TSTP Solution File: LCL676+1.005 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL676+1.005 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 0.69s 0.67s
% Output : Proof 0.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL676+1.005 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n023.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 00:20:49 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.33 Usage: tptp [options] [-file:]file
% 0.13/0.33 -h, -? prints this message.
% 0.13/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.33 -m, -model generate model.
% 0.13/0.33 -p, -proof generate proof.
% 0.13/0.33 -c, -core generate unsat core of named formulas.
% 0.13/0.33 -st, -statistics display statistics.
% 0.13/0.33 -t:timeout set timeout (in second).
% 0.13/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.33 -<param>:<value> configuration parameter and value.
% 0.13/0.33 -o:<output-file> file to place output in.
% 0.69/0.67 % SZS status Theorem
% 0.69/0.67 % SZS output start Proof
% 0.69/0.67 tff(r1_type, type, (
% 0.69/0.67 r1: ( $i * $i ) > $o)).
% 0.69/0.67 tff(tptp_fun_X_8_type, type, (
% 0.69/0.67 tptp_fun_X_8: $i > $i)).
% 0.69/0.67 tff(tptp_fun_X_21_type, type, (
% 0.69/0.67 tptp_fun_X_21: $i > $i)).
% 0.69/0.67 tff(tptp_fun_Y_7_type, type, (
% 0.69/0.67 tptp_fun_Y_7: $i)).
% 0.69/0.67 tff(p2_type, type, (
% 0.69/0.67 p2: $i > $o)).
% 0.69/0.67 tff(tptp_fun_Y_9_type, type, (
% 0.69/0.67 tptp_fun_Y_9: $i > $i)).
% 0.69/0.67 tff(tptp_fun_X_0_type, type, (
% 0.69/0.67 tptp_fun_X_0: $i)).
% 0.69/0.67 tff(tptp_fun_Y_26_type, type, (
% 0.69/0.67 tptp_fun_Y_26: $i > $i)).
% 0.69/0.67 tff(p1_type, type, (
% 0.69/0.67 p1: $i > $o)).
% 0.69/0.67 tff(tptp_fun_Y_31_type, type, (
% 0.69/0.67 tptp_fun_Y_31: $i)).
% 0.69/0.67 tff(tptp_fun_X_32_type, type, (
% 0.69/0.67 tptp_fun_X_32: $i)).
% 0.69/0.67 tff(tptp_fun_Y_29_type, type, (
% 0.69/0.67 tptp_fun_Y_29: $i)).
% 0.69/0.67 tff(tptp_fun_X_30_type, type, (
% 0.69/0.67 tptp_fun_X_30: $i)).
% 0.69/0.67 tff(p3_type, type, (
% 0.69/0.67 p3: $i > $o)).
% 0.69/0.67 tff(tptp_fun_Y_27_type, type, (
% 0.69/0.67 tptp_fun_Y_27: $i)).
% 0.69/0.67 tff(tptp_fun_X_28_type, type, (
% 0.69/0.67 tptp_fun_X_28: $i)).
% 0.69/0.67 tff(p4_type, type, (
% 0.69/0.67 p4: $i > $o)).
% 0.69/0.67 tff(tptp_fun_Y_24_type, type, (
% 0.69/0.67 tptp_fun_Y_24: $i)).
% 0.69/0.67 tff(tptp_fun_X_25_type, type, (
% 0.69/0.67 tptp_fun_X_25: $i)).
% 0.69/0.67 tff(tptp_fun_X_23_type, type, (
% 0.69/0.67 tptp_fun_X_23: $i > $i)).
% 0.69/0.67 tff(tptp_fun_Y_22_type, type, (
% 0.69/0.67 tptp_fun_Y_22: $i > $i)).
% 0.69/0.67 tff(tptp_fun_Y_18_type, type, (
% 0.69/0.67 tptp_fun_Y_18: $i)).
% 0.69/0.67 tff(tptp_fun_X_15_type, type, (
% 0.69/0.67 tptp_fun_X_15: $i > $i)).
% 0.69/0.67 tff(tptp_fun_Y_14_type, type, (
% 0.69/0.67 tptp_fun_Y_14: $i > $i)).
% 0.69/0.67 tff(tptp_fun_Y_20_type, type, (
% 0.69/0.67 tptp_fun_Y_20: $i)).
% 0.69/0.67 tff(tptp_fun_X_19_type, type, (
% 0.69/0.67 tptp_fun_X_19: $i)).
% 0.69/0.67 tff(tptp_fun_X_17_type, type, (
% 0.69/0.67 tptp_fun_X_17: $i)).
% 0.69/0.67 tff(tptp_fun_Y_16_type, type, (
% 0.69/0.67 tptp_fun_Y_16: $i)).
% 0.69/0.67 tff(tptp_fun_Y_13_type, type, (
% 0.69/0.67 tptp_fun_Y_13: $i)).
% 0.69/0.67 tff(tptp_fun_Y_12_type, type, (
% 0.69/0.67 tptp_fun_Y_12: $i > $i)).
% 0.69/0.67 tff(tptp_fun_X_11_type, type, (
% 0.69/0.67 tptp_fun_X_11: $i > $i)).
% 0.69/0.67 tff(p5_type, type, (
% 0.69/0.67 p5: $i > $o)).
% 0.69/0.67 tff(tptp_fun_X_10_type, type, (
% 0.69/0.67 tptp_fun_X_10: $i > $i)).
% 0.69/0.67 tff(tptp_fun_Y_5_type, type, (
% 0.69/0.67 tptp_fun_Y_5: $i)).
% 0.69/0.67 tff(tptp_fun_X_6_type, type, (
% 0.69/0.67 tptp_fun_X_6: $i)).
% 0.69/0.67 tff(tptp_fun_Y_4_type, type, (
% 0.69/0.67 tptp_fun_Y_4: $i > $i)).
% 0.69/0.67 tff(tptp_fun_X_3_type, type, (
% 0.69/0.67 tptp_fun_X_3: $i > $i)).
% 0.69/0.67 tff(tptp_fun_Y_2_type, type, (
% 0.69/0.67 tptp_fun_Y_2: $i)).
% 0.69/0.67 tff(tptp_fun_Y_1_type, type, (
% 0.69/0.67 tptp_fun_Y_1: $i)).
% 0.69/0.67 tff(1,plain,
% 0.69/0.67 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p2(tptp_fun_X_21(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p2(tptp_fun_X_21(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))),
% 0.69/0.67 inference(bind,[status(th)],[])).
% 0.69/0.67 tff(2,plain,
% 0.69/0.67 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p2(tptp_fun_X_21(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p2(tptp_fun_X_21(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.69/0.67 inference(quant_intro,[status(thm)],[1])).
% 0.69/0.67 tff(3,plain,
% 0.69/0.67 (^[Y: $i] : refl((p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p2(tptp_fun_X_21(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p2(tptp_fun_X_21(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))))))),
% 0.69/0.67 inference(bind,[status(th)],[])).
% 0.69/0.67 tff(4,plain,
% 0.69/0.67 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p2(tptp_fun_X_21(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p2(tptp_fun_X_21(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y)))))))),
% 0.69/0.67 inference(quant_intro,[status(thm)],[3])).
% 0.69/0.67 tff(5,plain,
% 0.69/0.67 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p2(tptp_fun_X_21(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p2(tptp_fun_X_21(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))))))),
% 0.69/0.67 inference(bind,[status(th)],[])).
% 0.69/0.67 tff(6,plain,
% 0.69/0.67 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p2(tptp_fun_X_21(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p2(tptp_fun_X_21(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y)))))))),
% 0.69/0.67 inference(quant_intro,[status(thm)],[5])).
% 0.69/0.67 tff(7,plain,
% 0.69/0.67 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p2(tptp_fun_X_21(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p2(tptp_fun_X_21(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y)))))))),
% 0.69/0.67 inference(transitivity,[status(thm)],[6, 4])).
% 0.69/0.67 tff(8,plain,
% 0.69/0.67 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p2(tptp_fun_X_21(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))))))),
% 0.69/0.67 inference(bind,[status(th)],[])).
% 0.69/0.67 tff(9,plain,
% 0.69/0.67 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p2(tptp_fun_X_21(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y)))))))),
% 0.69/0.67 inference(quant_intro,[status(thm)],[8])).
% 0.69/0.67 tff(10,plain,
% 0.69/0.67 (((~((~r1(X!0, Y!1)) | p3(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_3(Y)) & p3(tptp_fun_X_3(Y)) & (~(p3(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) & ((r1(X!0, Y!5) & r1(Y!5, X!6) & ![Y: $i] : ((~p5(Y)) | (~r1(X!6, Y))) & (~p1(Y!5))) | ((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | ((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_11(Y)) & p1(tptp_fun_X_11(Y)) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y)))))) & (((((r1(X!0, Y!13) & (~p2(Y!13)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!13, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_14(X)) & p2(tptp_fun_Y_14(X)) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X)))))))) & (p2(X!0) | (r1(X!0, Y!16) & p2(Y!16) & (~((~r1(Y!16, X!17)) | p2(X!17)))))) | (r1(X!0, Y!18) & ((r1(Y!18, X!19) & r1(X!19, Y!20) & (~p2(Y!20)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!20, X))) & ![X: $i] : (p2(X) | (~r1(Y!18, X)) | (r1(X, tptp_fun_Y_14(X)) & p2(tptp_fun_Y_14(X)) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X))))))) | ((~p2(Y!18)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!18, X))))) & ![X: $i] : ((~r1(Y!18, 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_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))) | (r1(Y, tptp_fun_X_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))) & r1(X, tptp_fun_Y_22(X)) & r1(tptp_fun_Y_22(X), tptp_fun_X_23(X)) & (~p2(tptp_fun_X_23(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_23(X), Y))))))) & (p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | p2(X!0) | p4(X!0) | (r1(X!0, Y!24) & (~p1(Y!24)) & (~p2(Y!24)) & (~p3(Y!24)) & (~p4(Y!24)) & r1(Y!24, X!25) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!24, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~p4(X)) & r1(X, tptp_fun_Y_26(X)))))) & (p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | p2(X!0) | (r1(X!0, Y!27) & (~p1(Y!27)) & (~p2(Y!27)) & (~p3(Y!27)) & r1(Y!27, X!28) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!27, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & r1(X, tptp_fun_Y_26(X)))))) & (![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | p2(X!0) | (r1(X!0, Y!29) & (~p1(Y!29)) & (~p2(Y!29)) & r1(Y!29, X!30) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!29, X)) | ((~p1(X)) & (~p2(X)) & r1(X, tptp_fun_Y_26(X)))))) & (![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | (r1(X!0, Y!31) & (~p1(Y!31)) & r1(Y!31, X!32) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!31, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_26(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))))) <=> ((~((~r1(X!0, Y!1)) | p3(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_3(Y)) & p3(tptp_fun_X_3(Y)) & (~(p3(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) & ((r1(X!0, Y!5) & r1(Y!5, X!6) & ![Y: $i] : ((~p5(Y)) | (~r1(X!6, Y))) & (~p1(Y!5))) | ((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | ((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_11(Y)) & p1(tptp_fun_X_11(Y)) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y)))))) & ((((r1(X!0, Y!13) & (~p2(Y!13)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!13, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_14(X)) & p2(tptp_fun_Y_14(X)) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X)))))))) & (p2(X!0) | (r1(X!0, Y!16) & p2(Y!16) & (~((~r1(Y!16, X!17)) | p2(X!17)))))) | (r1(X!0, Y!18) & ((r1(Y!18, X!19) & r1(X!19, Y!20) & (~p2(Y!20)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!20, X))) & ![X: $i] : (p2(X) | (~r1(Y!18, X)) | (r1(X, tptp_fun_Y_14(X)) & p2(tptp_fun_Y_14(X)) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X))))))) | ((~p2(Y!18)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!18, X))))) & ![X: $i] : ((~r1(Y!18, 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_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))) | (r1(Y, tptp_fun_X_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))) & r1(X, tptp_fun_Y_22(X)) & r1(tptp_fun_Y_22(X), tptp_fun_X_23(X)) & (~p2(tptp_fun_X_23(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_23(X), Y))))))) & (p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | p2(X!0) | p4(X!0) | (r1(X!0, Y!24) & (~p1(Y!24)) & (~p2(Y!24)) & (~p3(Y!24)) & (~p4(Y!24)) & r1(Y!24, X!25) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!24, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~p4(X)) & r1(X, tptp_fun_Y_26(X)))))) & (p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | p2(X!0) | (r1(X!0, Y!27) & (~p1(Y!27)) & (~p2(Y!27)) & (~p3(Y!27)) & r1(Y!27, X!28) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!27, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & r1(X, tptp_fun_Y_26(X)))))) & (![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | p2(X!0) | (r1(X!0, Y!29) & (~p1(Y!29)) & (~p2(Y!29)) & r1(Y!29, X!30) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!29, X)) | ((~p1(X)) & (~p2(X)) & r1(X, tptp_fun_Y_26(X)))))) & (![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | (r1(X!0, Y!31) & (~p1(Y!31)) & r1(Y!31, X!32) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!31, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_26(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))))),
% 0.69/0.68 inference(rewrite,[status(thm)],[])).
% 0.69/0.68 tff(11,plain,
% 0.69/0.68 (((((((~(~r1(X!0, Y!13))) & (~p2(Y!13)) & ![X: $i] : ((~r1(Y!13, 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_14(X)))) & (~(~p2(tptp_fun_Y_14(X)))) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X)))))))) & (p2(X!0) | ((~(~r1(X!0, Y!16))) & (~(~p2(Y!16))) & (~((~r1(Y!16, X!17)) | p2(X!17)))))) | ((~(~r1(X!0, Y!18))) & ((((~(~r1(Y!18, X!19))) & ((~(~r1(X!19, Y!20))) & (~p2(Y!20)) & ![X: $i] : ((~r1(Y!20, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!18, X)) | p2(X) | ((~(~r1(X, tptp_fun_Y_14(X)))) & (~(~p2(tptp_fun_Y_14(X)))) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X))))))) | ((~p2(Y!18)) & ![X: $i] : ((~r1(Y!18, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!18, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & (~(~p2(tptp_fun_X_8(Y)))) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))) | ((~(~r1(Y, tptp_fun_X_21(Y)))) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_21(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) & (p2(Y) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & (~(~p2(tptp_fun_X_8(Y)))) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) | ((![Y: $i] : ((~r1(X, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & (~(~p2(tptp_fun_X_8(Y)))) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))) & ((~(~r1(X, tptp_fun_Y_22(X)))) & ((~(~r1(tptp_fun_Y_22(X), tptp_fun_X_23(X)))) & (~p2(tptp_fun_X_23(X))) & ![Y: $i] : ((~r1(tptp_fun_X_23(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)))))))) & (p1(X!0) | p2(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~(~r1(X!0, Y!24))) & (~p1(Y!24)) & (~p2(Y!24)) & (~p3(Y!24)) & (~p4(Y!24)) & (~(~r1(Y!24, X!25))) & ![X: $i] : ((~r1(Y!24, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~p4(X)) & (~(~r1(X, tptp_fun_Y_26(X)))))))) & (p1(X!0) | p2(X!0) | p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~(~r1(X!0, Y!27))) & (~p1(Y!27)) & (~p2(Y!27)) & (~p3(Y!27)) & (~(~r1(Y!27, X!28))) & ![X: $i] : ((~r1(Y!27, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~(~r1(X, tptp_fun_Y_26(X)))))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~(~r1(X!0, Y!29))) & (~p1(Y!29)) & (~p2(Y!29)) & (~(~r1(Y!29, X!30))) & ![X: $i] : ((~r1(Y!29, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & (~p2(X)) & (~(~r1(X, tptp_fun_Y_26(X)))))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~(~r1(X!0, Y!31))) & (~p1(Y!31)) & (~(~r1(Y!31, X!32))) & ![X: $i] : ((~r1(Y!31, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & (~(~r1(X, tptp_fun_Y_26(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_21(Y)))) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_21(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) <=> (((((r1(X!0, Y!13) & (~p2(Y!13)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!13, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_14(X)) & p2(tptp_fun_Y_14(X)) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X)))))))) & (p2(X!0) | (r1(X!0, Y!16) & p2(Y!16) & (~((~r1(Y!16, X!17)) | p2(X!17)))))) | (r1(X!0, Y!18) & ((r1(Y!18, X!19) & r1(X!19, Y!20) & (~p2(Y!20)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!20, X))) & ![X: $i] : (p2(X) | (~r1(Y!18, X)) | (r1(X, tptp_fun_Y_14(X)) & p2(tptp_fun_Y_14(X)) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X))))))) | ((~p2(Y!18)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!18, X))))) & ![X: $i] : ((~r1(Y!18, 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_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))) | (r1(Y, tptp_fun_X_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))) & r1(X, tptp_fun_Y_22(X)) & r1(tptp_fun_Y_22(X), tptp_fun_X_23(X)) & (~p2(tptp_fun_X_23(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_23(X), Y))))))) & (p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | p2(X!0) | p4(X!0) | (r1(X!0, Y!24) & (~p1(Y!24)) & (~p2(Y!24)) & (~p3(Y!24)) & (~p4(Y!24)) & r1(Y!24, X!25) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!24, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~p4(X)) & r1(X, tptp_fun_Y_26(X)))))) & (p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | p2(X!0) | (r1(X!0, Y!27) & (~p1(Y!27)) & (~p2(Y!27)) & (~p3(Y!27)) & r1(Y!27, X!28) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!27, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & r1(X, tptp_fun_Y_26(X)))))) & (![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | p2(X!0) | (r1(X!0, Y!29) & (~p1(Y!29)) & (~p2(Y!29)) & r1(Y!29, X!30) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!29, X)) | ((~p1(X)) & (~p2(X)) & r1(X, tptp_fun_Y_26(X)))))) & (![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | (r1(X!0, Y!31) & (~p1(Y!31)) & r1(Y!31, X!32) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!31, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_26(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))))),
% 0.69/0.68 inference(rewrite,[status(thm)],[])).
% 0.69/0.68 tff(12,plain,
% 0.69/0.68 (^[Y: $i] : trans(monotonicity(rewrite(((~(~r1(Y, tptp_fun_X_11(Y)))) & (~(~p1(tptp_fun_X_11(Y)))) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y))))) <=> (r1(Y, tptp_fun_X_11(Y)) & p1(tptp_fun_X_11(Y)) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y)))))), (((~r1(X!0, Y)) | p1(Y) | ((~(~r1(Y, tptp_fun_X_11(Y)))) & (~(~p1(tptp_fun_X_11(Y)))) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y)))))) <=> ((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_11(Y)) & p1(tptp_fun_X_11(Y)) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y)))))))), rewrite(((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_11(Y)) & p1(tptp_fun_X_11(Y)) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y)))))) <=> (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_11(Y)) & p1(tptp_fun_X_11(Y)) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y))))))), (((~r1(X!0, Y)) | p1(Y) | ((~(~r1(Y, tptp_fun_X_11(Y)))) & (~(~p1(tptp_fun_X_11(Y)))) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y)))))) <=> (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_11(Y)) & p1(tptp_fun_X_11(Y)) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y))))))))),
% 0.69/0.68 inference(bind,[status(th)],[])).
% 0.69/0.68 tff(13,plain,
% 0.69/0.68 (![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | ((~(~r1(Y, tptp_fun_X_11(Y)))) & (~(~p1(tptp_fun_X_11(Y)))) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y)))))) <=> ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_11(Y)) & p1(tptp_fun_X_11(Y)) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y))))))),
% 0.69/0.68 inference(quant_intro,[status(thm)],[12])).
% 0.69/0.68 tff(14,plain,
% 0.69/0.68 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | ((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | ((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))))),
% 0.69/0.68 inference(rewrite,[status(thm)],[])).
% 0.69/0.68 tff(15,plain,
% 0.69/0.68 (((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & (~(~p2(tptp_fun_X_8(Y)))) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))) <=> ((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))),
% 0.69/0.68 inference(rewrite,[status(thm)],[])).
% 0.69/0.68 tff(16,plain,
% 0.69/0.68 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | ((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & (~(~p2(tptp_fun_X_8(Y)))) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | ((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))))),
% 0.69/0.68 inference(monotonicity,[status(thm)],[15])).
% 0.69/0.68 tff(17,plain,
% 0.69/0.68 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | ((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & (~(~p2(tptp_fun_X_8(Y)))) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | ((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))))),
% 0.69/0.68 inference(transitivity,[status(thm)],[16, 14])).
% 0.69/0.68 tff(18,plain,
% 0.69/0.68 (((r1(X!0, Y!5) & r1(Y!5, X!6) & ![Y: $i] : ((~p5(Y)) | (~r1(X!6, Y))) & (~p1(Y!5))) | ((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) <=> ((r1(X!0, Y!5) & r1(Y!5, X!6) & ![Y: $i] : ((~p5(Y)) | (~r1(X!6, Y))) & (~p1(Y!5))) | ((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))))),
% 0.69/0.68 inference(rewrite,[status(thm)],[])).
% 0.69/0.68 tff(19,plain,
% 0.69/0.68 ((r1(X!0, Y!5) & (r1(Y!5, X!6) & ![Y: $i] : ((~p5(Y)) | (~r1(X!6, Y)))) & (~p1(Y!5))) <=> (r1(X!0, Y!5) & r1(Y!5, X!6) & ![Y: $i] : ((~p5(Y)) | (~r1(X!6, Y))) & (~p1(Y!5)))),
% 0.69/0.68 inference(rewrite,[status(thm)],[])).
% 0.69/0.68 tff(20,plain,
% 0.69/0.68 (((~(~r1(Y!5, X!6))) & ![Y: $i] : ((~r1(X!6, Y)) | (~p5(Y)))) <=> (r1(Y!5, X!6) & ![Y: $i] : ((~p5(Y)) | (~r1(X!6, Y))))),
% 0.69/0.68 inference(rewrite,[status(thm)],[])).
% 0.69/0.68 tff(21,plain,
% 0.69/0.68 ((~(~r1(X!0, Y!5))) <=> r1(X!0, Y!5)),
% 0.69/0.68 inference(rewrite,[status(thm)],[])).
% 0.69/0.68 tff(22,plain,
% 0.69/0.68 (((~(~r1(X!0, Y!5))) & ((~(~r1(Y!5, X!6))) & ![Y: $i] : ((~r1(X!6, Y)) | (~p5(Y)))) & (~p1(Y!5))) <=> (r1(X!0, Y!5) & (r1(Y!5, X!6) & ![Y: $i] : ((~p5(Y)) | (~r1(X!6, Y)))) & (~p1(Y!5)))),
% 0.69/0.68 inference(monotonicity,[status(thm)],[21, 20])).
% 0.69/0.68 tff(23,plain,
% 0.69/0.68 (((~(~r1(X!0, Y!5))) & ((~(~r1(Y!5, X!6))) & ![Y: $i] : ((~r1(X!6, Y)) | (~p5(Y)))) & (~p1(Y!5))) <=> (r1(X!0, Y!5) & r1(Y!5, X!6) & ![Y: $i] : ((~p5(Y)) | (~r1(X!6, Y))) & (~p1(Y!5)))),
% 0.69/0.68 inference(transitivity,[status(thm)],[22, 19])).
% 0.69/0.68 tff(24,plain,
% 0.69/0.68 ((((~(~r1(X!0, Y!5))) & ((~(~r1(Y!5, X!6))) & ![Y: $i] : ((~r1(X!6, Y)) | (~p5(Y)))) & (~p1(Y!5))) | ((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & (~(~p2(tptp_fun_X_8(Y)))) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) <=> ((r1(X!0, Y!5) & r1(Y!5, X!6) & ![Y: $i] : ((~p5(Y)) | (~r1(X!6, Y))) & (~p1(Y!5))) | ((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))))),
% 0.69/0.68 inference(monotonicity,[status(thm)],[23, 15])).
% 0.69/0.68 tff(25,plain,
% 0.69/0.68 ((((~(~r1(X!0, Y!5))) & ((~(~r1(Y!5, X!6))) & ![Y: $i] : ((~r1(X!6, Y)) | (~p5(Y)))) & (~p1(Y!5))) | ((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & (~(~p2(tptp_fun_X_8(Y)))) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) <=> ((r1(X!0, Y!5) & r1(Y!5, X!6) & ![Y: $i] : ((~p5(Y)) | (~r1(X!6, Y))) & (~p1(Y!5))) | ((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))))),
% 0.69/0.68 inference(transitivity,[status(thm)],[24, 18])).
% 0.69/0.68 tff(26,plain,
% 0.69/0.68 (^[Y: $i] : trans(monotonicity(rewrite(((~(~r1(Y, tptp_fun_X_3(Y)))) & (~(~p3(tptp_fun_X_3(Y)))) & (~((~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | p3(tptp_fun_Y_4(Y))))) <=> (r1(Y, tptp_fun_X_3(Y)) & p3(tptp_fun_X_3(Y)) & (~(p3(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))), (((~r1(X!0, Y)) | p3(Y) | ((~(~r1(Y, tptp_fun_X_3(Y)))) & (~(~p3(tptp_fun_X_3(Y)))) & (~((~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | p3(tptp_fun_Y_4(Y)))))) <=> ((~r1(X!0, Y)) | p3(Y) | (r1(Y, tptp_fun_X_3(Y)) & p3(tptp_fun_X_3(Y)) & (~(p3(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))))), rewrite(((~r1(X!0, Y)) | p3(Y) | (r1(Y, tptp_fun_X_3(Y)) & p3(tptp_fun_X_3(Y)) & (~(p3(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) <=> (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_3(Y)) & p3(tptp_fun_X_3(Y)) & (~(p3(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))))), (((~r1(X!0, Y)) | p3(Y) | ((~(~r1(Y, tptp_fun_X_3(Y)))) & (~(~p3(tptp_fun_X_3(Y)))) & (~((~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | p3(tptp_fun_Y_4(Y)))))) <=> (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_3(Y)) & p3(tptp_fun_X_3(Y)) & (~(p3(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))))))),
% 0.69/0.68 inference(bind,[status(th)],[])).
% 0.69/0.68 tff(27,plain,
% 0.69/0.68 (![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | ((~(~r1(Y, tptp_fun_X_3(Y)))) & (~(~p3(tptp_fun_X_3(Y)))) & (~((~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | p3(tptp_fun_Y_4(Y)))))) <=> ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_3(Y)) & p3(tptp_fun_X_3(Y)) & (~(p3(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))))),
% 0.69/0.68 inference(quant_intro,[status(thm)],[26])).
% 0.69/0.68 tff(28,plain,
% 0.69/0.68 ((~((~r1(X!0, Y!2)) | p1(Y!2))) <=> (~((~r1(X!0, Y!2)) | p1(Y!2)))),
% 0.69/0.68 inference(rewrite,[status(thm)],[])).
% 0.69/0.68 tff(29,plain,
% 0.69/0.68 ((~((~r1(X!0, Y!1)) | p3(Y!1))) <=> (~((~r1(X!0, Y!1)) | p3(Y!1)))),
% 0.69/0.68 inference(rewrite,[status(thm)],[])).
% 0.69/0.68 tff(30,plain,
% 0.69/0.68 (((~((~r1(X!0, Y!1)) | p3(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | ((~(~r1(Y, tptp_fun_X_3(Y)))) & (~(~p3(tptp_fun_X_3(Y)))) & (~((~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | p3(tptp_fun_Y_4(Y)))))) & (((~(~r1(X!0, Y!5))) & ((~(~r1(Y!5, X!6))) & ![Y: $i] : ((~r1(X!6, Y)) | (~p5(Y)))) & (~p1(Y!5))) | ((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & (~(~p2(tptp_fun_X_8(Y)))) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | ((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & (~(~p2(tptp_fun_X_8(Y)))) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | ((~(~r1(Y, tptp_fun_X_11(Y)))) & (~(~p1(tptp_fun_X_11(Y)))) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y)))))) & ((((((~(~r1(X!0, Y!13))) & (~p2(Y!13)) & ![X: $i] : ((~r1(Y!13, 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_14(X)))) & (~(~p2(tptp_fun_Y_14(X)))) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X)))))))) & (p2(X!0) | ((~(~r1(X!0, Y!16))) & (~(~p2(Y!16))) & (~((~r1(Y!16, X!17)) | p2(X!17)))))) | ((~(~r1(X!0, Y!18))) & ((((~(~r1(Y!18, X!19))) & ((~(~r1(X!19, Y!20))) & (~p2(Y!20)) & ![X: $i] : ((~r1(Y!20, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!18, X)) | p2(X) | ((~(~r1(X, tptp_fun_Y_14(X)))) & (~(~p2(tptp_fun_Y_14(X)))) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X))))))) | ((~p2(Y!18)) & ![X: $i] : ((~r1(Y!18, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!18, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & (~(~p2(tptp_fun_X_8(Y)))) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))) | ((~(~r1(Y, tptp_fun_X_21(Y)))) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_21(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) & (p2(Y) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & (~(~p2(tptp_fun_X_8(Y)))) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) | ((![Y: $i] : ((~r1(X, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & (~(~p2(tptp_fun_X_8(Y)))) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))) & ((~(~r1(X, tptp_fun_Y_22(X)))) & ((~(~r1(tptp_fun_Y_22(X), tptp_fun_X_23(X)))) & (~p2(tptp_fun_X_23(X))) & ![Y: $i] : ((~r1(tptp_fun_X_23(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)))))))) & (p1(X!0) | p2(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~(~r1(X!0, Y!24))) & (~p1(Y!24)) & (~p2(Y!24)) & (~p3(Y!24)) & (~p4(Y!24)) & (~(~r1(Y!24, X!25))) & ![X: $i] : ((~r1(Y!24, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~p4(X)) & (~(~r1(X, tptp_fun_Y_26(X)))))))) & (p1(X!0) | p2(X!0) | p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~(~r1(X!0, Y!27))) & (~p1(Y!27)) & (~p2(Y!27)) & (~p3(Y!27)) & (~(~r1(Y!27, X!28))) & ![X: $i] : ((~r1(Y!27, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~(~r1(X, tptp_fun_Y_26(X)))))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~(~r1(X!0, Y!29))) & (~p1(Y!29)) & (~p2(Y!29)) & (~(~r1(Y!29, X!30))) & ![X: $i] : ((~r1(Y!29, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & (~p2(X)) & (~(~r1(X, tptp_fun_Y_26(X)))))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~(~r1(X!0, Y!31))) & (~p1(Y!31)) & (~(~r1(Y!31, X!32))) & ![X: $i] : ((~r1(Y!31, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & (~(~r1(X, tptp_fun_Y_26(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_21(Y)))) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_21(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) <=> ((~((~r1(X!0, Y!1)) | p3(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_3(Y)) & p3(tptp_fun_X_3(Y)) & (~(p3(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) & ((r1(X!0, Y!5) & r1(Y!5, X!6) & ![Y: $i] : ((~p5(Y)) | (~r1(X!6, Y))) & (~p1(Y!5))) | ((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | ((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_11(Y)) & p1(tptp_fun_X_11(Y)) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y)))))) & (((((r1(X!0, Y!13) & (~p2(Y!13)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!13, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_14(X)) & p2(tptp_fun_Y_14(X)) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X)))))))) & (p2(X!0) | (r1(X!0, Y!16) & p2(Y!16) & (~((~r1(Y!16, X!17)) | p2(X!17)))))) | (r1(X!0, Y!18) & ((r1(Y!18, X!19) & r1(X!19, Y!20) & (~p2(Y!20)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!20, X))) & ![X: $i] : (p2(X) | (~r1(Y!18, X)) | (r1(X, tptp_fun_Y_14(X)) & p2(tptp_fun_Y_14(X)) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X))))))) | ((~p2(Y!18)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!18, X))))) & ![X: $i] : ((~r1(Y!18, 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_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))) | (r1(Y, tptp_fun_X_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))) & r1(X, tptp_fun_Y_22(X)) & r1(tptp_fun_Y_22(X), tptp_fun_X_23(X)) & (~p2(tptp_fun_X_23(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_23(X), Y))))))) & (p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | p2(X!0) | p4(X!0) | (r1(X!0, Y!24) & (~p1(Y!24)) & (~p2(Y!24)) & (~p3(Y!24)) & (~p4(Y!24)) & r1(Y!24, X!25) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!24, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~p4(X)) & r1(X, tptp_fun_Y_26(X)))))) & (p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | p2(X!0) | (r1(X!0, Y!27) & (~p1(Y!27)) & (~p2(Y!27)) & (~p3(Y!27)) & r1(Y!27, X!28) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!27, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & r1(X, tptp_fun_Y_26(X)))))) & (![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | p2(X!0) | (r1(X!0, Y!29) & (~p1(Y!29)) & (~p2(Y!29)) & r1(Y!29, X!30) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!29, X)) | ((~p1(X)) & (~p2(X)) & r1(X, tptp_fun_Y_26(X)))))) & (![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | (r1(X!0, Y!31) & (~p1(Y!31)) & r1(Y!31, X!32) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!31, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_26(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y)))))))),
% 0.69/0.69 inference(monotonicity,[status(thm)],[29, 28, 27, 25, 17, 13, 11])).
% 0.69/0.69 tff(31,plain,
% 0.69/0.69 (((~((~r1(X!0, Y!1)) | p3(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | ((~(~r1(Y, tptp_fun_X_3(Y)))) & (~(~p3(tptp_fun_X_3(Y)))) & (~((~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | p3(tptp_fun_Y_4(Y)))))) & (((~(~r1(X!0, Y!5))) & ((~(~r1(Y!5, X!6))) & ![Y: $i] : ((~r1(X!6, Y)) | (~p5(Y)))) & (~p1(Y!5))) | ((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & (~(~p2(tptp_fun_X_8(Y)))) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | ((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & (~(~p2(tptp_fun_X_8(Y)))) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | ((~(~r1(Y, tptp_fun_X_11(Y)))) & (~(~p1(tptp_fun_X_11(Y)))) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y)))))) & ((((((~(~r1(X!0, Y!13))) & (~p2(Y!13)) & ![X: $i] : ((~r1(Y!13, 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_14(X)))) & (~(~p2(tptp_fun_Y_14(X)))) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X)))))))) & (p2(X!0) | ((~(~r1(X!0, Y!16))) & (~(~p2(Y!16))) & (~((~r1(Y!16, X!17)) | p2(X!17)))))) | ((~(~r1(X!0, Y!18))) & ((((~(~r1(Y!18, X!19))) & ((~(~r1(X!19, Y!20))) & (~p2(Y!20)) & ![X: $i] : ((~r1(Y!20, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!18, X)) | p2(X) | ((~(~r1(X, tptp_fun_Y_14(X)))) & (~(~p2(tptp_fun_Y_14(X)))) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X))))))) | ((~p2(Y!18)) & ![X: $i] : ((~r1(Y!18, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!18, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & (~(~p2(tptp_fun_X_8(Y)))) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))) | ((~(~r1(Y, tptp_fun_X_21(Y)))) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_21(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) & (p2(Y) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & (~(~p2(tptp_fun_X_8(Y)))) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) | ((![Y: $i] : ((~r1(X, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & (~(~p2(tptp_fun_X_8(Y)))) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))) & ((~(~r1(X, tptp_fun_Y_22(X)))) & ((~(~r1(tptp_fun_Y_22(X), tptp_fun_X_23(X)))) & (~p2(tptp_fun_X_23(X))) & ![Y: $i] : ((~r1(tptp_fun_X_23(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)))))))) & (p1(X!0) | p2(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~(~r1(X!0, Y!24))) & (~p1(Y!24)) & (~p2(Y!24)) & (~p3(Y!24)) & (~p4(Y!24)) & (~(~r1(Y!24, X!25))) & ![X: $i] : ((~r1(Y!24, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~p4(X)) & (~(~r1(X, tptp_fun_Y_26(X)))))))) & (p1(X!0) | p2(X!0) | p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~(~r1(X!0, Y!27))) & (~p1(Y!27)) & (~p2(Y!27)) & (~p3(Y!27)) & (~(~r1(Y!27, X!28))) & ![X: $i] : ((~r1(Y!27, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~(~r1(X, tptp_fun_Y_26(X)))))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~(~r1(X!0, Y!29))) & (~p1(Y!29)) & (~p2(Y!29)) & (~(~r1(Y!29, X!30))) & ![X: $i] : ((~r1(Y!29, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & (~p2(X)) & (~(~r1(X, tptp_fun_Y_26(X)))))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~(~r1(X!0, Y!31))) & (~p1(Y!31)) & (~(~r1(Y!31, X!32))) & ![X: $i] : ((~r1(Y!31, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & (~(~r1(X, tptp_fun_Y_26(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_21(Y)))) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_21(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) <=> ((~((~r1(X!0, Y!1)) | p3(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_3(Y)) & p3(tptp_fun_X_3(Y)) & (~(p3(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) & ((r1(X!0, Y!5) & r1(Y!5, X!6) & ![Y: $i] : ((~p5(Y)) | (~r1(X!6, Y))) & (~p1(Y!5))) | ((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | ((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_11(Y)) & p1(tptp_fun_X_11(Y)) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y)))))) & ((((r1(X!0, Y!13) & (~p2(Y!13)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!13, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_14(X)) & p2(tptp_fun_Y_14(X)) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X)))))))) & (p2(X!0) | (r1(X!0, Y!16) & p2(Y!16) & (~((~r1(Y!16, X!17)) | p2(X!17)))))) | (r1(X!0, Y!18) & ((r1(Y!18, X!19) & r1(X!19, Y!20) & (~p2(Y!20)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!20, X))) & ![X: $i] : (p2(X) | (~r1(Y!18, X)) | (r1(X, tptp_fun_Y_14(X)) & p2(tptp_fun_Y_14(X)) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X))))))) | ((~p2(Y!18)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!18, X))))) & ![X: $i] : ((~r1(Y!18, 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_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))) | (r1(Y, tptp_fun_X_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))) & r1(X, tptp_fun_Y_22(X)) & r1(tptp_fun_Y_22(X), tptp_fun_X_23(X)) & (~p2(tptp_fun_X_23(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_23(X), Y))))))) & (p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | p2(X!0) | p4(X!0) | (r1(X!0, Y!24) & (~p1(Y!24)) & (~p2(Y!24)) & (~p3(Y!24)) & (~p4(Y!24)) & r1(Y!24, X!25) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!24, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~p4(X)) & r1(X, tptp_fun_Y_26(X)))))) & (p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | p2(X!0) | (r1(X!0, Y!27) & (~p1(Y!27)) & (~p2(Y!27)) & (~p3(Y!27)) & r1(Y!27, X!28) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!27, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & r1(X, tptp_fun_Y_26(X)))))) & (![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | p2(X!0) | (r1(X!0, Y!29) & (~p1(Y!29)) & (~p2(Y!29)) & r1(Y!29, X!30) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!29, X)) | ((~p1(X)) & (~p2(X)) & r1(X, tptp_fun_Y_26(X)))))) & (![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | (r1(X!0, Y!31) & (~p1(Y!31)) & r1(Y!31, X!32) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!31, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_26(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))))),
% 0.69/0.69 inference(transitivity,[status(thm)],[30, 10])).
% 0.69/0.69 tff(32,plain,
% 0.69/0.69 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p5(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)) | (~p5(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)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(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)))))))))))) & (p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & ![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))))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p5(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)) | (~p5(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)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(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)))))))))))) & (p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & ![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)))))))))))),
% 0.69/0.69 inference(rewrite,[status(thm)],[])).
% 0.69/0.69 tff(33,plain,
% 0.69/0.69 ((~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p5(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)) | (~p5(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)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(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)))))))))))) & (p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & ![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))))))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p5(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)) | (~p5(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)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(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)))))))))))) & (p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & ![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)))))))))))),
% 0.69/0.70 inference(rewrite,[status(thm)],[])).
% 0.69/0.70 tff(34,plain,
% 0.69/0.70 ((~?[X: $i] : (~(((((((![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p5(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)) | p3(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p3(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p3(X))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p5(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)))))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ![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)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p5(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)) | (~p5(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)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(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)))))))))))) & (p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & ![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))))))))))))),
% 0.69/0.70 inference(rewrite,[status(thm)],[])).
% 0.69/0.70 tff(35,plain,
% 0.69/0.70 ((~(~?[X: $i] : (~(((((((![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p5(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)) | p3(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p3(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p3(X))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p5(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)))))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ![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)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p5(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)) | (~p5(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)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(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)))))))))))) & (p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & ![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)))))))))))))),
% 0.69/0.70 inference(monotonicity,[status(thm)],[34])).
% 0.69/0.70 tff(36,plain,
% 0.69/0.70 ((~(~?[X: $i] : (~(((((((![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p5(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)) | p3(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p3(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p3(X))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p5(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)))))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ![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)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p5(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)) | (~p5(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)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(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)))))))))))) & (p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & ![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)))))))))))),
% 0.69/0.71 inference(transitivity,[status(thm)],[35, 33])).
% 0.69/0.71 tff(37,axiom,(~(~?[X: $i] : (~(((((((![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p5(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)) | p3(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p3(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p3(X))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p5(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)))))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ![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/sandbox2/benchmark/theBenchmark.p','main')).
% 0.69/0.71 tff(38,plain,
% 0.69/0.71 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p5(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)) | (~p5(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)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(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)))))))))))) & (p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & ![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)))))))))))),
% 0.69/0.71 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.69/0.71 tff(39,plain,
% 0.69/0.71 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p5(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)) | (~p5(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)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(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)))))))))))) & (p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & ![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)))))))))))),
% 0.69/0.71 inference(modus_ponens,[status(thm)],[38, 32])).
% 0.69/0.71 tff(40,plain,
% 0.69/0.71 ((~((~r1(X!0, Y!1)) | p3(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_3(Y)) & p3(tptp_fun_X_3(Y)) & (~(p3(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) & ((r1(X!0, Y!5) & r1(Y!5, X!6) & ![Y: $i] : ((~p5(Y)) | (~r1(X!6, Y))) & (~p1(Y!5))) | ((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | ((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_11(Y)) & p1(tptp_fun_X_11(Y)) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y)))))) & ((((r1(X!0, Y!13) & (~p2(Y!13)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!13, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_14(X)) & p2(tptp_fun_Y_14(X)) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X)))))))) & (p2(X!0) | (r1(X!0, Y!16) & p2(Y!16) & (~((~r1(Y!16, X!17)) | p2(X!17)))))) | (r1(X!0, Y!18) & ((r1(Y!18, X!19) & r1(X!19, Y!20) & (~p2(Y!20)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!20, X))) & ![X: $i] : (p2(X) | (~r1(Y!18, X)) | (r1(X, tptp_fun_Y_14(X)) & p2(tptp_fun_Y_14(X)) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X))))))) | ((~p2(Y!18)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!18, X))))) & ![X: $i] : ((~r1(Y!18, 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_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))) | (r1(Y, tptp_fun_X_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))) & r1(X, tptp_fun_Y_22(X)) & r1(tptp_fun_Y_22(X), tptp_fun_X_23(X)) & (~p2(tptp_fun_X_23(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_23(X), Y))))))) & (p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | p2(X!0) | p4(X!0) | (r1(X!0, Y!24) & (~p1(Y!24)) & (~p2(Y!24)) & (~p3(Y!24)) & (~p4(Y!24)) & r1(Y!24, X!25) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!24, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~p4(X)) & r1(X, tptp_fun_Y_26(X)))))) & (p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | p2(X!0) | (r1(X!0, Y!27) & (~p1(Y!27)) & (~p2(Y!27)) & (~p3(Y!27)) & r1(Y!27, X!28) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!27, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & r1(X, tptp_fun_Y_26(X)))))) & (![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | p2(X!0) | (r1(X!0, Y!29) & (~p1(Y!29)) & (~p2(Y!29)) & r1(Y!29, X!30) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!29, X)) | ((~p1(X)) & (~p2(X)) & r1(X, tptp_fun_Y_26(X)))))) & (![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | (r1(X!0, Y!31) & (~p1(Y!31)) & r1(Y!31, X!32) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!31, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_26(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y)))))),
% 0.69/0.71 inference(modus_ponens,[status(thm)],[39, 31])).
% 0.69/0.71 tff(41,plain,
% 0.69/0.71 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y)))))),
% 0.69/0.71 inference(and_elim,[status(thm)],[40])).
% 0.69/0.71 tff(42,plain,
% 0.69/0.71 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p2(tptp_fun_X_21(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y)))))))),
% 0.69/0.71 inference(modus_ponens,[status(thm)],[41, 9])).
% 0.69/0.71 tff(43,plain,
% 0.69/0.71 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p2(tptp_fun_X_21(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y)))))))),
% 0.69/0.71 inference(modus_ponens,[status(thm)],[42, 7])).
% 0.69/0.71 tff(44,plain,
% 0.69/0.71 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p2(tptp_fun_X_21(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.69/0.71 inference(modus_ponens,[status(thm)],[43, 2])).
% 0.69/0.71 tff(45,assumption,((~r1(X!0, Y!7)) | p2(Y!7) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))), introduced(assumption)).
% 0.69/0.71 tff(46,plain,
% 0.69/0.71 (((~(p1(Y!5) | (~r1(X!0, Y!5)) | (~r1(Y!5, X!6)) | (~![Y: $i] : ((~p5(Y)) | (~r1(X!6, Y)))))) | (~((~r1(X!0, Y!7)) | p2(Y!7) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))))) <=> ((~(p1(Y!5) | (~r1(X!0, Y!5)) | (~r1(Y!5, X!6)) | (~![Y: $i] : ((~p5(Y)) | (~r1(X!6, Y)))))) | (~((~r1(X!0, Y!7)) | p2(Y!7) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))))),
% 0.69/0.71 inference(rewrite,[status(thm)],[])).
% 0.69/0.71 tff(47,plain,
% 0.69/0.71 (((r1(X!0, Y!5) & r1(Y!5, X!6) & ![Y: $i] : ((~p5(Y)) | (~r1(X!6, Y))) & (~p1(Y!5))) | ((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) <=> ((~(p1(Y!5) | (~r1(X!0, Y!5)) | (~r1(Y!5, X!6)) | (~![Y: $i] : ((~p5(Y)) | (~r1(X!6, Y)))))) | (~((~r1(X!0, Y!7)) | p2(Y!7) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))))),
% 0.69/0.71 inference(rewrite,[status(thm)],[])).
% 0.69/0.71 tff(48,plain,
% 0.69/0.71 ((r1(X!0, Y!5) & r1(Y!5, X!6) & ![Y: $i] : ((~p5(Y)) | (~r1(X!6, Y))) & (~p1(Y!5))) | ((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))),
% 0.69/0.71 inference(and_elim,[status(thm)],[40])).
% 0.69/0.71 tff(49,plain,
% 0.69/0.71 ((~(p1(Y!5) | (~r1(X!0, Y!5)) | (~r1(Y!5, X!6)) | (~![Y: $i] : ((~p5(Y)) | (~r1(X!6, Y)))))) | (~((~r1(X!0, Y!7)) | p2(Y!7) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))))),
% 0.69/0.71 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.69/0.71 tff(50,plain,
% 0.69/0.71 ((~(p1(Y!5) | (~r1(X!0, Y!5)) | (~r1(Y!5, X!6)) | (~![Y: $i] : ((~p5(Y)) | (~r1(X!6, Y)))))) | (~((~r1(X!0, Y!7)) | p2(Y!7) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))))),
% 0.69/0.71 inference(modus_ponens,[status(thm)],[49, 46])).
% 0.69/0.71 tff(51,plain,
% 0.69/0.71 (~(p1(Y!5) | (~r1(X!0, Y!5)) | (~r1(Y!5, X!6)) | (~![Y: $i] : ((~p5(Y)) | (~r1(X!6, Y)))))),
% 0.69/0.71 inference(unit_resolution,[status(thm)],[50, 45])).
% 0.69/0.71 tff(52,plain,
% 0.69/0.71 ((p1(Y!5) | (~r1(X!0, Y!5)) | (~r1(Y!5, X!6)) | (~![Y: $i] : ((~p5(Y)) | (~r1(X!6, Y))))) | r1(Y!5, X!6)),
% 0.69/0.71 inference(tautology,[status(thm)],[])).
% 0.69/0.71 tff(53,plain,
% 0.69/0.71 (r1(Y!5, X!6)),
% 0.69/0.71 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.69/0.71 tff(54,plain,
% 0.69/0.71 ((p1(Y!5) | (~r1(X!0, Y!5)) | (~r1(Y!5, X!6)) | (~![Y: $i] : ((~p5(Y)) | (~r1(X!6, Y))))) | r1(X!0, Y!5)),
% 0.69/0.71 inference(tautology,[status(thm)],[])).
% 0.69/0.71 tff(55,plain,
% 0.69/0.71 (r1(X!0, Y!5)),
% 0.69/0.71 inference(unit_resolution,[status(thm)],[54, 51])).
% 0.69/0.71 tff(56,plain,
% 0.69/0.71 (![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)))),
% 0.69/0.71 inference(rewrite,[status(thm)],[])).
% 0.69/0.71 tff(57,plain,
% 0.69/0.71 (^[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)))))),
% 0.69/0.72 inference(bind,[status(th)],[])).
% 0.69/0.72 tff(58,plain,
% 0.69/0.72 (![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)))),
% 0.69/0.72 inference(quant_intro,[status(thm)],[57])).
% 0.69/0.72 tff(59,plain,
% 0.69/0.72 (![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))),
% 0.69/0.72 inference(rewrite,[status(thm)],[])).
% 0.69/0.72 tff(60,plain,
% 0.69/0.72 (^[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)))),
% 0.69/0.72 inference(bind,[status(th)],[])).
% 0.69/0.72 tff(61,plain,
% 0.69/0.72 (![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))),
% 0.69/0.72 inference(quant_intro,[status(thm)],[60])).
% 0.69/0.72 tff(62,axiom,(![X: $i, Y: $i, Z: $i] : ((r1(X, Y) & r1(Y, Z)) => r1(X, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','transitivity')).
% 0.69/0.72 tff(63,plain,
% 0.69/0.72 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 0.69/0.72 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.69/0.72 tff(64,plain,
% 0.69/0.72 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 0.69/0.72 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.69/0.72 tff(65,plain,(
% 0.69/0.72 ![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 0.69/0.72 inference(skolemize,[status(sab)],[64])).
% 0.69/0.72 tff(66,plain,
% 0.69/0.72 (![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 0.69/0.72 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.69/0.72 tff(67,plain,
% 0.69/0.72 (![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 0.69/0.72 inference(modus_ponens,[status(thm)],[66, 56])).
% 0.69/0.72 tff(68,plain,
% 0.69/0.72 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, Y!5)) | (~r1(Y!5, X!6)) | r1(X!0, X!6))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!5)) | (~r1(Y!5, X!6)) | r1(X!0, X!6))),
% 0.69/0.72 inference(rewrite,[status(thm)],[])).
% 0.69/0.72 tff(69,plain,
% 0.69/0.72 ((r1(X!0, X!6) | (~r1(Y!5, X!6)) | (~r1(X!0, Y!5))) <=> ((~r1(X!0, Y!5)) | (~r1(Y!5, X!6)) | r1(X!0, X!6))),
% 0.69/0.72 inference(rewrite,[status(thm)],[])).
% 0.69/0.72 tff(70,plain,
% 0.69/0.72 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!6) | (~r1(Y!5, X!6)) | (~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, X!6)) | r1(X!0, X!6)))),
% 0.69/0.72 inference(monotonicity,[status(thm)],[69])).
% 0.69/0.72 tff(71,plain,
% 0.69/0.72 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!6) | (~r1(Y!5, X!6)) | (~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, X!6)) | r1(X!0, X!6))),
% 0.69/0.72 inference(transitivity,[status(thm)],[70, 68])).
% 0.69/0.72 tff(72,plain,
% 0.69/0.72 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!6) | (~r1(Y!5, X!6)) | (~r1(X!0, Y!5)))),
% 0.69/0.72 inference(quant_inst,[status(thm)],[])).
% 0.69/0.72 tff(73,plain,
% 0.69/0.72 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!5)) | (~r1(Y!5, X!6)) | r1(X!0, X!6)),
% 0.69/0.72 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.69/0.72 tff(74,plain,
% 0.69/0.72 (r1(X!0, X!6)),
% 0.69/0.72 inference(unit_resolution,[status(thm)],[73, 67, 55, 53])).
% 0.69/0.72 tff(75,plain,
% 0.69/0.72 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | (~((~r1(X!0, Y!7)) | p2(Y!7) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))))) <=> ((~((~r1(X!0, Y!7)) | p2(Y!7) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))))),
% 0.69/0.72 inference(rewrite,[status(thm)],[])).
% 0.69/0.72 tff(76,plain,
% 0.69/0.72 ((~((~r1(X!0, Y!7)) | p2(Y!7) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) <=> (~((~r1(X!0, Y!7)) | p2(Y!7) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))))),
% 0.69/0.72 inference(rewrite,[status(thm)],[])).
% 0.69/0.72 tff(77,plain,
% 0.69/0.72 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | (~((~r1(X!0, Y!7)) | p2(Y!7) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | (~((~r1(X!0, Y!7)) | p2(Y!7) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))))),
% 0.69/0.72 inference(monotonicity,[status(thm)],[76])).
% 0.69/0.72 tff(78,plain,
% 0.69/0.72 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | (~((~r1(X!0, Y!7)) | p2(Y!7) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))))) <=> ((~((~r1(X!0, Y!7)) | p2(Y!7) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))))),
% 0.69/0.72 inference(transitivity,[status(thm)],[77, 75])).
% 0.69/0.72 tff(79,plain,
% 0.69/0.72 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | (~((~r1(X!0, Y!7)) | p2(Y!7) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | (~((~r1(X!0, Y!7)) | p2(Y!7) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))))),
% 0.69/0.72 inference(rewrite,[status(thm)],[])).
% 0.69/0.72 tff(80,plain,
% 0.69/0.72 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | (~((~r1(X!0, Y!7)) | p2(Y!7) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | (~((~r1(X!0, Y!7)) | p2(Y!7) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))))),
% 0.69/0.72 inference(rewrite,[status(thm)],[])).
% 0.69/0.72 tff(81,plain,
% 0.69/0.72 (((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))) <=> (~((~r1(X!0, Y!7)) | p2(Y!7) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))))),
% 0.69/0.72 inference(rewrite,[status(thm)],[])).
% 0.69/0.72 tff(82,plain,
% 0.69/0.72 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))),
% 0.69/0.72 inference(bind,[status(th)],[])).
% 0.69/0.72 tff(83,plain,
% 0.69/0.72 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))),
% 0.69/0.72 inference(quant_intro,[status(thm)],[82])).
% 0.69/0.72 tff(84,plain,
% 0.69/0.72 ((~((~r1(X!0, Y!7)) | p2(Y!7))) <=> (~((~r1(X!0, Y!7)) | p2(Y!7)))),
% 0.69/0.72 inference(rewrite,[status(thm)],[])).
% 0.69/0.72 tff(85,plain,
% 0.69/0.72 (((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))) <=> ((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))),
% 0.69/0.72 inference(monotonicity,[status(thm)],[84, 83])).
% 0.69/0.72 tff(86,plain,
% 0.69/0.72 (((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))) <=> (~((~r1(X!0, Y!7)) | p2(Y!7) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))))),
% 0.69/0.72 inference(transitivity,[status(thm)],[85, 81])).
% 0.69/0.72 tff(87,plain,
% 0.69/0.72 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | ((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | (~((~r1(X!0, Y!7)) | p2(Y!7) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))))),
% 0.69/0.72 inference(monotonicity,[status(thm)],[86])).
% 0.69/0.72 tff(88,plain,
% 0.69/0.72 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | ((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | (~((~r1(X!0, Y!7)) | p2(Y!7) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))))),
% 0.69/0.72 inference(transitivity,[status(thm)],[87, 80])).
% 0.69/0.72 tff(89,plain,
% 0.69/0.72 (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | ((~((~r1(X!0, Y!7)) | p2(Y!7))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p2(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))),
% 0.69/0.72 inference(and_elim,[status(thm)],[40])).
% 0.69/0.72 tff(90,plain,
% 0.69/0.72 (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | (~((~r1(X!0, Y!7)) | p2(Y!7) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))))),
% 0.69/0.72 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.69/0.72 tff(91,plain,
% 0.69/0.72 (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | (~((~r1(X!0, Y!7)) | p2(Y!7) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))))),
% 0.69/0.72 inference(modus_ponens,[status(thm)],[90, 79])).
% 0.69/0.72 tff(92,plain,
% 0.69/0.72 ((~((~r1(X!0, Y!7)) | p2(Y!7) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y))))))),
% 0.69/0.72 inference(modus_ponens,[status(thm)],[91, 78])).
% 0.69/0.72 tff(93,plain,
% 0.69/0.72 (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y))))))),
% 0.69/0.72 inference(unit_resolution,[status(thm)],[92, 45])).
% 0.69/0.72 tff(94,plain,
% 0.69/0.72 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y))))))) | ((~r1(X!0, X!6)) | (~((~r1(X!6, tptp_fun_X_10(X!6))) | (~p5(tptp_fun_X_10(X!6))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y))))))) | (~r1(X!0, X!6)) | (~((~r1(X!6, tptp_fun_X_10(X!6))) | (~p5(tptp_fun_X_10(X!6))))))),
% 0.69/0.72 inference(rewrite,[status(thm)],[])).
% 0.69/0.72 tff(95,plain,
% 0.69/0.72 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y))))))) | ((~r1(X!0, X!6)) | (~((~r1(X!6, tptp_fun_X_10(X!6))) | (~p5(tptp_fun_X_10(X!6))))))),
% 0.69/0.72 inference(quant_inst,[status(thm)],[])).
% 0.69/0.72 tff(96,plain,
% 0.69/0.72 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y))))))) | (~r1(X!0, X!6)) | (~((~r1(X!6, tptp_fun_X_10(X!6))) | (~p5(tptp_fun_X_10(X!6)))))),
% 0.69/0.72 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.69/0.72 tff(97,plain,
% 0.69/0.72 (~((~r1(X!6, tptp_fun_X_10(X!6))) | (~p5(tptp_fun_X_10(X!6))))),
% 0.69/0.72 inference(unit_resolution,[status(thm)],[96, 93, 74])).
% 0.69/0.72 tff(98,plain,
% 0.69/0.72 (((~r1(X!6, tptp_fun_X_10(X!6))) | (~p5(tptp_fun_X_10(X!6)))) | p5(tptp_fun_X_10(X!6))),
% 0.69/0.72 inference(tautology,[status(thm)],[])).
% 0.69/0.72 tff(99,plain,
% 0.69/0.72 (p5(tptp_fun_X_10(X!6))),
% 0.69/0.72 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.69/0.72 tff(100,plain,
% 0.69/0.72 (((~r1(X!6, tptp_fun_X_10(X!6))) | (~p5(tptp_fun_X_10(X!6)))) | r1(X!6, tptp_fun_X_10(X!6))),
% 0.69/0.72 inference(tautology,[status(thm)],[])).
% 0.69/0.72 tff(101,plain,
% 0.69/0.72 (r1(X!6, tptp_fun_X_10(X!6))),
% 0.69/0.72 inference(unit_resolution,[status(thm)],[100, 97])).
% 0.69/0.72 tff(102,plain,
% 0.69/0.72 ((p1(Y!5) | (~r1(X!0, Y!5)) | (~r1(Y!5, X!6)) | (~![Y: $i] : ((~p5(Y)) | (~r1(X!6, Y))))) | ![Y: $i] : ((~p5(Y)) | (~r1(X!6, Y)))),
% 0.69/0.72 inference(tautology,[status(thm)],[])).
% 0.69/0.72 tff(103,plain,
% 0.69/0.72 (![Y: $i] : ((~p5(Y)) | (~r1(X!6, Y)))),
% 0.69/0.72 inference(unit_resolution,[status(thm)],[102, 51])).
% 0.69/0.72 tff(104,plain,
% 0.69/0.72 (((~![Y: $i] : ((~p5(Y)) | (~r1(X!6, Y)))) | ((~p5(tptp_fun_X_10(X!6))) | (~r1(X!6, tptp_fun_X_10(X!6))))) <=> ((~![Y: $i] : ((~p5(Y)) | (~r1(X!6, Y)))) | (~p5(tptp_fun_X_10(X!6))) | (~r1(X!6, tptp_fun_X_10(X!6))))),
% 0.69/0.72 inference(rewrite,[status(thm)],[])).
% 0.69/0.72 tff(105,plain,
% 0.69/0.72 ((~![Y: $i] : ((~p5(Y)) | (~r1(X!6, Y)))) | ((~p5(tptp_fun_X_10(X!6))) | (~r1(X!6, tptp_fun_X_10(X!6))))),
% 0.69/0.72 inference(quant_inst,[status(thm)],[])).
% 0.69/0.72 tff(106,plain,
% 0.69/0.72 ((~![Y: $i] : ((~p5(Y)) | (~r1(X!6, Y)))) | (~p5(tptp_fun_X_10(X!6))) | (~r1(X!6, tptp_fun_X_10(X!6)))),
% 0.69/0.72 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.69/0.72 tff(107,plain,
% 0.69/0.72 ($false),
% 0.69/0.72 inference(unit_resolution,[status(thm)],[106, 103, 101, 99])).
% 0.69/0.72 tff(108,plain,(~((~r1(X!0, Y!7)) | p2(Y!7) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))))), inference(lemma,lemma(discharge,[]))).
% 0.69/0.72 tff(109,plain,
% 0.69/0.72 (((~r1(X!0, Y!7)) | p2(Y!7) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))) | (~p2(Y!7))),
% 0.69/0.72 inference(tautology,[status(thm)],[])).
% 0.69/0.72 tff(110,plain,
% 0.69/0.72 (~p2(Y!7)),
% 0.69/0.72 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.69/0.72 tff(111,plain,
% 0.69/0.72 (((~r1(X!0, Y!7)) | p2(Y!7) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))) | r1(X!0, Y!7)),
% 0.69/0.72 inference(tautology,[status(thm)],[])).
% 0.69/0.72 tff(112,plain,
% 0.69/0.72 (r1(X!0, Y!7)),
% 0.69/0.72 inference(unit_resolution,[status(thm)],[111, 108])).
% 0.69/0.72 tff(113,plain,
% 0.69/0.72 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p2(tptp_fun_X_21(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | (p2(Y!7) | (~r1(X!0, Y!7)) | (~(p2(tptp_fun_X_21(Y!7)) | (~r1(Y!7, tptp_fun_X_21(Y!7))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!7), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p2(tptp_fun_X_21(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | p2(Y!7) | (~r1(X!0, Y!7)) | (~(p2(tptp_fun_X_21(Y!7)) | (~r1(Y!7, tptp_fun_X_21(Y!7))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!7), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.69/0.72 inference(rewrite,[status(thm)],[])).
% 0.69/0.72 tff(114,plain,
% 0.69/0.72 ((p2(Y!7) | (~r1(X!0, Y!7)) | (~((~r1(Y!7, tptp_fun_X_21(Y!7))) | p2(tptp_fun_X_21(Y!7)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!7), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) <=> (p2(Y!7) | (~r1(X!0, Y!7)) | (~(p2(tptp_fun_X_21(Y!7)) | (~r1(Y!7, tptp_fun_X_21(Y!7))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!7), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.69/0.72 inference(rewrite,[status(thm)],[])).
% 0.69/0.72 tff(115,plain,
% 0.69/0.72 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p2(tptp_fun_X_21(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | (p2(Y!7) | (~r1(X!0, Y!7)) | (~((~r1(Y!7, tptp_fun_X_21(Y!7))) | p2(tptp_fun_X_21(Y!7)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!7), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p2(tptp_fun_X_21(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | (p2(Y!7) | (~r1(X!0, Y!7)) | (~(p2(tptp_fun_X_21(Y!7)) | (~r1(Y!7, tptp_fun_X_21(Y!7))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!7), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))),
% 0.69/0.72 inference(monotonicity,[status(thm)],[114])).
% 0.69/0.72 tff(116,plain,
% 0.69/0.72 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p2(tptp_fun_X_21(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | (p2(Y!7) | (~r1(X!0, Y!7)) | (~((~r1(Y!7, tptp_fun_X_21(Y!7))) | p2(tptp_fun_X_21(Y!7)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!7), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p2(tptp_fun_X_21(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | p2(Y!7) | (~r1(X!0, Y!7)) | (~(p2(tptp_fun_X_21(Y!7)) | (~r1(Y!7, tptp_fun_X_21(Y!7))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!7), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.69/0.72 inference(transitivity,[status(thm)],[115, 113])).
% 0.69/0.72 tff(117,plain,
% 0.69/0.72 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p2(tptp_fun_X_21(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | (p2(Y!7) | (~r1(X!0, Y!7)) | (~((~r1(Y!7, tptp_fun_X_21(Y!7))) | p2(tptp_fun_X_21(Y!7)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!7), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.69/0.72 inference(quant_inst,[status(thm)],[])).
% 0.69/0.72 tff(118,plain,
% 0.69/0.72 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p2(tptp_fun_X_21(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | p2(Y!7) | (~r1(X!0, Y!7)) | (~(p2(tptp_fun_X_21(Y!7)) | (~r1(Y!7, tptp_fun_X_21(Y!7))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!7), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))),
% 0.69/0.72 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.69/0.72 tff(119,plain,
% 0.69/0.72 (~(p2(tptp_fun_X_21(Y!7)) | (~r1(Y!7, tptp_fun_X_21(Y!7))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!7), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))),
% 0.69/0.72 inference(unit_resolution,[status(thm)],[118, 112, 110, 44])).
% 0.69/0.72 tff(120,plain,
% 0.69/0.72 ((p2(tptp_fun_X_21(Y!7)) | (~r1(Y!7, tptp_fun_X_21(Y!7))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!7), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | r1(Y!7, tptp_fun_X_21(Y!7))),
% 0.69/0.72 inference(tautology,[status(thm)],[])).
% 0.69/0.72 tff(121,plain,
% 0.69/0.72 (r1(Y!7, tptp_fun_X_21(Y!7))),
% 0.69/0.72 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.69/0.72 tff(122,plain,
% 0.69/0.72 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, Y!7)) | (~r1(Y!7, tptp_fun_X_21(Y!7))) | r1(X!0, tptp_fun_X_21(Y!7)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!7)) | (~r1(Y!7, tptp_fun_X_21(Y!7))) | r1(X!0, tptp_fun_X_21(Y!7)))),
% 0.69/0.72 inference(rewrite,[status(thm)],[])).
% 0.69/0.72 tff(123,plain,
% 0.69/0.72 ((r1(X!0, tptp_fun_X_21(Y!7)) | (~r1(Y!7, tptp_fun_X_21(Y!7))) | (~r1(X!0, Y!7))) <=> ((~r1(X!0, Y!7)) | (~r1(Y!7, tptp_fun_X_21(Y!7))) | r1(X!0, tptp_fun_X_21(Y!7)))),
% 0.69/0.72 inference(rewrite,[status(thm)],[])).
% 0.69/0.72 tff(124,plain,
% 0.69/0.72 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_21(Y!7)) | (~r1(Y!7, tptp_fun_X_21(Y!7))) | (~r1(X!0, Y!7)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, Y!7)) | (~r1(Y!7, tptp_fun_X_21(Y!7))) | r1(X!0, tptp_fun_X_21(Y!7))))),
% 0.69/0.72 inference(monotonicity,[status(thm)],[123])).
% 0.69/0.72 tff(125,plain,
% 0.69/0.72 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_21(Y!7)) | (~r1(Y!7, tptp_fun_X_21(Y!7))) | (~r1(X!0, Y!7)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!7)) | (~r1(Y!7, tptp_fun_X_21(Y!7))) | r1(X!0, tptp_fun_X_21(Y!7)))),
% 0.69/0.72 inference(transitivity,[status(thm)],[124, 122])).
% 0.69/0.72 tff(126,plain,
% 0.69/0.72 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_21(Y!7)) | (~r1(Y!7, tptp_fun_X_21(Y!7))) | (~r1(X!0, Y!7)))),
% 0.69/0.72 inference(quant_inst,[status(thm)],[])).
% 0.69/0.72 tff(127,plain,
% 0.69/0.72 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!7)) | (~r1(Y!7, tptp_fun_X_21(Y!7))) | r1(X!0, tptp_fun_X_21(Y!7))),
% 0.69/0.72 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.69/0.72 tff(128,plain,
% 0.69/0.72 (r1(X!0, tptp_fun_X_21(Y!7))),
% 0.69/0.72 inference(unit_resolution,[status(thm)],[127, 67, 112, 121])).
% 0.69/0.72 tff(129,plain,
% 0.69/0.72 ((p2(tptp_fun_X_21(Y!7)) | (~r1(Y!7, tptp_fun_X_21(Y!7))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!7), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | (~p2(tptp_fun_X_21(Y!7)))),
% 0.69/0.72 inference(tautology,[status(thm)],[])).
% 0.69/0.72 tff(130,plain,
% 0.69/0.72 (~p2(tptp_fun_X_21(Y!7))),
% 0.69/0.72 inference(unit_resolution,[status(thm)],[129, 119])).
% 0.69/0.72 tff(131,plain,
% 0.69/0.72 (((~r1(X!0, Y!7)) | p2(Y!7) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y))))))) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))),
% 0.69/0.72 inference(tautology,[status(thm)],[])).
% 0.69/0.72 tff(132,plain,
% 0.69/0.72 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))),
% 0.69/0.72 inference(unit_resolution,[status(thm)],[131, 108])).
% 0.69/0.72 tff(133,plain,
% 0.69/0.72 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))) | (p2(tptp_fun_X_21(Y!7)) | (~r1(X!0, tptp_fun_X_21(Y!7))) | (~((~p2(tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_21(Y!7), tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), tptp_fun_Y_9(tptp_fun_X_21(Y!7)))) | p2(tptp_fun_Y_9(tptp_fun_X_21(Y!7))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))) | p2(tptp_fun_X_21(Y!7)) | (~r1(X!0, tptp_fun_X_21(Y!7))) | (~((~p2(tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_21(Y!7), tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), tptp_fun_Y_9(tptp_fun_X_21(Y!7)))) | p2(tptp_fun_Y_9(tptp_fun_X_21(Y!7))))))),
% 0.69/0.72 inference(rewrite,[status(thm)],[])).
% 0.69/0.72 tff(134,plain,
% 0.69/0.72 ((p2(tptp_fun_X_21(Y!7)) | (~r1(X!0, tptp_fun_X_21(Y!7))) | (~((~r1(tptp_fun_X_21(Y!7), tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~p2(tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), tptp_fun_Y_9(tptp_fun_X_21(Y!7)))) | p2(tptp_fun_Y_9(tptp_fun_X_21(Y!7)))))) <=> (p2(tptp_fun_X_21(Y!7)) | (~r1(X!0, tptp_fun_X_21(Y!7))) | (~((~p2(tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_21(Y!7), tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), tptp_fun_Y_9(tptp_fun_X_21(Y!7)))) | p2(tptp_fun_Y_9(tptp_fun_X_21(Y!7))))))),
% 0.69/0.72 inference(rewrite,[status(thm)],[])).
% 0.69/0.72 tff(135,plain,
% 0.69/0.72 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))) | (p2(tptp_fun_X_21(Y!7)) | (~r1(X!0, tptp_fun_X_21(Y!7))) | (~((~r1(tptp_fun_X_21(Y!7), tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~p2(tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), tptp_fun_Y_9(tptp_fun_X_21(Y!7)))) | p2(tptp_fun_Y_9(tptp_fun_X_21(Y!7))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))) | (p2(tptp_fun_X_21(Y!7)) | (~r1(X!0, tptp_fun_X_21(Y!7))) | (~((~p2(tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_21(Y!7), tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), tptp_fun_Y_9(tptp_fun_X_21(Y!7)))) | p2(tptp_fun_Y_9(tptp_fun_X_21(Y!7)))))))),
% 0.77/0.73 inference(monotonicity,[status(thm)],[134])).
% 0.77/0.73 tff(136,plain,
% 0.77/0.73 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))) | (p2(tptp_fun_X_21(Y!7)) | (~r1(X!0, tptp_fun_X_21(Y!7))) | (~((~r1(tptp_fun_X_21(Y!7), tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~p2(tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), tptp_fun_Y_9(tptp_fun_X_21(Y!7)))) | p2(tptp_fun_Y_9(tptp_fun_X_21(Y!7))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))) | p2(tptp_fun_X_21(Y!7)) | (~r1(X!0, tptp_fun_X_21(Y!7))) | (~((~p2(tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_21(Y!7), tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), tptp_fun_Y_9(tptp_fun_X_21(Y!7)))) | p2(tptp_fun_Y_9(tptp_fun_X_21(Y!7))))))),
% 0.77/0.73 inference(transitivity,[status(thm)],[135, 133])).
% 0.77/0.73 tff(137,plain,
% 0.77/0.73 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))) | (p2(tptp_fun_X_21(Y!7)) | (~r1(X!0, tptp_fun_X_21(Y!7))) | (~((~r1(tptp_fun_X_21(Y!7), tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~p2(tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), tptp_fun_Y_9(tptp_fun_X_21(Y!7)))) | p2(tptp_fun_Y_9(tptp_fun_X_21(Y!7))))))),
% 0.77/0.73 inference(quant_inst,[status(thm)],[])).
% 0.77/0.73 tff(138,plain,
% 0.77/0.73 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p2(tptp_fun_X_8(Y))) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p2(tptp_fun_Y_9(Y)))))) | p2(tptp_fun_X_21(Y!7)) | (~r1(X!0, tptp_fun_X_21(Y!7))) | (~((~p2(tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_21(Y!7), tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), tptp_fun_Y_9(tptp_fun_X_21(Y!7)))) | p2(tptp_fun_Y_9(tptp_fun_X_21(Y!7)))))),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.77/0.73 tff(139,plain,
% 0.77/0.73 ((~r1(X!0, tptp_fun_X_21(Y!7))) | (~((~p2(tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_21(Y!7), tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), tptp_fun_Y_9(tptp_fun_X_21(Y!7)))) | p2(tptp_fun_Y_9(tptp_fun_X_21(Y!7)))))),
% 0.77/0.73 inference(unit_resolution,[status(thm)],[138, 132, 130])).
% 0.77/0.73 tff(140,plain,
% 0.77/0.73 (~((~p2(tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_21(Y!7), tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), tptp_fun_Y_9(tptp_fun_X_21(Y!7)))) | p2(tptp_fun_Y_9(tptp_fun_X_21(Y!7))))),
% 0.77/0.73 inference(unit_resolution,[status(thm)],[139, 128])).
% 0.77/0.73 tff(141,plain,
% 0.77/0.73 (((~p2(tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_21(Y!7), tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), tptp_fun_Y_9(tptp_fun_X_21(Y!7)))) | p2(tptp_fun_Y_9(tptp_fun_X_21(Y!7)))) | r1(tptp_fun_X_21(Y!7), tptp_fun_X_8(tptp_fun_X_21(Y!7)))),
% 0.77/0.73 inference(tautology,[status(thm)],[])).
% 0.77/0.73 tff(142,plain,
% 0.77/0.73 (r1(tptp_fun_X_21(Y!7), tptp_fun_X_8(tptp_fun_X_21(Y!7)))),
% 0.77/0.73 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.77/0.73 tff(143,plain,
% 0.77/0.73 (((~p2(tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_21(Y!7), tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), tptp_fun_Y_9(tptp_fun_X_21(Y!7)))) | p2(tptp_fun_Y_9(tptp_fun_X_21(Y!7)))) | p2(tptp_fun_X_8(tptp_fun_X_21(Y!7)))),
% 0.77/0.73 inference(tautology,[status(thm)],[])).
% 0.77/0.73 tff(144,plain,
% 0.77/0.73 (p2(tptp_fun_X_8(tptp_fun_X_21(Y!7)))),
% 0.77/0.73 inference(unit_resolution,[status(thm)],[143, 140])).
% 0.77/0.73 tff(145,plain,
% 0.77/0.73 ((p2(tptp_fun_X_21(Y!7)) | (~r1(Y!7, tptp_fun_X_21(Y!7))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!7), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!7), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))),
% 0.77/0.73 inference(tautology,[status(thm)],[])).
% 0.77/0.73 tff(146,plain,
% 0.77/0.73 (![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!7), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))),
% 0.77/0.73 inference(unit_resolution,[status(thm)],[145, 119])).
% 0.77/0.73 tff(147,plain,
% 0.77/0.73 (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!7), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_21(Y!7), tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), X))))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!7), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_21(Y!7), tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), X))))),
% 0.77/0.73 inference(rewrite,[status(thm)],[])).
% 0.77/0.73 tff(148,plain,
% 0.77/0.73 (((~p2(tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_21(Y!7), tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | ![X: $i] : ((~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), X)) | p2(X))) <=> ((~p2(tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_21(Y!7), tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), X))))),
% 0.77/0.73 inference(rewrite,[status(thm)],[])).
% 0.77/0.73 tff(149,plain,
% 0.77/0.73 (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!7), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_21(Y!7), tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | ![X: $i] : ((~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), X)) | p2(X)))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!7), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_21(Y!7), tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), X)))))),
% 0.77/0.73 inference(monotonicity,[status(thm)],[148])).
% 0.77/0.73 tff(150,plain,
% 0.77/0.73 (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!7), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_21(Y!7), tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | ![X: $i] : ((~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), X)) | p2(X)))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!7), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_21(Y!7), tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), X))))),
% 0.77/0.73 inference(transitivity,[status(thm)],[149, 147])).
% 0.77/0.73 tff(151,plain,
% 0.77/0.73 ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!7), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_21(Y!7), tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | ![X: $i] : ((~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), X)) | p2(X)))),
% 0.77/0.73 inference(quant_inst,[status(thm)],[])).
% 0.77/0.73 tff(152,plain,
% 0.77/0.73 ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!7), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_21(Y!7), tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), X)))),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.77/0.73 tff(153,plain,
% 0.77/0.73 (![X: $i] : (p2(X) | (~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), X)))),
% 0.77/0.73 inference(unit_resolution,[status(thm)],[152, 146, 144, 142])).
% 0.77/0.73 tff(154,plain,
% 0.77/0.73 (((~p2(tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_21(Y!7), tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), tptp_fun_Y_9(tptp_fun_X_21(Y!7)))) | p2(tptp_fun_Y_9(tptp_fun_X_21(Y!7)))) | (~p2(tptp_fun_Y_9(tptp_fun_X_21(Y!7))))),
% 0.77/0.73 inference(tautology,[status(thm)],[])).
% 0.77/0.73 tff(155,plain,
% 0.77/0.73 (~p2(tptp_fun_Y_9(tptp_fun_X_21(Y!7)))),
% 0.77/0.73 inference(unit_resolution,[status(thm)],[154, 140])).
% 0.77/0.73 tff(156,plain,
% 0.77/0.73 (((~p2(tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_21(Y!7), tptp_fun_X_8(tptp_fun_X_21(Y!7)))) | (~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), tptp_fun_Y_9(tptp_fun_X_21(Y!7)))) | p2(tptp_fun_Y_9(tptp_fun_X_21(Y!7)))) | r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), tptp_fun_Y_9(tptp_fun_X_21(Y!7)))),
% 0.77/0.73 inference(tautology,[status(thm)],[])).
% 0.77/0.73 tff(157,plain,
% 0.77/0.73 (r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), tptp_fun_Y_9(tptp_fun_X_21(Y!7)))),
% 0.77/0.73 inference(unit_resolution,[status(thm)],[156, 140])).
% 0.77/0.73 tff(158,plain,
% 0.77/0.73 (((~![X: $i] : (p2(X) | (~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), X)))) | (p2(tptp_fun_Y_9(tptp_fun_X_21(Y!7))) | (~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), tptp_fun_Y_9(tptp_fun_X_21(Y!7)))))) <=> ((~![X: $i] : (p2(X) | (~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), X)))) | p2(tptp_fun_Y_9(tptp_fun_X_21(Y!7))) | (~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), tptp_fun_Y_9(tptp_fun_X_21(Y!7)))))),
% 0.77/0.73 inference(rewrite,[status(thm)],[])).
% 0.77/0.73 tff(159,plain,
% 0.77/0.73 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), X)))) | (p2(tptp_fun_Y_9(tptp_fun_X_21(Y!7))) | (~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), tptp_fun_Y_9(tptp_fun_X_21(Y!7)))))),
% 0.77/0.73 inference(quant_inst,[status(thm)],[])).
% 0.77/0.73 tff(160,plain,
% 0.77/0.73 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), X)))) | p2(tptp_fun_Y_9(tptp_fun_X_21(Y!7))) | (~r1(tptp_fun_X_8(tptp_fun_X_21(Y!7)), tptp_fun_Y_9(tptp_fun_X_21(Y!7))))),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.77/0.73 tff(161,plain,
% 0.77/0.73 ($false),
% 0.77/0.73 inference(unit_resolution,[status(thm)],[160, 157, 155, 153])).
% 0.77/0.73 % SZS output end Proof
%------------------------------------------------------------------------------