TSTP Solution File: LCL650+1.001 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL650+1.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 04:57:23 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL650+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n029.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
% 0.13/0.34 % DateTime : Thu Sep 1 23:13:29 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.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(p2_type, type, (
% 0.20/0.40 p2: $i > $o)).
% 0.20/0.40 tff(tptp_fun_X_11_type, type, (
% 0.20/0.40 tptp_fun_X_11: $i)).
% 0.20/0.40 tff(p1_type, type, (
% 0.20/0.40 p1: $i > $o)).
% 0.20/0.40 tff(r1_type, type, (
% 0.20/0.40 r1: ( $i * $i ) > $o)).
% 0.20/0.40 tff(tptp_fun_Y_10_type, type, (
% 0.20/0.40 tptp_fun_Y_10: $i)).
% 0.20/0.40 tff(tptp_fun_X_9_type, type, (
% 0.20/0.40 tptp_fun_X_9: $i)).
% 0.20/0.40 tff(p3_type, type, (
% 0.20/0.40 p3: $i > $o)).
% 0.20/0.40 tff(tptp_fun_Y_7_type, type, (
% 0.20/0.40 tptp_fun_Y_7: $i > $i)).
% 0.20/0.40 tff(tptp_fun_Y_8_type, type, (
% 0.20/0.40 tptp_fun_Y_8: $i)).
% 0.20/0.40 tff(tptp_fun_X_6_type, type, (
% 0.20/0.40 tptp_fun_X_6: $i > $i)).
% 0.20/0.40 tff(p4_type, type, (
% 0.20/0.40 p4: $i > $o)).
% 0.20/0.40 tff(tptp_fun_X_0_type, type, (
% 0.20/0.40 tptp_fun_X_0: $i)).
% 0.20/0.40 tff(tptp_fun_X_5_type, type, (
% 0.20/0.40 tptp_fun_X_5: $i)).
% 0.20/0.40 tff(p6_type, type, (
% 0.20/0.40 p6: $i > $o)).
% 0.20/0.40 tff(p8_type, type, (
% 0.20/0.40 p8: $i > $o)).
% 0.20/0.40 tff(tptp_fun_Y_4_type, type, (
% 0.20/0.40 tptp_fun_Y_4: $i)).
% 0.20/0.40 tff(tptp_fun_X_3_type, type, (
% 0.20/0.40 tptp_fun_X_3: $i)).
% 0.20/0.40 tff(tptp_fun_Y_2_type, type, (
% 0.20/0.40 tptp_fun_Y_2: $i)).
% 0.20/0.40 tff(tptp_fun_Y_1_type, type, (
% 0.20/0.40 tptp_fun_Y_1: $i)).
% 0.20/0.40 tff(p5_type, type, (
% 0.20/0.40 p5: $i > $o)).
% 0.20/0.40 tff(1,assumption,(~p1(X!11)), introduced(assumption)).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (((~(p5(Y!1) | (~r1(X!0, Y!1)))) & (r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X)))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))) & (r1(X!0, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11)))))) <=> ((~(p5(Y!1) | (~r1(X!0, Y!1)))) & r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X)))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))) & r1(X!0, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 ((r1(X!0, Y!8) & (r1(Y!8, X!9) & r1(X!9, Y!10) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11)))))) <=> (r1(X!0, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 ((r1(Y!8, X!9) & (r1(X!9, Y!10) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11)))))) <=> (r1(Y!8, X!9) & r1(X!9, Y!10) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (((~(~r1(X!9, Y!10))) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11))))) <=> (r1(X!9, Y!10) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 ((~(~r1(Y!8, X!9))) <=> r1(Y!8, X!9)),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (((~(~r1(Y!8, X!9))) & ((~(~r1(X!9, Y!10))) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11)))))) <=> (r1(Y!8, X!9) & (r1(X!9, Y!10) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[6, 5])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (((~(~r1(Y!8, X!9))) & ((~(~r1(X!9, Y!10))) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11)))))) <=> (r1(Y!8, X!9) & r1(X!9, Y!10) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11)))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[7, 4])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 ((~(~r1(X!0, Y!8))) <=> r1(X!0, Y!8)),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (((~(~r1(X!0, Y!8))) & ((~(~r1(Y!8, X!9))) & ((~(~r1(X!9, Y!10))) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11))))))) <=> (r1(X!0, Y!8) & (r1(Y!8, X!9) & r1(X!9, Y!10) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[9, 8])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (((~(~r1(X!0, Y!8))) & ((~(~r1(Y!8, X!9))) & ((~(~r1(X!9, Y!10))) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11))))))) <=> (r1(X!0, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11)))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[10, 3])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 ((r1(X!0, Y!2) & (r1(Y!2, X!3) & r1(X!3, Y!4) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5))))))) <=> (r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 ((r1(Y!2, X!3) & (r1(X!3, Y!4) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5))))))) <=> (r1(Y!2, X!3) & r1(X!3, Y!4) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (((~(~r1(X!3, Y!4))) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5)))))) <=> (r1(X!3, Y!4) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 ((~(~r1(Y!2, X!3))) <=> r1(Y!2, X!3)),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (((~(~r1(Y!2, X!3))) & ((~(~r1(X!3, Y!4))) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5))))))) <=> (r1(Y!2, X!3) & (r1(X!3, Y!4) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5)))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[15, 14])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (((~(~r1(Y!2, X!3))) & ((~(~r1(X!3, Y!4))) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5))))))) <=> (r1(Y!2, X!3) & r1(X!3, Y!4) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[16, 13])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 ((~(~r1(X!0, Y!2))) <=> r1(X!0, Y!2)),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (((~(~r1(X!0, Y!2))) & ((~(~r1(Y!2, X!3))) & ((~(~r1(X!3, Y!4))) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5)))))))) <=> (r1(X!0, Y!2) & (r1(Y!2, X!3) & r1(X!3, Y!4) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5)))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[18, 17])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 (((~(~r1(X!0, Y!2))) & ((~(~r1(Y!2, X!3))) & ((~(~r1(X!3, Y!4))) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5)))))))) <=> (r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[19, 12])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 ((~((~r1(X!0, Y!1)) | p5(Y!1))) <=> (~(p5(Y!1) | (~r1(X!0, Y!1))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (((~((~r1(X!0, Y!1)) | p5(Y!1))) & ((~(~r1(X!0, Y!2))) & ((~(~r1(Y!2, X!3))) & ((~(~r1(X!3, Y!4))) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X)))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))) & ((~(~r1(X!0, Y!8))) & ((~(~r1(Y!8, X!9))) & ((~(~r1(X!9, Y!10))) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11)))))))) <=> ((~(p5(Y!1) | (~r1(X!0, Y!1)))) & (r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X)))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))) & (r1(X!0, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[21, 20, 11])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 (((~((~r1(X!0, Y!1)) | p5(Y!1))) & ((~(~r1(X!0, Y!2))) & ((~(~r1(Y!2, X!3))) & ((~(~r1(X!3, Y!4))) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X)))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))) & ((~(~r1(X!0, Y!8))) & ((~(~r1(Y!8, X!9))) & ((~(~r1(X!9, Y!10))) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11)))))))) <=> ((~(p5(Y!1) | (~r1(X!0, Y!1)))) & r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X)))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))) & r1(X!0, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11)))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[22, 2])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X)))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p4(X) & p3(X) & p2(X) & p1(X)))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X)))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p4(X) & p3(X) & p2(X) & p1(X))))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 ((~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X)))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p4(X) & p3(X) & p2(X) & p1(X)))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X)))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p4(X) & p3(X) & p2(X) & p1(X))))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 ((~?[X: $i] : (~(((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((((~p8(X)) & (~p6(X))) & (~p4(X))) & (~p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y))) | (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p3(X)) & (~p1(X))) | (p1(X) & p3(X)))))))) | ![X: $i] : ((~r1(Y, X)) | p4(X))) | (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p2(X)) & (~p3(X))) | (p3(X) & p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~![Y: $i] : ((~r1(X, Y)) | (~(~![X: $i] : ((~r1(Y, X)) | (~(((~p1(X)) & (~p2(X))) | (p2(X) & p1(X)))))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((p4(X) & p3(X)) & p2(X)) & p1(X))))))))) <=> (~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X)))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p4(X) & p3(X) & p2(X) & p1(X)))))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 ((~(~?[X: $i] : (~(((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((((~p8(X)) & (~p6(X))) & (~p4(X))) & (~p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y))) | (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p3(X)) & (~p1(X))) | (p1(X) & p3(X)))))))) | ![X: $i] : ((~r1(Y, X)) | p4(X))) | (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p2(X)) & (~p3(X))) | (p3(X) & p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~![Y: $i] : ((~r1(X, Y)) | (~(~![X: $i] : ((~r1(Y, X)) | (~(((~p1(X)) & (~p2(X))) | (p2(X) & p1(X)))))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((p4(X) & p3(X)) & p2(X)) & p1(X)))))))))) <=> (~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X)))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p4(X) & p3(X) & p2(X) & p1(X))))))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[26])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 ((~(~?[X: $i] : (~(((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((((~p8(X)) & (~p6(X))) & (~p4(X))) & (~p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y))) | (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p3(X)) & (~p1(X))) | (p1(X) & p3(X)))))))) | ![X: $i] : ((~r1(Y, X)) | p4(X))) | (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p2(X)) & (~p3(X))) | (p3(X) & p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~![Y: $i] : ((~r1(X, Y)) | (~(~![X: $i] : ((~r1(Y, X)) | (~(((~p1(X)) & (~p2(X))) | (p2(X) & p1(X)))))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((p4(X) & p3(X)) & p2(X)) & p1(X)))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X)))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p4(X) & p3(X) & p2(X) & p1(X))))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[27, 25])).
% 0.20/0.41 tff(29,axiom,(~(~?[X: $i] : (~(((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((((~p8(X)) & (~p6(X))) & (~p4(X))) & (~p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y))) | (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p3(X)) & (~p1(X))) | (p1(X) & p3(X)))))))) | ![X: $i] : ((~r1(Y, X)) | p4(X))) | (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p2(X)) & (~p3(X))) | (p3(X) & p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~![Y: $i] : ((~r1(X, Y)) | (~(~![X: $i] : ((~r1(Y, X)) | (~(((~p1(X)) & (~p2(X))) | (p2(X) & p1(X)))))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((p4(X) & p3(X)) & p2(X)) & p1(X)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','main')).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X)))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p4(X) & p3(X) & p2(X) & p1(X))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X)))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p4(X) & p3(X) & p2(X) & p1(X))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[30, 24])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 ((~(p5(Y!1) | (~r1(X!0, Y!1)))) & r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X)))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))) & r1(X!0, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[31, 23])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 (r1(X!0, Y!8)),
% 0.20/0.42 inference(and_elim,[status(thm)],[32])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (^[Y: $i] : refl(((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))) <=> ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[34])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))) <=> ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[36])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[37, 35])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X)))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))) <=> ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 (![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X)))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 (![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X)))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X)))))))))))),
% 0.20/0.42 inference(and_elim,[status(thm)],[32])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))) | ((~r1(X!0, Y!8)) | (~(p4(tptp_fun_X_6(Y!8)) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | (~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))) | (~r1(X!0, Y!8)) | (~(p4(tptp_fun_X_6(Y!8)) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | (~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(45,plain,
% 0.20/0.43 (((~r1(X!0, Y!8)) | (~((~r1(Y!8, tptp_fun_X_6(Y!8))) | p4(tptp_fun_X_6(Y!8)) | (~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))) <=> ((~r1(X!0, Y!8)) | (~(p4(tptp_fun_X_6(Y!8)) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | (~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(46,plain,
% 0.20/0.43 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))) | ((~r1(X!0, Y!8)) | (~((~r1(Y!8, tptp_fun_X_6(Y!8))) | p4(tptp_fun_X_6(Y!8)) | (~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))) | ((~r1(X!0, Y!8)) | (~(p4(tptp_fun_X_6(Y!8)) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | (~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[45])).
% 0.20/0.43 tff(47,plain,
% 0.20/0.43 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))) | ((~r1(X!0, Y!8)) | (~((~r1(Y!8, tptp_fun_X_6(Y!8))) | p4(tptp_fun_X_6(Y!8)) | (~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))) | (~r1(X!0, Y!8)) | (~(p4(tptp_fun_X_6(Y!8)) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | (~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[46, 44])).
% 0.20/0.43 tff(48,plain,
% 0.20/0.43 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))) | ((~r1(X!0, Y!8)) | (~((~r1(Y!8, tptp_fun_X_6(Y!8))) | p4(tptp_fun_X_6(Y!8)) | (~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(49,plain,
% 0.20/0.43 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))) | (~r1(X!0, Y!8)) | (~(p4(tptp_fun_X_6(Y!8)) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | (~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.20/0.43 tff(50,plain,
% 0.20/0.43 (~(p4(tptp_fun_X_6(Y!8)) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | (~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[49, 43, 33])).
% 0.20/0.43 tff(51,plain,
% 0.20/0.43 ((p4(tptp_fun_X_6(Y!8)) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | (~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))) | ![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(52,plain,
% 0.20/0.43 (![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.20/0.43 tff(53,plain,
% 0.20/0.43 (r1(Y!8, X!9)),
% 0.20/0.43 inference(and_elim,[status(thm)],[32])).
% 0.20/0.43 tff(54,plain,
% 0.20/0.43 (((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))) | ((~r1(Y!8, X!9)) | (~((~r1(X!9, tptp_fun_Y_7(X!9))) | p3(tptp_fun_Y_7(X!9)) | (~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))) <=> ((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))) | (~r1(Y!8, X!9)) | (~((~r1(X!9, tptp_fun_Y_7(X!9))) | p3(tptp_fun_Y_7(X!9)) | (~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(55,plain,
% 0.20/0.44 ((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))) | ((~r1(Y!8, X!9)) | (~((~r1(X!9, tptp_fun_Y_7(X!9))) | p3(tptp_fun_Y_7(X!9)) | (~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(56,plain,
% 0.20/0.44 ((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))) | (~r1(Y!8, X!9)) | (~((~r1(X!9, tptp_fun_Y_7(X!9))) | p3(tptp_fun_Y_7(X!9)) | (~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.20/0.44 tff(57,plain,
% 0.20/0.44 (~((~r1(X!9, tptp_fun_Y_7(X!9))) | p3(tptp_fun_Y_7(X!9)) | (~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[56, 53, 52])).
% 0.20/0.44 tff(58,plain,
% 0.20/0.44 (((~r1(X!9, tptp_fun_Y_7(X!9))) | p3(tptp_fun_Y_7(X!9)) | (~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(59,plain,
% 0.20/0.44 (![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.20/0.44 tff(60,plain,
% 0.20/0.44 (r1(X!9, Y!10)),
% 0.20/0.44 inference(and_elim,[status(thm)],[32])).
% 0.20/0.44 tff(61,plain,
% 0.20/0.44 (((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))) | ((~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))) <=> ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))) | (~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(62,plain,
% 0.20/0.44 ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))) | ((~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(63,plain,
% 0.20/0.44 ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))) | (~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.44 tff(64,plain,
% 0.20/0.44 (![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[63, 60, 59])).
% 0.20/0.44 tff(65,plain,
% 0.20/0.44 (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11)))),
% 0.20/0.44 inference(and_elim,[status(thm)],[32])).
% 0.20/0.44 tff(66,plain,
% 0.20/0.44 (r1(Y!10, X!11)),
% 0.20/0.44 inference(or_elim,[status(thm)],[65])).
% 0.20/0.44 tff(67,plain,
% 0.20/0.44 (((~![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))) | ((~r1(Y!10, X!11)) | (~((~((~p2(X!11)) | (~p1(X!11)))) | (~(p1(X!11) | p2(X!11))))))) <=> ((~![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))) | (~r1(Y!10, X!11)) | (~((~((~p2(X!11)) | (~p1(X!11)))) | (~(p1(X!11) | p2(X!11))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(68,plain,
% 0.20/0.44 ((~![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))) | ((~r1(Y!10, X!11)) | (~((~((~p2(X!11)) | (~p1(X!11)))) | (~(p1(X!11) | p2(X!11))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(69,plain,
% 0.20/0.44 ((~![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))) | (~r1(Y!10, X!11)) | (~((~((~p2(X!11)) | (~p1(X!11)))) | (~(p1(X!11) | p2(X!11)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.44 tff(70,plain,
% 0.20/0.44 (~((~((~p2(X!11)) | (~p1(X!11)))) | (~(p1(X!11) | p2(X!11))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[69, 66, 64])).
% 0.20/0.44 tff(71,plain,
% 0.20/0.44 (((~((~p2(X!11)) | (~p1(X!11)))) | (~(p1(X!11) | p2(X!11)))) | (p1(X!11) | p2(X!11))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(72,plain,
% 0.20/0.44 (p1(X!11) | p2(X!11)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.20/0.44 tff(73,plain,
% 0.20/0.44 ((~(p1(X!11) | p2(X!11))) | p1(X!11) | p2(X!11)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(74,plain,
% 0.20/0.44 (p1(X!11) | p2(X!11)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.20/0.44 tff(75,plain,
% 0.20/0.44 (p2(X!11)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[74, 1])).
% 0.20/0.44 tff(76,plain,
% 0.20/0.44 ((p4(tptp_fun_X_6(Y!8)) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | (~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(77,plain,
% 0.20/0.44 (![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[76, 50])).
% 0.20/0.44 tff(78,plain,
% 0.20/0.44 (((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | ((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) <=> ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(79,plain,
% 0.20/0.44 ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | ((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(80,plain,
% 0.20/0.44 ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.44 tff(81,plain,
% 0.20/0.44 (![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X)))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[80, 53, 77])).
% 0.20/0.44 tff(82,plain,
% 0.20/0.44 (((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X)))))))) | ((~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X)))))))) <=> ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X)))))))) | (~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X)))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(83,plain,
% 0.20/0.44 ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X)))))))) | ((~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X)))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(84,plain,
% 0.20/0.44 ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X)))))))) | (~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.44 tff(85,plain,
% 0.20/0.44 (![X: $i] : ((~r1(Y!10, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[84, 60, 81])).
% 0.20/0.44 tff(86,plain,
% 0.20/0.44 (((~![X: $i] : ((~r1(Y!10, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))) | ((~r1(Y!10, X!11)) | (~((~((~p1(X!11)) | (~p3(X!11)))) | (~(p3(X!11) | p1(X!11))))))) <=> ((~![X: $i] : ((~r1(Y!10, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))) | (~r1(Y!10, X!11)) | (~((~((~p1(X!11)) | (~p3(X!11)))) | (~(p3(X!11) | p1(X!11))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(87,plain,
% 0.20/0.44 ((~![X: $i] : ((~r1(Y!10, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))) | ((~r1(Y!10, X!11)) | (~((~((~p1(X!11)) | (~p3(X!11)))) | (~(p3(X!11) | p1(X!11))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(88,plain,
% 0.20/0.44 ((~![X: $i] : ((~r1(Y!10, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))) | (~r1(Y!10, X!11)) | (~((~((~p1(X!11)) | (~p3(X!11)))) | (~(p3(X!11) | p1(X!11)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.44 tff(89,plain,
% 0.20/0.44 (~((~((~p1(X!11)) | (~p3(X!11)))) | (~(p3(X!11) | p1(X!11))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[88, 66, 85])).
% 0.20/0.44 tff(90,plain,
% 0.20/0.44 (((~((~p1(X!11)) | (~p3(X!11)))) | (~(p3(X!11) | p1(X!11)))) | (p3(X!11) | p1(X!11))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(91,plain,
% 0.20/0.44 (p3(X!11) | p1(X!11)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.20/0.44 tff(92,plain,
% 0.20/0.44 ((~(p3(X!11) | p1(X!11))) | p3(X!11) | p1(X!11)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(93,plain,
% 0.20/0.44 (p3(X!11) | p1(X!11)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.20/0.44 tff(94,plain,
% 0.20/0.44 (p3(X!11)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[93, 1])).
% 0.20/0.44 tff(95,plain,
% 0.20/0.44 (((~r1(X!9, tptp_fun_Y_7(X!9))) | p3(tptp_fun_Y_7(X!9)) | (~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(96,plain,
% 0.20/0.44 (![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[95, 57])).
% 0.20/0.44 tff(97,plain,
% 0.20/0.44 (((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | ((~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) <=> ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(98,plain,
% 0.20/0.44 ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | ((~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(99,plain,
% 0.20/0.44 ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.20/0.44 tff(100,plain,
% 0.20/0.44 (![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[99, 60, 96])).
% 0.20/0.44 tff(101,plain,
% 0.20/0.44 (((~![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))) | ((~r1(Y!10, X!11)) | (~((~((~p2(X!11)) | (~p3(X!11)))) | (~(p2(X!11) | p3(X!11))))))) <=> ((~![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))) | (~r1(Y!10, X!11)) | (~((~((~p2(X!11)) | (~p3(X!11)))) | (~(p2(X!11) | p3(X!11))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(102,plain,
% 0.20/0.44 ((~![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))) | ((~r1(Y!10, X!11)) | (~((~((~p2(X!11)) | (~p3(X!11)))) | (~(p2(X!11) | p3(X!11))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(103,plain,
% 0.20/0.44 ((~![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))) | (~r1(Y!10, X!11)) | (~((~((~p2(X!11)) | (~p3(X!11)))) | (~(p2(X!11) | p3(X!11)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.20/0.44 tff(104,plain,
% 0.20/0.44 (~((~((~p2(X!11)) | (~p3(X!11)))) | (~(p2(X!11) | p3(X!11))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[103, 66, 100])).
% 0.20/0.44 tff(105,plain,
% 0.20/0.44 (((~((~p2(X!11)) | (~p3(X!11)))) | (~(p2(X!11) | p3(X!11)))) | ((~p2(X!11)) | (~p3(X!11)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(106,plain,
% 0.20/0.45 ((~p2(X!11)) | (~p3(X!11))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.20/0.45 tff(107,plain,
% 0.20/0.45 ((~((~p2(X!11)) | (~p3(X!11)))) | (~p2(X!11)) | (~p3(X!11))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(108,plain,
% 0.20/0.45 ((~p2(X!11)) | (~p3(X!11))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.20/0.45 tff(109,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[108, 94, 75])).
% 0.20/0.45 tff(110,plain,(p1(X!11)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(111,plain,
% 0.20/0.45 (((~((~p2(X!11)) | (~p1(X!11)))) | (~(p1(X!11) | p2(X!11)))) | ((~p2(X!11)) | (~p1(X!11)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(112,plain,
% 0.20/0.45 ((~p2(X!11)) | (~p1(X!11))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[111, 70])).
% 0.20/0.45 tff(113,plain,
% 0.20/0.45 ((~((~p2(X!11)) | (~p1(X!11)))) | (~p2(X!11)) | (~p1(X!11))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(114,plain,
% 0.20/0.45 ((~p2(X!11)) | (~p1(X!11))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.20/0.45 tff(115,plain,
% 0.20/0.45 (~p2(X!11)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[114, 110])).
% 0.20/0.45 tff(116,plain,
% 0.20/0.45 (((~((~p1(X!11)) | (~p3(X!11)))) | (~(p3(X!11) | p1(X!11)))) | ((~p1(X!11)) | (~p3(X!11)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(117,plain,
% 0.20/0.45 ((~p1(X!11)) | (~p3(X!11))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[116, 89])).
% 0.20/0.45 tff(118,plain,
% 0.20/0.45 ((~((~p1(X!11)) | (~p3(X!11)))) | (~p1(X!11)) | (~p3(X!11))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(119,plain,
% 0.20/0.45 ((~p1(X!11)) | (~p3(X!11))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.20/0.45 tff(120,plain,
% 0.20/0.45 (~p3(X!11)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[119, 110])).
% 0.20/0.45 tff(121,plain,
% 0.20/0.45 (((~((~p2(X!11)) | (~p3(X!11)))) | (~(p2(X!11) | p3(X!11)))) | (p2(X!11) | p3(X!11))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(122,plain,
% 0.20/0.45 (p2(X!11) | p3(X!11)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[121, 104])).
% 0.20/0.45 tff(123,plain,
% 0.20/0.45 ((~(p2(X!11) | p3(X!11))) | p2(X!11) | p3(X!11)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(124,plain,
% 0.20/0.45 (p2(X!11) | p3(X!11)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.20/0.45 tff(125,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[124, 120, 115])).
% 0.20/0.45 % SZS output end Proof
%------------------------------------------------------------------------------