_fun_X_6(tptp_fun_X_19(Y!5)), tptp_fun_Y_7(tptp_fun_X_19(Y!5)))) | p2(tptp_fun_Y_7(tptp_fun_X_19(Y!5)))) | p2(tptp_fun_X_6(tptp_fun_X_19(Y!5)))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(85,plain,
% 0.19/0.49 (p2(tptp_fun_X_6(tptp_fun_X_19(Y!5)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.19/0.49 tff(86,plain,
% 0.19/0.49 (((~r1(tptp_fun_X_19(Y!5), tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | (~p2(tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | (~r1(tptp_fun_X_6(tptp_fun_X_19(Y!5)), tptp_fun_Y_7(tptp_fun_X_19(Y!5)))) | p2(tptp_fun_Y_7(tptp_fun_X_19(Y!5)))) | r1(tptp_fun_X_19(Y!5), tptp_fun_X_6(tptp_fun_X_19(Y!5)))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(87,plain,
% 0.19/0.49 (r1(tptp_fun_X_19(Y!5), tptp_fun_X_6(tptp_fun_X_19(Y!5)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[86, 83])).
% 0.19/0.49 tff(88,plain,
% 0.19/0.49 (((~r1(Y!5, tptp_fun_X_19(Y!5))) | p2(tptp_fun_X_19(Y!5)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(89,plain,
% 0.19/0.49 (![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[88, 53])).
% 0.19/0.49 tff(90,plain,
% 0.19/0.49 (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | (~r1(tptp_fun_X_19(Y!5), tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_X_6(tptp_fun_X_19(Y!5)), X))))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | (~r1(tptp_fun_X_19(Y!5), tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_X_6(tptp_fun_X_19(Y!5)), X))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(91,plain,
% 0.19/0.49 (((~p2(tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | (~r1(tptp_fun_X_19(Y!5), tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | ![X: $i] : ((~r1(tptp_fun_X_6(tptp_fun_X_19(Y!5)), X)) | p2(X))) <=> ((~p2(tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | (~r1(tptp_fun_X_19(Y!5), tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_X_6(tptp_fun_X_19(Y!5)), X))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(92,plain,
% 0.19/0.49 (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | (~r1(tptp_fun_X_19(Y!5), tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | ![X: $i] : ((~r1(tptp_fun_X_6(tptp_fun_X_19(Y!5)), X)) | p2(X)))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | (~r1(tptp_fun_X_19(Y!5), tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_X_6(tptp_fun_X_19(Y!5)), X)))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[91])).
% 0.19/0.49 tff(93,plain,
% 0.19/0.49 (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | (~r1(tptp_fun_X_19(Y!5), tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | ![X: $i] : ((~r1(tptp_fun_X_6(tptp_fun_X_19(Y!5)), X)) | p2(X)))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | (~r1(tptp_fun_X_19(Y!5), tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_X_6(tptp_fun_X_19(Y!5)), X))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[92, 90])).
% 0.19/0.49 tff(94,plain,
% 0.19/0.49 ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | (~r1(tptp_fun_X_19(Y!5), tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | ![X: $i] : ((~r1(tptp_fun_X_6(tptp_fun_X_19(Y!5)), X)) | p2(X)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(95,plain,
% 0.19/0.49 ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_19(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | (~r1(tptp_fun_X_19(Y!5), tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_X_6(tptp_fun_X_19(Y!5)), X)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.19/0.49 tff(96,plain,
% 0.19/0.49 (![X: $i] : (p2(X) | (~r1(tptp_fun_X_6(tptp_fun_X_19(Y!5)), X)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[95, 89, 87, 85])).
% 0.19/0.49 tff(97,plain,
% 0.19/0.49 (((~r1(tptp_fun_X_19(Y!5), tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | (~p2(tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | (~r1(tptp_fun_X_6(tptp_fun_X_19(Y!5)), tptp_fun_Y_7(tptp_fun_X_19(Y!5)))) | p2(tptp_fun_Y_7(tptp_fun_X_19(Y!5)))) | (~p2(tptp_fun_Y_7(tptp_fun_X_19(Y!5))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(98,plain,
% 0.19/0.49 (~p2(tptp_fun_Y_7(tptp_fun_X_19(Y!5)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[97, 83])).
% 0.19/0.49 tff(99,plain,
% 0.19/0.49 (((~r1(tptp_fun_X_19(Y!5), tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | (~p2(tptp_fun_X_6(tptp_fun_X_19(Y!5)))) | (~r1(tptp_fun_X_6(tptp_fun_X_19(Y!5)), tptp_fun_Y_7(tptp_fun_X_19(Y!5)))) | p2(tptp_fun_Y_7(tptp_fun_X_19(Y!5)))) | r1(tptp_fun_X_6(tptp_fun_X_19(Y!5)), tptp_fun_Y_7(tptp_fun_X_19(Y!5)))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(100,plain,
% 0.19/0.49 (r1(tptp_fun_X_6(tptp_fun_X_19(Y!5)), tptp_fun_Y_7(tptp_fun_X_19(Y!5)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[99, 83])).
% 0.19/0.49 tff(101,plain,
% 0.19/0.49 (((~![X: $i] : (p2(X) | (~r1(tptp_fun_X_6(tptp_fun_X_19(Y!5)), X)))) | (p2(tptp_fun_Y_7(tptp_fun_X_19(Y!5))) | (~r1(tptp_fun_X_6(tptp_fun_X_19(Y!5)), tptp_fun_Y_7(tptp_fun_X_19(Y!5)))))) <=> ((~![X: $i] : (p2(X) | (~r1(tptp_fun_X_6(tptp_fun_X_19(Y!5)), X)))) | p2(tptp_fun_Y_7(tptp_fun_X_19(Y!5))) | (~r1(tptp_fun_X_6(tptp_fun_X_19(Y!5)), tptp_fun_Y_7(tptp_fun_X_19(Y!5)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(102,plain,
% 0.19/0.49 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_X_6(tptp_fun_X_19(Y!5)), X)))) | (p2(tptp_fun_Y_7(tptp_fun_X_19(Y!5))) | (~r1(tptp_fun_X_6(tptp_fun_X_19(Y!5)), tptp_fun_Y_7(tptp_fun_X_19(Y!5)))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(103,plain,
% 0.19/0.49 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_X_6(tptp_fun_X_19(Y!5)), X)))) | p2(tptp_fun_Y_7(tptp_fun_X_19(Y!5))) | (~r1(tptp_fun_X_6(tptp_fun_X_19(Y!5)), tptp_fun_Y_7(tptp_fun_X_19(Y!5))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.19/0.49 tff(104,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[103, 100, 98, 96])).
% 0.19/0.49 tff(105,plain,((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(106,plain,
% 0.19/0.49 (((~((~r1(X!0, Y!3)) | p1(Y!3) | (~r1(Y!3, X!4)) | (~![Y: $i] : ((~p3(Y)) | (~r1(X!4, Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))) <=> ((~((~r1(X!0, Y!3)) | p1(Y!3) | (~r1(Y!3, X!4)) | (~![Y: $i] : ((~p3(Y)) | (~r1(X!4, Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(107,plain,
% 0.19/0.49 (((r1(X!0, Y!3) & r1(Y!3, X!4) & ![Y: $i] : ((~p3(Y)) | (~r1(X!4, Y))) & (~p1(Y!3))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) <=> ((~((~r1(X!0, Y!3)) | p1(Y!3) | (~r1(Y!3, X!4)) | (~![Y: $i] : ((~p3(Y)) | (~r1(X!4, Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(108,plain,
% 0.19/0.49 ((r1(X!0, Y!3) & r1(Y!3, X!4) & ![Y: $i] : ((~p3(Y)) | (~r1(X!4, Y))) & (~p1(Y!3))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))),
% 0.19/0.49 inference(and_elim,[status(thm)],[40])).
% 0.19/0.49 tff(109,plain,
% 0.19/0.49 ((~((~r1(X!0, Y!3)) | p1(Y!3) | (~r1(Y!3, X!4)) | (~![Y: $i] : ((~p3(Y)) | (~r1(X!4, Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.19/0.49 tff(110,plain,
% 0.19/0.49 ((~((~r1(X!0, Y!3)) | p1(Y!3) | (~r1(Y!3, X!4)) | (~![Y: $i] : ((~p3(Y)) | (~r1(X!4, Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[109, 106])).
% 0.19/0.49 tff(111,plain,
% 0.19/0.49 (~((~r1(X!0, Y!3)) | p1(Y!3) | (~r1(Y!3, X!4)) | (~![Y: $i] : ((~p3(Y)) | (~r1(X!4, Y)))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[110, 105])).
% 0.19/0.49 tff(112,plain,
% 0.19/0.49 (((~r1(X!0, Y!3)) | p1(Y!3) | (~r1(Y!3, X!4)) | (~![Y: $i] : ((~p3(Y)) | (~r1(X!4, Y))))) | r1(Y!3, X!4)),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(113,plain,
% 0.19/0.49 (r1(Y!3, X!4)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.19/0.49 tff(114,plain,
% 0.19/0.49 (((~r1(X!0, Y!3)) | p1(Y!3) | (~r1(Y!3, X!4)) | (~![Y: $i] : ((~p3(Y)) | (~r1(X!4, Y))))) | r1(X!0, Y!3)),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(115,plain,
% 0.19/0.49 (r1(X!0, Y!3)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[114, 111])).
% 0.19/0.49 tff(116,plain,
% 0.19/0.49 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, Y!3)) | (~r1(Y!3, X!4)) | r1(X!0, X!4))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!3)) | (~r1(Y!3, X!4)) | r1(X!0, X!4))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(117,plain,
% 0.19/0.49 ((r1(X!0, X!4) | (~r1(Y!3, X!4)) | (~r1(X!0, Y!3))) <=> ((~r1(X!0, Y!3)) | (~r1(Y!3, X!4)) | r1(X!0, X!4))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(118,plain,
% 0.19/0.49 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!4) | (~r1(Y!3, X!4)) | (~r1(X!0, Y!3)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, Y!3)) | (~r1(Y!3, X!4)) | r1(X!0, X!4)))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[117])).
% 0.19/0.49 tff(119,plain,
% 0.19/0.49 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!4) | (~r1(Y!3, X!4)) | (~r1(X!0, Y!3)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!3)) | (~r1(Y!3, X!4)) | r1(X!0, X!4))),
% 0.19/0.49 inference(transitivity,[status(thm)],[118, 116])).
% 0.19/0.49 tff(120,plain,
% 0.19/0.49 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!4) | (~r1(Y!3, X!4)) | (~r1(X!0, Y!3)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(121,plain,
% 0.19/0.49 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!3)) | (~r1(Y!3, X!4)) | r1(X!0, X!4)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.19/0.49 tff(122,plain,
% 0.19/0.49 (r1(X!0, X!4)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[121, 67, 115, 113])).
% 0.19/0.49 tff(123,plain,
% 0.19/0.49 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))) <=> ((~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y)))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(124,plain,
% 0.19/0.49 ((~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) <=> (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(125,plain,
% 0.19/0.49 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[124])).
% 0.19/0.49 tff(126,plain,
% 0.19/0.49 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))) <=> ((~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y)))))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[125, 123])).
% 0.19/0.49 tff(127,plain,
% 0.19/0.49 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(128,plain,
% 0.19/0.49 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(129,plain,
% 0.19/0.49 (((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) <=> (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(130,plain,
% 0.19/0.49 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(131,plain,
% 0.19/0.49 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[130])).
% 0.19/0.49 tff(132,plain,
% 0.19/0.49 ((~((~r1(X!0, Y!5)) | p2(Y!5))) <=> (~((~r1(X!0, Y!5)) | p2(Y!5)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(133,plain,
% 0.19/0.49 (((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) <=> ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[132, 131])).
% 0.19/0.49 tff(134,plain,
% 0.19/0.49 (((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) <=> (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[133, 129])).
% 0.19/0.49 tff(135,plain,
% 0.19/0.49 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[134])).
% 0.19/0.49 tff(136,plain,
% 0.19/0.49 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[135, 128])).
% 0.19/0.49 tff(137,plain,
% 0.19/0.49 (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))),
% 0.19/0.49 inference(and_elim,[status(thm)],[40])).
% 0.19/0.49 tff(138,plain,
% 0.19/0.49 (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.19/0.50 tff(139,plain,
% 0.19/0.50 (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[138, 127])).
% 0.19/0.50 tff(140,plain,
% 0.19/0.50 ((~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[139, 126])).
% 0.19/0.50 tff(141,plain,
% 0.19/0.50 (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[140, 105])).
% 0.19/0.50 tff(142,plain,
% 0.19/0.50 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y))))))) | ((~r1(X!0, X!4)) | (~((~r1(X!4, tptp_fun_X_8(X!4))) | (~p3(tptp_fun_X_8(X!4))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y))))))) | (~r1(X!0, X!4)) | (~((~r1(X!4, tptp_fun_X_8(X!4))) | (~p3(tptp_fun_X_8(X!4))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(143,plain,
% 0.19/0.50 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y))))))) | ((~r1(X!0, X!4)) | (~((~r1(X!4, tptp_fun_X_8(X!4))) | (~p3(tptp_fun_X_8(X!4))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(144,plain,
% 0.19/0.50 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p3(tptp_fun_X_8(Y))))))) | (~r1(X!0, X!4)) | (~((~r1(X!4, tptp_fun_X_8(X!4))) | (~p3(tptp_fun_X_8(X!4)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.19/0.50 tff(145,plain,
% 0.19/0.50 (~((~r1(X!4, tptp_fun_X_8(X!4))) | (~p3(tptp_fun_X_8(X!4))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[144, 141, 122])).
% 0.19/0.50 tff(146,plain,
% 0.19/0.50 (((~r1(X!4, tptp_fun_X_8(X!4))) | (~p3(tptp_fun_X_8(X!4)))) | p3(tptp_fun_X_8(X!4))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(147,plain,
% 0.19/0.50 (p3(tptp_fun_X_8(X!4))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.19/0.50 tff(148,plain,
% 0.19/0.50 (((~r1(X!4, tptp_fun_X_8(X!4))) | (~p3(tptp_fun_X_8(X!4)))) | r1(X!4, tptp_fun_X_8(X!4))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(149,plain,
% 0.19/0.50 (r1(X!4, tptp_fun_X_8(X!4))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[148, 145])).
% 0.19/0.50 tff(150,plain,
% 0.19/0.50 (((~r1(X!0, Y!3)) | p1(Y!3) | (~r1(Y!3, X!4)) | (~![Y: $i] : ((~p3(Y)) | (~r1(X!4, Y))))) | ![Y: $i] : ((~p3(Y)) | (~r1(X!4, Y)))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(151,plain,
% 0.19/0.50 (![Y: $i] : ((~p3(Y)) | (~r1(X!4, Y)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[150, 111])).
% 0.19/0.50 tff(152,plain,
% 0.19/0.50 (((~![Y: $i] : ((~p3(Y)) | (~r1(X!4, Y)))) | ((~p3(tptp_fun_X_8(X!4))) | (~r1(X!4, tptp_fun_X_8(X!4))))) <=> ((~![Y: $i] : ((~p3(Y)) | (~r1(X!4, Y)))) | (~p3(tptp_fun_X_8(X!4))) | (~r1(X!4, tptp_fun_X_8(X!4))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(153,plain,
% 0.19/0.50 ((~![Y: $i] : ((~p3(Y)) | (~r1(X!4, Y)))) | ((~p3(tptp_fun_X_8(X!4))) | (~r1(X!4, tptp_fun_X_8(X!4))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(154,plain,
% 0.19/0.50 ((~![Y: $i] : ((~p3(Y)) | (~r1(X!4, Y)))) | (~p3(tptp_fun_X_8(X!4))) | (~r1(X!4, tptp_fun_X_8(X!4)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.19/0.50 tff(155,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[154, 151, 149, 147])).
% 0.19/0.50 % SZS output end Proof
%------------------------------------------------------------------------------