TSTP Solution File: SET745+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET745+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 : Tue Sep 20 05:07:50 EDT 2022
% Result : Theorem 0.19s 0.42s
% Output : Proof 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET745+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n011.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 : Sat Sep 3 07:38:43 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 tff(apply_type, type, (
% 0.19/0.42 apply: ( $i * $i * $i ) > $o)).
% 0.19/0.42 tff(tptp_fun_Y1_46_type, type, (
% 0.19/0.42 tptp_fun_Y1_46: $i)).
% 0.19/0.42 tff(tptp_fun_X_47_type, type, (
% 0.19/0.42 tptp_fun_X_47: $i)).
% 0.19/0.42 tff(tptp_fun_F_42_type, type, (
% 0.19/0.42 tptp_fun_F_42: $i)).
% 0.19/0.42 tff(tptp_fun_F1_44_type, type, (
% 0.19/0.42 tptp_fun_F1_44: $i)).
% 0.19/0.42 tff(member_type, type, (
% 0.19/0.42 member: ( $i * $i ) > $o)).
% 0.19/0.42 tff(tptp_fun_A1_41_type, type, (
% 0.19/0.42 tptp_fun_A1_41: $i)).
% 0.19/0.42 tff(tptp_fun_F2_43_type, type, (
% 0.19/0.42 tptp_fun_F2_43: $i)).
% 0.19/0.42 tff(tptp_fun_A2_40_type, type, (
% 0.19/0.42 tptp_fun_A2_40: $i)).
% 0.19/0.42 tff(union_type, type, (
% 0.19/0.42 union: ( $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_Y2_45_type, type, (
% 0.19/0.42 tptp_fun_Y2_45: $i)).
% 0.19/0.42 tff(tptp_fun_B_39_type, type, (
% 0.19/0.42 tptp_fun_B_39: $i)).
% 0.19/0.42 tff(maps_type, type, (
% 0.19/0.42 maps: ( $i * $i * $i ) > $o)).
% 0.19/0.42 tff(tptp_fun_Y2_5_type, type, (
% 0.19/0.42 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_Y1_6_type, type, (
% 0.19/0.42 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_Y_3_type, type, (
% 0.19/0.42 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_X_7_type, type, (
% 0.19/0.42 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_X_4_type, type, (
% 0.19/0.42 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(1,assumption,((~(maps(F!42, union(A1!41, A2!40), B!39) | (~((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y)))))))) | (~((~maps(F!42, union(A1!41, A2!40), B!39)) | (~((~![X: $i] : ((~member(X, union(A1!41, A2!40))) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(Y1, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, union(A1!41, A2!40)))))))))), introduced(assumption)).
% 0.19/0.42 tff(2,plain,
% 0.19/0.42 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(3,plain,
% 0.19/0.42 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.42 tff(4,plain,
% 0.19/0.42 (^[F: $i, A: $i, B: $i] : refl((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(5,plain,
% 0.19/0.42 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.42 tff(6,plain,
% 0.19/0.42 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(7,plain,
% 0.19/0.42 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.42 tff(8,plain,
% 0.19/0.42 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[7, 5])).
% 0.19/0.42 tff(9,plain,
% 0.19/0.42 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) <=> ((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))), trans(monotonicity(rewrite((~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) <=> (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))), trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite((member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)) <=> (~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))), ((~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> (~(~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))), rewrite((~(~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))) <=> ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))), ((~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))), (![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))), ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))), rewrite((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))), ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))))), ((maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))))) <=> (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))), rewrite((maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))), ((maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))), ((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))))) <=> (((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B))))))) & (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))), rewrite((((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B))))))) & (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))), ((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(10,plain,
% 0.19/0.42 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[9])).
% 0.19/0.42 tff(11,plain,
% 0.19/0.42 (^[F: $i, A: $i, B: $i] : rewrite((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (((~(~member(tptp_fun_X_4(B, A, F), A))) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(12,plain,
% 0.19/0.42 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (((~(~member(tptp_fun_X_4(B, A, F), A))) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.42 tff(13,plain,
% 0.19/0.42 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) <=> ![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(14,plain,
% 0.19/0.42 (^[F: $i, A: $i, B: $i] : rewrite((maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2))))) <=> (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(15,plain,
% 0.19/0.42 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2))))) <=> ![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.43 tff(16,axiom,(![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2)))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','maps')).
% 0.19/0.43 tff(17,plain,
% 0.19/0.43 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.43 tff(18,plain,
% 0.19/0.43 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.19/0.43 tff(19,plain,(
% 0.19/0.43 ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (((~(~member(tptp_fun_X_4(B, A, F), A))) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[18])).
% 0.19/0.43 tff(20,plain,
% 0.19/0.43 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.19/0.43 tff(21,plain,
% 0.19/0.43 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[20, 10])).
% 0.19/0.43 tff(22,plain,
% 0.19/0.43 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[21, 8])).
% 0.19/0.43 tff(23,plain,
% 0.19/0.43 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[22, 3])).
% 0.19/0.43 tff(24,plain,
% 0.19/0.43 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~(maps(F!42, union(A1!41, A2!40), B!39) | (~((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y)))))))) | (~((~maps(F!42, union(A1!41, A2!40), B!39)) | (~((~![X: $i] : ((~member(X, union(A1!41, A2!40))) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(Y1, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, union(A1!41, A2!40)))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~(maps(F!42, union(A1!41, A2!40), B!39) | (~((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y)))))))) | (~((~maps(F!42, union(A1!41, A2!40), B!39)) | (~((~![X: $i] : ((~member(X, union(A1!41, A2!40))) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(Y1, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, union(A1!41, A2!40))))))))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(25,plain,
% 0.19/0.43 ((~((~((~maps(F!42, union(A1!41, A2!40), B!39)) | (~((~![X: $i] : ((~member(X, union(A1!41, A2!40))) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, union(A1!41, A2!40))) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!42, union(A1!41, A2!40), B!39) | (~((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y)))))))))) <=> (~((~(maps(F!42, union(A1!41, A2!40), B!39) | (~((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y)))))))) | (~((~maps(F!42, union(A1!41, A2!40), B!39)) | (~((~![X: $i] : ((~member(X, union(A1!41, A2!40))) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(Y1, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, union(A1!41, A2!40)))))))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(26,plain,
% 0.19/0.43 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, union(A1!41, A2!40), B!39)) | (~((~![X: $i] : ((~member(X, union(A1!41, A2!40))) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, union(A1!41, A2!40))) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!42, union(A1!41, A2!40), B!39) | (~((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~(maps(F!42, union(A1!41, A2!40), B!39) | (~((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y)))))))) | (~((~maps(F!42, union(A1!41, A2!40), B!39)) | (~((~![X: $i] : ((~member(X, union(A1!41, A2!40))) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(Y1, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, union(A1!41, A2!40))))))))))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[25])).
% 0.19/0.44 tff(27,plain,
% 0.19/0.44 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, union(A1!41, A2!40), B!39)) | (~((~![X: $i] : ((~member(X, union(A1!41, A2!40))) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, union(A1!41, A2!40))) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!42, union(A1!41, A2!40), B!39) | (~((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~(maps(F!42, union(A1!41, A2!40), B!39) | (~((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y)))))))) | (~((~maps(F!42, union(A1!41, A2!40), B!39)) | (~((~![X: $i] : ((~member(X, union(A1!41, A2!40))) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(Y1, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, union(A1!41, A2!40))))))))))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[26, 24])).
% 0.19/0.44 tff(28,plain,
% 0.19/0.44 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, union(A1!41, A2!40), B!39)) | (~((~![X: $i] : ((~member(X, union(A1!41, A2!40))) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, union(A1!41, A2!40))) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!42, union(A1!41, A2!40), B!39) | (~((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y))))))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(29,plain,
% 0.19/0.45 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~(maps(F!42, union(A1!41, A2!40), B!39) | (~((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y)))))))) | (~((~maps(F!42, union(A1!41, A2!40), B!39)) | (~((~![X: $i] : ((~member(X, union(A1!41, A2!40))) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(Y1, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, union(A1!41, A2!40)))))))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.45 tff(30,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[29, 23, 1])).
% 0.19/0.45 tff(31,plain,(~((~(maps(F!42, union(A1!41, A2!40), B!39) | (~((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y)))))))) | (~((~maps(F!42, union(A1!41, A2!40), B!39)) | (~((~![X: $i] : ((~member(X, union(A1!41, A2!40))) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(Y1, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, union(A1!41, A2!40))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(32,plain,
% 0.19/0.45 (((~(maps(F!42, union(A1!41, A2!40), B!39) | (~((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y)))))))) | (~((~maps(F!42, union(A1!41, A2!40), B!39)) | (~((~![X: $i] : ((~member(X, union(A1!41, A2!40))) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(Y1, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, union(A1!41, A2!40)))))))))) | (maps(F!42, union(A1!41, A2!40), B!39) | (~((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y)))))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(33,plain,
% 0.19/0.45 (maps(F!42, union(A1!41, A2!40), B!39) | (~((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.19/0.45 tff(34,assumption,(~maps(F!42, union(A1!41, A2!40), B!39)), introduced(assumption)).
% 0.19/0.45 tff(35,plain,
% 0.19/0.45 (^[X: $i, A: $i, B: $i] : refl((member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> (member(X, union(A, B)) <=> (member(X, B) | member(X, A))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(36,plain,
% 0.19/0.45 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[35])).
% 0.19/0.45 tff(37,plain,
% 0.19/0.45 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(38,plain,
% 0.19/0.45 (^[X: $i, A: $i, B: $i] : rewrite((member(X, union(A, B)) <=> (member(X, A) | member(X, B))) <=> (member(X, union(A, B)) <=> (member(X, B) | member(X, A))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(39,plain,
% 0.19/0.45 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[38])).
% 0.19/0.45 tff(40,axiom,(![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','union')).
% 0.19/0.45 tff(41,plain,
% 0.19/0.45 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.45 tff(42,plain,
% 0.19/0.45 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.19/0.45 tff(43,plain,(
% 0.19/0.45 ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[42])).
% 0.19/0.45 tff(44,plain,
% 0.19/0.45 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.19/0.45 tff(45,plain,
% 0.19/0.45 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40)) <=> (member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41) | member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40)) <=> (member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41) | member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(46,plain,
% 0.19/0.45 ((member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40)) <=> (member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40) | member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41))) <=> (member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40)) <=> (member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41) | member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(47,plain,
% 0.19/0.45 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40)) <=> (member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40) | member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40)) <=> (member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41) | member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[46])).
% 0.19/0.45 tff(48,plain,
% 0.19/0.45 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40)) <=> (member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40) | member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40)) <=> (member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41) | member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[47, 45])).
% 0.19/0.45 tff(49,plain,
% 0.19/0.45 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40)) <=> (member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40) | member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(50,plain,
% 0.19/0.45 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40)) <=> (member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41) | member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.45 tff(51,plain,
% 0.19/0.45 (member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40)) <=> (member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41) | member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[50, 44])).
% 0.19/0.46 tff(52,assumption,(~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y)))))), introduced(assumption)).
% 0.19/0.46 tff(53,plain,
% 0.19/0.46 (((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y))))) | member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(54,plain,
% 0.19/0.46 (member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.19/0.46 tff(55,plain,
% 0.19/0.46 ((~(member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40)) <=> (member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41) | member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)))) | (~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41) | member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(56,plain,
% 0.19/0.46 ((~(member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40)) <=> (member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41) | member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)))) | (member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41) | member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.19/0.46 tff(57,plain,
% 0.19/0.46 (member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41) | member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[56, 51])).
% 0.19/0.46 tff(58,plain,
% 0.19/0.46 (((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y))))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(59,plain,
% 0.19/0.46 (![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[58, 52])).
% 0.19/0.46 tff(60,assumption,(member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)), introduced(assumption)).
% 0.19/0.46 tff(61,plain,
% 0.19/0.46 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~(maps(F2!43, A2!40, B!39) | (~((tptp_fun_Y1_6(B!39, A2!40, F2!43) = tptp_fun_Y2_5(B!39, A2!40, F2!43)) | (~apply(F2!43, tptp_fun_X_7(B!39, A2!40, F2!43), tptp_fun_Y1_6(B!39, A2!40, F2!43))) | (~apply(F2!43, tptp_fun_X_7(B!39, A2!40, F2!43), tptp_fun_Y2_5(B!39, A2!40, F2!43))) | (~member(tptp_fun_X_7(B!39, A2!40, F2!43), A2!40)) | (~member(tptp_fun_Y1_6(B!39, A2!40, F2!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A2!40, F2!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A2!40, F2!43), A2!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!43, tptp_fun_X_4(B!39, A2!40, F2!43), Y)))))))) | (~((~maps(F2!43, A2!40, B!39)) | (~((~![X: $i] : ((~member(X, A2!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!43), B!39)) | (~apply(F2!43, X, tptp_fun_Y_3(X, B!39, F2!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~(maps(F2!43, A2!40, B!39) | (~((tptp_fun_Y1_6(B!39, A2!40, F2!43) = tptp_fun_Y2_5(B!39, A2!40, F2!43)) | (~apply(F2!43, tptp_fun_X_7(B!39, A2!40, F2!43), tptp_fun_Y1_6(B!39, A2!40, F2!43))) | (~apply(F2!43, tptp_fun_X_7(B!39, A2!40, F2!43), tptp_fun_Y2_5(B!39, A2!40, F2!43))) | (~member(tptp_fun_X_7(B!39, A2!40, F2!43), A2!40)) | (~member(tptp_fun_Y1_6(B!39, A2!40, F2!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A2!40, F2!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A2!40, F2!43), A2!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!43, tptp_fun_X_4(B!39, A2!40, F2!43), Y)))))))) | (~((~maps(F2!43, A2!40, B!39)) | (~((~![X: $i] : ((~member(X, A2!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!43), B!39)) | (~apply(F2!43, X, tptp_fun_Y_3(X, B!39, F2!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1)))))))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(62,plain,
% 0.19/0.46 ((~((~((~maps(F2!43, A2!40, B!39)) | (~((~![X: $i] : ((~member(X, A2!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!43), B!39)) | (~apply(F2!43, X, tptp_fun_Y_3(X, B!39, F2!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F2!43, X, Y1)) | (~apply(F2!43, X, Y2)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F2!43, A2!40, B!39) | (~((tptp_fun_Y1_6(B!39, A2!40, F2!43) = tptp_fun_Y2_5(B!39, A2!40, F2!43)) | (~apply(F2!43, tptp_fun_X_7(B!39, A2!40, F2!43), tptp_fun_Y1_6(B!39, A2!40, F2!43))) | (~apply(F2!43, tptp_fun_X_7(B!39, A2!40, F2!43), tptp_fun_Y2_5(B!39, A2!40, F2!43))) | (~member(tptp_fun_X_7(B!39, A2!40, F2!43), A2!40)) | (~member(tptp_fun_Y1_6(B!39, A2!40, F2!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A2!40, F2!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A2!40, F2!43), A2!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!43, tptp_fun_X_4(B!39, A2!40, F2!43), Y)))))))))) <=> (~((~(maps(F2!43, A2!40, B!39) | (~((tptp_fun_Y1_6(B!39, A2!40, F2!43) = tptp_fun_Y2_5(B!39, A2!40, F2!43)) | (~apply(F2!43, tptp_fun_X_7(B!39, A2!40, F2!43), tptp_fun_Y1_6(B!39, A2!40, F2!43))) | (~apply(F2!43, tptp_fun_X_7(B!39, A2!40, F2!43), tptp_fun_Y2_5(B!39, A2!40, F2!43))) | (~member(tptp_fun_X_7(B!39, A2!40, F2!43), A2!40)) | (~member(tptp_fun_Y1_6(B!39, A2!40, F2!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A2!40, F2!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A2!40, F2!43), A2!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!43, tptp_fun_X_4(B!39, A2!40, F2!43), Y)))))))) | (~((~maps(F2!43, A2!40, B!39)) | (~((~![X: $i] : ((~member(X, A2!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!43), B!39)) | (~apply(F2!43, X, tptp_fun_Y_3(X, B!39, F2!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1))))))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(63,plain,
% 0.19/0.46 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F2!43, A2!40, B!39)) | (~((~![X: $i] : ((~member(X, A2!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!43), B!39)) | (~apply(F2!43, X, tptp_fun_Y_3(X, B!39, F2!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F2!43, X, Y1)) | (~apply(F2!43, X, Y2)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F2!43, A2!40, B!39) | (~((tptp_fun_Y1_6(B!39, A2!40, F2!43) = tptp_fun_Y2_5(B!39, A2!40, F2!43)) | (~apply(F2!43, tptp_fun_X_7(B!39, A2!40, F2!43), tptp_fun_Y1_6(B!39, A2!40, F2!43))) | (~apply(F2!43, tptp_fun_X_7(B!39, A2!40, F2!43), tptp_fun_Y2_5(B!39, A2!40, F2!43))) | (~member(tptp_fun_X_7(B!39, A2!40, F2!43), A2!40)) | (~member(tptp_fun_Y1_6(B!39, A2!40, F2!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A2!40, F2!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A2!40, F2!43), A2!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!43, tptp_fun_X_4(B!39, A2!40, F2!43), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~(maps(F2!43, A2!40, B!39) | (~((tptp_fun_Y1_6(B!39, A2!40, F2!43) = tptp_fun_Y2_5(B!39, A2!40, F2!43)) | (~apply(F2!43, tptp_fun_X_7(B!39, A2!40, F2!43), tptp_fun_Y1_6(B!39, A2!40, F2!43))) | (~apply(F2!43, tptp_fun_X_7(B!39, A2!40, F2!43), tptp_fun_Y2_5(B!39, A2!40, F2!43))) | (~member(tptp_fun_X_7(B!39, A2!40, F2!43), A2!40)) | (~member(tptp_fun_Y1_6(B!39, A2!40, F2!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A2!40, F2!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A2!40, F2!43), A2!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!43, tptp_fun_X_4(B!39, A2!40, F2!43), Y)))))))) | (~((~maps(F2!43, A2!40, B!39)) | (~((~![X: $i] : ((~member(X, A2!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!43), B!39)) | (~apply(F2!43, X, tptp_fun_Y_3(X, B!39, F2!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1)))))))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[62])).
% 0.19/0.46 tff(64,plain,
% 0.19/0.46 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F2!43, A2!40, B!39)) | (~((~![X: $i] : ((~member(X, A2!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!43), B!39)) | (~apply(F2!43, X, tptp_fun_Y_3(X, B!39, F2!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F2!43, X, Y1)) | (~apply(F2!43, X, Y2)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F2!43, A2!40, B!39) | (~((tptp_fun_Y1_6(B!39, A2!40, F2!43) = tptp_fun_Y2_5(B!39, A2!40, F2!43)) | (~apply(F2!43, tptp_fun_X_7(B!39, A2!40, F2!43), tptp_fun_Y1_6(B!39, A2!40, F2!43))) | (~apply(F2!43, tptp_fun_X_7(B!39, A2!40, F2!43), tptp_fun_Y2_5(B!39, A2!40, F2!43))) | (~member(tptp_fun_X_7(B!39, A2!40, F2!43), A2!40)) | (~member(tptp_fun_Y1_6(B!39, A2!40, F2!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A2!40, F2!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A2!40, F2!43), A2!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!43, tptp_fun_X_4(B!39, A2!40, F2!43), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~(maps(F2!43, A2!40, B!39) | (~((tptp_fun_Y1_6(B!39, A2!40, F2!43) = tptp_fun_Y2_5(B!39, A2!40, F2!43)) | (~apply(F2!43, tptp_fun_X_7(B!39, A2!40, F2!43), tptp_fun_Y1_6(B!39, A2!40, F2!43))) | (~apply(F2!43, tptp_fun_X_7(B!39, A2!40, F2!43), tptp_fun_Y2_5(B!39, A2!40, F2!43))) | (~member(tptp_fun_X_7(B!39, A2!40, F2!43), A2!40)) | (~member(tptp_fun_Y1_6(B!39, A2!40, F2!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A2!40, F2!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A2!40, F2!43), A2!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!43, tptp_fun_X_4(B!39, A2!40, F2!43), Y)))))))) | (~((~maps(F2!43, A2!40, B!39)) | (~((~![X: $i] : ((~member(X, A2!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!43), B!39)) | (~apply(F2!43, X, tptp_fun_Y_3(X, B!39, F2!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1)))))))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[63, 61])).
% 0.19/0.47 tff(65,plain,
% 0.19/0.47 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F2!43, A2!40, B!39)) | (~((~![X: $i] : ((~member(X, A2!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!43), B!39)) | (~apply(F2!43, X, tptp_fun_Y_3(X, B!39, F2!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F2!43, X, Y1)) | (~apply(F2!43, X, Y2)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F2!43, A2!40, B!39) | (~((tptp_fun_Y1_6(B!39, A2!40, F2!43) = tptp_fun_Y2_5(B!39, A2!40, F2!43)) | (~apply(F2!43, tptp_fun_X_7(B!39, A2!40, F2!43), tptp_fun_Y1_6(B!39, A2!40, F2!43))) | (~apply(F2!43, tptp_fun_X_7(B!39, A2!40, F2!43), tptp_fun_Y2_5(B!39, A2!40, F2!43))) | (~member(tptp_fun_X_7(B!39, A2!40, F2!43), A2!40)) | (~member(tptp_fun_Y1_6(B!39, A2!40, F2!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A2!40, F2!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A2!40, F2!43), A2!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!43, tptp_fun_X_4(B!39, A2!40, F2!43), Y))))))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(66,plain,
% 0.19/0.47 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~(maps(F2!43, A2!40, B!39) | (~((tptp_fun_Y1_6(B!39, A2!40, F2!43) = tptp_fun_Y2_5(B!39, A2!40, F2!43)) | (~apply(F2!43, tptp_fun_X_7(B!39, A2!40, F2!43), tptp_fun_Y1_6(B!39, A2!40, F2!43))) | (~apply(F2!43, tptp_fun_X_7(B!39, A2!40, F2!43), tptp_fun_Y2_5(B!39, A2!40, F2!43))) | (~member(tptp_fun_X_7(B!39, A2!40, F2!43), A2!40)) | (~member(tptp_fun_Y1_6(B!39, A2!40, F2!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A2!40, F2!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A2!40, F2!43), A2!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!43, tptp_fun_X_4(B!39, A2!40, F2!43), Y)))))))) | (~((~maps(F2!43, A2!40, B!39)) | (~((~![X: $i] : ((~member(X, A2!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!43), B!39)) | (~apply(F2!43, X, tptp_fun_Y_3(X, B!39, F2!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1))))))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.19/0.47 tff(67,plain,
% 0.19/0.47 (~((~(maps(F2!43, A2!40, B!39) | (~((tptp_fun_Y1_6(B!39, A2!40, F2!43) = tptp_fun_Y2_5(B!39, A2!40, F2!43)) | (~apply(F2!43, tptp_fun_X_7(B!39, A2!40, F2!43), tptp_fun_Y1_6(B!39, A2!40, F2!43))) | (~apply(F2!43, tptp_fun_X_7(B!39, A2!40, F2!43), tptp_fun_Y2_5(B!39, A2!40, F2!43))) | (~member(tptp_fun_X_7(B!39, A2!40, F2!43), A2!40)) | (~member(tptp_fun_Y1_6(B!39, A2!40, F2!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A2!40, F2!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A2!40, F2!43), A2!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!43, tptp_fun_X_4(B!39, A2!40, F2!43), Y)))))))) | (~((~maps(F2!43, A2!40, B!39)) | (~((~![X: $i] : ((~member(X, A2!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!43), B!39)) | (~apply(F2!43, X, tptp_fun_Y_3(X, B!39, F2!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1)))))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[66, 23])).
% 0.19/0.47 tff(68,plain,
% 0.19/0.47 (((~(maps(F2!43, A2!40, B!39) | (~((tptp_fun_Y1_6(B!39, A2!40, F2!43) = tptp_fun_Y2_5(B!39, A2!40, F2!43)) | (~apply(F2!43, tptp_fun_X_7(B!39, A2!40, F2!43), tptp_fun_Y1_6(B!39, A2!40, F2!43))) | (~apply(F2!43, tptp_fun_X_7(B!39, A2!40, F2!43), tptp_fun_Y2_5(B!39, A2!40, F2!43))) | (~member(tptp_fun_X_7(B!39, A2!40, F2!43), A2!40)) | (~member(tptp_fun_Y1_6(B!39, A2!40, F2!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A2!40, F2!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A2!40, F2!43), A2!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!43, tptp_fun_X_4(B!39, A2!40, F2!43), Y)))))))) | (~((~maps(F2!43, A2!40, B!39)) | (~((~![X: $i] : ((~member(X, A2!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!43), B!39)) | (~apply(F2!43, X, tptp_fun_Y_3(X, B!39, F2!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1))))))))) | ((~maps(F2!43, A2!40, B!39)) | (~((~![X: $i] : ((~member(X, A2!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!43), B!39)) | (~apply(F2!43, X, tptp_fun_Y_3(X, B!39, F2!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1)))))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(69,plain,
% 0.19/0.47 ((~maps(F2!43, A2!40, B!39)) | (~((~![X: $i] : ((~member(X, A2!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!43), B!39)) | (~apply(F2!43, X, tptp_fun_Y_3(X, B!39, F2!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.19/0.47 tff(70,plain,
% 0.19/0.47 (((maps(F1!44, A1!41, B!39) & maps(F2!43, A2!40, B!39) & ![X: $i, Y: $i] : ((~(member(X, union(A1!41, A2!40)) & member(Y, B!39))) | (apply(F!42, X, Y) <=> ((member(X, A2!40) & apply(F2!43, X, Y)) | (member(X, A1!41) & apply(F1!44, X, Y)))))) & ((maps(F!42, union(A1!41, A2!40), B!39) | ![X: $i, Y1: $i, Y2: $i] : ((~(member(X, A1!41) & member(X, A2!40) & member(Y1, B!39) & member(Y2, B!39) & apply(F1!44, X, Y1) & apply(F2!43, X, Y2))) | (Y1 = Y2))) & ((~maps(F!42, union(A1!41, A2!40), B!39)) | (~((~(member(X!47, A1!41) & member(X!47, A2!40) & member(Y1!46, B!39) & member(Y2!45, B!39) & apply(F1!44, X!47, Y1!46) & apply(F2!43, X!47, Y2!45))) | (Y1!46 = Y2!45)))))) <=> (maps(F1!44, A1!41, B!39) & maps(F2!43, A2!40, B!39) & ![X: $i, Y: $i] : ((~(member(X, union(A1!41, A2!40)) & member(Y, B!39))) | (apply(F!42, X, Y) <=> ((member(X, A2!40) & apply(F2!43, X, Y)) | (member(X, A1!41) & apply(F1!44, X, Y))))) & (maps(F!42, union(A1!41, A2!40), B!39) | ![X: $i, Y1: $i, Y2: $i] : ((~(member(X, A1!41) & member(X, A2!40) & member(Y1, B!39) & member(Y2, B!39) & apply(F1!44, X, Y1) & apply(F2!43, X, Y2))) | (Y1 = Y2))) & ((~maps(F!42, union(A1!41, A2!40), B!39)) | (~((~(member(X!47, A1!41) & member(X!47, A2!40) & member(Y1!46, B!39) & member(Y2!45, B!39) & apply(F1!44, X!47, Y1!46) & apply(F2!43, X!47, Y2!45))) | (Y1!46 = Y2!45)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(71,plain,
% 0.19/0.47 ((maps(F!42, union(A1!41, A2!40), B!39) | ![X: $i, Y1: $i, Y2: $i] : ((~(member(X, A1!41) & member(X, A2!40) & member(Y1, B!39) & member(Y2, B!39) & apply(F1!44, X, Y1) & apply(F2!43, X, Y2))) | (Y1 = Y2))) <=> (maps(F!42, union(A1!41, A2!40), B!39) | ![X: $i, Y1: $i, Y2: $i] : ((~(member(X, A1!41) & member(X, A2!40) & member(Y1, B!39) & member(Y2, B!39) & apply(F1!44, X, Y1) & apply(F2!43, X, Y2))) | (Y1 = Y2)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(72,plain,
% 0.19/0.47 (((maps(F!42, union(A1!41, A2!40), B!39) | ![X: $i, Y1: $i, Y2: $i] : ((~(member(X, A1!41) & member(X, A2!40) & member(Y1, B!39) & member(Y2, B!39) & apply(F1!44, X, Y1) & apply(F2!43, X, Y2))) | (Y1 = Y2))) & ((~maps(F!42, union(A1!41, A2!40), B!39)) | (~((~(member(X!47, A1!41) & member(X!47, A2!40) & member(Y1!46, B!39) & member(Y2!45, B!39) & apply(F1!44, X!47, Y1!46) & apply(F2!43, X!47, Y2!45))) | (Y1!46 = Y2!45))))) <=> ((maps(F!42, union(A1!41, A2!40), B!39) | ![X: $i, Y1: $i, Y2: $i] : ((~(member(X, A1!41) & member(X, A2!40) & member(Y1, B!39) & member(Y2, B!39) & apply(F1!44, X, Y1) & apply(F2!43, X, Y2))) | (Y1 = Y2))) & ((~maps(F!42, union(A1!41, A2!40), B!39)) | (~((~(member(X!47, A1!41) & member(X!47, A2!40) & member(Y1!46, B!39) & member(Y2!45, B!39) & apply(F1!44, X!47, Y1!46) & apply(F2!43, X!47, Y2!45))) | (Y1!46 = Y2!45)))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[71])).
% 0.19/0.47 tff(73,plain,
% 0.19/0.47 ((maps(F1!44, A1!41, B!39) & maps(F2!43, A2!40, B!39) & ![X: $i, Y: $i] : ((~(member(X, union(A1!41, A2!40)) & member(Y, B!39))) | (apply(F!42, X, Y) <=> ((member(X, A2!40) & apply(F2!43, X, Y)) | (member(X, A1!41) & apply(F1!44, X, Y)))))) <=> (maps(F1!44, A1!41, B!39) & maps(F2!43, A2!40, B!39) & ![X: $i, Y: $i] : ((~(member(X, union(A1!41, A2!40)) & member(Y, B!39))) | (apply(F!42, X, Y) <=> ((member(X, A2!40) & apply(F2!43, X, Y)) | (member(X, A1!41) & apply(F1!44, X, Y))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(74,plain,
% 0.19/0.47 (((maps(F1!44, A1!41, B!39) & maps(F2!43, A2!40, B!39) & ![X: $i, Y: $i] : ((~(member(X, union(A1!41, A2!40)) & member(Y, B!39))) | (apply(F!42, X, Y) <=> ((member(X, A2!40) & apply(F2!43, X, Y)) | (member(X, A1!41) & apply(F1!44, X, Y)))))) & ((maps(F!42, union(A1!41, A2!40), B!39) | ![X: $i, Y1: $i, Y2: $i] : ((~(member(X, A1!41) & member(X, A2!40) & member(Y1, B!39) & member(Y2, B!39) & apply(F1!44, X, Y1) & apply(F2!43, X, Y2))) | (Y1 = Y2))) & ((~maps(F!42, union(A1!41, A2!40), B!39)) | (~((~(member(X!47, A1!41) & member(X!47, A2!40) & member(Y1!46, B!39) & member(Y2!45, B!39) & apply(F1!44, X!47, Y1!46) & apply(F2!43, X!47, Y2!45))) | (Y1!46 = Y2!45)))))) <=> ((maps(F1!44, A1!41, B!39) & maps(F2!43, A2!40, B!39) & ![X: $i, Y: $i] : ((~(member(X, union(A1!41, A2!40)) & member(Y, B!39))) | (apply(F!42, X, Y) <=> ((member(X, A2!40) & apply(F2!43, X, Y)) | (member(X, A1!41) & apply(F1!44, X, Y)))))) & ((maps(F!42, union(A1!41, A2!40), B!39) | ![X: $i, Y1: $i, Y2: $i] : ((~(member(X, A1!41) & member(X, A2!40) & member(Y1, B!39) & member(Y2, B!39) & apply(F1!44, X, Y1) & apply(F2!43, X, Y2))) | (Y1 = Y2))) & ((~maps(F!42, union(A1!41, A2!40), B!39)) | (~((~(member(X!47, A1!41) & member(X!47, A2!40) & member(Y1!46, B!39) & member(Y2!45, B!39) & apply(F1!44, X!47, Y1!46) & apply(F2!43, X!47, Y2!45))) | (Y1!46 = Y2!45))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[73, 72])).
% 0.19/0.47 tff(75,plain,
% 0.19/0.47 (((maps(F1!44, A1!41, B!39) & maps(F2!43, A2!40, B!39) & ![X: $i, Y: $i] : ((~(member(X, union(A1!41, A2!40)) & member(Y, B!39))) | (apply(F!42, X, Y) <=> ((member(X, A2!40) & apply(F2!43, X, Y)) | (member(X, A1!41) & apply(F1!44, X, Y)))))) & ((maps(F!42, union(A1!41, A2!40), B!39) | ![X: $i, Y1: $i, Y2: $i] : ((~(member(X, A1!41) & member(X, A2!40) & member(Y1, B!39) & member(Y2, B!39) & apply(F1!44, X, Y1) & apply(F2!43, X, Y2))) | (Y1 = Y2))) & ((~maps(F!42, union(A1!41, A2!40), B!39)) | (~((~(member(X!47, A1!41) & member(X!47, A2!40) & member(Y1!46, B!39) & member(Y2!45, B!39) & apply(F1!44, X!47, Y1!46) & apply(F2!43, X!47, Y2!45))) | (Y1!46 = Y2!45)))))) <=> (maps(F1!44, A1!41, B!39) & maps(F2!43, A2!40, B!39) & ![X: $i, Y: $i] : ((~(member(X, union(A1!41, A2!40)) & member(Y, B!39))) | (apply(F!42, X, Y) <=> ((member(X, A2!40) & apply(F2!43, X, Y)) | (member(X, A1!41) & apply(F1!44, X, Y))))) & (maps(F!42, union(A1!41, A2!40), B!39) | ![X: $i, Y1: $i, Y2: $i] : ((~(member(X, A1!41) & member(X, A2!40) & member(Y1, B!39) & member(Y2, B!39) & apply(F1!44, X, Y1) & apply(F2!43, X, Y2))) | (Y1 = Y2))) & ((~maps(F!42, union(A1!41, A2!40), B!39)) | (~((~(member(X!47, A1!41) & member(X!47, A2!40) & member(Y1!46, B!39) & member(Y2!45, B!39) & apply(F1!44, X!47, Y1!46) & apply(F2!43, X!47, Y2!45))) | (Y1!46 = Y2!45)))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[74, 70])).
% 0.19/0.47 tff(76,plain,
% 0.19/0.47 ((~![F1: $i, F2: $i, F: $i, A1: $i, A2: $i, B: $i] : ((~(maps(F1, A1, B) & maps(F2, A2, B) & ![X: $i, Y: $i] : ((~(member(X, union(A1, A2)) & member(Y, B))) | (apply(F, X, Y) <=> ((member(X, A2) & apply(F2, X, Y)) | (member(X, A1) & apply(F1, X, Y))))))) | (maps(F, union(A1, A2), B) <=> ![X: $i, Y1: $i, Y2: $i] : ((~(member(X, A1) & member(X, A2) & member(Y1, B) & member(Y2, B) & apply(F1, X, Y1) & apply(F2, X, Y2))) | (Y1 = Y2))))) <=> (~![F1: $i, F2: $i, F: $i, A1: $i, A2: $i, B: $i] : ((~(maps(F1, A1, B) & maps(F2, A2, B) & ![X: $i, Y: $i] : ((~(member(X, union(A1, A2)) & member(Y, B))) | (apply(F, X, Y) <=> ((member(X, A2) & apply(F2, X, Y)) | (member(X, A1) & apply(F1, X, Y))))))) | (maps(F, union(A1, A2), B) <=> ![X: $i, Y1: $i, Y2: $i] : ((~(member(X, A1) & member(X, A2) & member(Y1, B) & member(Y2, B) & apply(F1, X, Y1) & apply(F2, X, Y2))) | (Y1 = Y2)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(77,plain,
% 0.19/0.47 ((~![F1: $i, F2: $i, F: $i, A1: $i, A2: $i, B: $i] : (((maps(F1, A1, B) & maps(F2, A2, B)) & ![X: $i, Y: $i] : ((member(X, union(A1, A2)) & member(Y, B)) => (apply(F, X, Y) <=> ((member(X, A1) & apply(F1, X, Y)) | (member(X, A2) & apply(F2, X, Y)))))) => (maps(F, union(A1, A2), B) <=> ![X: $i, Y1: $i, Y2: $i] : ((((((member(X, A1) & member(X, A2)) & member(Y1, B)) & member(Y2, B)) & apply(F1, X, Y1)) & apply(F2, X, Y2)) => (Y1 = Y2))))) <=> (~![F1: $i, F2: $i, F: $i, A1: $i, A2: $i, B: $i] : ((~(maps(F1, A1, B) & maps(F2, A2, B) & ![X: $i, Y: $i] : ((~(member(X, union(A1, A2)) & member(Y, B))) | (apply(F, X, Y) <=> ((member(X, A2) & apply(F2, X, Y)) | (member(X, A1) & apply(F1, X, Y))))))) | (maps(F, union(A1, A2), B) <=> ![X: $i, Y1: $i, Y2: $i] : ((~(member(X, A1) & member(X, A2) & member(Y1, B) & member(Y2, B) & apply(F1, X, Y1) & apply(F2, X, Y2))) | (Y1 = Y2)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(78,axiom,(~![F1: $i, F2: $i, F: $i, A1: $i, A2: $i, B: $i] : (((maps(F1, A1, B) & maps(F2, A2, B)) & ![X: $i, Y: $i] : ((member(X, union(A1, A2)) & member(Y, B)) => (apply(F, X, Y) <=> ((member(X, A1) & apply(F1, X, Y)) | (member(X, A2) & apply(F2, X, Y)))))) => (maps(F, union(A1, A2), B) <=> ![X: $i, Y1: $i, Y2: $i] : ((((((member(X, A1) & member(X, A2)) & member(Y1, B)) & member(Y2, B)) & apply(F1, X, Y1)) & apply(F2, X, Y2)) => (Y1 = Y2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thII36')).
% 0.19/0.47 tff(79,plain,
% 0.19/0.47 (~![F1: $i, F2: $i, F: $i, A1: $i, A2: $i, B: $i] : ((~(maps(F1, A1, B) & maps(F2, A2, B) & ![X: $i, Y: $i] : ((~(member(X, union(A1, A2)) & member(Y, B))) | (apply(F, X, Y) <=> ((member(X, A2) & apply(F2, X, Y)) | (member(X, A1) & apply(F1, X, Y))))))) | (maps(F, union(A1, A2), B) <=> ![X: $i, Y1: $i, Y2: $i] : ((~(member(X, A1) & member(X, A2) & member(Y1, B) & member(Y2, B) & apply(F1, X, Y1) & apply(F2, X, Y2))) | (Y1 = Y2))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.19/0.47 tff(80,plain,
% 0.19/0.47 (~![F1: $i, F2: $i, F: $i, A1: $i, A2: $i, B: $i] : ((~(maps(F1, A1, B) & maps(F2, A2, B) & ![X: $i, Y: $i] : ((~(member(X, union(A1, A2)) & member(Y, B))) | (apply(F, X, Y) <=> ((member(X, A2) & apply(F2, X, Y)) | (member(X, A1) & apply(F1, X, Y))))))) | (maps(F, union(A1, A2), B) <=> ![X: $i, Y1: $i, Y2: $i] : ((~(member(X, A1) & member(X, A2) & member(Y1, B) & member(Y2, B) & apply(F1, X, Y1) & apply(F2, X, Y2))) | (Y1 = Y2))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[79, 76])).
% 0.19/0.47 tff(81,plain,
% 0.19/0.47 (~![F1: $i, F2: $i, F: $i, A1: $i, A2: $i, B: $i] : ((~(maps(F1, A1, B) & maps(F2, A2, B) & ![X: $i, Y: $i] : ((~(member(X, union(A1, A2)) & member(Y, B))) | (apply(F, X, Y) <=> ((member(X, A2) & apply(F2, X, Y)) | (member(X, A1) & apply(F1, X, Y))))))) | (maps(F, union(A1, A2), B) <=> ![X: $i, Y1: $i, Y2: $i] : ((~(member(X, A1) & member(X, A2) & member(Y1, B) & member(Y2, B) & apply(F1, X, Y1) & apply(F2, X, Y2))) | (Y1 = Y2))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.19/0.47 tff(82,plain,
% 0.19/0.47 (~![F1: $i, F2: $i, F: $i, A1: $i, A2: $i, B: $i] : ((~(maps(F1, A1, B) & maps(F2, A2, B) & ![X: $i, Y: $i] : ((~(member(X, union(A1, A2)) & member(Y, B))) | (apply(F, X, Y) <=> ((member(X, A2) & apply(F2, X, Y)) | (member(X, A1) & apply(F1, X, Y))))))) | (maps(F, union(A1, A2), B) <=> ![X: $i, Y1: $i, Y2: $i] : ((~(member(X, A1) & member(X, A2) & member(Y1, B) & member(Y2, B) & apply(F1, X, Y1) & apply(F2, X, Y2))) | (Y1 = Y2))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[81, 76])).
% 0.19/0.47 tff(83,plain,
% 0.19/0.47 (~![F1: $i, F2: $i, F: $i, A1: $i, A2: $i, B: $i] : ((~(maps(F1, A1, B) & maps(F2, A2, B) & ![X: $i, Y: $i] : ((~(member(X, union(A1, A2)) & member(Y, B))) | (apply(F, X, Y) <=> ((member(X, A2) & apply(F2, X, Y)) | (member(X, A1) & apply(F1, X, Y))))))) | (maps(F, union(A1, A2), B) <=> ![X: $i, Y1: $i, Y2: $i] : ((~(member(X, A1) & member(X, A2) & member(Y1, B) & member(Y2, B) & apply(F1, X, Y1) & apply(F2, X, Y2))) | (Y1 = Y2))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[82, 76])).
% 0.19/0.47 tff(84,plain,
% 0.19/0.47 (~![F1: $i, F2: $i, F: $i, A1: $i, A2: $i, B: $i] : ((~(maps(F1, A1, B) & maps(F2, A2, B) & ![X: $i, Y: $i] : ((~(member(X, union(A1, A2)) & member(Y, B))) | (apply(F, X, Y) <=> ((member(X, A2) & apply(F2, X, Y)) | (member(X, A1) & apply(F1, X, Y))))))) | (maps(F, union(A1, A2), B) <=> ![X: $i, Y1: $i, Y2: $i] : ((~(member(X, A1) & member(X, A2) & member(Y1, B) & member(Y2, B) & apply(F1, X, Y1) & apply(F2, X, Y2))) | (Y1 = Y2))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.19/0.48 tff(85,plain,
% 0.19/0.48 (~![F1: $i, F2: $i, F: $i, A1: $i, A2: $i, B: $i] : ((~(maps(F1, A1, B) & maps(F2, A2, B) & ![X: $i, Y: $i] : ((~(member(X, union(A1, A2)) & member(Y, B))) | (apply(F, X, Y) <=> ((member(X, A2) & apply(F2, X, Y)) | (member(X, A1) & apply(F1, X, Y))))))) | (maps(F, union(A1, A2), B) <=> ![X: $i, Y1: $i, Y2: $i] : ((~(member(X, A1) & member(X, A2) & member(Y1, B) & member(Y2, B) & apply(F1, X, Y1) & apply(F2, X, Y2))) | (Y1 = Y2))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[84, 76])).
% 0.19/0.48 tff(86,plain,
% 0.19/0.48 (maps(F1!44, A1!41, B!39) & maps(F2!43, A2!40, B!39) & ![X: $i, Y: $i] : ((~(member(X, union(A1!41, A2!40)) & member(Y, B!39))) | (apply(F!42, X, Y) <=> ((member(X, A2!40) & apply(F2!43, X, Y)) | (member(X, A1!41) & apply(F1!44, X, Y))))) & (maps(F!42, union(A1!41, A2!40), B!39) | ![X: $i, Y1: $i, Y2: $i] : ((~(member(X, A1!41) & member(X, A2!40) & member(Y1, B!39) & member(Y2, B!39) & apply(F1!44, X, Y1) & apply(F2!43, X, Y2))) | (Y1 = Y2))) & ((~maps(F!42, union(A1!41, A2!40), B!39)) | (~((~(member(X!47, A1!41) & member(X!47, A2!40) & member(Y1!46, B!39) & member(Y2!45, B!39) & apply(F1!44, X!47, Y1!46) & apply(F2!43, X!47, Y2!45))) | (Y1!46 = Y2!45))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[85, 75])).
% 0.19/0.48 tff(87,plain,
% 0.19/0.48 (maps(F2!43, A2!40, B!39)),
% 0.19/0.48 inference(and_elim,[status(thm)],[86])).
% 0.19/0.48 tff(88,plain,
% 0.19/0.48 ((~((~maps(F2!43, A2!40, B!39)) | (~((~![X: $i] : ((~member(X, A2!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!43), B!39)) | (~apply(F2!43, X, tptp_fun_Y_3(X, B!39, F2!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1)))))))) | (~maps(F2!43, A2!40, B!39)) | (~((~![X: $i] : ((~member(X, A2!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!43), B!39)) | (~apply(F2!43, X, tptp_fun_Y_3(X, B!39, F2!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1))))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(89,plain,
% 0.19/0.48 ((~((~maps(F2!43, A2!40, B!39)) | (~((~![X: $i] : ((~member(X, A2!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!43), B!39)) | (~apply(F2!43, X, tptp_fun_Y_3(X, B!39, F2!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1)))))))) | (~((~![X: $i] : ((~member(X, A2!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!43), B!39)) | (~apply(F2!43, X, tptp_fun_Y_3(X, B!39, F2!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.19/0.48 tff(90,plain,
% 0.19/0.48 (~((~![X: $i] : ((~member(X, A2!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!43), B!39)) | (~apply(F2!43, X, tptp_fun_Y_3(X, B!39, F2!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1)))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[89, 69])).
% 0.19/0.48 tff(91,plain,
% 0.19/0.48 (((~![X: $i] : ((~member(X, A2!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!43), B!39)) | (~apply(F2!43, X, tptp_fun_Y_3(X, B!39, F2!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1))))) | ![X: $i] : ((~member(X, A2!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!43), B!39)) | (~apply(F2!43, X, tptp_fun_Y_3(X, B!39, F2!43))))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(92,plain,
% 0.19/0.48 (![X: $i] : ((~member(X, A2!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!43), B!39)) | (~apply(F2!43, X, tptp_fun_Y_3(X, B!39, F2!43))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.19/0.48 tff(93,plain,
% 0.19/0.48 (((~![X: $i] : ((~member(X, A2!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!43), B!39)) | (~apply(F2!43, X, tptp_fun_Y_3(X, B!39, F2!43))))))) | ((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))))) <=> ((~![X: $i] : ((~member(X, A2!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!43), B!39)) | (~apply(F2!43, X, tptp_fun_Y_3(X, B!39, F2!43))))))) | (~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(94,plain,
% 0.19/0.48 ((~![X: $i] : ((~member(X, A2!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!43), B!39)) | (~apply(F2!43, X, tptp_fun_Y_3(X, B!39, F2!43))))))) | ((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(95,plain,
% 0.19/0.48 ((~![X: $i] : ((~member(X, A2!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!43), B!39)) | (~apply(F2!43, X, tptp_fun_Y_3(X, B!39, F2!43))))))) | (~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.19/0.48 tff(96,plain,
% 0.19/0.48 (~((~member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[95, 92, 60])).
% 0.19/0.48 tff(97,plain,
% 0.19/0.48 (((~member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)))) | member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(98,plain,
% 0.19/0.48 (member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.19/0.48 tff(99,assumption,(member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))), introduced(assumption)).
% 0.19/0.48 tff(100,plain,
% 0.19/0.48 (^[X: $i, Y: $i] : refl(((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y))))))) <=> ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(101,plain,
% 0.19/0.48 (![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y))))))) <=> ![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[100])).
% 0.19/0.48 tff(102,plain,
% 0.19/0.48 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((member(X, union(A1!41, A2!40)) & member(Y, B!39)) <=> (~((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39))))), ((~(member(X, union(A1!41, A2!40)) & member(Y, B!39))) <=> (~(~((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39))))))), rewrite((~(~((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39))))) <=> ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)))), ((~(member(X, union(A1!41, A2!40)) & member(Y, B!39))) <=> ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39))))), rewrite((apply(F!42, X, Y) <=> ((member(X, A2!40) & apply(F2!43, X, Y)) | (member(X, A1!41) & apply(F1!44, X, Y)))) <=> (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y))))))), (((~(member(X, union(A1!41, A2!40)) & member(Y, B!39))) | (apply(F!42, X, Y) <=> ((member(X, A2!40) & apply(F2!43, X, Y)) | (member(X, A1!41) & apply(F1!44, X, Y))))) <=> (((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39))) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y))))))))), rewrite((((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39))) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y))))))) <=> ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))), (((~(member(X, union(A1!41, A2!40)) & member(Y, B!39))) | (apply(F!42, X, Y) <=> ((member(X, A2!40) & apply(F2!43, X, Y)) | (member(X, A1!41) & apply(F1!44, X, Y))))) <=> ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(103,plain,
% 0.19/0.48 (![X: $i, Y: $i] : ((~(member(X, union(A1!41, A2!40)) & member(Y, B!39))) | (apply(F!42, X, Y) <=> ((member(X, A2!40) & apply(F2!43, X, Y)) | (member(X, A1!41) & apply(F1!44, X, Y))))) <=> ![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[102])).
% 0.19/0.48 tff(104,plain,
% 0.19/0.48 (![X: $i, Y: $i] : ((~(member(X, union(A1!41, A2!40)) & member(Y, B!39))) | (apply(F!42, X, Y) <=> ((member(X, A2!40) & apply(F2!43, X, Y)) | (member(X, A1!41) & apply(F1!44, X, Y)))))),
% 0.19/0.48 inference(and_elim,[status(thm)],[86])).
% 0.19/0.48 tff(105,plain,
% 0.19/0.48 (![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.48 tff(106,plain,
% 0.19/0.48 (![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.19/0.48 tff(107,plain,
% 0.19/0.48 (((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | ((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)) <=> ((~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))))))) <=> ((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | (~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)) <=> ((~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(108,plain,
% 0.19/0.48 ((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | ((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)) <=> ((~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(109,plain,
% 0.19/0.48 ((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | (~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)) <=> ((~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.19/0.48 tff(110,plain,
% 0.19/0.48 (apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)) <=> ((~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[109, 106, 99, 98])).
% 0.19/0.48 tff(111,assumption,(![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y)))), introduced(assumption)).
% 0.19/0.48 tff(112,plain,
% 0.19/0.48 (((~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y)))) | ((~member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))) <=> ((~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y)))) | (~member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(113,plain,
% 0.19/0.49 ((~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y)))) | ((~member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(114,plain,
% 0.19/0.49 ((~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y)))) | (~member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.19/0.49 tff(115,plain,
% 0.19/0.49 (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[114, 111, 98])).
% 0.19/0.49 tff(116,plain,
% 0.19/0.49 (((~member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)))) | apply(F2!43, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(117,plain,
% 0.19/0.49 (apply(F2!43, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[116, 96])).
% 0.19/0.49 tff(118,plain,
% 0.19/0.49 ((~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))) | (~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(119,plain,
% 0.19/0.49 (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[118, 60, 117])).
% 0.19/0.49 tff(120,plain,
% 0.19/0.49 (((~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)))))) | ((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(121,plain,
% 0.19/0.49 ((~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.19/0.49 tff(122,plain,
% 0.19/0.49 ((~(apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)) <=> ((~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)))))))) | apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)) | (~((~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)))))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(123,plain,
% 0.19/0.49 ((~(apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)) <=> ((~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)))))))) | apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.19/0.49 tff(124,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[123, 115, 110])).
% 0.19/0.49 tff(125,plain,((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y)))) | (~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(126,plain,
% 0.19/0.49 (~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[125, 59, 54])).
% 0.19/0.49 tff(127,plain,
% 0.19/0.49 ((~(member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41) | member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40))) | member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41) | member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(128,plain,
% 0.19/0.49 (member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[127, 126, 57])).
% 0.19/0.49 tff(129,plain,
% 0.19/0.49 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~(maps(F1!44, A1!41, B!39) | (~((tptp_fun_Y1_6(B!39, A1!41, F1!44) = tptp_fun_Y2_5(B!39, A1!41, F1!44)) | (~apply(F1!44, tptp_fun_X_7(B!39, A1!41, F1!44), tptp_fun_Y1_6(B!39, A1!41, F1!44))) | (~apply(F1!44, tptp_fun_X_7(B!39, A1!41, F1!44), tptp_fun_Y2_5(B!39, A1!41, F1!44))) | (~member(tptp_fun_X_7(B!39, A1!41, F1!44), A1!41)) | (~member(tptp_fun_Y1_6(B!39, A1!41, F1!44), B!39)) | (~member(tptp_fun_Y2_5(B!39, A1!41, F1!44), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A1!41, F1!44), A1!41)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!44, tptp_fun_X_4(B!39, A1!41, F1!44), Y)))))))) | (~((~maps(F1!44, A1!41, B!39)) | (~((~![X: $i] : ((~member(X, A1!41)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!44), B!39)) | (~apply(F1!44, X, tptp_fun_Y_3(X, B!39, F1!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~(maps(F1!44, A1!41, B!39) | (~((tptp_fun_Y1_6(B!39, A1!41, F1!44) = tptp_fun_Y2_5(B!39, A1!41, F1!44)) | (~apply(F1!44, tptp_fun_X_7(B!39, A1!41, F1!44), tptp_fun_Y1_6(B!39, A1!41, F1!44))) | (~apply(F1!44, tptp_fun_X_7(B!39, A1!41, F1!44), tptp_fun_Y2_5(B!39, A1!41, F1!44))) | (~member(tptp_fun_X_7(B!39, A1!41, F1!44), A1!41)) | (~member(tptp_fun_Y1_6(B!39, A1!41, F1!44), B!39)) | (~member(tptp_fun_Y2_5(B!39, A1!41, F1!44), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A1!41, F1!44), A1!41)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!44, tptp_fun_X_4(B!39, A1!41, F1!44), Y)))))))) | (~((~maps(F1!44, A1!41, B!39)) | (~((~![X: $i] : ((~member(X, A1!41)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!44), B!39)) | (~apply(F1!44, X, tptp_fun_Y_3(X, B!39, F1!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2)))))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(130,plain,
% 0.19/0.49 ((~((~((~maps(F1!44, A1!41, B!39)) | (~((~![X: $i] : ((~member(X, A1!41)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!44), B!39)) | (~apply(F1!44, X, tptp_fun_Y_3(X, B!39, F1!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F1!44, A1!41, B!39) | (~((tptp_fun_Y1_6(B!39, A1!41, F1!44) = tptp_fun_Y2_5(B!39, A1!41, F1!44)) | (~apply(F1!44, tptp_fun_X_7(B!39, A1!41, F1!44), tptp_fun_Y1_6(B!39, A1!41, F1!44))) | (~apply(F1!44, tptp_fun_X_7(B!39, A1!41, F1!44), tptp_fun_Y2_5(B!39, A1!41, F1!44))) | (~member(tptp_fun_X_7(B!39, A1!41, F1!44), A1!41)) | (~member(tptp_fun_Y1_6(B!39, A1!41, F1!44), B!39)) | (~member(tptp_fun_Y2_5(B!39, A1!41, F1!44), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A1!41, F1!44), A1!41)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!44, tptp_fun_X_4(B!39, A1!41, F1!44), Y)))))))))) <=> (~((~(maps(F1!44, A1!41, B!39) | (~((tptp_fun_Y1_6(B!39, A1!41, F1!44) = tptp_fun_Y2_5(B!39, A1!41, F1!44)) | (~apply(F1!44, tptp_fun_X_7(B!39, A1!41, F1!44), tptp_fun_Y1_6(B!39, A1!41, F1!44))) | (~apply(F1!44, tptp_fun_X_7(B!39, A1!41, F1!44), tptp_fun_Y2_5(B!39, A1!41, F1!44))) | (~member(tptp_fun_X_7(B!39, A1!41, F1!44), A1!41)) | (~member(tptp_fun_Y1_6(B!39, A1!41, F1!44), B!39)) | (~member(tptp_fun_Y2_5(B!39, A1!41, F1!44), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A1!41, F1!44), A1!41)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!44, tptp_fun_X_4(B!39, A1!41, F1!44), Y)))))))) | (~((~maps(F1!44, A1!41, B!39)) | (~((~![X: $i] : ((~member(X, A1!41)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!44), B!39)) | (~apply(F1!44, X, tptp_fun_Y_3(X, B!39, F1!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2))))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(131,plain,
% 0.19/0.49 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F1!44, A1!41, B!39)) | (~((~![X: $i] : ((~member(X, A1!41)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!44), B!39)) | (~apply(F1!44, X, tptp_fun_Y_3(X, B!39, F1!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F1!44, A1!41, B!39) | (~((tptp_fun_Y1_6(B!39, A1!41, F1!44) = tptp_fun_Y2_5(B!39, A1!41, F1!44)) | (~apply(F1!44, tptp_fun_X_7(B!39, A1!41, F1!44), tptp_fun_Y1_6(B!39, A1!41, F1!44))) | (~apply(F1!44, tptp_fun_X_7(B!39, A1!41, F1!44), tptp_fun_Y2_5(B!39, A1!41, F1!44))) | (~member(tptp_fun_X_7(B!39, A1!41, F1!44), A1!41)) | (~member(tptp_fun_Y1_6(B!39, A1!41, F1!44), B!39)) | (~member(tptp_fun_Y2_5(B!39, A1!41, F1!44), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A1!41, F1!44), A1!41)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!44, tptp_fun_X_4(B!39, A1!41, F1!44), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~(maps(F1!44, A1!41, B!39) | (~((tptp_fun_Y1_6(B!39, A1!41, F1!44) = tptp_fun_Y2_5(B!39, A1!41, F1!44)) | (~apply(F1!44, tptp_fun_X_7(B!39, A1!41, F1!44), tptp_fun_Y1_6(B!39, A1!41, F1!44))) | (~apply(F1!44, tptp_fun_X_7(B!39, A1!41, F1!44), tptp_fun_Y2_5(B!39, A1!41, F1!44))) | (~member(tptp_fun_X_7(B!39, A1!41, F1!44), A1!41)) | (~member(tptp_fun_Y1_6(B!39, A1!41, F1!44), B!39)) | (~member(tptp_fun_Y2_5(B!39, A1!41, F1!44), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A1!41, F1!44), A1!41)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!44, tptp_fun_X_4(B!39, A1!41, F1!44), Y)))))))) | (~((~maps(F1!44, A1!41, B!39)) | (~((~![X: $i] : ((~member(X, A1!41)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!44), B!39)) | (~apply(F1!44, X, tptp_fun_Y_3(X, B!39, F1!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2)))))))))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[130])).
% 0.19/0.49 tff(132,plain,
% 0.19/0.49 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F1!44, A1!41, B!39)) | (~((~![X: $i] : ((~member(X, A1!41)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!44), B!39)) | (~apply(F1!44, X, tptp_fun_Y_3(X, B!39, F1!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F1!44, A1!41, B!39) | (~((tptp_fun_Y1_6(B!39, A1!41, F1!44) = tptp_fun_Y2_5(B!39, A1!41, F1!44)) | (~apply(F1!44, tptp_fun_X_7(B!39, A1!41, F1!44), tptp_fun_Y1_6(B!39, A1!41, F1!44))) | (~apply(F1!44, tptp_fun_X_7(B!39, A1!41, F1!44), tptp_fun_Y2_5(B!39, A1!41, F1!44))) | (~member(tptp_fun_X_7(B!39, A1!41, F1!44), A1!41)) | (~member(tptp_fun_Y1_6(B!39, A1!41, F1!44), B!39)) | (~member(tptp_fun_Y2_5(B!39, A1!41, F1!44), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A1!41, F1!44), A1!41)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!44, tptp_fun_X_4(B!39, A1!41, F1!44), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~(maps(F1!44, A1!41, B!39) | (~((tptp_fun_Y1_6(B!39, A1!41, F1!44) = tptp_fun_Y2_5(B!39, A1!41, F1!44)) | (~apply(F1!44, tptp_fun_X_7(B!39, A1!41, F1!44), tptp_fun_Y1_6(B!39, A1!41, F1!44))) | (~apply(F1!44, tptp_fun_X_7(B!39, A1!41, F1!44), tptp_fun_Y2_5(B!39, A1!41, F1!44))) | (~member(tptp_fun_X_7(B!39, A1!41, F1!44), A1!41)) | (~member(tptp_fun_Y1_6(B!39, A1!41, F1!44), B!39)) | (~member(tptp_fun_Y2_5(B!39, A1!41, F1!44), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A1!41, F1!44), A1!41)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!44, tptp_fun_X_4(B!39, A1!41, F1!44), Y)))))))) | (~((~maps(F1!44, A1!41, B!39)) | (~((~![X: $i] : ((~member(X, A1!41)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!44), B!39)) | (~apply(F1!44, X, tptp_fun_Y_3(X, B!39, F1!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2)))))))))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[131, 129])).
% 0.19/0.50 tff(133,plain,
% 0.19/0.50 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F1!44, A1!41, B!39)) | (~((~![X: $i] : ((~member(X, A1!41)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!44), B!39)) | (~apply(F1!44, X, tptp_fun_Y_3(X, B!39, F1!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F1!44, A1!41, B!39) | (~((tptp_fun_Y1_6(B!39, A1!41, F1!44) = tptp_fun_Y2_5(B!39, A1!41, F1!44)) | (~apply(F1!44, tptp_fun_X_7(B!39, A1!41, F1!44), tptp_fun_Y1_6(B!39, A1!41, F1!44))) | (~apply(F1!44, tptp_fun_X_7(B!39, A1!41, F1!44), tptp_fun_Y2_5(B!39, A1!41, F1!44))) | (~member(tptp_fun_X_7(B!39, A1!41, F1!44), A1!41)) | (~member(tptp_fun_Y1_6(B!39, A1!41, F1!44), B!39)) | (~member(tptp_fun_Y2_5(B!39, A1!41, F1!44), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A1!41, F1!44), A1!41)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!44, tptp_fun_X_4(B!39, A1!41, F1!44), Y))))))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(134,plain,
% 0.19/0.50 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~(maps(F1!44, A1!41, B!39) | (~((tptp_fun_Y1_6(B!39, A1!41, F1!44) = tptp_fun_Y2_5(B!39, A1!41, F1!44)) | (~apply(F1!44, tptp_fun_X_7(B!39, A1!41, F1!44), tptp_fun_Y1_6(B!39, A1!41, F1!44))) | (~apply(F1!44, tptp_fun_X_7(B!39, A1!41, F1!44), tptp_fun_Y2_5(B!39, A1!41, F1!44))) | (~member(tptp_fun_X_7(B!39, A1!41, F1!44), A1!41)) | (~member(tptp_fun_Y1_6(B!39, A1!41, F1!44), B!39)) | (~member(tptp_fun_Y2_5(B!39, A1!41, F1!44), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A1!41, F1!44), A1!41)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!44, tptp_fun_X_4(B!39, A1!41, F1!44), Y)))))))) | (~((~maps(F1!44, A1!41, B!39)) | (~((~![X: $i] : ((~member(X, A1!41)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!44), B!39)) | (~apply(F1!44, X, tptp_fun_Y_3(X, B!39, F1!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2))))))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.19/0.50 tff(135,plain,
% 0.19/0.50 (~((~(maps(F1!44, A1!41, B!39) | (~((tptp_fun_Y1_6(B!39, A1!41, F1!44) = tptp_fun_Y2_5(B!39, A1!41, F1!44)) | (~apply(F1!44, tptp_fun_X_7(B!39, A1!41, F1!44), tptp_fun_Y1_6(B!39, A1!41, F1!44))) | (~apply(F1!44, tptp_fun_X_7(B!39, A1!41, F1!44), tptp_fun_Y2_5(B!39, A1!41, F1!44))) | (~member(tptp_fun_X_7(B!39, A1!41, F1!44), A1!41)) | (~member(tptp_fun_Y1_6(B!39, A1!41, F1!44), B!39)) | (~member(tptp_fun_Y2_5(B!39, A1!41, F1!44), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A1!41, F1!44), A1!41)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!44, tptp_fun_X_4(B!39, A1!41, F1!44), Y)))))))) | (~((~maps(F1!44, A1!41, B!39)) | (~((~![X: $i] : ((~member(X, A1!41)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!44), B!39)) | (~apply(F1!44, X, tptp_fun_Y_3(X, B!39, F1!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2)))))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[134, 23])).
% 0.19/0.50 tff(136,plain,
% 0.19/0.50 (((~(maps(F1!44, A1!41, B!39) | (~((tptp_fun_Y1_6(B!39, A1!41, F1!44) = tptp_fun_Y2_5(B!39, A1!41, F1!44)) | (~apply(F1!44, tptp_fun_X_7(B!39, A1!41, F1!44), tptp_fun_Y1_6(B!39, A1!41, F1!44))) | (~apply(F1!44, tptp_fun_X_7(B!39, A1!41, F1!44), tptp_fun_Y2_5(B!39, A1!41, F1!44))) | (~member(tptp_fun_X_7(B!39, A1!41, F1!44), A1!41)) | (~member(tptp_fun_Y1_6(B!39, A1!41, F1!44), B!39)) | (~member(tptp_fun_Y2_5(B!39, A1!41, F1!44), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A1!41, F1!44), A1!41)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!44, tptp_fun_X_4(B!39, A1!41, F1!44), Y)))))))) | (~((~maps(F1!44, A1!41, B!39)) | (~((~![X: $i] : ((~member(X, A1!41)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!44), B!39)) | (~apply(F1!44, X, tptp_fun_Y_3(X, B!39, F1!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2))))))))) | ((~maps(F1!44, A1!41, B!39)) | (~((~![X: $i] : ((~member(X, A1!41)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!44), B!39)) | (~apply(F1!44, X, tptp_fun_Y_3(X, B!39, F1!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2)))))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(137,plain,
% 0.19/0.50 ((~maps(F1!44, A1!41, B!39)) | (~((~![X: $i] : ((~member(X, A1!41)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!44), B!39)) | (~apply(F1!44, X, tptp_fun_Y_3(X, B!39, F1!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.19/0.50 tff(138,plain,
% 0.19/0.50 (maps(F1!44, A1!41, B!39)),
% 0.19/0.50 inference(and_elim,[status(thm)],[86])).
% 0.19/0.50 tff(139,plain,
% 0.19/0.50 ((~((~maps(F1!44, A1!41, B!39)) | (~((~![X: $i] : ((~member(X, A1!41)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!44), B!39)) | (~apply(F1!44, X, tptp_fun_Y_3(X, B!39, F1!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2)))))))) | (~maps(F1!44, A1!41, B!39)) | (~((~![X: $i] : ((~member(X, A1!41)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!44), B!39)) | (~apply(F1!44, X, tptp_fun_Y_3(X, B!39, F1!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2))))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(140,plain,
% 0.19/0.50 ((~((~maps(F1!44, A1!41, B!39)) | (~((~![X: $i] : ((~member(X, A1!41)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!44), B!39)) | (~apply(F1!44, X, tptp_fun_Y_3(X, B!39, F1!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2)))))))) | (~((~![X: $i] : ((~member(X, A1!41)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!44), B!39)) | (~apply(F1!44, X, tptp_fun_Y_3(X, B!39, F1!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.19/0.50 tff(141,plain,
% 0.19/0.50 (~((~![X: $i] : ((~member(X, A1!41)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!44), B!39)) | (~apply(F1!44, X, tptp_fun_Y_3(X, B!39, F1!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2)))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[140, 137])).
% 0.19/0.50 tff(142,plain,
% 0.19/0.50 (((~![X: $i] : ((~member(X, A1!41)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!44), B!39)) | (~apply(F1!44, X, tptp_fun_Y_3(X, B!39, F1!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2))))) | ![X: $i] : ((~member(X, A1!41)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!44), B!39)) | (~apply(F1!44, X, tptp_fun_Y_3(X, B!39, F1!44))))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(143,plain,
% 0.19/0.50 (![X: $i] : ((~member(X, A1!41)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!44), B!39)) | (~apply(F1!44, X, tptp_fun_Y_3(X, B!39, F1!44))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[142, 141])).
% 0.19/0.50 tff(144,plain,
% 0.19/0.50 (((~![X: $i] : ((~member(X, A1!41)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!44), B!39)) | (~apply(F1!44, X, tptp_fun_Y_3(X, B!39, F1!44))))))) | ((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))))))) <=> ((~![X: $i] : ((~member(X, A1!41)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!44), B!39)) | (~apply(F1!44, X, tptp_fun_Y_3(X, B!39, F1!44))))))) | (~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(145,plain,
% 0.19/0.50 ((~![X: $i] : ((~member(X, A1!41)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!44), B!39)) | (~apply(F1!44, X, tptp_fun_Y_3(X, B!39, F1!44))))))) | ((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(146,plain,
% 0.19/0.50 ((~![X: $i] : ((~member(X, A1!41)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!44), B!39)) | (~apply(F1!44, X, tptp_fun_Y_3(X, B!39, F1!44))))))) | (~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.19/0.50 tff(147,plain,
% 0.19/0.50 (~((~member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[146, 143, 128])).
% 0.19/0.50 tff(148,plain,
% 0.19/0.50 (((~member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)))) | member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(149,plain,
% 0.19/0.50 (member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.19/0.50 tff(150,plain,
% 0.19/0.50 (((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | ((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)) <=> ((~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))))))))) <=> ((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | (~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)) <=> ((~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(151,plain,
% 0.19/0.51 ((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | ((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)) <=> ((~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))))))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(152,plain,
% 0.19/0.51 ((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | (~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)) <=> ((~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.19/0.51 tff(153,plain,
% 0.19/0.51 (apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)) <=> ((~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[152, 106, 54, 149])).
% 0.19/0.51 tff(154,plain,
% 0.19/0.51 (((~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y)))) | ((~member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))))) <=> ((~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y)))) | (~member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(155,plain,
% 0.19/0.51 ((~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y)))) | ((~member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(156,plain,
% 0.19/0.51 ((~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y)))) | (~member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.19/0.51 tff(157,plain,
% 0.19/0.51 (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[156, 59, 149])).
% 0.19/0.51 tff(158,plain,
% 0.19/0.51 (((~member(tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)))) | apply(F1!44, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(159,plain,
% 0.19/0.51 (apply(F1!44, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[158, 147])).
% 0.19/0.51 tff(160,plain,
% 0.19/0.51 ((~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))))) | (~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(161,plain,
% 0.19/0.51 (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[160, 128, 159])).
% 0.19/0.51 tff(162,plain,
% 0.19/0.51 (((~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)))))) | ((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(163,plain,
% 0.19/0.51 ((~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[162, 161])).
% 0.19/0.51 tff(164,plain,
% 0.19/0.51 ((~(apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)) <=> ((~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)))))))) | apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)) | (~((~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)))))))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(165,plain,
% 0.19/0.51 ((~(apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)) <=> ((~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)))))))) | apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.19/0.51 tff(166,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[165, 157, 153])).
% 0.19/0.51 tff(167,plain,((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51 tff(168,plain,
% 0.19/0.51 ((~(maps(F!42, union(A1!41, A2!40), B!39) | (~((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y)))))))) | maps(F!42, union(A1!41, A2!40), B!39) | (~((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y))))))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(169,plain,
% 0.19/0.51 ((~(maps(F!42, union(A1!41, A2!40), B!39) | (~((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y)))))))) | maps(F!42, union(A1!41, A2!40), B!39) | (~((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[168, 167])).
% 0.19/0.52 tff(170,plain,
% 0.19/0.52 (~((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[169, 34, 33])).
% 0.19/0.52 tff(171,plain,
% 0.19/0.52 (((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39))) | member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(172,plain,
% 0.19/0.52 (member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.19/0.52 tff(173,plain,
% 0.19/0.52 (((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39))) | member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(174,plain,
% 0.19/0.52 (member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[173, 170])).
% 0.19/0.52 tff(175,plain,
% 0.19/0.52 (((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | ((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42)) <=> ((~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))))))))) <=> ((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42)) <=> ((~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(176,plain,
% 0.19/0.52 ((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | ((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42)) <=> ((~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))))))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(177,plain,
% 0.19/0.52 ((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42)) <=> ((~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42)))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.19/0.52 tff(178,plain,
% 0.19/0.52 (apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42)) <=> ((~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[177, 106, 174, 172])).
% 0.19/0.52 tff(179,plain,
% 0.19/0.52 (((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39))) | apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(180,plain,
% 0.19/0.52 (apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[179, 170])).
% 0.19/0.52 tff(181,plain,
% 0.19/0.52 ((~(apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42)) <=> ((~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42)))))))) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | ((~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))))))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(182,plain,
% 0.19/0.52 ((~(apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42)) <=> ((~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42)))))))) | ((~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[181, 180])).
% 0.19/0.52 tff(183,plain,
% 0.19/0.52 ((~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42)))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[182, 178])).
% 0.19/0.52 tff(184,plain,
% 0.19/0.52 (((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39))) | (~(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(185,plain,
% 0.19/0.52 (~(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[184, 170])).
% 0.19/0.52 tff(186,plain,
% 0.19/0.52 ((maps(F!42, union(A1!41, A2!40), B!39) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F2!43, X, Y2)))) <=> (maps(F!42, union(A1!41, A2!40), B!39) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F2!43, X, Y2))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(187,plain,
% 0.19/0.52 ((maps(F!42, union(A1!41, A2!40), B!39) | ![X: $i, Y1: $i, Y2: $i] : ((~(member(X, A1!41) & member(X, A2!40) & member(Y1, B!39) & member(Y2, B!39) & apply(F1!44, X, Y1) & apply(F2!43, X, Y2))) | (Y1 = Y2))) <=> (maps(F!42, union(A1!41, A2!40), B!39) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F2!43, X, Y2))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(188,plain,
% 0.19/0.52 (maps(F!42, union(A1!41, A2!40), B!39) | ![X: $i, Y1: $i, Y2: $i] : ((~(member(X, A1!41) & member(X, A2!40) & member(Y1, B!39) & member(Y2, B!39) & apply(F1!44, X, Y1) & apply(F2!43, X, Y2))) | (Y1 = Y2))),
% 0.19/0.52 inference(and_elim,[status(thm)],[86])).
% 0.19/0.52 tff(189,plain,
% 0.19/0.52 (maps(F!42, union(A1!41, A2!40), B!39) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F2!43, X, Y2)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.19/0.52 tff(190,plain,
% 0.19/0.52 (maps(F!42, union(A1!41, A2!40), B!39) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F2!43, X, Y2)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[189, 186])).
% 0.19/0.52 tff(191,plain,
% 0.19/0.52 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F2!43, X, Y2)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[190, 34])).
% 0.19/0.52 tff(192,plain,
% 0.19/0.52 (((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39))) | member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(193,plain,
% 0.19/0.52 (member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[192, 170])).
% 0.19/0.52 tff(194,plain,
% 0.19/0.52 (((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | ((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) <=> ((~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))))))) <=> ((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) <=> ((~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(195,plain,
% 0.19/0.52 (((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) <=> ((~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)))))))) <=> ((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) <=> ((~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(196,plain,
% 0.19/0.53 (((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | ((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) <=> ((~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))))))) <=> ((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | ((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) <=> ((~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)))))))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[195])).
% 0.19/0.53 tff(197,plain,
% 0.19/0.53 (((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | ((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) <=> ((~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))))))) <=> ((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) <=> ((~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))))))),
% 0.19/0.53 inference(transitivity,[status(thm)],[196, 194])).
% 0.19/0.53 tff(198,plain,
% 0.19/0.53 ((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | ((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) <=> ((~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(199,plain,
% 0.19/0.53 ((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) <=> ((~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)))))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.19/0.53 tff(200,plain,
% 0.19/0.53 (apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) <=> ((~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[199, 106, 174, 193])).
% 0.19/0.53 tff(201,plain,
% 0.19/0.53 (((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39))) | apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(202,plain,
% 0.19/0.53 (apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[201, 170])).
% 0.19/0.53 tff(203,plain,
% 0.19/0.53 ((~(apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) <=> ((~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)))))))) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | ((~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(204,plain,
% 0.19/0.53 ((~(apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) <=> ((~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)))))))) | ((~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[203, 202])).
% 0.19/0.53 tff(205,plain,
% 0.19/0.53 ((~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[204, 200])).
% 0.19/0.53 tff(206,assumption,(~(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))), introduced(assumption)).
% 0.19/0.53 tff(207,assumption,(~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))))), introduced(assumption)).
% 0.19/0.53 tff(208,plain,
% 0.19/0.53 (((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42)))) | member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(209,plain,
% 0.19/0.53 (member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[208, 207])).
% 0.19/0.53 tff(210,plain,
% 0.19/0.53 (((~![X: $i] : ((~member(X, A1!41)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!44), B!39)) | (~apply(F1!44, X, tptp_fun_Y_3(X, B!39, F1!44))))))) | ((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))))))) <=> ((~![X: $i] : ((~member(X, A1!41)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!44), B!39)) | (~apply(F1!44, X, tptp_fun_Y_3(X, B!39, F1!44))))))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(211,plain,
% 0.19/0.53 ((~![X: $i] : ((~member(X, A1!41)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!44), B!39)) | (~apply(F1!44, X, tptp_fun_Y_3(X, B!39, F1!44))))))) | ((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(212,plain,
% 0.19/0.53 ((~![X: $i] : ((~member(X, A1!41)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!44), B!39)) | (~apply(F1!44, X, tptp_fun_Y_3(X, B!39, F1!44))))))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.19/0.54 tff(213,plain,
% 0.19/0.54 (~((~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[212, 143, 209])).
% 0.19/0.54 tff(214,plain,
% 0.19/0.54 (((~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)))) | apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(215,plain,
% 0.19/0.54 (apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[214, 213])).
% 0.19/0.54 tff(216,plain,
% 0.19/0.54 (((~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)))) | member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(217,plain,
% 0.19/0.54 (member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[216, 213])).
% 0.19/0.54 tff(218,plain,
% 0.19/0.54 (((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42)))) | apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(219,plain,
% 0.19/0.54 (apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[218, 207])).
% 0.19/0.54 tff(220,assumption,(member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)), introduced(assumption)).
% 0.19/0.54 tff(221,plain,
% 0.19/0.54 (((~![X: $i] : ((~member(X, A1!41)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!44), B!39)) | (~apply(F1!44, X, tptp_fun_Y_3(X, B!39, F1!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2)))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(222,plain,
% 0.19/0.54 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2)))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[221, 141])).
% 0.19/0.54 tff(223,plain,
% 0.19/0.54 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2)))) | ((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))) | (tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2)))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))) | (tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(224,plain,
% 0.19/0.54 (((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)))) <=> ((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))) | (tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(225,plain,
% 0.19/0.54 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2)))) | ((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2)))) | ((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))) | (tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[224])).
% 0.19/0.54 tff(226,plain,
% 0.19/0.54 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2)))) | ((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2)))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))) | (tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)))),
% 0.19/0.54 inference(transitivity,[status(thm)],[225, 223])).
% 0.19/0.54 tff(227,plain,
% 0.19/0.54 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2)))) | ((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(228,plain,
% 0.19/0.54 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2)))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))) | (tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.19/0.54 tff(229,plain,
% 0.19/0.54 (tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[228, 222, 220, 209, 219, 217, 215])).
% 0.19/0.54 tff(230,assumption,(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)), introduced(assumption)).
% 0.19/0.54 tff(231,assumption,(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)), introduced(assumption)).
% 0.19/0.54 tff(232,plain,
% 0.19/0.54 (tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)),
% 0.19/0.54 inference(transitivity,[status(thm)],[231, 230])).
% 0.19/0.54 tff(233,plain,
% 0.19/0.54 ($false),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[206, 232])).
% 0.19/0.54 tff(234,plain,((~(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.54 tff(235,plain,
% 0.19/0.54 (~(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[234, 229, 206])).
% 0.19/0.54 tff(236,assumption,((~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)))))), introduced(assumption)).
% 0.19/0.54 tff(237,assumption,(![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F2!43, X, Y2)))), introduced(assumption)).
% 0.19/0.54 tff(238,assumption,(member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)), introduced(assumption)).
% 0.19/0.54 tff(239,assumption,(~(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))), introduced(assumption)).
% 0.19/0.54 tff(240,assumption,(member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)), introduced(assumption)).
% 0.19/0.54 tff(241,plain,
% 0.19/0.54 (~((~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[212, 143, 240])).
% 0.19/0.54 tff(242,plain,
% 0.19/0.54 (apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[214, 241])).
% 0.19/0.54 tff(243,plain,
% 0.19/0.54 (member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[216, 241])).
% 0.19/0.54 tff(244,assumption,(~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))), introduced(assumption)).
% 0.19/0.54 tff(245,plain,
% 0.19/0.54 (((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)))) | apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(246,plain,
% 0.19/0.54 (apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[245, 244])).
% 0.19/0.54 tff(247,plain,
% 0.19/0.54 (((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)))) | member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(248,plain,
% 0.19/0.54 (member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[247, 244])).
% 0.19/0.54 tff(249,plain,
% 0.19/0.54 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F2!43, X, Y2)))) | ((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))) | (tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F2!43, X, Y2)))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))) | (tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(250,plain,
% 0.19/0.55 (((tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)))) <=> ((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))) | (tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(251,plain,
% 0.19/0.55 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F2!43, X, Y2)))) | ((tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F2!43, X, Y2)))) | ((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))) | (tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[250])).
% 0.19/0.55 tff(252,plain,
% 0.19/0.55 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F2!43, X, Y2)))) | ((tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F2!43, X, Y2)))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))) | (tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)))),
% 0.19/0.55 inference(transitivity,[status(thm)],[251, 249])).
% 0.19/0.55 tff(253,plain,
% 0.19/0.55 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F2!43, X, Y2)))) | ((tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(254,plain,
% 0.19/0.55 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F2!43, X, Y2)))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))) | (tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[253, 252])).
% 0.19/0.55 tff(255,plain,
% 0.19/0.55 ($false),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[254, 237, 238, 248, 240, 246, 243, 242, 239])).
% 0.19/0.55 tff(256,plain,(((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F2!43, X, Y2)))) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.55 tff(257,plain,
% 0.19/0.55 ((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[256, 209, 238, 237, 235])).
% 0.19/0.55 tff(258,plain,
% 0.19/0.55 ((~((~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)))))),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(259,plain,
% 0.19/0.55 (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[258, 257, 236])).
% 0.19/0.55 tff(260,plain,
% 0.19/0.55 (((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)))) | apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(261,plain,
% 0.19/0.55 (apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[260, 259])).
% 0.19/0.55 tff(262,plain,
% 0.19/0.55 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2)))) | ((~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))) | (tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2)))) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))) | (tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(263,plain,
% 0.19/0.55 (((tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)))) <=> ((~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))) | (tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(264,plain,
% 0.19/0.56 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2)))) | ((tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2)))) | ((~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))) | (tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[263])).
% 0.19/0.56 tff(265,plain,
% 0.19/0.56 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2)))) | ((tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2)))) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))) | (tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)))),
% 0.19/0.56 inference(transitivity,[status(thm)],[264, 262])).
% 0.19/0.56 tff(266,plain,
% 0.19/0.56 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2)))) | ((tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(267,plain,
% 0.19/0.56 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F1!44, X, Y2)))) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44))) | (tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F1!44) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.19/0.56 tff(268,plain,
% 0.19/0.56 ($false),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[267, 222, 238, 209, 261, 217, 215, 235])).
% 0.19/0.56 tff(269,plain,(((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42)))) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~((~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F2!43, X, Y2)))) | (tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.56 tff(270,plain,
% 0.19/0.56 ((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42)))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[269, 193, 205, 191, 185, 172])).
% 0.19/0.56 tff(271,plain,
% 0.19/0.56 ((~((~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))))) | (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42)))))),
% 0.19/0.56 inference(tautology,[status(thm)],[])).
% 0.19/0.56 tff(272,plain,
% 0.19/0.56 (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[271, 270, 183])).
% 0.19/0.56 tff(273,plain,
% 0.19/0.56 (((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42)))) | member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)),
% 0.19/0.56 inference(tautology,[status(thm)],[])).
% 0.19/0.56 tff(274,plain,
% 0.19/0.56 (member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[273, 272])).
% 0.19/0.56 tff(275,plain,
% 0.19/0.56 (((~![X: $i] : ((~member(X, A2!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!43), B!39)) | (~apply(F2!43, X, tptp_fun_Y_3(X, B!39, F2!43))))))) | ((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))))) <=> ((~![X: $i] : ((~member(X, A2!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!43), B!39)) | (~apply(F2!43, X, tptp_fun_Y_3(X, B!39, F2!43))))))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(276,plain,
% 0.19/0.56 ((~![X: $i] : ((~member(X, A2!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!43), B!39)) | (~apply(F2!43, X, tptp_fun_Y_3(X, B!39, F2!43))))))) | ((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(277,plain,
% 0.19/0.56 ((~![X: $i] : ((~member(X, A2!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!43), B!39)) | (~apply(F2!43, X, tptp_fun_Y_3(X, B!39, F2!43))))))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[276, 275])).
% 0.19/0.56 tff(278,plain,
% 0.19/0.56 (~((~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[277, 92, 274])).
% 0.19/0.56 tff(279,plain,
% 0.19/0.56 (((~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)))) | apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))),
% 0.19/0.56 inference(tautology,[status(thm)],[])).
% 0.19/0.56 tff(280,plain,
% 0.19/0.56 (apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[279, 278])).
% 0.19/0.56 tff(281,plain,
% 0.19/0.56 (((~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)))) | member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)),
% 0.19/0.56 inference(tautology,[status(thm)],[])).
% 0.19/0.56 tff(282,plain,
% 0.19/0.56 (member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[281, 278])).
% 0.19/0.56 tff(283,plain,
% 0.19/0.56 (((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42)))) | apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))),
% 0.19/0.56 inference(tautology,[status(thm)],[])).
% 0.19/0.56 tff(284,plain,
% 0.19/0.56 (apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[283, 272])).
% 0.19/0.56 tff(285,plain,
% 0.19/0.56 (((~![X: $i] : ((~member(X, A2!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!43), B!39)) | (~apply(F2!43, X, tptp_fun_Y_3(X, B!39, F2!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1)))),
% 0.19/0.56 inference(tautology,[status(thm)],[])).
% 0.19/0.56 tff(286,plain,
% 0.19/0.56 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1)))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[285, 90])).
% 0.19/0.56 tff(287,plain,
% 0.19/0.56 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1)))) | ((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1)))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(288,plain,
% 0.19/0.56 (((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42)))) <=> ((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(289,plain,
% 0.19/0.56 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1)))) | ((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1)))) | ((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)))))),
% 0.19/0.57 inference(monotonicity,[status(thm)],[288])).
% 0.19/0.57 tff(290,plain,
% 0.19/0.57 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1)))) | ((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1)))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))),
% 0.19/0.57 inference(transitivity,[status(thm)],[289, 287])).
% 0.19/0.57 tff(291,plain,
% 0.19/0.57 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1)))) | ((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(292,plain,
% 0.19/0.57 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1)))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.19/0.57 tff(293,plain,
% 0.19/0.57 (tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[292, 286, 172, 274, 284, 282, 280])).
% 0.19/0.57 tff(294,assumption,(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)), introduced(assumption)).
% 0.19/0.57 tff(295,assumption,(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)), introduced(assumption)).
% 0.19/0.57 tff(296,plain,
% 0.19/0.57 (tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)),
% 0.19/0.57 inference(transitivity,[status(thm)],[295, 294])).
% 0.19/0.57 tff(297,plain,
% 0.19/0.57 ($false),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[206, 296])).
% 0.19/0.57 tff(298,plain,((~(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.57 tff(299,plain,
% 0.19/0.57 (~(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[298, 185, 293])).
% 0.19/0.57 tff(300,assumption,(~(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))), introduced(assumption)).
% 0.19/0.57 tff(301,assumption,(member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)), introduced(assumption)).
% 0.19/0.57 tff(302,plain,
% 0.19/0.57 (~((~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[277, 92, 301])).
% 0.19/0.57 tff(303,plain,
% 0.19/0.57 (apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[279, 302])).
% 0.19/0.57 tff(304,plain,
% 0.19/0.57 (member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[281, 302])).
% 0.19/0.57 tff(305,assumption,(apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))), introduced(assumption)).
% 0.19/0.57 tff(306,plain,
% 0.19/0.57 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1)))) | ((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))) | (tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1)))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))) | (tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(307,plain,
% 0.19/0.57 (((tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)))) <=> ((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))) | (tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(308,plain,
% 0.19/0.57 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1)))) | ((tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1)))) | ((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))) | (tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))),
% 0.19/0.57 inference(monotonicity,[status(thm)],[307])).
% 0.19/0.57 tff(309,plain,
% 0.19/0.57 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1)))) | ((tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1)))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))) | (tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)))),
% 0.19/0.58 inference(transitivity,[status(thm)],[308, 306])).
% 0.19/0.58 tff(310,plain,
% 0.19/0.58 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1)))) | ((tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(311,plain,
% 0.19/0.58 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F2!43, X, Y2)) | (~apply(F2!43, X, Y1)))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))) | (tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.19/0.58 tff(312,plain,
% 0.19/0.58 ($false),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[311, 286, 238, 301, 305, 304, 303, 300])).
% 0.19/0.58 tff(313,plain,((~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.58 tff(314,plain,
% 0.19/0.58 (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[313, 193, 274, 299])).
% 0.19/0.58 tff(315,plain,
% 0.19/0.58 ((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[245, 314])).
% 0.19/0.58 tff(316,plain,
% 0.19/0.58 (~((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[258, 315, 205])).
% 0.19/0.58 tff(317,plain,
% 0.19/0.58 (apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[260, 316])).
% 0.19/0.58 tff(318,plain,
% 0.19/0.58 (((~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)))) | member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)),
% 0.19/0.58 inference(tautology,[status(thm)],[])).
% 0.19/0.58 tff(319,plain,
% 0.19/0.58 (member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[318, 316])).
% 0.19/0.58 tff(320,plain,
% 0.19/0.58 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F2!43, X, Y2)))) | ((~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))) | (tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F2!43, X, Y2)))) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))) | (tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(321,plain,
% 0.19/0.58 (((tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)))) <=> ((~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))) | (tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(322,plain,
% 0.19/0.58 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F2!43, X, Y2)))) | ((tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F2!43, X, Y2)))) | ((~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))) | (tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))),
% 0.44/0.58 inference(monotonicity,[status(thm)],[321])).
% 0.44/0.58 tff(323,plain,
% 0.44/0.58 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F2!43, X, Y2)))) | ((tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F2!43, X, Y2)))) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))) | (tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)))),
% 0.44/0.58 inference(transitivity,[status(thm)],[322, 320])).
% 0.44/0.58 tff(324,plain,
% 0.44/0.58 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F2!43, X, Y2)))) | ((tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))))),
% 0.44/0.58 inference(quant_inst,[status(thm)],[])).
% 0.44/0.58 tff(325,plain,
% 0.44/0.58 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A1!41)) | (~member(X, A2!40)) | (~member(Y1, B!39)) | (~apply(F1!44, X, Y1)) | (~apply(F2!43, X, Y2)))) | (~apply(F1!44, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A1!41)) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), A2!40)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43), B!39)) | (~apply(F2!43, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))) | (tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43))),
% 0.44/0.58 inference(modus_ponens,[status(thm)],[324, 323])).
% 0.44/0.58 tff(326,plain,
% 0.44/0.58 (tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43)),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[325, 191, 193, 274, 319, 317, 282, 280])).
% 0.44/0.58 tff(327,plain,
% 0.44/0.58 (tptp_fun_Y_3(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), B!39, F2!43) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)),
% 0.44/0.58 inference(symmetry,[status(thm)],[326])).
% 0.44/0.58 tff(328,plain,
% 0.44/0.58 (tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)),
% 0.44/0.58 inference(transitivity,[status(thm)],[293, 327])).
% 0.44/0.58 tff(329,plain,
% 0.44/0.58 ($false),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[185, 328])).
% 0.44/0.58 tff(330,plain,(maps(F!42, union(A1!41, A2!40), B!39)), inference(lemma,lemma(discharge,[]))).
% 0.44/0.58 tff(331,plain,
% 0.44/0.58 (((~maps(F!42, union(A1!41, A2!40), B!39)) | (~((~(member(X!47, A1!41) & member(X!47, A2!40) & member(Y1!46, B!39) & member(Y2!45, B!39) & apply(F1!44, X!47, Y1!46) & apply(F2!43, X!47, Y2!45))) | (Y1!46 = Y2!45)))) <=> ((~maps(F!42, union(A1!41, A2!40), B!39)) | (~((Y1!46 = Y2!45) | (~member(X!47, A1!41)) | (~member(X!47, A2!40)) | (~member(Y1!46, B!39)) | (~member(Y2!45, B!39)) | (~apply(F1!44, X!47, Y1!46)) | (~apply(F2!43, X!47, Y2!45)))))),
% 0.44/0.58 inference(rewrite,[status(thm)],[])).
% 0.44/0.58 tff(332,plain,
% 0.44/0.58 ((~maps(F!42, union(A1!41, A2!40), B!39)) | (~((~(member(X!47, A1!41) & member(X!47, A2!40) & member(Y1!46, B!39) & member(Y2!45, B!39) & apply(F1!44, X!47, Y1!46) & apply(F2!43, X!47, Y2!45))) | (Y1!46 = Y2!45)))),
% 0.44/0.58 inference(and_elim,[status(thm)],[86])).
% 0.44/0.58 tff(333,plain,
% 0.44/0.58 ((~maps(F!42, union(A1!41, A2!40), B!39)) | (~((Y1!46 = Y2!45) | (~member(X!47, A1!41)) | (~member(X!47, A2!40)) | (~member(Y1!46, B!39)) | (~member(Y2!45, B!39)) | (~apply(F1!44, X!47, Y1!46)) | (~apply(F2!43, X!47, Y2!45))))),
% 0.44/0.58 inference(modus_ponens,[status(thm)],[332, 331])).
% 0.44/0.58 tff(334,plain,
% 0.44/0.58 (~((Y1!46 = Y2!45) | (~member(X!47, A1!41)) | (~member(X!47, A2!40)) | (~member(Y1!46, B!39)) | (~member(Y2!45, B!39)) | (~apply(F1!44, X!47, Y1!46)) | (~apply(F2!43, X!47, Y2!45)))),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[333, 330])).
% 0.44/0.58 tff(335,plain,
% 0.44/0.58 (((Y1!46 = Y2!45) | (~member(X!47, A1!41)) | (~member(X!47, A2!40)) | (~member(Y1!46, B!39)) | (~member(Y2!45, B!39)) | (~apply(F1!44, X!47, Y1!46)) | (~apply(F2!43, X!47, Y2!45))) | member(X!47, A1!41)),
% 0.44/0.58 inference(tautology,[status(thm)],[])).
% 0.44/0.58 tff(336,plain,
% 0.44/0.58 (member(X!47, A1!41)),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[335, 334])).
% 0.44/0.58 tff(337,plain,
% 0.44/0.58 ((member(X!47, A1!41) | member(X!47, A2!40)) | (~member(X!47, A1!41))),
% 0.44/0.58 inference(tautology,[status(thm)],[])).
% 0.44/0.58 tff(338,plain,
% 0.44/0.58 (member(X!47, A1!41) | member(X!47, A2!40)),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[337, 336])).
% 0.44/0.58 tff(339,assumption,(~(member(X!47, union(A1!41, A2!40)) <=> (member(X!47, A1!41) | member(X!47, A2!40)))), introduced(assumption)).
% 0.44/0.58 tff(340,plain,
% 0.44/0.58 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(X!47, union(A1!41, A2!40)) <=> (member(X!47, A1!41) | member(X!47, A2!40)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(X!47, union(A1!41, A2!40)) <=> (member(X!47, A1!41) | member(X!47, A2!40))))),
% 0.44/0.59 inference(rewrite,[status(thm)],[])).
% 0.44/0.59 tff(341,plain,
% 0.44/0.59 ((member(X!47, union(A1!41, A2!40)) <=> (member(X!47, A2!40) | member(X!47, A1!41))) <=> (member(X!47, union(A1!41, A2!40)) <=> (member(X!47, A1!41) | member(X!47, A2!40)))),
% 0.44/0.59 inference(rewrite,[status(thm)],[])).
% 0.44/0.59 tff(342,plain,
% 0.44/0.59 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(X!47, union(A1!41, A2!40)) <=> (member(X!47, A2!40) | member(X!47, A1!41)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(X!47, union(A1!41, A2!40)) <=> (member(X!47, A1!41) | member(X!47, A2!40))))),
% 0.44/0.59 inference(monotonicity,[status(thm)],[341])).
% 0.44/0.59 tff(343,plain,
% 0.44/0.59 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(X!47, union(A1!41, A2!40)) <=> (member(X!47, A2!40) | member(X!47, A1!41)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(X!47, union(A1!41, A2!40)) <=> (member(X!47, A1!41) | member(X!47, A2!40))))),
% 0.44/0.59 inference(transitivity,[status(thm)],[342, 340])).
% 0.44/0.59 tff(344,plain,
% 0.44/0.59 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(X!47, union(A1!41, A2!40)) <=> (member(X!47, A2!40) | member(X!47, A1!41)))),
% 0.44/0.59 inference(quant_inst,[status(thm)],[])).
% 0.44/0.59 tff(345,plain,
% 0.44/0.59 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(X!47, union(A1!41, A2!40)) <=> (member(X!47, A1!41) | member(X!47, A2!40)))),
% 0.44/0.59 inference(modus_ponens,[status(thm)],[344, 343])).
% 0.44/0.59 tff(346,plain,
% 0.44/0.59 ($false),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[345, 44, 339])).
% 0.44/0.59 tff(347,plain,(member(X!47, union(A1!41, A2!40)) <=> (member(X!47, A1!41) | member(X!47, A2!40))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.59 tff(348,plain,
% 0.44/0.59 ((~(member(X!47, union(A1!41, A2!40)) <=> (member(X!47, A1!41) | member(X!47, A2!40)))) | member(X!47, union(A1!41, A2!40)) | (~(member(X!47, A1!41) | member(X!47, A2!40)))),
% 0.44/0.59 inference(tautology,[status(thm)],[])).
% 0.44/0.59 tff(349,plain,
% 0.44/0.59 (member(X!47, union(A1!41, A2!40)) | (~(member(X!47, A1!41) | member(X!47, A2!40)))),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[348, 347])).
% 0.44/0.59 tff(350,plain,
% 0.44/0.59 (member(X!47, union(A1!41, A2!40))),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[349, 338])).
% 0.44/0.59 tff(351,plain,
% 0.44/0.59 (((Y1!46 = Y2!45) | (~member(X!47, A1!41)) | (~member(X!47, A2!40)) | (~member(Y1!46, B!39)) | (~member(Y2!45, B!39)) | (~apply(F1!44, X!47, Y1!46)) | (~apply(F2!43, X!47, Y2!45))) | member(Y1!46, B!39)),
% 0.44/0.59 inference(tautology,[status(thm)],[])).
% 0.44/0.59 tff(352,plain,
% 0.44/0.59 (member(Y1!46, B!39)),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[351, 334])).
% 0.44/0.59 tff(353,plain,
% 0.44/0.59 (((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | ((~member(Y1!46, B!39)) | (~member(X!47, union(A1!41, A2!40))) | (apply(F!42, X!47, Y1!46) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y1!46)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y1!46)))))))) <=> ((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | (~member(Y1!46, B!39)) | (~member(X!47, union(A1!41, A2!40))) | (apply(F!42, X!47, Y1!46) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y1!46)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y1!46)))))))),
% 0.44/0.59 inference(rewrite,[status(thm)],[])).
% 0.44/0.59 tff(354,plain,
% 0.44/0.59 (((~member(X!47, union(A1!41, A2!40))) | (~member(Y1!46, B!39)) | (apply(F!42, X!47, Y1!46) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y1!46)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y1!46))))))) <=> ((~member(Y1!46, B!39)) | (~member(X!47, union(A1!41, A2!40))) | (apply(F!42, X!47, Y1!46) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y1!46)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y1!46)))))))),
% 0.44/0.59 inference(rewrite,[status(thm)],[])).
% 0.44/0.59 tff(355,plain,
% 0.44/0.59 ((apply(F!42, X!47, Y1!46) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y1!46)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y1!46)))))) <=> (apply(F!42, X!47, Y1!46) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y1!46)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y1!46))))))),
% 0.44/0.59 inference(rewrite,[status(thm)],[])).
% 0.44/0.59 tff(356,plain,
% 0.44/0.59 (((~member(X!47, union(A1!41, A2!40))) | (~member(Y1!46, B!39)) | (apply(F!42, X!47, Y1!46) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y1!46)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y1!46))))))) <=> ((~member(X!47, union(A1!41, A2!40))) | (~member(Y1!46, B!39)) | (apply(F!42, X!47, Y1!46) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y1!46)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y1!46)))))))),
% 0.44/0.59 inference(monotonicity,[status(thm)],[355])).
% 0.44/0.59 tff(357,plain,
% 0.44/0.59 (((~member(X!47, union(A1!41, A2!40))) | (~member(Y1!46, B!39)) | (apply(F!42, X!47, Y1!46) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y1!46)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y1!46))))))) <=> ((~member(Y1!46, B!39)) | (~member(X!47, union(A1!41, A2!40))) | (apply(F!42, X!47, Y1!46) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y1!46)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y1!46)))))))),
% 0.44/0.59 inference(transitivity,[status(thm)],[356, 354])).
% 0.44/0.59 tff(358,plain,
% 0.44/0.59 (((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | ((~member(X!47, union(A1!41, A2!40))) | (~member(Y1!46, B!39)) | (apply(F!42, X!47, Y1!46) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y1!46)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y1!46)))))))) <=> ((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | ((~member(Y1!46, B!39)) | (~member(X!47, union(A1!41, A2!40))) | (apply(F!42, X!47, Y1!46) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y1!46)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y1!46))))))))),
% 0.44/0.59 inference(monotonicity,[status(thm)],[357])).
% 0.44/0.59 tff(359,plain,
% 0.44/0.59 (((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | ((~member(X!47, union(A1!41, A2!40))) | (~member(Y1!46, B!39)) | (apply(F!42, X!47, Y1!46) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y1!46)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y1!46)))))))) <=> ((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | (~member(Y1!46, B!39)) | (~member(X!47, union(A1!41, A2!40))) | (apply(F!42, X!47, Y1!46) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y1!46)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y1!46)))))))),
% 0.44/0.59 inference(transitivity,[status(thm)],[358, 353])).
% 0.44/0.59 tff(360,plain,
% 0.44/0.59 ((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | ((~member(X!47, union(A1!41, A2!40))) | (~member(Y1!46, B!39)) | (apply(F!42, X!47, Y1!46) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y1!46)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y1!46)))))))),
% 0.44/0.59 inference(quant_inst,[status(thm)],[])).
% 0.44/0.59 tff(361,plain,
% 0.44/0.59 ((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | (~member(Y1!46, B!39)) | (~member(X!47, union(A1!41, A2!40))) | (apply(F!42, X!47, Y1!46) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y1!46)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y1!46))))))),
% 0.44/0.59 inference(modus_ponens,[status(thm)],[360, 359])).
% 0.44/0.59 tff(362,plain,
% 0.44/0.59 (apply(F!42, X!47, Y1!46) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y1!46)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y1!46)))))),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[361, 106, 352, 350])).
% 0.44/0.59 tff(363,plain,
% 0.44/0.59 (((Y1!46 = Y2!45) | (~member(X!47, A1!41)) | (~member(X!47, A2!40)) | (~member(Y1!46, B!39)) | (~member(Y2!45, B!39)) | (~apply(F1!44, X!47, Y1!46)) | (~apply(F2!43, X!47, Y2!45))) | apply(F1!44, X!47, Y1!46)),
% 0.44/0.59 inference(tautology,[status(thm)],[])).
% 0.44/0.59 tff(364,plain,
% 0.44/0.59 (apply(F1!44, X!47, Y1!46)),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[363, 334])).
% 0.44/0.59 tff(365,plain,
% 0.44/0.59 ((~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y1!46)))) | (~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y1!46))),
% 0.44/0.59 inference(tautology,[status(thm)],[])).
% 0.44/0.59 tff(366,plain,
% 0.44/0.59 (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y1!46)))),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[365, 336, 364])).
% 0.44/0.59 tff(367,plain,
% 0.44/0.59 (((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y1!46)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y1!46))))) | ((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y1!46)))),
% 0.44/0.59 inference(tautology,[status(thm)],[])).
% 0.44/0.59 tff(368,plain,
% 0.44/0.59 ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y1!46)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y1!46))))),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[367, 366])).
% 0.44/0.59 tff(369,plain,
% 0.44/0.59 ((~(apply(F!42, X!47, Y1!46) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y1!46)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y1!46))))))) | apply(F!42, X!47, Y1!46) | (~((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y1!46)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y1!46))))))),
% 0.44/0.59 inference(tautology,[status(thm)],[])).
% 0.44/0.59 tff(370,plain,
% 0.44/0.59 ((~(apply(F!42, X!47, Y1!46) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y1!46)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y1!46))))))) | apply(F!42, X!47, Y1!46)),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[369, 368])).
% 0.44/0.59 tff(371,plain,
% 0.44/0.59 (apply(F!42, X!47, Y1!46)),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[370, 362])).
% 0.44/0.59 tff(372,plain,
% 0.44/0.59 (((Y1!46 = Y2!45) | (~member(X!47, A1!41)) | (~member(X!47, A2!40)) | (~member(Y1!46, B!39)) | (~member(Y2!45, B!39)) | (~apply(F1!44, X!47, Y1!46)) | (~apply(F2!43, X!47, Y2!45))) | member(Y2!45, B!39)),
% 0.44/0.59 inference(tautology,[status(thm)],[])).
% 0.44/0.59 tff(373,plain,
% 0.44/0.59 (member(Y2!45, B!39)),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[372, 334])).
% 0.44/0.59 tff(374,plain,
% 0.44/0.59 (((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | ((~member(Y2!45, B!39)) | (~member(X!47, union(A1!41, A2!40))) | (apply(F!42, X!47, Y2!45) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y2!45)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y2!45)))))))) <=> ((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | (~member(Y2!45, B!39)) | (~member(X!47, union(A1!41, A2!40))) | (apply(F!42, X!47, Y2!45) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y2!45)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y2!45)))))))),
% 0.44/0.59 inference(rewrite,[status(thm)],[])).
% 0.44/0.59 tff(375,plain,
% 0.44/0.59 (((~member(X!47, union(A1!41, A2!40))) | (~member(Y2!45, B!39)) | (apply(F!42, X!47, Y2!45) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y2!45)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y2!45))))))) <=> ((~member(Y2!45, B!39)) | (~member(X!47, union(A1!41, A2!40))) | (apply(F!42, X!47, Y2!45) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y2!45)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y2!45)))))))),
% 0.44/0.59 inference(rewrite,[status(thm)],[])).
% 0.44/0.59 tff(376,plain,
% 0.44/0.59 ((apply(F!42, X!47, Y2!45) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y2!45)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y2!45)))))) <=> (apply(F!42, X!47, Y2!45) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y2!45)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y2!45))))))),
% 0.44/0.59 inference(rewrite,[status(thm)],[])).
% 0.44/0.59 tff(377,plain,
% 0.44/0.59 (((~member(X!47, union(A1!41, A2!40))) | (~member(Y2!45, B!39)) | (apply(F!42, X!47, Y2!45) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y2!45)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y2!45))))))) <=> ((~member(X!47, union(A1!41, A2!40))) | (~member(Y2!45, B!39)) | (apply(F!42, X!47, Y2!45) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y2!45)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y2!45)))))))),
% 0.44/0.59 inference(monotonicity,[status(thm)],[376])).
% 0.44/0.59 tff(378,plain,
% 0.44/0.59 (((~member(X!47, union(A1!41, A2!40))) | (~member(Y2!45, B!39)) | (apply(F!42, X!47, Y2!45) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y2!45)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y2!45))))))) <=> ((~member(Y2!45, B!39)) | (~member(X!47, union(A1!41, A2!40))) | (apply(F!42, X!47, Y2!45) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y2!45)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y2!45)))))))),
% 0.44/0.59 inference(transitivity,[status(thm)],[377, 375])).
% 0.44/0.59 tff(379,plain,
% 0.44/0.59 (((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | ((~member(X!47, union(A1!41, A2!40))) | (~member(Y2!45, B!39)) | (apply(F!42, X!47, Y2!45) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y2!45)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y2!45)))))))) <=> ((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | ((~member(Y2!45, B!39)) | (~member(X!47, union(A1!41, A2!40))) | (apply(F!42, X!47, Y2!45) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y2!45)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y2!45))))))))),
% 0.44/0.59 inference(monotonicity,[status(thm)],[378])).
% 0.44/0.59 tff(380,plain,
% 0.44/0.59 (((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | ((~member(X!47, union(A1!41, A2!40))) | (~member(Y2!45, B!39)) | (apply(F!42, X!47, Y2!45) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y2!45)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y2!45)))))))) <=> ((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | (~member(Y2!45, B!39)) | (~member(X!47, union(A1!41, A2!40))) | (apply(F!42, X!47, Y2!45) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y2!45)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y2!45)))))))),
% 0.44/0.59 inference(transitivity,[status(thm)],[379, 374])).
% 0.44/0.59 tff(381,plain,
% 0.44/0.59 ((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | ((~member(X!47, union(A1!41, A2!40))) | (~member(Y2!45, B!39)) | (apply(F!42, X!47, Y2!45) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y2!45)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y2!45)))))))),
% 0.44/0.59 inference(quant_inst,[status(thm)],[])).
% 0.44/0.59 tff(382,plain,
% 0.44/0.59 ((~![X: $i, Y: $i] : ((~member(X, union(A1!41, A2!40))) | (~member(Y, B!39)) | (apply(F!42, X, Y) <=> ((~((~member(X, A2!40)) | (~apply(F2!43, X, Y)))) | (~((~member(X, A1!41)) | (~apply(F1!44, X, Y)))))))) | (~member(Y2!45, B!39)) | (~member(X!47, union(A1!41, A2!40))) | (apply(F!42, X!47, Y2!45) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y2!45)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y2!45))))))),
% 0.46/0.60 inference(modus_ponens,[status(thm)],[381, 380])).
% 0.46/0.60 tff(383,plain,
% 0.46/0.60 (apply(F!42, X!47, Y2!45) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y2!45)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y2!45)))))),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[382, 106, 373, 350])).
% 0.46/0.60 tff(384,plain,
% 0.46/0.60 (((Y1!46 = Y2!45) | (~member(X!47, A1!41)) | (~member(X!47, A2!40)) | (~member(Y1!46, B!39)) | (~member(Y2!45, B!39)) | (~apply(F1!44, X!47, Y1!46)) | (~apply(F2!43, X!47, Y2!45))) | apply(F2!43, X!47, Y2!45)),
% 0.46/0.60 inference(tautology,[status(thm)],[])).
% 0.46/0.60 tff(385,plain,
% 0.46/0.60 (apply(F2!43, X!47, Y2!45)),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[384, 334])).
% 0.46/0.60 tff(386,plain,
% 0.46/0.60 (((Y1!46 = Y2!45) | (~member(X!47, A1!41)) | (~member(X!47, A2!40)) | (~member(Y1!46, B!39)) | (~member(Y2!45, B!39)) | (~apply(F1!44, X!47, Y1!46)) | (~apply(F2!43, X!47, Y2!45))) | member(X!47, A2!40)),
% 0.46/0.60 inference(tautology,[status(thm)],[])).
% 0.46/0.60 tff(387,plain,
% 0.46/0.60 (member(X!47, A2!40)),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[386, 334])).
% 0.46/0.60 tff(388,plain,
% 0.46/0.60 ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y2!45)))) | (~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y2!45))),
% 0.46/0.60 inference(tautology,[status(thm)],[])).
% 0.46/0.60 tff(389,plain,
% 0.46/0.60 (~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y2!45)))),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[388, 387, 385])).
% 0.46/0.60 tff(390,plain,
% 0.46/0.60 (((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y2!45)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y2!45))))) | ((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y2!45)))),
% 0.46/0.60 inference(tautology,[status(thm)],[])).
% 0.46/0.60 tff(391,plain,
% 0.46/0.60 ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y2!45)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y2!45))))),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[390, 389])).
% 0.46/0.60 tff(392,plain,
% 0.46/0.60 ((~(apply(F!42, X!47, Y2!45) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y2!45)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y2!45))))))) | apply(F!42, X!47, Y2!45) | (~((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y2!45)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y2!45))))))),
% 0.46/0.60 inference(tautology,[status(thm)],[])).
% 0.46/0.60 tff(393,plain,
% 0.46/0.60 ((~(apply(F!42, X!47, Y2!45) <=> ((~((~member(X!47, A2!40)) | (~apply(F2!43, X!47, Y2!45)))) | (~((~member(X!47, A1!41)) | (~apply(F1!44, X!47, Y2!45))))))) | apply(F!42, X!47, Y2!45)),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[392, 391])).
% 0.46/0.60 tff(394,plain,
% 0.46/0.60 (apply(F!42, X!47, Y2!45)),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[393, 383])).
% 0.46/0.60 tff(395,plain,
% 0.46/0.60 (((~(maps(F!42, union(A1!41, A2!40), B!39) | (~((tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42) = tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42))) | (~member(tptp_fun_X_7(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~member(tptp_fun_Y1_6(B!39, union(A1!41, A2!40), F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, union(A1!41, A2!40), F!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), union(A1!41, A2!40))) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, union(A1!41, A2!40), F!42), Y)))))))) | (~((~maps(F!42, union(A1!41, A2!40), B!39)) | (~((~![X: $i] : ((~member(X, union(A1!41, A2!40))) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(Y1, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, union(A1!41, A2!40)))))))))) | ((~maps(F!42, union(A1!41, A2!40), B!39)) | (~((~![X: $i] : ((~member(X, union(A1!41, A2!40))) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(Y1, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, union(A1!41, A2!40))))))))),
% 0.46/0.60 inference(tautology,[status(thm)],[])).
% 0.46/0.60 tff(396,plain,
% 0.46/0.60 ((~maps(F!42, union(A1!41, A2!40), B!39)) | (~((~![X: $i] : ((~member(X, union(A1!41, A2!40))) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(Y1, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, union(A1!41, A2!40)))))))),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[395, 31])).
% 0.46/0.60 tff(397,plain,
% 0.46/0.60 ((~((~maps(F!42, union(A1!41, A2!40), B!39)) | (~((~![X: $i] : ((~member(X, union(A1!41, A2!40))) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(Y1, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, union(A1!41, A2!40))))))))) | (~maps(F!42, union(A1!41, A2!40), B!39)) | (~((~![X: $i] : ((~member(X, union(A1!41, A2!40))) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(Y1, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, union(A1!41, A2!40)))))))),
% 0.46/0.60 inference(tautology,[status(thm)],[])).
% 0.46/0.60 tff(398,plain,
% 0.46/0.60 (~((~![X: $i] : ((~member(X, union(A1!41, A2!40))) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(Y1, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, union(A1!41, A2!40))))))),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[397, 330, 396])).
% 0.46/0.60 tff(399,plain,
% 0.46/0.60 (((~![X: $i] : ((~member(X, union(A1!41, A2!40))) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(Y1, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, union(A1!41, A2!40)))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(Y1, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, union(A1!41, A2!40))))),
% 0.46/0.60 inference(tautology,[status(thm)],[])).
% 0.46/0.60 tff(400,plain,
% 0.46/0.60 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(Y1, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, union(A1!41, A2!40))))),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[399, 398])).
% 0.46/0.60 tff(401,plain,
% 0.46/0.60 (((Y1!46 = Y2!45) | (~member(X!47, A1!41)) | (~member(X!47, A2!40)) | (~member(Y1!46, B!39)) | (~member(Y2!45, B!39)) | (~apply(F1!44, X!47, Y1!46)) | (~apply(F2!43, X!47, Y2!45))) | (~(Y1!46 = Y2!45))),
% 0.46/0.60 inference(tautology,[status(thm)],[])).
% 0.46/0.60 tff(402,plain,
% 0.46/0.60 (~(Y1!46 = Y2!45)),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[401, 334])).
% 0.46/0.60 tff(403,plain,
% 0.46/0.60 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(Y1, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, union(A1!41, A2!40))))) | ((Y1!46 = Y2!45) | (~member(Y1!46, B!39)) | (~member(Y2!45, B!39)) | (~member(X!47, union(A1!41, A2!40))) | (~apply(F!42, X!47, Y2!45)) | (~apply(F!42, X!47, Y1!46)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(Y1, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, union(A1!41, A2!40))))) | (Y1!46 = Y2!45) | (~member(Y1!46, B!39)) | (~member(Y2!45, B!39)) | (~member(X!47, union(A1!41, A2!40))) | (~apply(F!42, X!47, Y2!45)) | (~apply(F!42, X!47, Y1!46)))),
% 0.46/0.60 inference(rewrite,[status(thm)],[])).
% 0.46/0.60 tff(404,plain,
% 0.46/0.60 (((Y1!46 = Y2!45) | (~member(Y2!45, B!39)) | (~member(Y1!46, B!39)) | (~apply(F!42, X!47, Y1!46)) | (~apply(F!42, X!47, Y2!45)) | (~member(X!47, union(A1!41, A2!40)))) <=> ((Y1!46 = Y2!45) | (~member(Y1!46, B!39)) | (~member(Y2!45, B!39)) | (~member(X!47, union(A1!41, A2!40))) | (~apply(F!42, X!47, Y2!45)) | (~apply(F!42, X!47, Y1!46)))),
% 0.46/0.60 inference(rewrite,[status(thm)],[])).
% 0.46/0.60 tff(405,plain,
% 0.46/0.60 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(Y1, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, union(A1!41, A2!40))))) | ((Y1!46 = Y2!45) | (~member(Y2!45, B!39)) | (~member(Y1!46, B!39)) | (~apply(F!42, X!47, Y1!46)) | (~apply(F!42, X!47, Y2!45)) | (~member(X!47, union(A1!41, A2!40))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(Y1, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, union(A1!41, A2!40))))) | ((Y1!46 = Y2!45) | (~member(Y1!46, B!39)) | (~member(Y2!45, B!39)) | (~member(X!47, union(A1!41, A2!40))) | (~apply(F!42, X!47, Y2!45)) | (~apply(F!42, X!47, Y1!46))))),
% 0.46/0.60 inference(monotonicity,[status(thm)],[404])).
% 0.46/0.60 tff(406,plain,
% 0.46/0.60 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(Y1, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, union(A1!41, A2!40))))) | ((Y1!46 = Y2!45) | (~member(Y2!45, B!39)) | (~member(Y1!46, B!39)) | (~apply(F!42, X!47, Y1!46)) | (~apply(F!42, X!47, Y2!45)) | (~member(X!47, union(A1!41, A2!40))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(Y1, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, union(A1!41, A2!40))))) | (Y1!46 = Y2!45) | (~member(Y1!46, B!39)) | (~member(Y2!45, B!39)) | (~member(X!47, union(A1!41, A2!40))) | (~apply(F!42, X!47, Y2!45)) | (~apply(F!42, X!47, Y1!46)))),
% 0.46/0.60 inference(transitivity,[status(thm)],[405, 403])).
% 0.46/0.60 tff(407,plain,
% 0.46/0.60 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(Y1, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, union(A1!41, A2!40))))) | ((Y1!46 = Y2!45) | (~member(Y2!45, B!39)) | (~member(Y1!46, B!39)) | (~apply(F!42, X!47, Y1!46)) | (~apply(F!42, X!47, Y2!45)) | (~member(X!47, union(A1!41, A2!40))))),
% 0.46/0.60 inference(quant_inst,[status(thm)],[])).
% 0.46/0.60 tff(408,plain,
% 0.46/0.60 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(Y1, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, union(A1!41, A2!40))))) | (Y1!46 = Y2!45) | (~member(Y1!46, B!39)) | (~member(Y2!45, B!39)) | (~member(X!47, union(A1!41, A2!40))) | (~apply(F!42, X!47, Y2!45)) | (~apply(F!42, X!47, Y1!46))),
% 0.46/0.60 inference(modus_ponens,[status(thm)],[407, 406])).
% 0.46/0.60 tff(409,plain,
% 0.46/0.60 ($false),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[408, 402, 352, 373, 350, 400, 394, 371])).
% 0.46/0.60 % SZS output end Proof
%------------------------------------------------------------------------------