TSTP Solution File: SEU418+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU418+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 07:29:29 EDT 2022
% Result : Theorem 5.23s 3.57s
% Output : Proof 5.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SEU418+1 : TPTP v8.1.0. Released v3.4.0.
% 0.07/0.15 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.35 % Computer : n028.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sat Sep 3 13:57:38 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.36 Usage: tptp [options] [-file:]file
% 0.15/0.36 -h, -? prints this message.
% 0.15/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.36 -m, -model generate model.
% 0.15/0.36 -p, -proof generate proof.
% 0.15/0.36 -c, -core generate unsat core of named formulas.
% 0.15/0.36 -st, -statistics display statistics.
% 0.15/0.36 -t:timeout set timeout (in second).
% 0.15/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.36 -<param>:<value> configuration parameter and value.
% 0.15/0.36 -o:<output-file> file to place output in.
% 5.23/3.57 % SZS status Theorem
% 5.23/3.57 % SZS output start Proof
% 5.23/3.57 tff(r2_hidden_type, type, (
% 5.23/3.57 r2_hidden: ( $i * $i ) > $o)).
% 5.23/3.57 tff(tptp_fun_B_1_type, type, (
% 5.23/3.57 tptp_fun_B_1: $i)).
% 5.23/3.57 tff(k4_tarski_type, type, (
% 5.23/3.57 k4_tarski: ( $i * $i ) > $i)).
% 5.23/3.57 tff(tptp_fun_F_8_type, type, (
% 5.23/3.57 tptp_fun_F_8: ( $i * $i * $i * $i ) > $i)).
% 5.23/3.57 tff(k3_xboole_0_type, type, (
% 5.23/3.57 k3_xboole_0: ( $i * $i ) > $i)).
% 5.23/3.57 tff(tptp_fun_A_0_type, type, (
% 5.23/3.57 tptp_fun_A_0: $i)).
% 5.23/3.57 tff(tptp_fun_C_2_type, type, (
% 5.23/3.57 tptp_fun_C_2: $i)).
% 5.23/3.57 tff(tptp_fun_C_4_type, type, (
% 5.23/3.57 tptp_fun_C_4: $i > $i)).
% 5.23/3.57 tff(tptp_fun_C_6_type, type, (
% 5.23/3.57 tptp_fun_C_6: ( $i * $i ) > $i)).
% 5.23/3.57 tff(k5_relat_1_type, type, (
% 5.23/3.57 k5_relat_1: ( $i * $i ) > $i)).
% 5.23/3.57 tff(tptp_fun_D_3_type, type, (
% 5.23/3.57 tptp_fun_D_3: $i > $i)).
% 5.23/3.57 tff(tptp_fun_D_7_type, type, (
% 5.23/3.57 tptp_fun_D_7: ( $i * $i * $i ) > $i)).
% 5.23/3.57 tff(tptp_fun_E_9_type, type, (
% 5.23/3.57 tptp_fun_E_9: ( $i * $i * $i ) > $i)).
% 5.23/3.57 tff(tptp_fun_D_10_type, type, (
% 5.23/3.57 tptp_fun_D_10: ( $i * $i * $i ) > $i)).
% 5.23/3.57 tff(tptp_fun_F_11_type, type, (
% 5.23/3.57 tptp_fun_F_11: ( $i * $i * $i ) > $i)).
% 5.23/3.57 tff(v1_relat_1_type, type, (
% 5.23/3.57 v1_relat_1: $i > $o)).
% 5.23/3.57 tff(r1_tarski_type, type, (
% 5.23/3.57 r1_tarski: ( $i * $i ) > $o)).
% 5.23/3.57 tff(tptp_fun_B_5_type, type, (
% 5.23/3.57 tptp_fun_B_5: $i > $i)).
% 5.23/3.57 tff(1,plain,
% 5.23/3.57 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B)))))))) <=> (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B)))))))))),
% 5.23/3.57 inference(bind,[status(th)],[])).
% 5.23/3.57 tff(2,plain,
% 5.23/3.57 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))))),
% 5.23/3.57 inference(quant_intro,[status(thm)],[1])).
% 5.23/3.57 tff(3,plain,
% 5.23/3.57 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))))),
% 5.23/3.57 inference(pull_quant,[status(thm)],[])).
% 5.23/3.57 tff(4,plain,
% 5.23/3.57 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A)))))) <=> ![D: $i] : ((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))), ((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) <=> (~![D: $i] : ((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))))), pull_quant((~![D: $i] : ((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) <=> ?[D: $i] : (~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A)))))))), ((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) <=> ?[D: $i] : (~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))))), (((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))) <=> (?[D: $i] : (~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))))), pull_quant((?[D: $i] : (~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))) <=> ?[D: $i] : ((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B)))))))), (((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))) <=> ?[D: $i] : ((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))))), ((~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B)))))))) <=> (~?[D: $i] : ((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B)))))))))), pull_quant((~?[D: $i] : ((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B)))))))) <=> ![D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))))), ((~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B)))))))) <=> ![D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))))))),
% 5.23/3.57 inference(bind,[status(th)],[])).
% 5.23/3.57 tff(5,plain,
% 5.23/3.57 (![A: $i, B: $i, C: $i] : (~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))))),
% 5.23/3.57 inference(quant_intro,[status(thm)],[4])).
% 5.23/3.58 tff(6,plain,
% 5.23/3.58 (![A: $i, B: $i, C: $i] : (~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))))),
% 5.23/3.58 inference(transitivity,[status(thm)],[5, 3])).
% 5.23/3.58 tff(7,plain,
% 5.23/3.58 (![A: $i, B: $i, C: $i] : (~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))))),
% 5.23/3.58 inference(transitivity,[status(thm)],[6, 2])).
% 5.23/3.58 tff(8,plain,
% 5.23/3.58 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B)))))))) <=> (~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B)))))))))),
% 5.23/3.58 inference(bind,[status(th)],[])).
% 5.23/3.58 tff(9,plain,
% 5.23/3.58 (![A: $i, B: $i, C: $i] : (~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))))),
% 5.23/3.58 inference(quant_intro,[status(thm)],[8])).
% 5.23/3.58 tff(10,plain,
% 5.23/3.58 (![A: $i, B: $i, C: $i] : (~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))))),
% 5.23/3.58 inference(transitivity,[status(thm)],[9, 7])).
% 5.23/3.58 tff(11,plain,
% 5.23/3.58 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B)))) <=> ((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))), rewrite(((C = k3_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_7(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_7(C, B, A), A) & r2_hidden(tptp_fun_D_7(C, B, A), B)))) <=> ((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B)))))), ((((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B)))) & ((C = k3_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_7(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_7(C, B, A), A) & r2_hidden(tptp_fun_D_7(C, B, A), B))))) <=> (((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A)))))) & ((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B)))))))), rewrite((((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A)))))) & ((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B)))))) <=> (~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))))), ((((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B)))) & ((C = k3_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_7(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_7(C, B, A), A) & r2_hidden(tptp_fun_D_7(C, B, A), B))))) <=> (~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))))))),
% 5.23/3.58 inference(bind,[status(th)],[])).
% 5.23/3.58 tff(12,plain,
% 5.23/3.58 (![A: $i, B: $i, C: $i] : (((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B)))) & ((C = k3_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_7(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_7(C, B, A), A) & r2_hidden(tptp_fun_D_7(C, B, A), B))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))))),
% 5.23/3.58 inference(quant_intro,[status(thm)],[11])).
% 5.23/3.58 tff(13,plain,
% 5.23/3.58 (^[A: $i, B: $i, C: $i] : rewrite((((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B)))) & ((C = k3_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_7(C, B, A), C) <=> (r2_hidden(tptp_fun_D_7(C, B, A), A) & r2_hidden(tptp_fun_D_7(C, B, A), B)))))) <=> (((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B)))) & ((C = k3_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_7(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_7(C, B, A), A) & r2_hidden(tptp_fun_D_7(C, B, A), B))))))),
% 5.23/3.58 inference(bind,[status(th)],[])).
% 5.23/3.58 tff(14,plain,
% 5.23/3.58 (![A: $i, B: $i, C: $i] : (((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B)))) & ((C = k3_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_7(C, B, A), C) <=> (r2_hidden(tptp_fun_D_7(C, B, A), A) & r2_hidden(tptp_fun_D_7(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B)))) & ((C = k3_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_7(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_7(C, B, A), A) & r2_hidden(tptp_fun_D_7(C, B, A), B)))))),
% 5.23/3.58 inference(quant_intro,[status(thm)],[13])).
% 5.23/3.58 tff(15,plain,
% 5.23/3.58 (![A: $i, B: $i, C: $i] : ((C = k3_xboole_0(A, B)) <=> ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = k3_xboole_0(A, B)) <=> ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B))))),
% 5.23/3.58 inference(rewrite,[status(thm)],[])).
% 5.23/3.58 tff(16,axiom,(![A: $i, B: $i, C: $i] : ((C = k3_xboole_0(A, B)) <=> ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_xboole_0')).
% 5.23/3.58 tff(17,plain,
% 5.23/3.58 (![A: $i, B: $i, C: $i] : ((C = k3_xboole_0(A, B)) <=> ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B))))),
% 5.23/3.58 inference(modus_ponens,[status(thm)],[16, 15])).
% 5.23/3.58 tff(18,plain,(
% 5.23/3.58 ![A: $i, B: $i, C: $i] : (((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B)))) & ((C = k3_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_7(C, B, A), C) <=> (r2_hidden(tptp_fun_D_7(C, B, A), A) & r2_hidden(tptp_fun_D_7(C, B, A), B))))))),
% 5.23/3.58 inference(skolemize,[status(sab)],[17])).
% 5.23/3.58 tff(19,plain,
% 5.23/3.58 (![A: $i, B: $i, C: $i] : (((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B)))) & ((C = k3_xboole_0(A, B)) | ((~r2_hidden(tptp_fun_D_7(C, B, A), C)) <=> (r2_hidden(tptp_fun_D_7(C, B, A), A) & r2_hidden(tptp_fun_D_7(C, B, A), B)))))),
% 5.23/3.58 inference(modus_ponens,[status(thm)],[18, 14])).
% 5.23/3.58 tff(20,plain,
% 5.23/3.58 (![A: $i, B: $i, C: $i] : (~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))))),
% 5.23/3.58 inference(modus_ponens,[status(thm)],[19, 12])).
% 5.23/3.58 tff(21,plain,
% 5.23/3.58 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))))),
% 5.23/3.58 inference(modus_ponens,[status(thm)],[20, 10])).
% 5.23/3.58 tff(22,plain,
% 5.23/3.58 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))))) | ((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) <=> ((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))))) | ((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) <=> ((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1)))))),
% 5.23/3.58 inference(rewrite,[status(thm)],[])).
% 5.23/3.58 tff(23,plain,
% 5.23/3.58 ((~(r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0)) <=> ((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1))))) <=> ((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) <=> ((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1))))),
% 5.23/3.58 inference(rewrite,[status(thm)],[])).
% 5.23/3.58 tff(24,plain,
% 5.23/3.58 (((r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0)) <=> ((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1)))) | $false) <=> (r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0)) <=> ((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1))))),
% 5.23/3.58 inference(rewrite,[status(thm)],[])).
% 5.23/3.58 tff(25,plain,
% 5.23/3.58 ((~$true) <=> $false),
% 5.23/3.58 inference(rewrite,[status(thm)],[])).
% 5.23/3.58 tff(26,plain,
% 5.23/3.58 (($true | (r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), k3_xboole_0(B!1, A!0)) <=> ((~r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), B!1)) | (~r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), A!0))))) <=> $true),
% 5.23/3.58 inference(rewrite,[status(thm)],[])).
% 5.23/3.58 tff(27,plain,
% 5.23/3.58 ((r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), k3_xboole_0(B!1, A!0)) <=> ((~r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), B!1)) | (~r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), A!0)))) <=> (r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), k3_xboole_0(B!1, A!0)) <=> ((~r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), B!1)) | (~r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), A!0))))),
% 5.23/3.58 inference(rewrite,[status(thm)],[])).
% 5.23/3.58 tff(28,plain,
% 5.23/3.58 ((k3_xboole_0(B!1, A!0) = k3_xboole_0(B!1, A!0)) <=> $true),
% 5.23/3.58 inference(rewrite,[status(thm)],[])).
% 5.23/3.58 tff(29,plain,
% 5.23/3.58 (((k3_xboole_0(B!1, A!0) = k3_xboole_0(B!1, A!0)) | (r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), k3_xboole_0(B!1, A!0)) <=> ((~r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), B!1)) | (~r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), A!0))))) <=> ($true | (r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), k3_xboole_0(B!1, A!0)) <=> ((~r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), B!1)) | (~r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), A!0)))))),
% 5.23/3.58 inference(monotonicity,[status(thm)],[28, 27])).
% 5.23/3.58 tff(30,plain,
% 5.23/3.58 (((k3_xboole_0(B!1, A!0) = k3_xboole_0(B!1, A!0)) | (r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), k3_xboole_0(B!1, A!0)) <=> ((~r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), B!1)) | (~r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), A!0))))) <=> $true),
% 5.23/3.58 inference(transitivity,[status(thm)],[29, 26])).
% 5.23/3.58 tff(31,plain,
% 5.23/3.58 ((~((k3_xboole_0(B!1, A!0) = k3_xboole_0(B!1, A!0)) | (r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), k3_xboole_0(B!1, A!0)) <=> ((~r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), B!1)) | (~r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), A!0)))))) <=> (~$true)),
% 5.23/3.58 inference(monotonicity,[status(thm)],[30])).
% 5.23/3.58 tff(32,plain,
% 5.23/3.58 ((~((k3_xboole_0(B!1, A!0) = k3_xboole_0(B!1, A!0)) | (r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), k3_xboole_0(B!1, A!0)) <=> ((~r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), B!1)) | (~r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), A!0)))))) <=> $false),
% 5.23/3.58 inference(transitivity,[status(thm)],[31, 25])).
% 5.23/3.58 tff(33,plain,
% 5.23/3.58 ((~(r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0)) <=> (~((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1)))))) <=> (r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0)) <=> ((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1))))),
% 5.23/3.58 inference(rewrite,[status(thm)],[])).
% 5.23/3.58 tff(34,plain,
% 5.23/3.58 (($false | (r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0)) <=> (~((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1)))))) <=> (r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0)) <=> (~((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1)))))),
% 5.23/3.59 inference(rewrite,[status(thm)],[])).
% 5.23/3.59 tff(35,plain,
% 5.23/3.59 ((~(k3_xboole_0(B!1, A!0) = k3_xboole_0(B!1, A!0))) <=> (~$true)),
% 5.23/3.59 inference(monotonicity,[status(thm)],[28])).
% 5.23/3.59 tff(36,plain,
% 5.23/3.59 ((~(k3_xboole_0(B!1, A!0) = k3_xboole_0(B!1, A!0))) <=> $false),
% 5.23/3.59 inference(transitivity,[status(thm)],[35, 25])).
% 5.23/3.59 tff(37,plain,
% 5.23/3.59 (((~(k3_xboole_0(B!1, A!0) = k3_xboole_0(B!1, A!0))) | (r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0)) <=> (~((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1)))))) <=> ($false | (r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0)) <=> (~((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1))))))),
% 5.23/3.59 inference(monotonicity,[status(thm)],[36])).
% 5.23/3.59 tff(38,plain,
% 5.23/3.59 (((~(k3_xboole_0(B!1, A!0) = k3_xboole_0(B!1, A!0))) | (r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0)) <=> (~((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1)))))) <=> (r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0)) <=> (~((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1)))))),
% 5.23/3.59 inference(transitivity,[status(thm)],[37, 34])).
% 5.23/3.59 tff(39,plain,
% 5.23/3.59 ((~((~(k3_xboole_0(B!1, A!0) = k3_xboole_0(B!1, A!0))) | (r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0)) <=> (~((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1))))))) <=> (~(r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0)) <=> (~((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1))))))),
% 5.23/3.59 inference(monotonicity,[status(thm)],[38])).
% 5.23/3.59 tff(40,plain,
% 5.23/3.59 ((~((~(k3_xboole_0(B!1, A!0) = k3_xboole_0(B!1, A!0))) | (r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0)) <=> (~((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1))))))) <=> (r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0)) <=> ((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1))))),
% 5.23/3.59 inference(transitivity,[status(thm)],[39, 33])).
% 5.23/3.59 tff(41,plain,
% 5.23/3.59 (((~((~(k3_xboole_0(B!1, A!0) = k3_xboole_0(B!1, A!0))) | (r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0)) <=> (~((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1))))))) | (~((k3_xboole_0(B!1, A!0) = k3_xboole_0(B!1, A!0)) | (r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), k3_xboole_0(B!1, A!0)) <=> ((~r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), B!1)) | (~r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), A!0))))))) <=> ((r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0)) <=> ((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1)))) | $false)),
% 5.23/3.59 inference(monotonicity,[status(thm)],[40, 32])).
% 5.23/3.59 tff(42,plain,
% 5.23/3.59 (((~((~(k3_xboole_0(B!1, A!0) = k3_xboole_0(B!1, A!0))) | (r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0)) <=> (~((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1))))))) | (~((k3_xboole_0(B!1, A!0) = k3_xboole_0(B!1, A!0)) | (r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), k3_xboole_0(B!1, A!0)) <=> ((~r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), B!1)) | (~r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), A!0))))))) <=> (r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0)) <=> ((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1))))),
% 5.23/3.59 inference(transitivity,[status(thm)],[41, 24])).
% 5.23/3.59 tff(43,plain,
% 5.23/3.59 ((~((~((~(k3_xboole_0(B!1, A!0) = k3_xboole_0(B!1, A!0))) | (r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0)) <=> (~((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1))))))) | (~((k3_xboole_0(B!1, A!0) = k3_xboole_0(B!1, A!0)) | (r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), k3_xboole_0(B!1, A!0)) <=> ((~r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), B!1)) | (~r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), A!0)))))))) <=> (~(r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0)) <=> ((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1)))))),
% 5.23/3.59 inference(monotonicity,[status(thm)],[42])).
% 5.23/3.59 tff(44,plain,
% 5.23/3.59 ((~((~((~(k3_xboole_0(B!1, A!0) = k3_xboole_0(B!1, A!0))) | (r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0)) <=> (~((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1))))))) | (~((k3_xboole_0(B!1, A!0) = k3_xboole_0(B!1, A!0)) | (r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), k3_xboole_0(B!1, A!0)) <=> ((~r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), B!1)) | (~r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), A!0)))))))) <=> ((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) <=> ((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1))))),
% 5.23/3.60 inference(transitivity,[status(thm)],[43, 23])).
% 5.23/3.60 tff(45,plain,
% 5.23/3.60 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))))) | (~((~((~(k3_xboole_0(B!1, A!0) = k3_xboole_0(B!1, A!0))) | (r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0)) <=> (~((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1))))))) | (~((k3_xboole_0(B!1, A!0) = k3_xboole_0(B!1, A!0)) | (r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), k3_xboole_0(B!1, A!0)) <=> ((~r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), B!1)) | (~r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), A!0))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))))) | ((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) <=> ((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1)))))),
% 5.23/3.60 inference(monotonicity,[status(thm)],[44])).
% 5.23/3.60 tff(46,plain,
% 5.23/3.60 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))))) | (~((~((~(k3_xboole_0(B!1, A!0) = k3_xboole_0(B!1, A!0))) | (r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0)) <=> (~((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1))))))) | (~((k3_xboole_0(B!1, A!0) = k3_xboole_0(B!1, A!0)) | (r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), k3_xboole_0(B!1, A!0)) <=> ((~r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), B!1)) | (~r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), A!0))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))))) | ((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) <=> ((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1)))))),
% 5.23/3.60 inference(transitivity,[status(thm)],[45, 22])).
% 5.23/3.60 tff(47,plain,
% 5.23/3.60 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))))) | (~((~((~(k3_xboole_0(B!1, A!0) = k3_xboole_0(B!1, A!0))) | (r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0)) <=> (~((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1))))))) | (~((k3_xboole_0(B!1, A!0) = k3_xboole_0(B!1, A!0)) | (r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), k3_xboole_0(B!1, A!0)) <=> ((~r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), B!1)) | (~r2_hidden(tptp_fun_D_7(k3_xboole_0(B!1, A!0), A!0, B!1), A!0))))))))),
% 5.23/3.60 inference(quant_inst,[status(thm)],[])).
% 5.23/3.60 tff(48,plain,
% 5.23/3.60 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))))) | ((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) <=> ((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1))))),
% 5.23/3.60 inference(modus_ponens,[status(thm)],[47, 46])).
% 5.23/3.60 tff(49,plain,
% 5.23/3.60 ((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) <=> ((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1)))),
% 5.23/3.60 inference(unit_resolution,[status(thm)],[48, 21])).
% 5.23/3.60 tff(50,plain,
% 5.23/3.60 (^[A: $i, B: $i] : refl((k3_xboole_0(A, B) = k3_xboole_0(B, A)) <=> (k3_xboole_0(A, B) = k3_xboole_0(B, A)))),
% 5.23/3.60 inference(bind,[status(th)],[])).
% 5.23/3.60 tff(51,plain,
% 5.23/3.60 (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A)) <=> ![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 5.23/3.60 inference(quant_intro,[status(thm)],[50])).
% 5.23/3.60 tff(52,plain,
% 5.23/3.60 (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A)) <=> ![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 5.23/3.60 inference(rewrite,[status(thm)],[])).
% 5.23/3.60 tff(53,axiom,(![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 5.23/3.60 tff(54,plain,
% 5.23/3.60 (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 5.23/3.60 inference(modus_ponens,[status(thm)],[53, 52])).
% 5.23/3.60 tff(55,plain,(
% 5.23/3.60 ![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 5.23/3.60 inference(skolemize,[status(sab)],[54])).
% 5.23/3.60 tff(56,plain,
% 5.23/3.60 (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 5.23/3.60 inference(modus_ponens,[status(thm)],[55, 51])).
% 5.23/3.60 tff(57,plain,
% 5.23/3.60 ((~![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))) | (k3_xboole_0(A!0, B!1) = k3_xboole_0(B!1, A!0))),
% 5.23/3.60 inference(quant_inst,[status(thm)],[])).
% 5.23/3.60 tff(58,plain,
% 5.23/3.60 (k3_xboole_0(A!0, B!1) = k3_xboole_0(B!1, A!0)),
% 5.23/3.60 inference(unit_resolution,[status(thm)],[57, 56])).
% 5.23/3.60 tff(59,plain,
% 5.23/3.60 (k3_xboole_0(B!1, A!0) = k3_xboole_0(A!0, B!1)),
% 5.23/3.60 inference(symmetry,[status(thm)],[58])).
% 5.23/3.60 tff(60,plain,
% 5.23/3.60 (v1_relat_1(k3_xboole_0(B!1, A!0)) <=> v1_relat_1(k3_xboole_0(A!0, B!1))),
% 5.23/3.60 inference(monotonicity,[status(thm)],[59])).
% 5.23/3.60 tff(61,plain,
% 5.23/3.60 (v1_relat_1(k3_xboole_0(A!0, B!1)) <=> v1_relat_1(k3_xboole_0(B!1, A!0))),
% 5.23/3.60 inference(symmetry,[status(thm)],[60])).
% 5.23/3.60 tff(62,plain,
% 5.23/3.60 (^[A: $i, B: $i] : refl((v1_relat_1(k3_xboole_0(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A))) <=> (v1_relat_1(k3_xboole_0(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A))))),
% 5.23/3.60 inference(bind,[status(th)],[])).
% 5.23/3.60 tff(63,plain,
% 5.23/3.60 (![A: $i, B: $i] : (v1_relat_1(k3_xboole_0(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A))) <=> ![A: $i, B: $i] : (v1_relat_1(k3_xboole_0(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))),
% 5.23/3.60 inference(quant_intro,[status(thm)],[62])).
% 5.23/3.60 tff(64,plain,
% 5.23/3.60 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_relat_1(A) & v1_relat_1(B)) <=> (~((~v1_relat_1(B)) | (~v1_relat_1(A))))), ((~(v1_relat_1(A) & v1_relat_1(B))) <=> (~(~((~v1_relat_1(B)) | (~v1_relat_1(A))))))), rewrite((~(~((~v1_relat_1(B)) | (~v1_relat_1(A))))) <=> ((~v1_relat_1(B)) | (~v1_relat_1(A)))), ((~(v1_relat_1(A) & v1_relat_1(B))) <=> ((~v1_relat_1(B)) | (~v1_relat_1(A))))), ((v1_relat_1(k3_xboole_0(A, B)) | (~(v1_relat_1(A) & v1_relat_1(B)))) <=> (v1_relat_1(k3_xboole_0(A, B)) | ((~v1_relat_1(B)) | (~v1_relat_1(A)))))), rewrite((v1_relat_1(k3_xboole_0(A, B)) | ((~v1_relat_1(B)) | (~v1_relat_1(A)))) <=> (v1_relat_1(k3_xboole_0(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))), ((v1_relat_1(k3_xboole_0(A, B)) | (~(v1_relat_1(A) & v1_relat_1(B)))) <=> (v1_relat_1(k3_xboole_0(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))))),
% 5.23/3.60 inference(bind,[status(th)],[])).
% 5.23/3.60 tff(65,plain,
% 5.23/3.60 (![A: $i, B: $i] : (v1_relat_1(k3_xboole_0(A, B)) | (~(v1_relat_1(A) & v1_relat_1(B)))) <=> ![A: $i, B: $i] : (v1_relat_1(k3_xboole_0(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))),
% 5.23/3.60 inference(quant_intro,[status(thm)],[64])).
% 5.23/3.60 tff(66,plain,
% 5.23/3.60 (![A: $i, B: $i] : (v1_relat_1(k3_xboole_0(A, B)) | (~(v1_relat_1(A) & v1_relat_1(B)))) <=> ![A: $i, B: $i] : (v1_relat_1(k3_xboole_0(A, B)) | (~(v1_relat_1(A) & v1_relat_1(B))))),
% 5.23/3.60 inference(rewrite,[status(thm)],[])).
% 5.23/3.60 tff(67,plain,
% 5.23/3.60 (^[A: $i, B: $i] : rewrite(((v1_relat_1(A) & v1_relat_1(B)) => v1_relat_1(k3_xboole_0(A, B))) <=> (v1_relat_1(k3_xboole_0(A, B)) | (~(v1_relat_1(A) & v1_relat_1(B)))))),
% 5.23/3.60 inference(bind,[status(th)],[])).
% 5.23/3.60 tff(68,plain,
% 5.23/3.60 (![A: $i, B: $i] : ((v1_relat_1(A) & v1_relat_1(B)) => v1_relat_1(k3_xboole_0(A, B))) <=> ![A: $i, B: $i] : (v1_relat_1(k3_xboole_0(A, B)) | (~(v1_relat_1(A) & v1_relat_1(B))))),
% 5.23/3.60 inference(quant_intro,[status(thm)],[67])).
% 5.23/3.60 tff(69,axiom,(![A: $i, B: $i] : ((v1_relat_1(A) & v1_relat_1(B)) => v1_relat_1(k3_xboole_0(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_relat_1')).
% 5.23/3.60 tff(70,plain,
% 5.23/3.60 (![A: $i, B: $i] : (v1_relat_1(k3_xboole_0(A, B)) | (~(v1_relat_1(A) & v1_relat_1(B))))),
% 5.23/3.60 inference(modus_ponens,[status(thm)],[69, 68])).
% 5.23/3.60 tff(71,plain,
% 5.23/3.60 (![A: $i, B: $i] : (v1_relat_1(k3_xboole_0(A, B)) | (~(v1_relat_1(A) & v1_relat_1(B))))),
% 5.23/3.60 inference(modus_ponens,[status(thm)],[70, 66])).
% 5.23/3.60 tff(72,plain,(
% 5.23/3.60 ![A: $i, B: $i] : (v1_relat_1(k3_xboole_0(A, B)) | (~(v1_relat_1(A) & v1_relat_1(B))))),
% 5.23/3.60 inference(skolemize,[status(sab)],[71])).
% 5.23/3.60 tff(73,plain,
% 5.23/3.60 (![A: $i, B: $i] : (v1_relat_1(k3_xboole_0(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))),
% 5.23/3.60 inference(modus_ponens,[status(thm)],[72, 65])).
% 5.23/3.60 tff(74,plain,
% 5.23/3.60 (![A: $i, B: $i] : (v1_relat_1(k3_xboole_0(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))),
% 5.23/3.60 inference(modus_ponens,[status(thm)],[73, 63])).
% 5.23/3.60 tff(75,plain,
% 5.23/3.60 ((v1_relat_1(A!0) & (v1_relat_1(B!1) & (~((~v1_relat_1(C!2)) | r1_tarski(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2))))))) <=> (v1_relat_1(A!0) & v1_relat_1(B!1) & (~((~v1_relat_1(C!2)) | r1_tarski(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2))))))),
% 5.23/3.60 inference(rewrite,[status(thm)],[])).
% 5.23/3.60 tff(76,plain,
% 5.23/3.60 (((~(~v1_relat_1(B!1))) & (~((~v1_relat_1(C!2)) | r1_tarski(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)))))) <=> (v1_relat_1(B!1) & (~((~v1_relat_1(C!2)) | r1_tarski(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2))))))),
% 5.23/3.60 inference(rewrite,[status(thm)],[])).
% 5.23/3.60 tff(77,plain,
% 5.23/3.60 ((~(~v1_relat_1(A!0))) <=> v1_relat_1(A!0)),
% 5.23/3.60 inference(rewrite,[status(thm)],[])).
% 5.23/3.60 tff(78,plain,
% 5.23/3.60 (((~(~v1_relat_1(A!0))) & ((~(~v1_relat_1(B!1))) & (~((~v1_relat_1(C!2)) | r1_tarski(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2))))))) <=> (v1_relat_1(A!0) & (v1_relat_1(B!1) & (~((~v1_relat_1(C!2)) | r1_tarski(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)))))))),
% 5.23/3.60 inference(monotonicity,[status(thm)],[77, 76])).
% 5.23/3.60 tff(79,plain,
% 5.23/3.60 (((~(~v1_relat_1(A!0))) & ((~(~v1_relat_1(B!1))) & (~((~v1_relat_1(C!2)) | r1_tarski(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2))))))) <=> (v1_relat_1(A!0) & v1_relat_1(B!1) & (~((~v1_relat_1(C!2)) | r1_tarski(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2))))))),
% 5.23/3.60 inference(transitivity,[status(thm)],[78, 75])).
% 5.23/3.60 tff(80,plain,
% 5.23/3.60 ((~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | r1_tarski(k5_relat_1(k3_xboole_0(A, B), C), k3_xboole_0(k5_relat_1(A, C), k5_relat_1(B, C))))))) <=> (~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | r1_tarski(k5_relat_1(k3_xboole_0(A, B), C), k3_xboole_0(k5_relat_1(A, C), k5_relat_1(B, C)))))))),
% 5.23/3.60 inference(rewrite,[status(thm)],[])).
% 5.23/3.60 tff(81,plain,
% 5.23/3.60 ((~![A: $i] : (v1_relat_1(A) => ![B: $i] : (v1_relat_1(B) => ![C: $i] : (v1_relat_1(C) => r1_tarski(k5_relat_1(k3_xboole_0(A, B), C), k3_xboole_0(k5_relat_1(A, C), k5_relat_1(B, C))))))) <=> (~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | r1_tarski(k5_relat_1(k3_xboole_0(A, B), C), k3_xboole_0(k5_relat_1(A, C), k5_relat_1(B, C)))))))),
% 5.23/3.60 inference(rewrite,[status(thm)],[])).
% 5.23/3.60 tff(82,axiom,(~![A: $i] : (v1_relat_1(A) => ![B: $i] : (v1_relat_1(B) => ![C: $i] : (v1_relat_1(C) => r1_tarski(k5_relat_1(k3_xboole_0(A, B), C), k3_xboole_0(k5_relat_1(A, C), k5_relat_1(B, C))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t8_relset_2')).
% 5.23/3.60 tff(83,plain,
% 5.23/3.60 (~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | r1_tarski(k5_relat_1(k3_xboole_0(A, B), C), k3_xboole_0(k5_relat_1(A, C), k5_relat_1(B, C))))))),
% 5.23/3.60 inference(modus_ponens,[status(thm)],[82, 81])).
% 5.23/3.60 tff(84,plain,
% 5.23/3.60 (~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | r1_tarski(k5_relat_1(k3_xboole_0(A, B), C), k3_xboole_0(k5_relat_1(A, C), k5_relat_1(B, C))))))),
% 5.23/3.60 inference(modus_ponens,[status(thm)],[83, 80])).
% 5.23/3.60 tff(85,plain,
% 5.23/3.60 (~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | r1_tarski(k5_relat_1(k3_xboole_0(A, B), C), k3_xboole_0(k5_relat_1(A, C), k5_relat_1(B, C))))))),
% 5.23/3.60 inference(modus_ponens,[status(thm)],[84, 80])).
% 5.23/3.60 tff(86,plain,
% 5.23/3.60 (~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | r1_tarski(k5_relat_1(k3_xboole_0(A, B), C), k3_xboole_0(k5_relat_1(A, C), k5_relat_1(B, C))))))),
% 5.23/3.60 inference(modus_ponens,[status(thm)],[85, 80])).
% 5.23/3.60 tff(87,plain,
% 5.23/3.60 (~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | r1_tarski(k5_relat_1(k3_xboole_0(A, B), C), k3_xboole_0(k5_relat_1(A, C), k5_relat_1(B, C))))))),
% 5.23/3.60 inference(modus_ponens,[status(thm)],[86, 80])).
% 5.23/3.60 tff(88,plain,
% 5.23/3.60 (~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | r1_tarski(k5_relat_1(k3_xboole_0(A, B), C), k3_xboole_0(k5_relat_1(A, C), k5_relat_1(B, C))))))),
% 5.23/3.60 inference(modus_ponens,[status(thm)],[87, 80])).
% 5.23/3.60 tff(89,plain,
% 5.23/3.60 (~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | r1_tarski(k5_relat_1(k3_xboole_0(A, B), C), k3_xboole_0(k5_relat_1(A, C), k5_relat_1(B, C))))))),
% 5.23/3.60 inference(modus_ponens,[status(thm)],[88, 80])).
% 5.23/3.60 tff(90,plain,
% 5.23/3.60 (v1_relat_1(A!0) & v1_relat_1(B!1) & (~((~v1_relat_1(C!2)) | r1_tarski(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)))))),
% 5.23/3.60 inference(modus_ponens,[status(thm)],[89, 79])).
% 5.23/3.60 tff(91,plain,
% 5.23/3.60 (v1_relat_1(B!1)),
% 5.23/3.60 inference(and_elim,[status(thm)],[90])).
% 5.23/3.60 tff(92,plain,
% 5.23/3.60 (v1_relat_1(A!0)),
% 5.23/3.60 inference(and_elim,[status(thm)],[90])).
% 5.23/3.60 tff(93,plain,
% 5.23/3.60 (((~![A: $i, B: $i] : (v1_relat_1(k3_xboole_0(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))) | ((~v1_relat_1(A!0)) | (~v1_relat_1(B!1)) | v1_relat_1(k3_xboole_0(A!0, B!1)))) <=> ((~![A: $i, B: $i] : (v1_relat_1(k3_xboole_0(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))) | (~v1_relat_1(A!0)) | (~v1_relat_1(B!1)) | v1_relat_1(k3_xboole_0(A!0, B!1)))),
% 5.23/3.60 inference(rewrite,[status(thm)],[])).
% 5.23/3.61 tff(94,plain,
% 5.23/3.61 ((v1_relat_1(k3_xboole_0(A!0, B!1)) | (~v1_relat_1(B!1)) | (~v1_relat_1(A!0))) <=> ((~v1_relat_1(A!0)) | (~v1_relat_1(B!1)) | v1_relat_1(k3_xboole_0(A!0, B!1)))),
% 5.23/3.61 inference(rewrite,[status(thm)],[])).
% 5.23/3.61 tff(95,plain,
% 5.23/3.61 (((~![A: $i, B: $i] : (v1_relat_1(k3_xboole_0(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))) | (v1_relat_1(k3_xboole_0(A!0, B!1)) | (~v1_relat_1(B!1)) | (~v1_relat_1(A!0)))) <=> ((~![A: $i, B: $i] : (v1_relat_1(k3_xboole_0(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))) | ((~v1_relat_1(A!0)) | (~v1_relat_1(B!1)) | v1_relat_1(k3_xboole_0(A!0, B!1))))),
% 5.23/3.61 inference(monotonicity,[status(thm)],[94])).
% 5.23/3.61 tff(96,plain,
% 5.23/3.61 (((~![A: $i, B: $i] : (v1_relat_1(k3_xboole_0(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))) | (v1_relat_1(k3_xboole_0(A!0, B!1)) | (~v1_relat_1(B!1)) | (~v1_relat_1(A!0)))) <=> ((~![A: $i, B: $i] : (v1_relat_1(k3_xboole_0(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))) | (~v1_relat_1(A!0)) | (~v1_relat_1(B!1)) | v1_relat_1(k3_xboole_0(A!0, B!1)))),
% 5.23/3.61 inference(transitivity,[status(thm)],[95, 93])).
% 5.23/3.61 tff(97,plain,
% 5.23/3.61 ((~![A: $i, B: $i] : (v1_relat_1(k3_xboole_0(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))) | (v1_relat_1(k3_xboole_0(A!0, B!1)) | (~v1_relat_1(B!1)) | (~v1_relat_1(A!0)))),
% 5.23/3.61 inference(quant_inst,[status(thm)],[])).
% 5.23/3.61 tff(98,plain,
% 5.23/3.61 ((~![A: $i, B: $i] : (v1_relat_1(k3_xboole_0(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))) | (~v1_relat_1(A!0)) | (~v1_relat_1(B!1)) | v1_relat_1(k3_xboole_0(A!0, B!1))),
% 5.23/3.61 inference(modus_ponens,[status(thm)],[97, 96])).
% 5.23/3.61 tff(99,plain,
% 5.23/3.61 (v1_relat_1(k3_xboole_0(A!0, B!1))),
% 5.23/3.61 inference(unit_resolution,[status(thm)],[98, 92, 91, 74])).
% 5.23/3.61 tff(100,plain,
% 5.23/3.61 (v1_relat_1(k3_xboole_0(B!1, A!0))),
% 5.23/3.61 inference(modus_ponens,[status(thm)],[99, 61])).
% 5.23/3.61 tff(101,plain,
% 5.23/3.61 (^[A: $i] : rewrite(((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))) | (~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B)))))))))))))) <=> ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))) | (~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B)))))))))))))))),
% 5.23/3.61 inference(bind,[status(th)],[])).
% 5.23/3.61 tff(102,plain,
% 5.23/3.61 (![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))) | (~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B)))))))))))))) <=> ![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))) | (~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))),
% 5.23/3.61 inference(quant_intro,[status(thm)],[101])).
% 5.23/3.61 tff(103,plain,
% 5.23/3.61 (^[A: $i] : refl(((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))) | (~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B)))))))))))))) <=> ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))) | (~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B)))))))))))))))),
% 5.23/3.61 inference(bind,[status(th)],[])).
% 5.23/3.61 tff(104,plain,
% 5.23/3.61 (![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))) | (~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B)))))))))))))) <=> ![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))) | (~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))))))))),
% 5.23/3.61 inference(quant_intro,[status(thm)],[103])).
% 5.23/3.61 tff(105,plain,
% 5.23/3.61 (^[A: $i] : rewrite(((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))) | (~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B)))))))))))))) <=> ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))) | (~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B)))))))))))))))),
% 5.23/3.61 inference(bind,[status(th)],[])).
% 5.23/3.61 tff(106,plain,
% 5.23/3.61 (![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))) | (~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B)))))))))))))) <=> ![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))) | (~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))))))))),
% 5.23/3.61 inference(quant_intro,[status(thm)],[105])).
% 5.23/3.61 tff(107,plain,
% 5.23/3.61 (![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))) | (~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B)))))))))))))) <=> ![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))) | (~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))))))))),
% 5.23/3.61 inference(transitivity,[status(thm)],[106, 104])).
% 5.23/3.61 tff(108,plain,
% 5.23/3.61 (^[A: $i] : rewrite(((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (((~r2_hidden(k4_tarski(D, E), C)) | (r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A) & r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B))) & (r2_hidden(k4_tarski(D, E), C) | ![F: $i] : (~(r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B)))))) & ((C = k5_relat_1(A, B)) | ((r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A) & r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B))) & ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : (~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A) & r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B)))))))))) <=> ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))) | (~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B)))))))))))))))),
% 5.23/3.61 inference(bind,[status(th)],[])).
% 5.23/3.61 tff(109,plain,
% 5.23/3.61 (![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (((~r2_hidden(k4_tarski(D, E), C)) | (r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A) & r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B))) & (r2_hidden(k4_tarski(D, E), C) | ![F: $i] : (~(r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B)))))) & ((C = k5_relat_1(A, B)) | ((r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A) & r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B))) & ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : (~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A) & r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B)))))))))) <=> ![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))) | (~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))))))))),
% 5.23/3.61 inference(quant_intro,[status(thm)],[108])).
% 5.23/3.61 tff(110,plain,
% 5.23/3.61 (![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | ((C = k5_relat_1(A, B)) <=> ![D: $i, E: $i] : (r2_hidden(k4_tarski(D, E), C) <=> ?[F: $i] : (r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B))))))) <=> ![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | ((C = k5_relat_1(A, B)) <=> ![D: $i, E: $i] : (r2_hidden(k4_tarski(D, E), C) <=> ?[F: $i] : (r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B)))))))),
% 5.23/3.61 inference(rewrite,[status(thm)],[])).
% 5.23/3.61 tff(111,plain,
% 5.23/3.61 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((C = k5_relat_1(A, B)) <=> ![D: $i, E: $i] : (r2_hidden(k4_tarski(D, E), C) <=> ?[F: $i] : (r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B)))) <=> ((C = k5_relat_1(A, B)) <=> ![D: $i, E: $i] : (r2_hidden(k4_tarski(D, E), C) <=> ?[F: $i] : (r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B))))), ((v1_relat_1(C) => ((C = k5_relat_1(A, B)) <=> ![D: $i, E: $i] : (r2_hidden(k4_tarski(D, E), C) <=> ?[F: $i] : (r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B))))) <=> (v1_relat_1(C) => ((C = k5_relat_1(A, B)) <=> ![D: $i, E: $i] : (r2_hidden(k4_tarski(D, E), C) <=> ?[F: $i] : (r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B))))))), rewrite((v1_relat_1(C) => ((C = k5_relat_1(A, B)) <=> ![D: $i, E: $i] : (r2_hidden(k4_tarski(D, E), C) <=> ?[F: $i] : (r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B))))) <=> ((~v1_relat_1(C)) | ((C = k5_relat_1(A, B)) <=> ![D: $i, E: $i] : (r2_hidden(k4_tarski(D, E), C) <=> ?[F: $i] : (r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B)))))), ((v1_relat_1(C) => ((C = k5_relat_1(A, B)) <=> ![D: $i, E: $i] : (r2_hidden(k4_tarski(D, E), C) <=> ?[F: $i] : (r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B))))) <=> ((~v1_relat_1(C)) | ((C = k5_relat_1(A, B)) <=> ![D: $i, E: $i] : (r2_hidden(k4_tarski(D, E), C) <=> ?[F: $i] : (r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B)))))))), (![C: $i] : (v1_relat_1(C) => ((C = k5_relat_1(A, B)) <=> ![D: $i, E: $i] : (r2_hidden(k4_tarski(D, E), C) <=> ?[F: $i] : (r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B))))) <=> ![C: $i] : ((~v1_relat_1(C)) | ((C = k5_relat_1(A, B)) <=> ![D: $i, E: $i] : (r2_hidden(k4_tarski(D, E), C) <=> ?[F: $i] : (r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B))))))), ((v1_relat_1(B) => ![C: $i] : (v1_relat_1(C) => ((C = k5_relat_1(A, B)) <=> ![D: $i, E: $i] : (r2_hidden(k4_tarski(D, E), C) <=> ?[F: $i] : (r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B)))))) <=> (v1_relat_1(B) => ![C: $i] : ((~v1_relat_1(C)) | ((C = k5_relat_1(A, B)) <=> ![D: $i, E: $i] : (r2_hidden(k4_tarski(D, E), C) <=> ?[F: $i] : (r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B)))))))), rewrite((v1_relat_1(B) => ![C: $i] : ((~v1_relat_1(C)) | ((C = k5_relat_1(A, B)) <=> ![D: $i, E: $i] : (r2_hidden(k4_tarski(D, E), C) <=> ?[F: $i] : (r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B)))))) <=> ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | ((C = k5_relat_1(A, B)) <=> ![D: $i, E: $i] : (r2_hidden(k4_tarski(D, E), C) <=> ?[F: $i] : (r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B))))))), ((v1_relat_1(B) => ![C: $i] : (v1_relat_1(C) => ((C = k5_relat_1(A, B)) <=> ![D: $i, E: $i] : (r2_hidden(k4_tarski(D, E), C) <=> ?[F: $i] : (r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B)))))) <=> ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | ((C = k5_relat_1(A, B)) <=> ![D: $i, E: $i] : (r2_hidden(k4_tarski(D, E), C) <=> ?[F: $i] : (r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B))))))))), (![B: $i] : (v1_relat_1(B) => ![C: $i] : (v1_relat_1(C) => ((C = k5_relat_1(A, B)) <=> ![D: $i, E: $i] : (r2_hidden(k4_tarski(D, E), C) <=> ?[F: $i] : (r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B)))))) <=> ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | ((C = k5_relat_1(A, B)) <=> ![D: $i, E: $i] : (r2_hidden(k4_tarski(D, E), C) <=> ?[F: $i] : (r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B)))))))), ((v1_relat_1(A) => ![B: $i] : (v1_relat_1(B) => ![C: $i] : (v1_relat_1(C) => ((C = k5_relat_1(A, B)) <=> ![D: $i, E: $i] : (r2_hidden(k4_tarski(D, E), C) <=> ?[F: $i] : (r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B))))))) <=> (v1_relat_1(A) => ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | ((C = k5_relat_1(A, B)) <=> ![D: $i, E: $i] : (r2_hidden(k4_tarski(D, E), C) <=> ?[F: $i] : (r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B))))))))), rewrite((v1_relat_1(A) => ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | ((C = k5_relat_1(A, B)) <=> ![D: $i, E: $i] : (r2_hidden(k4_tarski(D, E), C) <=> ?[F: $i] : (r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B))))))) <=> ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | ((C = k5_relat_1(A, B)) <=> ![D: $i, E: $i] : (r2_hidden(k4_tarski(D, E), C) <=> ?[F: $i] : (r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B)))))))), ((v1_relat_1(A) => ![B: $i] : (v1_relat_1(B) => ![C: $i] : (v1_relat_1(C) => ((C = k5_relat_1(A, B)) <=> ![D: $i, E: $i] : (r2_hidden(k4_tarski(D, E), C) <=> ?[F: $i] : (r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B))))))) <=> ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | ((C = k5_relat_1(A, B)) <=> ![D: $i, E: $i] : (r2_hidden(k4_tarski(D, E), C) <=> ?[F: $i] : (r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B)))))))))),
% 5.23/3.61 inference(bind,[status(th)],[])).
% 5.23/3.61 tff(112,plain,
% 5.23/3.61 (![A: $i] : (v1_relat_1(A) => ![B: $i] : (v1_relat_1(B) => ![C: $i] : (v1_relat_1(C) => ((C = k5_relat_1(A, B)) <=> ![D: $i, E: $i] : (r2_hidden(k4_tarski(D, E), C) <=> ?[F: $i] : (r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B))))))) <=> ![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | ((C = k5_relat_1(A, B)) <=> ![D: $i, E: $i] : (r2_hidden(k4_tarski(D, E), C) <=> ?[F: $i] : (r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B)))))))),
% 5.23/3.61 inference(quant_intro,[status(thm)],[111])).
% 5.23/3.61 tff(113,axiom,(![A: $i] : (v1_relat_1(A) => ![B: $i] : (v1_relat_1(B) => ![C: $i] : (v1_relat_1(C) => ((C = k5_relat_1(A, B)) <=> ![D: $i, E: $i] : (r2_hidden(k4_tarski(D, E), C) <=> ?[F: $i] : (r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d8_relat_1')).
% 5.23/3.61 tff(114,plain,
% 5.23/3.61 (![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | ((C = k5_relat_1(A, B)) <=> ![D: $i, E: $i] : (r2_hidden(k4_tarski(D, E), C) <=> ?[F: $i] : (r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B)))))))),
% 5.23/3.61 inference(modus_ponens,[status(thm)],[113, 112])).
% 5.23/3.61 tff(115,plain,
% 5.23/3.61 (![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | ((C = k5_relat_1(A, B)) <=> ![D: $i, E: $i] : (r2_hidden(k4_tarski(D, E), C) <=> ?[F: $i] : (r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B)))))))),
% 5.23/3.61 inference(modus_ponens,[status(thm)],[114, 110])).
% 5.23/3.61 tff(116,plain,(
% 5.23/3.61 ![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (((~r2_hidden(k4_tarski(D, E), C)) | (r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A) & r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B))) & (r2_hidden(k4_tarski(D, E), C) | ![F: $i] : (~(r2_hidden(k4_tarski(D, F), A) & r2_hidden(k4_tarski(F, E), B)))))) & ((C = k5_relat_1(A, B)) | ((r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A) & r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B))) & ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : (~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A) & r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))))),
% 5.23/3.61 inference(skolemize,[status(sab)],[115])).
% 5.23/3.61 tff(117,plain,
% 5.23/3.61 (![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))) | (~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))))))))),
% 5.23/3.61 inference(modus_ponens,[status(thm)],[116, 109])).
% 5.23/3.61 tff(118,plain,
% 5.23/3.61 (![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))) | (~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))))))))),
% 5.23/3.61 inference(modus_ponens,[status(thm)],[117, 107])).
% 5.23/3.61 tff(119,plain,
% 5.23/3.61 (![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))) | (~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))),
% 5.23/3.61 inference(modus_ponens,[status(thm)],[118, 102])).
% 5.23/3.61 tff(120,plain,
% 5.23/3.61 (((~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))) | (~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))) | ((~v1_relat_1(k3_xboole_0(B!1, A!0))) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(k3_xboole_0(B!1, A!0), B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_F_11(C, B, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), B))))))))) | (~((~(C = k5_relat_1(k3_xboole_0(B!1, A!0), B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, k3_xboole_0(B!1, A!0)), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0)))))))))))))))) <=> ((~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))) | (~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))) | (~v1_relat_1(k3_xboole_0(B!1, A!0))) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(k3_xboole_0(B!1, A!0), B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_F_11(C, B, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), B))))))))) | (~((~(C = k5_relat_1(k3_xboole_0(B!1, A!0), B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, k3_xboole_0(B!1, A!0)), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0)))))))))))))))),
% 5.23/3.61 inference(rewrite,[status(thm)],[])).
% 5.23/3.61 tff(121,plain,
% 5.23/3.61 (((~v1_relat_1(k3_xboole_0(B!1, A!0))) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(k3_xboole_0(B!1, A!0), B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_F_11(C, B, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), B))))))))) | (~((~(C = k5_relat_1(k3_xboole_0(B!1, A!0), B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, k3_xboole_0(B!1, A!0)), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, E), B)))))))))))))) <=> ((~v1_relat_1(k3_xboole_0(B!1, A!0))) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(k3_xboole_0(B!1, A!0), B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_F_11(C, B, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), B))))))))) | (~((~(C = k5_relat_1(k3_xboole_0(B!1, A!0), B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, k3_xboole_0(B!1, A!0)), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0)))))))))))))))),
% 5.23/3.61 inference(rewrite,[status(thm)],[])).
% 5.23/3.61 tff(122,plain,
% 5.23/3.61 (((~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))) | (~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))) | ((~v1_relat_1(k3_xboole_0(B!1, A!0))) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(k3_xboole_0(B!1, A!0), B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_F_11(C, B, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), B))))))))) | (~((~(C = k5_relat_1(k3_xboole_0(B!1, A!0), B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, k3_xboole_0(B!1, A!0)), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))) <=> ((~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))) | (~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))) | ((~v1_relat_1(k3_xboole_0(B!1, A!0))) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(k3_xboole_0(B!1, A!0), B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_F_11(C, B, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), B))))))))) | (~((~(C = k5_relat_1(k3_xboole_0(B!1, A!0), B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, k3_xboole_0(B!1, A!0)), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0))))))))))))))))),
% 5.23/3.61 inference(monotonicity,[status(thm)],[121])).
% 5.23/3.61 tff(123,plain,
% 5.23/3.61 (((~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))) | (~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))) | ((~v1_relat_1(k3_xboole_0(B!1, A!0))) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(k3_xboole_0(B!1, A!0), B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_F_11(C, B, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), B))))))))) | (~((~(C = k5_relat_1(k3_xboole_0(B!1, A!0), B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, k3_xboole_0(B!1, A!0)), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))) <=> ((~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))) | (~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))) | (~v1_relat_1(k3_xboole_0(B!1, A!0))) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(k3_xboole_0(B!1, A!0), B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_F_11(C, B, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), B))))))))) | (~((~(C = k5_relat_1(k3_xboole_0(B!1, A!0), B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, k3_xboole_0(B!1, A!0)), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0)))))))))))))))),
% 5.23/3.62 inference(transitivity,[status(thm)],[122, 120])).
% 5.23/3.62 tff(124,plain,
% 5.23/3.62 ((~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))) | (~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))) | ((~v1_relat_1(k3_xboole_0(B!1, A!0))) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(k3_xboole_0(B!1, A!0), B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_F_11(C, B, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), B))))))))) | (~((~(C = k5_relat_1(k3_xboole_0(B!1, A!0), B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, k3_xboole_0(B!1, A!0)), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))),
% 5.23/3.62 inference(quant_inst,[status(thm)],[])).
% 5.23/3.62 tff(125,plain,
% 5.23/3.62 ((~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))) | (~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))) | (~v1_relat_1(k3_xboole_0(B!1, A!0))) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(k3_xboole_0(B!1, A!0), B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_F_11(C, B, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), B))))))))) | (~((~(C = k5_relat_1(k3_xboole_0(B!1, A!0), B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, k3_xboole_0(B!1, A!0)), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0))))))))))))))),
% 5.23/3.62 inference(modus_ponens,[status(thm)],[124, 123])).
% 5.23/3.62 tff(126,plain,
% 5.23/3.62 ((~v1_relat_1(k3_xboole_0(B!1, A!0))) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(k3_xboole_0(B!1, A!0), B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_F_11(C, B, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), B))))))))) | (~((~(C = k5_relat_1(k3_xboole_0(B!1, A!0), B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, k3_xboole_0(B!1, A!0)), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0))))))))))))))),
% 5.23/3.62 inference(unit_resolution,[status(thm)],[125, 119])).
% 5.23/3.62 tff(127,plain,
% 5.23/3.62 (![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(k3_xboole_0(B!1, A!0), B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_F_11(C, B, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), B))))))))) | (~((~(C = k5_relat_1(k3_xboole_0(B!1, A!0), B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, k3_xboole_0(B!1, A!0)), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0))))))))))))))),
% 5.23/3.62 inference(unit_resolution,[status(thm)],[126, 100])).
% 5.23/3.62 tff(128,plain,
% 5.23/3.62 (~((~v1_relat_1(C!2)) | r1_tarski(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2))))),
% 5.23/3.62 inference(and_elim,[status(thm)],[90])).
% 5.23/3.62 tff(129,plain,
% 5.23/3.62 (v1_relat_1(C!2)),
% 5.23/3.62 inference(or_elim,[status(thm)],[128])).
% 5.23/3.62 tff(130,plain,
% 5.23/3.62 (((~![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(k3_xboole_0(B!1, A!0), B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_F_11(C, B, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), B))))))))) | (~((~(C = k5_relat_1(k3_xboole_0(B!1, A!0), B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, k3_xboole_0(B!1, A!0)), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0))))))))))))))) | ((~v1_relat_1(C!2)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(k3_xboole_0(B!1, A!0), C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_F_11(C, C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C!2))))))))) | (~((~(C = k5_relat_1(k3_xboole_0(B!1, A!0), C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0)), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0))))))))))))))) <=> ((~![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(k3_xboole_0(B!1, A!0), B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_F_11(C, B, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), B))))))))) | (~((~(C = k5_relat_1(k3_xboole_0(B!1, A!0), B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, k3_xboole_0(B!1, A!0)), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0))))))))))))))) | (~v1_relat_1(C!2)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(k3_xboole_0(B!1, A!0), C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_F_11(C, C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C!2))))))))) | (~((~(C = k5_relat_1(k3_xboole_0(B!1, A!0), C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0)), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0))))))))))))))),
% 5.23/3.62 inference(rewrite,[status(thm)],[])).
% 5.23/3.62 tff(131,plain,
% 5.23/3.62 ((~![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(k3_xboole_0(B!1, A!0), B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_F_11(C, B, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), B))))))))) | (~((~(C = k5_relat_1(k3_xboole_0(B!1, A!0), B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, k3_xboole_0(B!1, A!0)), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0))))))))))))))) | ((~v1_relat_1(C!2)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(k3_xboole_0(B!1, A!0), C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_F_11(C, C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C!2))))))))) | (~((~(C = k5_relat_1(k3_xboole_0(B!1, A!0), C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0)), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0))))))))))))))),
% 5.23/3.62 inference(quant_inst,[status(thm)],[])).
% 5.23/3.62 tff(132,plain,
% 5.23/3.62 ((~![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(k3_xboole_0(B!1, A!0), B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_F_11(C, B, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, k3_xboole_0(B!1, A!0)), F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, k3_xboole_0(B!1, A!0))), B))))))))) | (~((~(C = k5_relat_1(k3_xboole_0(B!1, A!0), B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, k3_xboole_0(B!1, A!0)), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0))))))))))))))) | (~v1_relat_1(C!2)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(k3_xboole_0(B!1, A!0), C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_F_11(C, C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C!2))))))))) | (~((~(C = k5_relat_1(k3_xboole_0(B!1, A!0), C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0)), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0)))))))))))))),
% 5.23/3.62 inference(modus_ponens,[status(thm)],[131, 130])).
% 5.23/3.62 tff(133,plain,
% 5.23/3.62 (![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(k3_xboole_0(B!1, A!0), C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_F_11(C, C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C!2))))))))) | (~((~(C = k5_relat_1(k3_xboole_0(B!1, A!0), C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0)), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0)))))))))))))),
% 5.23/3.62 inference(unit_resolution,[status(thm)],[132, 129, 127])).
% 5.23/3.62 tff(134,plain,
% 5.23/3.62 (^[A: $i, B: $i] : refl((v1_relat_1(k5_relat_1(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A))) <=> (v1_relat_1(k5_relat_1(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A))))),
% 5.23/3.62 inference(bind,[status(th)],[])).
% 5.23/3.62 tff(135,plain,
% 5.23/3.62 (![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A))) <=> ![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))),
% 5.23/3.62 inference(quant_intro,[status(thm)],[134])).
% 5.23/3.62 tff(136,plain,
% 5.23/3.62 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_relat_1(A) & v1_relat_1(B)) <=> (~((~v1_relat_1(B)) | (~v1_relat_1(A))))), ((~(v1_relat_1(A) & v1_relat_1(B))) <=> (~(~((~v1_relat_1(B)) | (~v1_relat_1(A))))))), rewrite((~(~((~v1_relat_1(B)) | (~v1_relat_1(A))))) <=> ((~v1_relat_1(B)) | (~v1_relat_1(A)))), ((~(v1_relat_1(A) & v1_relat_1(B))) <=> ((~v1_relat_1(B)) | (~v1_relat_1(A))))), ((v1_relat_1(k5_relat_1(A, B)) | (~(v1_relat_1(A) & v1_relat_1(B)))) <=> (v1_relat_1(k5_relat_1(A, B)) | ((~v1_relat_1(B)) | (~v1_relat_1(A)))))), rewrite((v1_relat_1(k5_relat_1(A, B)) | ((~v1_relat_1(B)) | (~v1_relat_1(A)))) <=> (v1_relat_1(k5_relat_1(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))), ((v1_relat_1(k5_relat_1(A, B)) | (~(v1_relat_1(A) & v1_relat_1(B)))) <=> (v1_relat_1(k5_relat_1(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))))),
% 5.23/3.62 inference(bind,[status(th)],[])).
% 5.23/3.62 tff(137,plain,
% 5.23/3.62 (![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~(v1_relat_1(A) & v1_relat_1(B)))) <=> ![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))),
% 5.23/3.62 inference(quant_intro,[status(thm)],[136])).
% 5.23/3.62 tff(138,plain,
% 5.23/3.62 (![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~(v1_relat_1(A) & v1_relat_1(B)))) <=> ![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~(v1_relat_1(A) & v1_relat_1(B))))),
% 5.23/3.62 inference(rewrite,[status(thm)],[])).
% 5.23/3.62 tff(139,plain,
% 5.23/3.62 (^[A: $i, B: $i] : rewrite(((v1_relat_1(A) & v1_relat_1(B)) => v1_relat_1(k5_relat_1(A, B))) <=> (v1_relat_1(k5_relat_1(A, B)) | (~(v1_relat_1(A) & v1_relat_1(B)))))),
% 5.23/3.62 inference(bind,[status(th)],[])).
% 5.23/3.62 tff(140,plain,
% 5.23/3.62 (![A: $i, B: $i] : ((v1_relat_1(A) & v1_relat_1(B)) => v1_relat_1(k5_relat_1(A, B))) <=> ![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~(v1_relat_1(A) & v1_relat_1(B))))),
% 5.23/3.62 inference(quant_intro,[status(thm)],[139])).
% 5.23/3.62 tff(141,axiom,(![A: $i, B: $i] : ((v1_relat_1(A) & v1_relat_1(B)) => v1_relat_1(k5_relat_1(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k5_relat_1')).
% 5.23/3.62 tff(142,plain,
% 5.23/3.62 (![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~(v1_relat_1(A) & v1_relat_1(B))))),
% 5.23/3.62 inference(modus_ponens,[status(thm)],[141, 140])).
% 5.23/3.62 tff(143,plain,
% 5.23/3.62 (![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~(v1_relat_1(A) & v1_relat_1(B))))),
% 5.23/3.62 inference(modus_ponens,[status(thm)],[142, 138])).
% 5.23/3.62 tff(144,plain,(
% 5.23/3.62 ![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~(v1_relat_1(A) & v1_relat_1(B))))),
% 5.23/3.62 inference(skolemize,[status(sab)],[143])).
% 5.23/3.62 tff(145,plain,
% 5.23/3.62 (![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))),
% 5.23/3.62 inference(modus_ponens,[status(thm)],[144, 137])).
% 5.23/3.62 tff(146,plain,
% 5.23/3.62 (![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))),
% 5.23/3.62 inference(modus_ponens,[status(thm)],[145, 135])).
% 5.23/3.62 tff(147,plain,
% 5.23/3.62 (((~![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))) | ((~v1_relat_1(C!2)) | v1_relat_1(k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | (~v1_relat_1(k3_xboole_0(A!0, B!1))))) <=> ((~![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))) | (~v1_relat_1(C!2)) | v1_relat_1(k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | (~v1_relat_1(k3_xboole_0(A!0, B!1))))),
% 5.23/3.62 inference(rewrite,[status(thm)],[])).
% 5.23/3.62 tff(148,plain,
% 5.23/3.62 ((v1_relat_1(k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | (~v1_relat_1(C!2)) | (~v1_relat_1(k3_xboole_0(A!0, B!1)))) <=> ((~v1_relat_1(C!2)) | v1_relat_1(k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | (~v1_relat_1(k3_xboole_0(A!0, B!1))))),
% 5.23/3.62 inference(rewrite,[status(thm)],[])).
% 5.23/3.62 tff(149,plain,
% 5.23/3.62 (((~![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))) | (v1_relat_1(k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | (~v1_relat_1(C!2)) | (~v1_relat_1(k3_xboole_0(A!0, B!1))))) <=> ((~![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))) | ((~v1_relat_1(C!2)) | v1_relat_1(k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | (~v1_relat_1(k3_xboole_0(A!0, B!1)))))),
% 5.23/3.62 inference(monotonicity,[status(thm)],[148])).
% 5.23/3.62 tff(150,plain,
% 5.23/3.62 (((~![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))) | (v1_relat_1(k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | (~v1_relat_1(C!2)) | (~v1_relat_1(k3_xboole_0(A!0, B!1))))) <=> ((~![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))) | (~v1_relat_1(C!2)) | v1_relat_1(k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | (~v1_relat_1(k3_xboole_0(A!0, B!1))))),
% 5.23/3.62 inference(transitivity,[status(thm)],[149, 147])).
% 5.23/3.62 tff(151,plain,
% 5.23/3.62 ((~![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))) | (v1_relat_1(k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | (~v1_relat_1(C!2)) | (~v1_relat_1(k3_xboole_0(A!0, B!1))))),
% 5.23/3.62 inference(quant_inst,[status(thm)],[])).
% 5.23/3.62 tff(152,plain,
% 5.23/3.62 ((~![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))) | (~v1_relat_1(C!2)) | v1_relat_1(k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | (~v1_relat_1(k3_xboole_0(A!0, B!1)))),
% 5.23/3.62 inference(modus_ponens,[status(thm)],[151, 150])).
% 5.23/3.62 tff(153,plain,
% 5.23/3.62 (v1_relat_1(k5_relat_1(k3_xboole_0(A!0, B!1), C!2))),
% 5.23/3.62 inference(unit_resolution,[status(thm)],[152, 129, 146, 99])).
% 5.23/3.62 tff(154,plain,
% 5.23/3.62 (((~![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(k3_xboole_0(B!1, A!0), C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_F_11(C, C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C!2))))))))) | (~((~(C = k5_relat_1(k3_xboole_0(B!1, A!0), C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0)), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0)))))))))))))) | ((~v1_relat_1(k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (~((~((k5_relat_1(k3_xboole_0(A!0, B!1), C!2) = k5_relat_1(k3_xboole_0(B!1, A!0), C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0))), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_F_11(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(tptp_fun_F_11(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0))), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0))), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0)), F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0))), C!2))))))))) | (~((~(k5_relat_1(k3_xboole_0(A!0, B!1), C!2) = k5_relat_1(k3_xboole_0(B!1, A!0), C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0)), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0)))))))))))))) <=> ((~![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(k3_xboole_0(B!1, A!0), C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_F_11(C, C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C!2))))))))) | (~((~(C = k5_relat_1(k3_xboole_0(B!1, A!0), C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0)), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0)))))))))))))) | (~v1_relat_1(k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (~((~((k5_relat_1(k3_xboole_0(A!0, B!1), C!2) = k5_relat_1(k3_xboole_0(B!1, A!0), C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0))), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_F_11(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(tptp_fun_F_11(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0))), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0))), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0)), F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0))), C!2))))))))) | (~((~(k5_relat_1(k3_xboole_0(A!0, B!1), C!2) = k5_relat_1(k3_xboole_0(B!1, A!0), C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0)), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0)))))))))))))),
% 5.23/3.63 inference(rewrite,[status(thm)],[])).
% 5.23/3.63 tff(155,plain,
% 5.23/3.63 ((~![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(k3_xboole_0(B!1, A!0), C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_F_11(C, C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C!2))))))))) | (~((~(C = k5_relat_1(k3_xboole_0(B!1, A!0), C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0)), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0)))))))))))))) | ((~v1_relat_1(k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (~((~((k5_relat_1(k3_xboole_0(A!0, B!1), C!2) = k5_relat_1(k3_xboole_0(B!1, A!0), C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0))), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_F_11(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(tptp_fun_F_11(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0))), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0))), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0)), F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0))), C!2))))))))) | (~((~(k5_relat_1(k3_xboole_0(A!0, B!1), C!2) = k5_relat_1(k3_xboole_0(B!1, A!0), C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0)), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0)))))))))))))),
% 5.23/3.63 inference(quant_inst,[status(thm)],[])).
% 5.23/3.63 tff(156,plain,
% 5.23/3.63 ((~![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(k3_xboole_0(B!1, A!0), C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_F_11(C, C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, k3_xboole_0(B!1, A!0)), F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, k3_xboole_0(B!1, A!0))), C!2))))))))) | (~((~(C = k5_relat_1(k3_xboole_0(B!1, A!0), C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0)), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0)))))))))))))) | (~v1_relat_1(k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (~((~((k5_relat_1(k3_xboole_0(A!0, B!1), C!2) = k5_relat_1(k3_xboole_0(B!1, A!0), C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0))), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_F_11(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(tptp_fun_F_11(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0))), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0))), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0)), F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0))), C!2))))))))) | (~((~(k5_relat_1(k3_xboole_0(A!0, B!1), C!2) = k5_relat_1(k3_xboole_0(B!1, A!0), C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0)), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0))))))))))))),
% 5.23/3.63 inference(modus_ponens,[status(thm)],[155, 154])).
% 5.23/3.63 tff(157,plain,
% 5.23/3.63 (~((~((k5_relat_1(k3_xboole_0(A!0, B!1), C!2) = k5_relat_1(k3_xboole_0(B!1, A!0), C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0))), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_F_11(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(tptp_fun_F_11(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0))), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0))), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0)), F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0))), C!2))))))))) | (~((~(k5_relat_1(k3_xboole_0(A!0, B!1), C!2) = k5_relat_1(k3_xboole_0(B!1, A!0), C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0)), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0)))))))))))),
% 5.23/3.63 inference(unit_resolution,[status(thm)],[156, 153, 133])).
% 5.23/3.63 tff(158,plain,
% 5.23/3.63 (((~((k5_relat_1(k3_xboole_0(A!0, B!1), C!2) = k5_relat_1(k3_xboole_0(B!1, A!0), C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0))), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_F_11(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(tptp_fun_F_11(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0))), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_E_9(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0))), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0)), F), k3_xboole_0(B!1, A!0))) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), C!2, k3_xboole_0(B!1, A!0))), C!2))))))))) | (~((~(k5_relat_1(k3_xboole_0(A!0, B!1), C!2) = k5_relat_1(k3_xboole_0(B!1, A!0), C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0)), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0))))))))))) | ((~(k5_relat_1(k3_xboole_0(A!0, B!1), C!2) = k5_relat_1(k3_xboole_0(B!1, A!0), C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0)), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0)))))))))),
% 5.23/3.63 inference(tautology,[status(thm)],[])).
% 5.23/3.63 tff(159,plain,
% 5.23/3.63 ((~(k5_relat_1(k3_xboole_0(A!0, B!1), C!2) = k5_relat_1(k3_xboole_0(B!1, A!0), C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0)), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0))))))))),
% 5.23/3.63 inference(unit_resolution,[status(thm)],[158, 157])).
% 5.23/3.63 tff(160,plain,
% 5.23/3.63 (k5_relat_1(k3_xboole_0(B!1, A!0), C!2) = k5_relat_1(k3_xboole_0(A!0, B!1), C!2)),
% 5.23/3.63 inference(monotonicity,[status(thm)],[59])).
% 5.23/3.63 tff(161,plain,
% 5.23/3.63 (k5_relat_1(k3_xboole_0(A!0, B!1), C!2) = k5_relat_1(k3_xboole_0(B!1, A!0), C!2)),
% 5.23/3.63 inference(symmetry,[status(thm)],[160])).
% 5.23/3.63 tff(162,plain,
% 5.23/3.63 ((~((~(k5_relat_1(k3_xboole_0(A!0, B!1), C!2) = k5_relat_1(k3_xboole_0(B!1, A!0), C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0)), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0)))))))))) | (~(k5_relat_1(k3_xboole_0(A!0, B!1), C!2) = k5_relat_1(k3_xboole_0(B!1, A!0), C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0)), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0))))))))),
% 5.23/3.63 inference(tautology,[status(thm)],[])).
% 5.23/3.63 tff(163,plain,
% 5.23/3.63 (![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0)), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0))))))))),
% 5.23/3.63 inference(unit_resolution,[status(thm)],[162, 161, 159])).
% 5.23/3.63 tff(164,plain,
% 5.23/3.63 ((~![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0)), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), k3_xboole_0(B!1, A!0))))))))) | (~((~((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), F), k3_xboole_0(B!1, A!0))))))))),
% 5.23/3.63 inference(quant_inst,[status(thm)],[])).
% 5.23/3.63 tff(165,plain,
% 5.23/3.63 (~((~((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), F), k3_xboole_0(B!1, A!0)))))))),
% 5.23/3.64 inference(unit_resolution,[status(thm)],[164, 163])).
% 5.23/3.64 tff(166,plain,
% 5.23/3.64 (((~((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~(r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), F), k3_xboole_0(B!1, A!0))))))) | ((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))),
% 5.23/3.64 inference(tautology,[status(thm)],[])).
% 5.23/3.64 tff(167,plain,
% 5.23/3.64 ((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0)))))),
% 5.23/3.64 inference(unit_resolution,[status(thm)],[166, 165])).
% 5.23/3.64 tff(168,plain,
% 5.23/3.64 (^[A: $i] : refl((~((~((~v1_relat_1(A)) | ![B: $i] : ((~r2_hidden(B, A)) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B)))))) | (~(v1_relat_1(A) | (~((~r2_hidden(tptp_fun_B_5(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_5(A) = k4_tarski(C, D)))))))))) <=> (~((~((~v1_relat_1(A)) | ![B: $i] : ((~r2_hidden(B, A)) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B)))))) | (~(v1_relat_1(A) | (~((~r2_hidden(tptp_fun_B_5(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_5(A) = k4_tarski(C, D)))))))))))),
% 5.23/3.64 inference(bind,[status(th)],[])).
% 5.23/3.64 tff(169,plain,
% 5.23/3.64 (![A: $i] : (~((~((~v1_relat_1(A)) | ![B: $i] : ((~r2_hidden(B, A)) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B)))))) | (~(v1_relat_1(A) | (~((~r2_hidden(tptp_fun_B_5(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_5(A) = k4_tarski(C, D)))))))))) <=> ![A: $i] : (~((~((~v1_relat_1(A)) | ![B: $i] : ((~r2_hidden(B, A)) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B)))))) | (~(v1_relat_1(A) | (~((~r2_hidden(tptp_fun_B_5(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_5(A) = k4_tarski(C, D))))))))))),
% 5.23/3.64 inference(quant_intro,[status(thm)],[168])).
% 5.23/3.64 tff(170,plain,
% 5.23/3.64 (^[A: $i] : rewrite((~((~((~v1_relat_1(A)) | ![B: $i] : ((~r2_hidden(B, A)) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B)))))) | (~(v1_relat_1(A) | (~((~r2_hidden(tptp_fun_B_5(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_5(A) = k4_tarski(C, D)))))))))) <=> (~((~((~v1_relat_1(A)) | ![B: $i] : ((~r2_hidden(B, A)) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B)))))) | (~(v1_relat_1(A) | (~((~r2_hidden(tptp_fun_B_5(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_5(A) = k4_tarski(C, D)))))))))))),
% 5.23/3.64 inference(bind,[status(th)],[])).
% 5.23/3.64 tff(171,plain,
% 5.23/3.64 (![A: $i] : (~((~((~v1_relat_1(A)) | ![B: $i] : ((~r2_hidden(B, A)) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B)))))) | (~(v1_relat_1(A) | (~((~r2_hidden(tptp_fun_B_5(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_5(A) = k4_tarski(C, D)))))))))) <=> ![A: $i] : (~((~((~v1_relat_1(A)) | ![B: $i] : ((~r2_hidden(B, A)) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B)))))) | (~(v1_relat_1(A) | (~((~r2_hidden(tptp_fun_B_5(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_5(A) = k4_tarski(C, D))))))))))),
% 5.23/3.64 inference(quant_intro,[status(thm)],[170])).
% 5.23/3.64 tff(172,plain,
% 5.23/3.64 (![A: $i] : (~((~((~v1_relat_1(A)) | ![B: $i] : ((~r2_hidden(B, A)) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B)))))) | (~(v1_relat_1(A) | (~((~r2_hidden(tptp_fun_B_5(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_5(A) = k4_tarski(C, D)))))))))) <=> ![A: $i] : (~((~((~v1_relat_1(A)) | ![B: $i] : ((~r2_hidden(B, A)) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B)))))) | (~(v1_relat_1(A) | (~((~r2_hidden(tptp_fun_B_5(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_5(A) = k4_tarski(C, D))))))))))),
% 5.23/3.64 inference(transitivity,[status(thm)],[171, 169])).
% 5.23/3.64 tff(173,plain,
% 5.23/3.64 (^[A: $i] : trans(monotonicity(rewrite(((~v1_relat_1(A)) | ![B: $i] : ((~r2_hidden(B, A)) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B))))) <=> ((~v1_relat_1(A)) | ![B: $i] : ((~r2_hidden(B, A)) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B)))))), rewrite((v1_relat_1(A) | (r2_hidden(tptp_fun_B_5(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_5(A) = k4_tarski(C, D))))) <=> (v1_relat_1(A) | (~((~r2_hidden(tptp_fun_B_5(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_5(A) = k4_tarski(C, D)))))))), ((((~v1_relat_1(A)) | ![B: $i] : ((~r2_hidden(B, A)) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B))))) & (v1_relat_1(A) | (r2_hidden(tptp_fun_B_5(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_5(A) = k4_tarski(C, D)))))) <=> (((~v1_relat_1(A)) | ![B: $i] : ((~r2_hidden(B, A)) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B))))) & (v1_relat_1(A) | (~((~r2_hidden(tptp_fun_B_5(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_5(A) = k4_tarski(C, D)))))))))), rewrite((((~v1_relat_1(A)) | ![B: $i] : ((~r2_hidden(B, A)) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B))))) & (v1_relat_1(A) | (~((~r2_hidden(tptp_fun_B_5(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_5(A) = k4_tarski(C, D)))))))) <=> (~((~((~v1_relat_1(A)) | ![B: $i] : ((~r2_hidden(B, A)) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B)))))) | (~(v1_relat_1(A) | (~((~r2_hidden(tptp_fun_B_5(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_5(A) = k4_tarski(C, D))))))))))), ((((~v1_relat_1(A)) | ![B: $i] : ((~r2_hidden(B, A)) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B))))) & (v1_relat_1(A) | (r2_hidden(tptp_fun_B_5(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_5(A) = k4_tarski(C, D)))))) <=> (~((~((~v1_relat_1(A)) | ![B: $i] : ((~r2_hidden(B, A)) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B)))))) | (~(v1_relat_1(A) | (~((~r2_hidden(tptp_fun_B_5(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_5(A) = k4_tarski(C, D))))))))))))),
% 5.23/3.64 inference(bind,[status(th)],[])).
% 5.23/3.64 tff(174,plain,
% 5.23/3.64 (![A: $i] : (((~v1_relat_1(A)) | ![B: $i] : ((~r2_hidden(B, A)) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B))))) & (v1_relat_1(A) | (r2_hidden(tptp_fun_B_5(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_5(A) = k4_tarski(C, D)))))) <=> ![A: $i] : (~((~((~v1_relat_1(A)) | ![B: $i] : ((~r2_hidden(B, A)) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B)))))) | (~(v1_relat_1(A) | (~((~r2_hidden(tptp_fun_B_5(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_5(A) = k4_tarski(C, D))))))))))),
% 5.23/3.64 inference(quant_intro,[status(thm)],[173])).
% 5.23/3.64 tff(175,plain,
% 5.23/3.64 (^[A: $i] : rewrite((((~v1_relat_1(A)) | ![B: $i] : ((~r2_hidden(B, A)) | (~(~(B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B))))))) & (v1_relat_1(A) | (r2_hidden(tptp_fun_B_5(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_5(A) = k4_tarski(C, D)))))) <=> (((~v1_relat_1(A)) | ![B: $i] : ((~r2_hidden(B, A)) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B))))) & (v1_relat_1(A) | (r2_hidden(tptp_fun_B_5(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_5(A) = k4_tarski(C, D)))))))),
% 5.23/3.64 inference(bind,[status(th)],[])).
% 5.23/3.64 tff(176,plain,
% 5.23/3.64 (![A: $i] : (((~v1_relat_1(A)) | ![B: $i] : ((~r2_hidden(B, A)) | (~(~(B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B))))))) & (v1_relat_1(A) | (r2_hidden(tptp_fun_B_5(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_5(A) = k4_tarski(C, D)))))) <=> ![A: $i] : (((~v1_relat_1(A)) | ![B: $i] : ((~r2_hidden(B, A)) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B))))) & (v1_relat_1(A) | (r2_hidden(tptp_fun_B_5(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_5(A) = k4_tarski(C, D))))))),
% 5.23/3.64 inference(quant_intro,[status(thm)],[175])).
% 5.23/3.64 tff(177,plain,
% 5.23/3.64 (![A: $i] : (v1_relat_1(A) <=> ![B: $i] : (~(r2_hidden(B, A) & ![C: $i, D: $i] : (~(B = k4_tarski(C, D)))))) <=> ![A: $i] : (v1_relat_1(A) <=> ![B: $i] : (~(r2_hidden(B, A) & ![C: $i, D: $i] : (~(B = k4_tarski(C, D))))))),
% 5.23/3.64 inference(rewrite,[status(thm)],[])).
% 5.23/3.64 tff(178,axiom,(![A: $i] : (v1_relat_1(A) <=> ![B: $i] : (~(r2_hidden(B, A) & ![C: $i, D: $i] : (~(B = k4_tarski(C, D))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_relat_1')).
% 5.23/3.64 tff(179,plain,
% 5.23/3.64 (![A: $i] : (v1_relat_1(A) <=> ![B: $i] : (~(r2_hidden(B, A) & ![C: $i, D: $i] : (~(B = k4_tarski(C, D))))))),
% 5.23/3.64 inference(modus_ponens,[status(thm)],[178, 177])).
% 5.23/3.64 tff(180,plain,(
% 5.23/3.64 ![A: $i] : (((~v1_relat_1(A)) | ![B: $i] : ((~r2_hidden(B, A)) | (~(~(B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B))))))) & (v1_relat_1(A) | (r2_hidden(tptp_fun_B_5(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_5(A) = k4_tarski(C, D))))))),
% 5.23/3.64 inference(skolemize,[status(sab)],[179])).
% 5.23/3.64 tff(181,plain,
% 5.23/3.64 (![A: $i] : (((~v1_relat_1(A)) | ![B: $i] : ((~r2_hidden(B, A)) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B))))) & (v1_relat_1(A) | (r2_hidden(tptp_fun_B_5(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_5(A) = k4_tarski(C, D))))))),
% 5.23/3.64 inference(modus_ponens,[status(thm)],[180, 176])).
% 5.23/3.64 tff(182,plain,
% 5.23/3.64 (![A: $i] : (~((~((~v1_relat_1(A)) | ![B: $i] : ((~r2_hidden(B, A)) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B)))))) | (~(v1_relat_1(A) | (~((~r2_hidden(tptp_fun_B_5(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_5(A) = k4_tarski(C, D))))))))))),
% 5.23/3.64 inference(modus_ponens,[status(thm)],[181, 174])).
% 5.23/3.64 tff(183,plain,
% 5.23/3.64 (![A: $i] : (~((~((~v1_relat_1(A)) | ![B: $i] : ((~r2_hidden(B, A)) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B)))))) | (~(v1_relat_1(A) | (~((~r2_hidden(tptp_fun_B_5(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_5(A) = k4_tarski(C, D))))))))))),
% 5.23/3.64 inference(modus_ponens,[status(thm)],[182, 172])).
% 5.23/3.64 tff(184,plain,
% 5.23/3.64 ((~![A: $i] : (~((~((~v1_relat_1(A)) | ![B: $i] : ((~r2_hidden(B, A)) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B)))))) | (~(v1_relat_1(A) | (~((~r2_hidden(tptp_fun_B_5(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_5(A) = k4_tarski(C, D))))))))))) | (~((~((~v1_relat_1(k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | ![B: $i] : ((~r2_hidden(B, k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B)))))) | (~(v1_relat_1(k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | (~((~r2_hidden(tptp_fun_B_5(k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (~![C: $i, D: $i] : (~(tptp_fun_B_5(k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) = k4_tarski(C, D))))))))))),
% 5.23/3.64 inference(quant_inst,[status(thm)],[])).
% 5.23/3.64 tff(185,plain,
% 5.23/3.64 (~((~((~v1_relat_1(k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | ![B: $i] : ((~r2_hidden(B, k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B)))))) | (~(v1_relat_1(k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | (~((~r2_hidden(tptp_fun_B_5(k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (~![C: $i, D: $i] : (~(tptp_fun_B_5(k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) = k4_tarski(C, D)))))))))),
% 5.23/3.64 inference(unit_resolution,[status(thm)],[184, 183])).
% 5.23/3.64 tff(186,plain,
% 5.23/3.64 (((~((~v1_relat_1(k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | ![B: $i] : ((~r2_hidden(B, k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B)))))) | (~(v1_relat_1(k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) | (~((~r2_hidden(tptp_fun_B_5(k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (~![C: $i, D: $i] : (~(tptp_fun_B_5(k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) = k4_tarski(C, D))))))))) | ((~v1_relat_1(k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | ![B: $i] : ((~r2_hidden(B, k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B)))))),
% 5.23/3.64 inference(tautology,[status(thm)],[])).
% 5.23/3.64 tff(187,plain,
% 5.23/3.64 ((~v1_relat_1(k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | ![B: $i] : ((~r2_hidden(B, k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B))))),
% 5.23/3.64 inference(unit_resolution,[status(thm)],[186, 185])).
% 5.23/3.64 tff(188,plain,
% 5.23/3.64 ((~((~v1_relat_1(k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | ![B: $i] : ((~r2_hidden(B, k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B)))))) | (~v1_relat_1(k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | ![B: $i] : ((~r2_hidden(B, k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B))))),
% 5.23/3.64 inference(tautology,[status(thm)],[])).
% 5.23/3.64 tff(189,plain,
% 5.23/3.64 ((~((~v1_relat_1(k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | ![B: $i] : ((~r2_hidden(B, k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B)))))) | ![B: $i] : ((~r2_hidden(B, k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B))))),
% 5.23/3.64 inference(unit_resolution,[status(thm)],[188, 153])).
% 5.23/3.64 tff(190,plain,
% 5.23/3.64 (![B: $i] : ((~r2_hidden(B, k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B))))),
% 5.23/3.64 inference(unit_resolution,[status(thm)],[189, 187])).
% 5.23/3.64 tff(191,plain,
% 5.23/3.64 (^[A: $i, B: $i] : refl((~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_6(B, A), A)) | r2_hidden(tptp_fun_C_6(B, A), B))))))) <=> (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_6(B, A), A)) | r2_hidden(tptp_fun_C_6(B, A), B))))))))),
% 5.23/3.64 inference(bind,[status(th)],[])).
% 5.23/3.64 tff(192,plain,
% 5.23/3.64 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_6(B, A), A)) | r2_hidden(tptp_fun_C_6(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_6(B, A), A)) | r2_hidden(tptp_fun_C_6(B, A), B)))))))),
% 5.23/3.64 inference(quant_intro,[status(thm)],[191])).
% 5.23/3.64 tff(193,plain,
% 5.23/3.64 (^[A: $i, B: $i] : rewrite((~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_6(B, A), A)) | r2_hidden(tptp_fun_C_6(B, A), B))))))) <=> (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_6(B, A), A)) | r2_hidden(tptp_fun_C_6(B, A), B))))))))),
% 5.23/3.64 inference(bind,[status(th)],[])).
% 5.23/3.64 tff(194,plain,
% 5.23/3.64 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_6(B, A), A)) | r2_hidden(tptp_fun_C_6(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_6(B, A), A)) | r2_hidden(tptp_fun_C_6(B, A), B)))))))),
% 5.23/3.64 inference(quant_intro,[status(thm)],[193])).
% 5.23/3.64 tff(195,plain,
% 5.23/3.64 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_6(B, A), A)) | r2_hidden(tptp_fun_C_6(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_6(B, A), A)) | r2_hidden(tptp_fun_C_6(B, A), B)))))))),
% 5.23/3.64 inference(transitivity,[status(thm)],[194, 192])).
% 5.23/3.64 tff(196,plain,
% 5.23/3.64 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) <=> ((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))), rewrite((r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_6(B, A), A)) | r2_hidden(tptp_fun_C_6(B, A), B)))) <=> (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_6(B, A), A)) | r2_hidden(tptp_fun_C_6(B, A), B))))), ((((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_6(B, A), A)) | r2_hidden(tptp_fun_C_6(B, A), B))))) <=> (((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_6(B, A), A)) | r2_hidden(tptp_fun_C_6(B, A), B))))))), rewrite((((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_6(B, A), A)) | r2_hidden(tptp_fun_C_6(B, A), B))))) <=> (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_6(B, A), A)) | r2_hidden(tptp_fun_C_6(B, A), B)))))))), ((((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_6(B, A), A)) | r2_hidden(tptp_fun_C_6(B, A), B))))) <=> (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_6(B, A), A)) | r2_hidden(tptp_fun_C_6(B, A), B)))))))))),
% 5.23/3.64 inference(bind,[status(th)],[])).
% 5.23/3.64 tff(197,plain,
% 5.23/3.64 (![A: $i, B: $i] : (((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_6(B, A), A)) | r2_hidden(tptp_fun_C_6(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_6(B, A), A)) | r2_hidden(tptp_fun_C_6(B, A), B)))))))),
% 5.23/3.64 inference(quant_intro,[status(thm)],[196])).
% 5.23/3.64 tff(198,plain,
% 5.23/3.64 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) <=> ![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 5.23/3.64 inference(rewrite,[status(thm)],[])).
% 5.23/3.64 tff(199,plain,
% 5.23/3.64 (^[A: $i, B: $i] : rewrite((r1_tarski(A, B) <=> ![C: $i] : (r2_hidden(C, A) => r2_hidden(C, B))) <=> (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))))),
% 5.23/3.64 inference(bind,[status(th)],[])).
% 5.23/3.64 tff(200,plain,
% 5.23/3.64 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : (r2_hidden(C, A) => r2_hidden(C, B))) <=> ![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 5.23/3.64 inference(quant_intro,[status(thm)],[199])).
% 5.23/3.64 tff(201,axiom,(![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : (r2_hidden(C, A) => r2_hidden(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_tarski')).
% 5.23/3.64 tff(202,plain,
% 5.23/3.64 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 5.23/3.64 inference(modus_ponens,[status(thm)],[201, 200])).
% 5.23/3.64 tff(203,plain,
% 5.23/3.64 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 5.23/3.64 inference(modus_ponens,[status(thm)],[202, 198])).
% 5.23/3.64 tff(204,plain,(
% 5.23/3.64 ![A: $i, B: $i] : (((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_6(B, A), A)) | r2_hidden(tptp_fun_C_6(B, A), B)))))),
% 5.23/3.64 inference(skolemize,[status(sab)],[203])).
% 5.23/3.64 tff(205,plain,
% 5.23/3.64 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_6(B, A), A)) | r2_hidden(tptp_fun_C_6(B, A), B)))))))),
% 5.23/3.64 inference(modus_ponens,[status(thm)],[204, 197])).
% 5.23/3.64 tff(206,plain,
% 5.23/3.64 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_6(B, A), A)) | r2_hidden(tptp_fun_C_6(B, A), B)))))))),
% 5.23/3.64 inference(modus_ponens,[status(thm)],[205, 195])).
% 5.23/3.64 tff(207,plain,
% 5.23/3.64 ((~![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_6(B, A), A)) | r2_hidden(tptp_fun_C_6(B, A), B)))))))) | (~((~((~r1_tarski(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)))) | ![C: $i] : ((~r2_hidden(C, k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | r2_hidden(C, k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)))))) | (~(r1_tarski(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2))) | (~((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)))))))))),
% 5.23/3.64 inference(quant_inst,[status(thm)],[])).
% 5.23/3.64 tff(208,plain,
% 5.23/3.64 (~((~((~r1_tarski(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)))) | ![C: $i] : ((~r2_hidden(C, k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | r2_hidden(C, k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)))))) | (~(r1_tarski(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2))) | (~((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2))))))))),
% 5.23/3.64 inference(unit_resolution,[status(thm)],[207, 206])).
% 5.23/3.64 tff(209,plain,
% 5.23/3.64 (((~((~r1_tarski(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)))) | ![C: $i] : ((~r2_hidden(C, k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | r2_hidden(C, k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)))))) | (~(r1_tarski(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2))) | (~((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)))))))) | (r1_tarski(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2))) | (~((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2))))))),
% 5.23/3.64 inference(tautology,[status(thm)],[])).
% 5.23/3.64 tff(210,plain,
% 5.23/3.64 (r1_tarski(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2))) | (~((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)))))),
% 5.23/3.64 inference(unit_resolution,[status(thm)],[209, 208])).
% 5.23/3.64 tff(211,plain,
% 5.23/3.64 (~r1_tarski(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)))),
% 5.23/3.64 inference(or_elim,[status(thm)],[128])).
% 5.23/3.64 tff(212,plain,
% 5.23/3.64 ((~(r1_tarski(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2))) | (~((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2))))))) | r1_tarski(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2))) | (~((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)))))),
% 5.23/3.65 inference(tautology,[status(thm)],[])).
% 5.23/3.65 tff(213,plain,
% 5.23/3.65 ((~(r1_tarski(k5_relat_1(k3_xboole_0(A!0, B!1), C!2), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2))) | (~((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2))))))) | (~((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)))))),
% 5.23/3.65 inference(unit_resolution,[status(thm)],[212, 211])).
% 5.23/3.65 tff(214,plain,
% 5.23/3.65 (~((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2))))),
% 5.23/3.65 inference(unit_resolution,[status(thm)],[213, 210])).
% 5.23/3.65 tff(215,plain,
% 5.23/3.65 (((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)))) | r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))),
% 5.23/3.65 inference(tautology,[status(thm)],[])).
% 5.23/3.65 tff(216,plain,
% 5.23/3.65 (r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))),
% 5.23/3.65 inference(unit_resolution,[status(thm)],[215, 214])).
% 5.23/3.65 tff(217,plain,
% 5.23/3.65 (((~![B: $i] : ((~r2_hidden(B, k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B))))) | ((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) = k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))))))) <=> ((~![B: $i] : ((~r2_hidden(B, k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B))))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) = k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))))))),
% 5.23/3.65 inference(rewrite,[status(thm)],[])).
% 5.23/3.65 tff(218,plain,
% 5.23/3.65 ((~![B: $i] : ((~r2_hidden(B, k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B))))) | ((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) = k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))))))),
% 5.23/3.65 inference(quant_inst,[status(thm)],[])).
% 5.23/3.65 tff(219,plain,
% 5.23/3.65 ((~![B: $i] : ((~r2_hidden(B, k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (B = k4_tarski(tptp_fun_C_4(B), tptp_fun_D_3(B))))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) = k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))))),
% 5.23/3.65 inference(modus_ponens,[status(thm)],[218, 217])).
% 5.23/3.65 tff(220,plain,
% 5.23/3.65 (tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) = k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))))),
% 5.23/3.65 inference(unit_resolution,[status(thm)],[219, 216, 190])).
% 5.23/3.65 tff(221,plain,
% 5.23/3.65 (k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))) = tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))),
% 5.23/3.65 inference(symmetry,[status(thm)],[220])).
% 5.23/3.65 tff(222,plain,
% 5.23/3.65 (r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) <=> r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))),
% 5.23/3.65 inference(monotonicity,[status(thm)],[221])).
% 5.23/3.65 tff(223,plain,
% 5.23/3.65 (r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)) <=> r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))),
% 5.23/3.65 inference(symmetry,[status(thm)],[222])).
% 5.23/3.65 tff(224,plain,
% 5.23/3.65 (r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))),
% 5.23/3.65 inference(modus_ponens,[status(thm)],[216, 223])).
% 5.23/3.65 tff(225,plain,
% 5.23/3.65 ((~((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))))) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0)))))),
% 5.23/3.65 inference(tautology,[status(thm)],[])).
% 5.23/3.65 tff(226,plain,
% 5.23/3.65 (~((~r2_hidden(k4_tarski(tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))))),
% 5.23/3.65 inference(unit_resolution,[status(thm)],[225, 224, 167])).
% 5.23/3.65 tff(227,plain,
% 5.23/3.65 (((~r2_hidden(k4_tarski(tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0)))) | r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))),
% 5.23/3.65 inference(tautology,[status(thm)],[])).
% 5.23/3.65 tff(228,plain,
% 5.23/3.65 (r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))),
% 5.23/3.65 inference(unit_resolution,[status(thm)],[227, 226])).
% 5.23/3.65 tff(229,plain,
% 5.23/3.65 ((~((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) <=> ((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1))))) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) | (~((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1))))),
% 5.23/3.65 inference(tautology,[status(thm)],[])).
% 5.23/3.65 tff(230,plain,
% 5.23/3.65 ((~((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0))) <=> ((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1))))) | (~((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1))))),
% 5.23/3.65 inference(unit_resolution,[status(thm)],[229, 228])).
% 5.23/3.65 tff(231,plain,
% 5.23/3.65 (~((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1)))),
% 5.23/3.65 inference(unit_resolution,[status(thm)],[230, 49])).
% 5.23/3.65 tff(232,plain,
% 5.23/3.65 (((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1))) | r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1)),
% 5.23/3.66 inference(tautology,[status(thm)],[])).
% 5.23/3.66 tff(233,plain,
% 5.23/3.66 (r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1)),
% 5.23/3.66 inference(unit_resolution,[status(thm)],[232, 231])).
% 5.23/3.66 tff(234,plain,
% 5.23/3.66 (((~r2_hidden(k4_tarski(tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), k3_xboole_0(B!1, A!0)))) | r2_hidden(k4_tarski(tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)),
% 5.23/3.66 inference(tautology,[status(thm)],[])).
% 5.23/3.66 tff(235,plain,
% 5.23/3.66 (r2_hidden(k4_tarski(tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)),
% 5.23/3.66 inference(unit_resolution,[status(thm)],[234, 226])).
% 5.23/3.66 tff(236,plain,
% 5.23/3.66 (r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(B!1, C!2)) <=> r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2))),
% 5.23/3.66 inference(monotonicity,[status(thm)],[221])).
% 5.23/3.66 tff(237,plain,
% 5.23/3.66 (r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2)) <=> r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(B!1, C!2))),
% 5.23/3.66 inference(symmetry,[status(thm)],[236])).
% 5.23/3.66 tff(238,plain,
% 5.23/3.66 ((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2))) <=> (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(B!1, C!2)))),
% 5.23/3.66 inference(monotonicity,[status(thm)],[237])).
% 5.23/3.66 tff(239,plain,
% 5.23/3.66 (r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(A!0, C!2)) <=> r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))),
% 5.23/3.66 inference(monotonicity,[status(thm)],[221])).
% 5.23/3.66 tff(240,plain,
% 5.23/3.66 (((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1))) | r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)),
% 5.23/3.66 inference(tautology,[status(thm)],[])).
% 5.23/3.66 tff(241,plain,
% 5.23/3.66 (r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)),
% 5.23/3.66 inference(unit_resolution,[status(thm)],[240, 231])).
% 5.23/3.66 tff(242,assumption,(![F: $i] : ((~r2_hidden(k4_tarski(F, tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), F), A!0)))), introduced(assumption)).
% 5.23/3.66 tff(243,plain,
% 5.23/3.66 (((~![F: $i] : ((~r2_hidden(k4_tarski(F, tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), F), A!0)))) | ((~r2_hidden(k4_tarski(tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)))) <=> ((~![F: $i] : ((~r2_hidden(k4_tarski(F, tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), F), A!0)))) | (~r2_hidden(k4_tarski(tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)))),
% 5.23/3.66 inference(rewrite,[status(thm)],[])).
% 5.23/3.66 tff(244,plain,
% 5.23/3.66 ((~![F: $i] : ((~r2_hidden(k4_tarski(F, tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), F), A!0)))) | ((~r2_hidden(k4_tarski(tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0)))),
% 5.23/3.66 inference(quant_inst,[status(thm)],[])).
% 5.23/3.66 tff(245,plain,
% 5.23/3.66 ((~![F: $i] : ((~r2_hidden(k4_tarski(F, tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), F), A!0)))) | (~r2_hidden(k4_tarski(tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), A!0))),
% 5.23/3.66 inference(modus_ponens,[status(thm)],[244, 243])).
% 5.23/3.66 tff(246,plain,
% 5.23/3.66 ($false),
% 5.23/3.66 inference(unit_resolution,[status(thm)],[245, 242, 235, 241])).
% 5.23/3.66 tff(247,plain,(~![F: $i] : ((~r2_hidden(k4_tarski(F, tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), F), A!0)))), inference(lemma,lemma(discharge,[]))).
% 5.23/3.66 tff(248,plain,
% 5.23/3.66 (((~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))) | (~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))) | ((~v1_relat_1(A!0)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A!0, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_E_9(C, B, A!0)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_F_11(C, B, A!0)), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A!0), tptp_fun_E_9(C, B, A!0)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_E_9(C, B, A!0)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), F), A!0)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A!0)), B))))))))) | (~((~(C = k5_relat_1(A!0, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A!0), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), A!0))))))))))))))) <=> ((~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))) | (~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))) | (~v1_relat_1(A!0)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A!0, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_E_9(C, B, A!0)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_F_11(C, B, A!0)), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A!0), tptp_fun_E_9(C, B, A!0)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_E_9(C, B, A!0)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), F), A!0)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A!0)), B))))))))) | (~((~(C = k5_relat_1(A!0, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A!0), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), A!0))))))))))))))),
% 5.23/3.66 inference(rewrite,[status(thm)],[])).
% 5.23/3.66 tff(249,plain,
% 5.23/3.66 (((~v1_relat_1(A!0)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A!0, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_E_9(C, B, A!0)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_F_11(C, B, A!0)), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A!0), tptp_fun_E_9(C, B, A!0)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_E_9(C, B, A!0)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), F), A!0)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A!0)), B))))))))) | (~((~(C = k5_relat_1(A!0, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A!0), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A!0)) | (~r2_hidden(k4_tarski(F, E), B)))))))))))))) <=> ((~v1_relat_1(A!0)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A!0, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_E_9(C, B, A!0)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_F_11(C, B, A!0)), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A!0), tptp_fun_E_9(C, B, A!0)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_E_9(C, B, A!0)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), F), A!0)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A!0)), B))))))))) | (~((~(C = k5_relat_1(A!0, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A!0), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), A!0))))))))))))))),
% 5.23/3.66 inference(rewrite,[status(thm)],[])).
% 5.23/3.66 tff(250,plain,
% 5.23/3.66 (((~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))) | (~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))) | ((~v1_relat_1(A!0)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A!0, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_E_9(C, B, A!0)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_F_11(C, B, A!0)), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A!0), tptp_fun_E_9(C, B, A!0)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_E_9(C, B, A!0)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), F), A!0)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A!0)), B))))))))) | (~((~(C = k5_relat_1(A!0, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A!0), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A!0)) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))) <=> ((~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))) | (~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))) | ((~v1_relat_1(A!0)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A!0, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_E_9(C, B, A!0)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_F_11(C, B, A!0)), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A!0), tptp_fun_E_9(C, B, A!0)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_E_9(C, B, A!0)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), F), A!0)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A!0)), B))))))))) | (~((~(C = k5_relat_1(A!0, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A!0), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), A!0)))))))))))))))),
% 5.23/3.66 inference(monotonicity,[status(thm)],[249])).
% 5.23/3.66 tff(251,plain,
% 5.23/3.66 (((~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))) | (~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))) | ((~v1_relat_1(A!0)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A!0, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_E_9(C, B, A!0)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_F_11(C, B, A!0)), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A!0), tptp_fun_E_9(C, B, A!0)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_E_9(C, B, A!0)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), F), A!0)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A!0)), B))))))))) | (~((~(C = k5_relat_1(A!0, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A!0), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A!0)) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))) <=> ((~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))) | (~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))) | (~v1_relat_1(A!0)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A!0, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_E_9(C, B, A!0)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_F_11(C, B, A!0)), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A!0), tptp_fun_E_9(C, B, A!0)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_E_9(C, B, A!0)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), F), A!0)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A!0)), B))))))))) | (~((~(C = k5_relat_1(A!0, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A!0), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), A!0))))))))))))))),
% 5.23/3.66 inference(transitivity,[status(thm)],[250, 248])).
% 5.23/3.66 tff(252,plain,
% 5.23/3.66 ((~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))) | (~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))) | ((~v1_relat_1(A!0)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A!0, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_E_9(C, B, A!0)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_F_11(C, B, A!0)), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A!0), tptp_fun_E_9(C, B, A!0)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_E_9(C, B, A!0)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), F), A!0)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A!0)), B))))))))) | (~((~(C = k5_relat_1(A!0, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A!0), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A!0)) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))),
% 5.23/3.66 inference(quant_inst,[status(thm)],[])).
% 5.23/3.66 tff(253,plain,
% 5.23/3.66 ((~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))) | (~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))) | (~v1_relat_1(A!0)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A!0, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_E_9(C, B, A!0)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_F_11(C, B, A!0)), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A!0), tptp_fun_E_9(C, B, A!0)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_E_9(C, B, A!0)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), F), A!0)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A!0)), B))))))))) | (~((~(C = k5_relat_1(A!0, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A!0), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), A!0)))))))))))))),
% 5.32/3.67 inference(modus_ponens,[status(thm)],[252, 251])).
% 5.32/3.67 tff(254,plain,
% 5.32/3.67 (![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A!0, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_E_9(C, B, A!0)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_F_11(C, B, A!0)), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A!0), tptp_fun_E_9(C, B, A!0)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_E_9(C, B, A!0)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), F), A!0)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A!0)), B))))))))) | (~((~(C = k5_relat_1(A!0, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A!0), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), A!0)))))))))))))),
% 5.32/3.67 inference(unit_resolution,[status(thm)],[253, 92, 119])).
% 5.32/3.67 tff(255,plain,
% 5.32/3.67 (((~![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A!0, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_E_9(C, B, A!0)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_F_11(C, B, A!0)), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A!0), tptp_fun_E_9(C, B, A!0)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_E_9(C, B, A!0)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), F), A!0)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A!0)), B))))))))) | (~((~(C = k5_relat_1(A!0, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A!0), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), A!0)))))))))))))) | ((~v1_relat_1(C!2)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A!0, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_F_11(C, C!2, A!0)), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), F), A!0)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, A!0)), C!2))))))))) | (~((~(C = k5_relat_1(A!0, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, A!0), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), A!0)))))))))))))) <=> ((~![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A!0, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_E_9(C, B, A!0)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_F_11(C, B, A!0)), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A!0), tptp_fun_E_9(C, B, A!0)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_E_9(C, B, A!0)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), F), A!0)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A!0)), B))))))))) | (~((~(C = k5_relat_1(A!0, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A!0), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), A!0)))))))))))))) | (~v1_relat_1(C!2)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A!0, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_F_11(C, C!2, A!0)), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), F), A!0)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, A!0)), C!2))))))))) | (~((~(C = k5_relat_1(A!0, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, A!0), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), A!0)))))))))))))),
% 5.32/3.67 inference(rewrite,[status(thm)],[])).
% 5.32/3.67 tff(256,plain,
% 5.32/3.67 ((~![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A!0, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_E_9(C, B, A!0)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_F_11(C, B, A!0)), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A!0), tptp_fun_E_9(C, B, A!0)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_E_9(C, B, A!0)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), F), A!0)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A!0)), B))))))))) | (~((~(C = k5_relat_1(A!0, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A!0), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), A!0)))))))))))))) | ((~v1_relat_1(C!2)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A!0, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_F_11(C, C!2, A!0)), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), F), A!0)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, A!0)), C!2))))))))) | (~((~(C = k5_relat_1(A!0, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, A!0), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), A!0)))))))))))))),
% 5.32/3.67 inference(quant_inst,[status(thm)],[])).
% 5.32/3.67 tff(257,plain,
% 5.32/3.67 ((~![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A!0, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_E_9(C, B, A!0)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_F_11(C, B, A!0)), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A!0), tptp_fun_E_9(C, B, A!0)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), tptp_fun_E_9(C, B, A!0)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A!0), F), A!0)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A!0)), B))))))))) | (~((~(C = k5_relat_1(A!0, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A!0), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), A!0)))))))))))))) | (~v1_relat_1(C!2)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A!0, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_F_11(C, C!2, A!0)), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), F), A!0)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, A!0)), C!2))))))))) | (~((~(C = k5_relat_1(A!0, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, A!0), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), A!0))))))))))))),
% 5.32/3.67 inference(modus_ponens,[status(thm)],[256, 255])).
% 5.32/3.67 tff(258,plain,
% 5.32/3.67 (![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A!0, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_F_11(C, C!2, A!0)), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), F), A!0)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, A!0)), C!2))))))))) | (~((~(C = k5_relat_1(A!0, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, A!0), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), A!0))))))))))))),
% 5.32/3.67 inference(unit_resolution,[status(thm)],[257, 129, 254])).
% 5.32/3.67 tff(259,plain,
% 5.32/3.67 (((~![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))) | ((~v1_relat_1(A!0)) | (~v1_relat_1(C!2)) | v1_relat_1(k5_relat_1(A!0, C!2)))) <=> ((~![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))) | (~v1_relat_1(A!0)) | (~v1_relat_1(C!2)) | v1_relat_1(k5_relat_1(A!0, C!2)))),
% 5.32/3.67 inference(rewrite,[status(thm)],[])).
% 5.32/3.67 tff(260,plain,
% 5.32/3.67 ((v1_relat_1(k5_relat_1(A!0, C!2)) | (~v1_relat_1(C!2)) | (~v1_relat_1(A!0))) <=> ((~v1_relat_1(A!0)) | (~v1_relat_1(C!2)) | v1_relat_1(k5_relat_1(A!0, C!2)))),
% 5.32/3.67 inference(rewrite,[status(thm)],[])).
% 5.32/3.67 tff(261,plain,
% 5.32/3.67 (((~![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))) | (v1_relat_1(k5_relat_1(A!0, C!2)) | (~v1_relat_1(C!2)) | (~v1_relat_1(A!0)))) <=> ((~![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))) | ((~v1_relat_1(A!0)) | (~v1_relat_1(C!2)) | v1_relat_1(k5_relat_1(A!0, C!2))))),
% 5.32/3.67 inference(monotonicity,[status(thm)],[260])).
% 5.32/3.67 tff(262,plain,
% 5.32/3.67 (((~![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))) | (v1_relat_1(k5_relat_1(A!0, C!2)) | (~v1_relat_1(C!2)) | (~v1_relat_1(A!0)))) <=> ((~![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))) | (~v1_relat_1(A!0)) | (~v1_relat_1(C!2)) | v1_relat_1(k5_relat_1(A!0, C!2)))),
% 5.32/3.67 inference(transitivity,[status(thm)],[261, 259])).
% 5.32/3.67 tff(263,plain,
% 5.32/3.67 ((~![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))) | (v1_relat_1(k5_relat_1(A!0, C!2)) | (~v1_relat_1(C!2)) | (~v1_relat_1(A!0)))),
% 5.32/3.67 inference(quant_inst,[status(thm)],[])).
% 5.32/3.67 tff(264,plain,
% 5.32/3.67 ((~![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))) | (~v1_relat_1(A!0)) | (~v1_relat_1(C!2)) | v1_relat_1(k5_relat_1(A!0, C!2))),
% 5.32/3.67 inference(modus_ponens,[status(thm)],[263, 262])).
% 5.32/3.67 tff(265,plain,
% 5.32/3.67 (v1_relat_1(k5_relat_1(A!0, C!2))),
% 5.32/3.67 inference(unit_resolution,[status(thm)],[264, 92, 129, 146])).
% 5.32/3.67 tff(266,plain,
% 5.32/3.67 (((~![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A!0, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_F_11(C, C!2, A!0)), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), F), A!0)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, A!0)), C!2))))))))) | (~((~(C = k5_relat_1(A!0, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, A!0), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), A!0))))))))))))) | ((~v1_relat_1(k5_relat_1(A!0, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(A!0, C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, A!0), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(A!0, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), A!0))))))))) <=> ((~![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A!0, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_F_11(C, C!2, A!0)), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), F), A!0)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, A!0)), C!2))))))))) | (~((~(C = k5_relat_1(A!0, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, A!0), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), A!0))))))))))))) | (~v1_relat_1(k5_relat_1(A!0, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(A!0, C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, A!0), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(A!0, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), A!0))))))))),
% 5.32/3.67 inference(rewrite,[status(thm)],[])).
% 5.32/3.67 tff(267,plain,
% 5.32/3.67 (((~v1_relat_1(k5_relat_1(A!0, C!2))) | (~((~((k5_relat_1(A!0, C!2) = k5_relat_1(A!0, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(A!0, C!2), C!2, A!0), tptp_fun_E_9(k5_relat_1(A!0, C!2), C!2, A!0)), k5_relat_1(A!0, C!2)) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(A!0, C!2), C!2, A!0), tptp_fun_F_11(k5_relat_1(A!0, C!2), C!2, A!0)), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(k5_relat_1(A!0, C!2), C!2, A!0), tptp_fun_E_9(k5_relat_1(A!0, C!2), C!2, A!0)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(A!0, C!2), C!2, A!0), tptp_fun_E_9(k5_relat_1(A!0, C!2), C!2, A!0)), k5_relat_1(A!0, C!2))) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(A!0, C!2), C!2, A!0), F), A!0)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(k5_relat_1(A!0, C!2), C!2, A!0)), C!2))))))))) | (~((~(k5_relat_1(A!0, C!2) = k5_relat_1(A!0, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(A!0, C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, A!0), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(A!0, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), A!0)))))))))))) <=> ((~v1_relat_1(k5_relat_1(A!0, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(A!0, C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, A!0), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(A!0, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), A!0))))))))),
% 5.32/3.67 inference(rewrite,[status(thm)],[])).
% 5.32/3.67 tff(268,plain,
% 5.32/3.67 (((~![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A!0, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_F_11(C, C!2, A!0)), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), F), A!0)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, A!0)), C!2))))))))) | (~((~(C = k5_relat_1(A!0, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, A!0), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), A!0))))))))))))) | ((~v1_relat_1(k5_relat_1(A!0, C!2))) | (~((~((k5_relat_1(A!0, C!2) = k5_relat_1(A!0, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(A!0, C!2), C!2, A!0), tptp_fun_E_9(k5_relat_1(A!0, C!2), C!2, A!0)), k5_relat_1(A!0, C!2)) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(A!0, C!2), C!2, A!0), tptp_fun_F_11(k5_relat_1(A!0, C!2), C!2, A!0)), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(k5_relat_1(A!0, C!2), C!2, A!0), tptp_fun_E_9(k5_relat_1(A!0, C!2), C!2, A!0)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(A!0, C!2), C!2, A!0), tptp_fun_E_9(k5_relat_1(A!0, C!2), C!2, A!0)), k5_relat_1(A!0, C!2))) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(A!0, C!2), C!2, A!0), F), A!0)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(k5_relat_1(A!0, C!2), C!2, A!0)), C!2))))))))) | (~((~(k5_relat_1(A!0, C!2) = k5_relat_1(A!0, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(A!0, C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, A!0), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(A!0, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), A!0))))))))))))) <=> ((~![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A!0, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_F_11(C, C!2, A!0)), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), F), A!0)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, A!0)), C!2))))))))) | (~((~(C = k5_relat_1(A!0, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, A!0), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), A!0))))))))))))) | ((~v1_relat_1(k5_relat_1(A!0, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(A!0, C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, A!0), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(A!0, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), A!0)))))))))),
% 5.32/3.67 inference(monotonicity,[status(thm)],[267])).
% 5.32/3.67 tff(269,plain,
% 5.32/3.67 (((~![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A!0, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_F_11(C, C!2, A!0)), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), F), A!0)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, A!0)), C!2))))))))) | (~((~(C = k5_relat_1(A!0, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, A!0), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), A!0))))))))))))) | ((~v1_relat_1(k5_relat_1(A!0, C!2))) | (~((~((k5_relat_1(A!0, C!2) = k5_relat_1(A!0, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(A!0, C!2), C!2, A!0), tptp_fun_E_9(k5_relat_1(A!0, C!2), C!2, A!0)), k5_relat_1(A!0, C!2)) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(A!0, C!2), C!2, A!0), tptp_fun_F_11(k5_relat_1(A!0, C!2), C!2, A!0)), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(k5_relat_1(A!0, C!2), C!2, A!0), tptp_fun_E_9(k5_relat_1(A!0, C!2), C!2, A!0)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(A!0, C!2), C!2, A!0), tptp_fun_E_9(k5_relat_1(A!0, C!2), C!2, A!0)), k5_relat_1(A!0, C!2))) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(A!0, C!2), C!2, A!0), F), A!0)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(k5_relat_1(A!0, C!2), C!2, A!0)), C!2))))))))) | (~((~(k5_relat_1(A!0, C!2) = k5_relat_1(A!0, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(A!0, C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, A!0), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(A!0, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), A!0))))))))))))) <=> ((~![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A!0, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_F_11(C, C!2, A!0)), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), F), A!0)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, A!0)), C!2))))))))) | (~((~(C = k5_relat_1(A!0, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, A!0), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), A!0))))))))))))) | (~v1_relat_1(k5_relat_1(A!0, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(A!0, C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, A!0), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(A!0, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), A!0))))))))),
% 5.32/3.67 inference(transitivity,[status(thm)],[268, 266])).
% 5.32/3.67 tff(270,plain,
% 5.32/3.68 ((~![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A!0, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_F_11(C, C!2, A!0)), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), F), A!0)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, A!0)), C!2))))))))) | (~((~(C = k5_relat_1(A!0, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, A!0), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), A!0))))))))))))) | ((~v1_relat_1(k5_relat_1(A!0, C!2))) | (~((~((k5_relat_1(A!0, C!2) = k5_relat_1(A!0, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(A!0, C!2), C!2, A!0), tptp_fun_E_9(k5_relat_1(A!0, C!2), C!2, A!0)), k5_relat_1(A!0, C!2)) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(A!0, C!2), C!2, A!0), tptp_fun_F_11(k5_relat_1(A!0, C!2), C!2, A!0)), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(k5_relat_1(A!0, C!2), C!2, A!0), tptp_fun_E_9(k5_relat_1(A!0, C!2), C!2, A!0)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(A!0, C!2), C!2, A!0), tptp_fun_E_9(k5_relat_1(A!0, C!2), C!2, A!0)), k5_relat_1(A!0, C!2))) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(A!0, C!2), C!2, A!0), F), A!0)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(k5_relat_1(A!0, C!2), C!2, A!0)), C!2))))))))) | (~((~(k5_relat_1(A!0, C!2) = k5_relat_1(A!0, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(A!0, C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, A!0), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(A!0, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), A!0))))))))))))),
% 5.32/3.68 inference(quant_inst,[status(thm)],[])).
% 5.32/3.68 tff(271,plain,
% 5.32/3.68 ((~![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A!0, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_F_11(C, C!2, A!0)), A!0)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), tptp_fun_E_9(C, C!2, A!0)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, A!0), F), A!0)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, A!0)), C!2))))))))) | (~((~(C = k5_relat_1(A!0, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, A!0), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), A!0))))))))))))) | (~v1_relat_1(k5_relat_1(A!0, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(A!0, C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, A!0), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(A!0, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), A!0)))))))),
% 5.32/3.68 inference(modus_ponens,[status(thm)],[270, 269])).
% 5.32/3.68 tff(272,plain,
% 5.32/3.68 (![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(A!0, C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, A!0), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(A!0, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), A!0)))))))),
% 5.32/3.68 inference(unit_resolution,[status(thm)],[271, 265, 258])).
% 5.32/3.68 tff(273,plain,
% 5.32/3.68 ((~![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(A!0, C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, A!0), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(A!0, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), A!0)))))))) | (~((~((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(A!0, C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, A!0), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(A!0, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), F), A!0)))))))),
% 5.32/3.68 inference(quant_inst,[status(thm)],[])).
% 5.32/3.68 tff(274,plain,
% 5.32/3.68 (~((~((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(A!0, C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, A!0), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(A!0, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), F), A!0))))))),
% 5.32/3.68 inference(unit_resolution,[status(thm)],[273, 272])).
% 5.32/3.68 tff(275,plain,
% 5.32/3.68 (((~((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(A!0, C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, A!0), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, A!0)), A!0)))))) | (~(r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(A!0, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), F), A!0)))))) | (r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(A!0, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), F), A!0))))),
% 5.32/3.68 inference(tautology,[status(thm)],[])).
% 5.32/3.68 tff(276,plain,
% 5.32/3.68 (r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(A!0, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), F), A!0)))),
% 5.32/3.68 inference(unit_resolution,[status(thm)],[275, 274])).
% 5.32/3.68 tff(277,plain,
% 5.32/3.68 ((~(r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(A!0, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), F), A!0))))) | r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(A!0, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), F), A!0)))),
% 5.32/3.68 inference(tautology,[status(thm)],[])).
% 5.32/3.68 tff(278,plain,
% 5.32/3.68 (r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(A!0, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), F), A!0)))),
% 5.32/3.68 inference(unit_resolution,[status(thm)],[277, 276])).
% 5.32/3.68 tff(279,plain,
% 5.32/3.68 (r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(A!0, C!2))),
% 5.32/3.68 inference(unit_resolution,[status(thm)],[278, 247])).
% 5.32/3.68 tff(280,plain,
% 5.32/3.68 (r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))),
% 5.32/3.68 inference(modus_ponens,[status(thm)],[279, 239])).
% 5.32/3.68 tff(281,plain,
% 5.32/3.68 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))))) | ((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)))) <=> ((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))))) | ((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)))) <=> ((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2))))))),
% 5.32/3.68 inference(rewrite,[status(thm)],[])).
% 5.32/3.68 tff(282,plain,
% 5.32/3.68 ((~(r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> ((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2)))))) <=> ((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)))) <=> ((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2)))))),
% 5.32/3.68 inference(rewrite,[status(thm)],[])).
% 5.32/3.68 tff(283,plain,
% 5.32/3.68 (((r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> ((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2))))) | $false) <=> (r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> ((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2)))))),
% 5.32/3.68 inference(rewrite,[status(thm)],[])).
% 5.32/3.68 tff(284,plain,
% 5.32/3.68 (($true | (r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> ((~r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(B!1, C!2))) | (~r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(A!0, C!2)))))) <=> $true),
% 5.32/3.68 inference(rewrite,[status(thm)],[])).
% 5.32/3.68 tff(285,plain,
% 5.32/3.68 ((r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> ((~r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(B!1, C!2))) | (~r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(A!0, C!2))))) <=> (r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> ((~r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(B!1, C!2))) | (~r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(A!0, C!2)))))),
% 5.32/3.68 inference(rewrite,[status(thm)],[])).
% 5.32/3.68 tff(286,plain,
% 5.32/3.68 ((k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)) = k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> $true),
% 5.32/3.68 inference(rewrite,[status(thm)],[])).
% 5.32/3.68 tff(287,plain,
% 5.32/3.68 (((k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)) = k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) | (r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> ((~r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(B!1, C!2))) | (~r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(A!0, C!2)))))) <=> ($true | (r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> ((~r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(B!1, C!2))) | (~r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(A!0, C!2))))))),
% 5.32/3.69 inference(monotonicity,[status(thm)],[286, 285])).
% 5.32/3.69 tff(288,plain,
% 5.32/3.69 (((k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)) = k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) | (r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> ((~r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(B!1, C!2))) | (~r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(A!0, C!2)))))) <=> $true),
% 5.32/3.69 inference(transitivity,[status(thm)],[287, 284])).
% 5.32/3.69 tff(289,plain,
% 5.32/3.69 ((~((k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)) = k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) | (r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> ((~r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(B!1, C!2))) | (~r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(A!0, C!2))))))) <=> (~$true)),
% 5.32/3.69 inference(monotonicity,[status(thm)],[288])).
% 5.32/3.69 tff(290,plain,
% 5.32/3.69 ((~((k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)) = k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) | (r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> ((~r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(B!1, C!2))) | (~r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(A!0, C!2))))))) <=> $false),
% 5.32/3.69 inference(transitivity,[status(thm)],[289, 25])).
% 5.32/3.69 tff(291,plain,
% 5.32/3.69 ((~(r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> (~((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2))))))) <=> (r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> ((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2)))))),
% 5.32/3.69 inference(rewrite,[status(thm)],[])).
% 5.32/3.69 tff(292,plain,
% 5.32/3.69 (($false | (r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> (~((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2))))))) <=> (r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> (~((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2))))))),
% 5.32/3.69 inference(rewrite,[status(thm)],[])).
% 5.32/3.69 tff(293,plain,
% 5.32/3.69 ((~(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)) = k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)))) <=> (~$true)),
% 5.32/3.69 inference(monotonicity,[status(thm)],[286])).
% 5.32/3.69 tff(294,plain,
% 5.32/3.69 ((~(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)) = k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)))) <=> $false),
% 5.32/3.69 inference(transitivity,[status(thm)],[293, 25])).
% 5.32/3.69 tff(295,plain,
% 5.32/3.69 (((~(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)) = k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)))) | (r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> (~((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2))))))) <=> ($false | (r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> (~((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2)))))))),
% 5.32/3.69 inference(monotonicity,[status(thm)],[294])).
% 5.32/3.69 tff(296,plain,
% 5.32/3.69 (((~(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)) = k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)))) | (r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> (~((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2))))))) <=> (r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> (~((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2))))))),
% 5.32/3.69 inference(transitivity,[status(thm)],[295, 292])).
% 5.32/3.69 tff(297,plain,
% 5.32/3.69 ((~((~(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)) = k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)))) | (r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> (~((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2)))))))) <=> (~(r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> (~((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2)))))))),
% 5.35/3.69 inference(monotonicity,[status(thm)],[296])).
% 5.35/3.69 tff(298,plain,
% 5.35/3.69 ((~((~(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)) = k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)))) | (r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> (~((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2)))))))) <=> (r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> ((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2)))))),
% 5.35/3.69 inference(transitivity,[status(thm)],[297, 291])).
% 5.35/3.69 tff(299,plain,
% 5.35/3.69 (((~((~(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)) = k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)))) | (r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> (~((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2)))))))) | (~((k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)) = k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) | (r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> ((~r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(B!1, C!2))) | (~r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(A!0, C!2)))))))) <=> ((r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> ((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2))))) | $false)),
% 5.35/3.69 inference(monotonicity,[status(thm)],[298, 290])).
% 5.35/3.69 tff(300,plain,
% 5.35/3.69 (((~((~(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)) = k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)))) | (r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> (~((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2)))))))) | (~((k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)) = k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) | (r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> ((~r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(B!1, C!2))) | (~r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(A!0, C!2)))))))) <=> (r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> ((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2)))))),
% 5.35/3.69 inference(transitivity,[status(thm)],[299, 283])).
% 5.35/3.69 tff(301,plain,
% 5.35/3.69 ((~((~((~(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)) = k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)))) | (r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> (~((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2)))))))) | (~((k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)) = k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) | (r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> ((~r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(B!1, C!2))) | (~r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(A!0, C!2))))))))) <=> (~(r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> ((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2))))))),
% 5.35/3.69 inference(monotonicity,[status(thm)],[300])).
% 5.35/3.69 tff(302,plain,
% 5.35/3.69 ((~((~((~(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)) = k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)))) | (r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> (~((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2)))))))) | (~((k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)) = k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) | (r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> ((~r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(B!1, C!2))) | (~r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(A!0, C!2))))))))) <=> ((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)))) <=> ((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2)))))),
% 5.35/3.69 inference(transitivity,[status(thm)],[301, 282])).
% 5.35/3.69 tff(303,plain,
% 5.35/3.69 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))))) | (~((~((~(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)) = k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)))) | (r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> (~((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2)))))))) | (~((k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)) = k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) | (r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> ((~r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(B!1, C!2))) | (~r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(A!0, C!2)))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))))) | ((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)))) <=> ((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2))))))),
% 5.35/3.69 inference(monotonicity,[status(thm)],[302])).
% 5.35/3.69 tff(304,plain,
% 5.35/3.69 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))))) | (~((~((~(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)) = k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)))) | (r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> (~((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2)))))))) | (~((k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)) = k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) | (r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> ((~r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(B!1, C!2))) | (~r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(A!0, C!2)))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))))) | ((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)))) <=> ((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2))))))),
% 5.35/3.69 inference(transitivity,[status(thm)],[303, 281])).
% 5.35/3.69 tff(305,plain,
% 5.35/3.69 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))))) | (~((~((~(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)) = k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)))) | (r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> (~((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2)))))))) | (~((k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)) = k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) | (r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> ((~r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(B!1, C!2))) | (~r2_hidden(tptp_fun_D_7(k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)), k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(A!0, C!2)))))))))),
% 5.35/3.69 inference(quant_inst,[status(thm)],[])).
% 5.35/3.69 tff(306,plain,
% 5.35/3.69 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (r2_hidden(D, C) <=> (~((~r2_hidden(D, B)) | (~r2_hidden(D, A))))))) | (~((C = k3_xboole_0(A, B)) | (r2_hidden(tptp_fun_D_7(C, B, A), C) <=> ((~r2_hidden(tptp_fun_D_7(C, B, A), A)) | (~r2_hidden(tptp_fun_D_7(C, B, A), B))))))))) | ((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)))) <=> ((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2)))))),
% 5.35/3.69 inference(modus_ponens,[status(thm)],[305, 304])).
% 5.35/3.69 tff(307,plain,
% 5.35/3.69 ((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)))) <=> ((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2))))),
% 5.35/3.69 inference(unit_resolution,[status(thm)],[306, 21])).
% 5.35/3.69 tff(308,plain,
% 5.35/3.69 ((~![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))) | (k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)) = k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)))),
% 5.35/3.70 inference(quant_inst,[status(thm)],[])).
% 5.35/3.70 tff(309,plain,
% 5.35/3.70 (k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)) = k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))),
% 5.35/3.70 inference(unit_resolution,[status(thm)],[308, 56])).
% 5.35/3.70 tff(310,plain,
% 5.35/3.70 (k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)) = k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2))),
% 5.35/3.70 inference(symmetry,[status(thm)],[309])).
% 5.35/3.70 tff(311,plain,
% 5.35/3.70 (r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) <=> r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)))),
% 5.35/3.70 inference(monotonicity,[status(thm)],[310])).
% 5.35/3.70 tff(312,plain,
% 5.35/3.70 (r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2))) <=> r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)))),
% 5.35/3.70 inference(symmetry,[status(thm)],[311])).
% 5.35/3.70 tff(313,plain,
% 5.35/3.70 ((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)))) <=> (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))))),
% 5.35/3.70 inference(monotonicity,[status(thm)],[312])).
% 5.35/3.70 tff(314,plain,
% 5.35/3.70 (((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))) | r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2))))),
% 5.35/3.70 inference(tautology,[status(thm)],[])).
% 5.35/3.70 tff(315,plain,
% 5.35/3.70 (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)))),
% 5.35/3.70 inference(unit_resolution,[status(thm)],[314, 214])).
% 5.35/3.70 tff(316,plain,
% 5.35/3.70 (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)))),
% 5.35/3.70 inference(modus_ponens,[status(thm)],[315, 313])).
% 5.35/3.70 tff(317,plain,
% 5.35/3.70 ((~((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2)))) <=> ((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2)))))) | r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k3_xboole_0(k5_relat_1(B!1, C!2), k5_relat_1(A!0, C!2))) | ((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2))))),
% 5.35/3.70 inference(tautology,[status(thm)],[])).
% 5.35/3.70 tff(318,plain,
% 5.35/3.70 ((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2)))),
% 5.35/3.70 inference(unit_resolution,[status(thm)],[317, 316, 307])).
% 5.35/3.70 tff(319,plain,
% 5.35/3.70 ((~((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2))))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2)))),
% 5.35/3.70 inference(tautology,[status(thm)],[])).
% 5.35/3.70 tff(320,plain,
% 5.35/3.70 ((~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(A!0, C!2))) | (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2)))),
% 5.35/3.70 inference(unit_resolution,[status(thm)],[319, 318])).
% 5.35/3.70 tff(321,plain,
% 5.35/3.70 (~r2_hidden(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)), k5_relat_1(B!1, C!2))),
% 5.35/3.70 inference(unit_resolution,[status(thm)],[320, 280])).
% 5.35/3.70 tff(322,plain,
% 5.35/3.70 (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(B!1, C!2))),
% 5.35/3.70 inference(modus_ponens,[status(thm)],[321, 238])).
% 5.35/3.70 tff(323,plain,
% 5.35/3.70 (((~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))) | (~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))) | ((~v1_relat_1(B!1)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(B!1, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_E_9(C, B, B!1)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_F_11(C, B, B!1)), B!1)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, B!1), tptp_fun_E_9(C, B, B!1)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_E_9(C, B, B!1)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), F), B!1)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, B!1)), B))))))))) | (~((~(C = k5_relat_1(B!1, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, B!1), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), B!1))))))))))))))) <=> ((~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))) | (~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))) | (~v1_relat_1(B!1)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(B!1, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_E_9(C, B, B!1)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_F_11(C, B, B!1)), B!1)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, B!1), tptp_fun_E_9(C, B, B!1)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_E_9(C, B, B!1)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), F), B!1)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, B!1)), B))))))))) | (~((~(C = k5_relat_1(B!1, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, B!1), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), B!1))))))))))))))),
% 5.35/3.70 inference(rewrite,[status(thm)],[])).
% 5.35/3.70 tff(324,plain,
% 5.35/3.70 (((~v1_relat_1(B!1)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(B!1, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_E_9(C, B, B!1)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_F_11(C, B, B!1)), B!1)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, B!1), tptp_fun_E_9(C, B, B!1)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_E_9(C, B, B!1)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), F), B!1)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, B!1)), B))))))))) | (~((~(C = k5_relat_1(B!1, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, B!1), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), B!1)) | (~r2_hidden(k4_tarski(F, E), B)))))))))))))) <=> ((~v1_relat_1(B!1)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(B!1, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_E_9(C, B, B!1)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_F_11(C, B, B!1)), B!1)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, B!1), tptp_fun_E_9(C, B, B!1)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_E_9(C, B, B!1)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), F), B!1)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, B!1)), B))))))))) | (~((~(C = k5_relat_1(B!1, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, B!1), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), B!1))))))))))))))),
% 5.35/3.70 inference(rewrite,[status(thm)],[])).
% 5.35/3.70 tff(325,plain,
% 5.35/3.70 (((~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))) | (~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))) | ((~v1_relat_1(B!1)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(B!1, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_E_9(C, B, B!1)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_F_11(C, B, B!1)), B!1)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, B!1), tptp_fun_E_9(C, B, B!1)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_E_9(C, B, B!1)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), F), B!1)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, B!1)), B))))))))) | (~((~(C = k5_relat_1(B!1, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, B!1), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), B!1)) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))) <=> ((~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))) | (~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))) | ((~v1_relat_1(B!1)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(B!1, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_E_9(C, B, B!1)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_F_11(C, B, B!1)), B!1)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, B!1), tptp_fun_E_9(C, B, B!1)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_E_9(C, B, B!1)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), F), B!1)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, B!1)), B))))))))) | (~((~(C = k5_relat_1(B!1, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, B!1), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), B!1)))))))))))))))),
% 5.35/3.70 inference(monotonicity,[status(thm)],[324])).
% 5.35/3.70 tff(326,plain,
% 5.35/3.70 (((~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))) | (~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))) | ((~v1_relat_1(B!1)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(B!1, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_E_9(C, B, B!1)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_F_11(C, B, B!1)), B!1)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, B!1), tptp_fun_E_9(C, B, B!1)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_E_9(C, B, B!1)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), F), B!1)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, B!1)), B))))))))) | (~((~(C = k5_relat_1(B!1, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, B!1), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), B!1)) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))) <=> ((~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))) | (~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))) | (~v1_relat_1(B!1)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(B!1, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_E_9(C, B, B!1)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_F_11(C, B, B!1)), B!1)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, B!1), tptp_fun_E_9(C, B, B!1)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_E_9(C, B, B!1)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), F), B!1)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, B!1)), B))))))))) | (~((~(C = k5_relat_1(B!1, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, B!1), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), B!1))))))))))))))),
% 5.35/3.70 inference(transitivity,[status(thm)],[325, 323])).
% 5.35/3.70 tff(327,plain,
% 5.35/3.70 ((~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))) | (~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))) | ((~v1_relat_1(B!1)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(B!1, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_E_9(C, B, B!1)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_F_11(C, B, B!1)), B!1)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, B!1), tptp_fun_E_9(C, B, B!1)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_E_9(C, B, B!1)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), F), B!1)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, B!1)), B))))))))) | (~((~(C = k5_relat_1(B!1, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, B!1), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), B!1)) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))),
% 5.35/3.70 inference(quant_inst,[status(thm)],[])).
% 5.35/3.70 tff(328,plain,
% 5.35/3.70 ((~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(A, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_F_11(C, B, A)), A)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, A), tptp_fun_E_9(C, B, A)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), tptp_fun_E_9(C, B, A)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, A), F), A)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, A)), B))))))))) | (~((~(C = k5_relat_1(A, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, A), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, A)), A)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(D, F), A)) | (~r2_hidden(k4_tarski(F, E), B))))))))))))))) | (~v1_relat_1(B!1)) | ![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(B!1, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_E_9(C, B, B!1)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_F_11(C, B, B!1)), B!1)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, B!1), tptp_fun_E_9(C, B, B!1)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_E_9(C, B, B!1)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), F), B!1)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, B!1)), B))))))))) | (~((~(C = k5_relat_1(B!1, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, B!1), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), B!1)))))))))))))),
% 5.35/3.70 inference(modus_ponens,[status(thm)],[327, 326])).
% 5.35/3.70 tff(329,plain,
% 5.35/3.70 (![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(B!1, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_E_9(C, B, B!1)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_F_11(C, B, B!1)), B!1)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, B!1), tptp_fun_E_9(C, B, B!1)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_E_9(C, B, B!1)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), F), B!1)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, B!1)), B))))))))) | (~((~(C = k5_relat_1(B!1, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, B!1), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), B!1)))))))))))))),
% 5.35/3.70 inference(unit_resolution,[status(thm)],[328, 91, 119])).
% 5.35/3.70 tff(330,plain,
% 5.35/3.70 (((~![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(B!1, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_E_9(C, B, B!1)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_F_11(C, B, B!1)), B!1)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, B!1), tptp_fun_E_9(C, B, B!1)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_E_9(C, B, B!1)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), F), B!1)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, B!1)), B))))))))) | (~((~(C = k5_relat_1(B!1, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, B!1), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), B!1)))))))))))))) | ((~v1_relat_1(C!2)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(B!1, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_F_11(C, C!2, B!1)), B!1)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), F), B!1)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, B!1)), C!2))))))))) | (~((~(C = k5_relat_1(B!1, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, B!1), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), B!1)))))))))))))) <=> ((~![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(B!1, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_E_9(C, B, B!1)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_F_11(C, B, B!1)), B!1)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, B!1), tptp_fun_E_9(C, B, B!1)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_E_9(C, B, B!1)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), F), B!1)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, B!1)), B))))))))) | (~((~(C = k5_relat_1(B!1, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, B!1), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), B!1)))))))))))))) | (~v1_relat_1(C!2)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(B!1, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_F_11(C, C!2, B!1)), B!1)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), F), B!1)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, B!1)), C!2))))))))) | (~((~(C = k5_relat_1(B!1, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, B!1), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), B!1)))))))))))))),
% 5.35/3.70 inference(rewrite,[status(thm)],[])).
% 5.35/3.70 tff(331,plain,
% 5.35/3.70 ((~![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(B!1, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_E_9(C, B, B!1)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_F_11(C, B, B!1)), B!1)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, B!1), tptp_fun_E_9(C, B, B!1)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_E_9(C, B, B!1)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), F), B!1)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, B!1)), B))))))))) | (~((~(C = k5_relat_1(B!1, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, B!1), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), B!1)))))))))))))) | ((~v1_relat_1(C!2)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(B!1, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_F_11(C, C!2, B!1)), B!1)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), F), B!1)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, B!1)), C!2))))))))) | (~((~(C = k5_relat_1(B!1, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, B!1), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), B!1)))))))))))))),
% 5.35/3.71 inference(quant_inst,[status(thm)],[])).
% 5.35/3.71 tff(332,plain,
% 5.35/3.71 ((~![B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(B!1, B)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_E_9(C, B, B!1)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_F_11(C, B, B!1)), B!1)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, B, B!1), tptp_fun_E_9(C, B, B!1)), B)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), tptp_fun_E_9(C, B, B!1)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, B, B!1), F), B!1)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, B, B!1)), B))))))))) | (~((~(C = k5_relat_1(B!1, B))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, B, B!1), E), B)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, B, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), B)) | (~r2_hidden(k4_tarski(D, F), B!1)))))))))))))) | (~v1_relat_1(C!2)) | ![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(B!1, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_F_11(C, C!2, B!1)), B!1)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), F), B!1)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, B!1)), C!2))))))))) | (~((~(C = k5_relat_1(B!1, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, B!1), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), B!1))))))))))))),
% 5.35/3.71 inference(modus_ponens,[status(thm)],[331, 330])).
% 5.35/3.71 tff(333,plain,
% 5.35/3.71 (![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(B!1, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_F_11(C, C!2, B!1)), B!1)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), F), B!1)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, B!1)), C!2))))))))) | (~((~(C = k5_relat_1(B!1, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, B!1), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), B!1))))))))))))),
% 5.35/3.71 inference(unit_resolution,[status(thm)],[332, 129, 329])).
% 5.35/3.71 tff(334,plain,
% 5.35/3.71 (((~![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))) | ((~v1_relat_1(B!1)) | (~v1_relat_1(C!2)) | v1_relat_1(k5_relat_1(B!1, C!2)))) <=> ((~![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))) | (~v1_relat_1(B!1)) | (~v1_relat_1(C!2)) | v1_relat_1(k5_relat_1(B!1, C!2)))),
% 5.35/3.71 inference(rewrite,[status(thm)],[])).
% 5.35/3.71 tff(335,plain,
% 5.35/3.71 ((v1_relat_1(k5_relat_1(B!1, C!2)) | (~v1_relat_1(C!2)) | (~v1_relat_1(B!1))) <=> ((~v1_relat_1(B!1)) | (~v1_relat_1(C!2)) | v1_relat_1(k5_relat_1(B!1, C!2)))),
% 5.35/3.71 inference(rewrite,[status(thm)],[])).
% 5.35/3.71 tff(336,plain,
% 5.35/3.71 (((~![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))) | (v1_relat_1(k5_relat_1(B!1, C!2)) | (~v1_relat_1(C!2)) | (~v1_relat_1(B!1)))) <=> ((~![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))) | ((~v1_relat_1(B!1)) | (~v1_relat_1(C!2)) | v1_relat_1(k5_relat_1(B!1, C!2))))),
% 5.35/3.71 inference(monotonicity,[status(thm)],[335])).
% 5.35/3.71 tff(337,plain,
% 5.35/3.71 (((~![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))) | (v1_relat_1(k5_relat_1(B!1, C!2)) | (~v1_relat_1(C!2)) | (~v1_relat_1(B!1)))) <=> ((~![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))) | (~v1_relat_1(B!1)) | (~v1_relat_1(C!2)) | v1_relat_1(k5_relat_1(B!1, C!2)))),
% 5.35/3.71 inference(transitivity,[status(thm)],[336, 334])).
% 5.35/3.71 tff(338,plain,
% 5.35/3.71 ((~![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))) | (v1_relat_1(k5_relat_1(B!1, C!2)) | (~v1_relat_1(C!2)) | (~v1_relat_1(B!1)))),
% 5.35/3.71 inference(quant_inst,[status(thm)],[])).
% 5.35/3.71 tff(339,plain,
% 5.35/3.71 ((~![A: $i, B: $i] : (v1_relat_1(k5_relat_1(A, B)) | (~v1_relat_1(B)) | (~v1_relat_1(A)))) | (~v1_relat_1(B!1)) | (~v1_relat_1(C!2)) | v1_relat_1(k5_relat_1(B!1, C!2))),
% 5.35/3.71 inference(modus_ponens,[status(thm)],[338, 337])).
% 5.35/3.71 tff(340,plain,
% 5.35/3.71 (v1_relat_1(k5_relat_1(B!1, C!2))),
% 5.35/3.71 inference(unit_resolution,[status(thm)],[339, 91, 129, 146])).
% 5.35/3.71 tff(341,plain,
% 5.35/3.71 (((~![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(B!1, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_F_11(C, C!2, B!1)), B!1)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), F), B!1)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, B!1)), C!2))))))))) | (~((~(C = k5_relat_1(B!1, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, B!1), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), B!1))))))))))))) | ((~v1_relat_1(k5_relat_1(B!1, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(B!1, C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, B!1), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(B!1, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), B!1))))))))) <=> ((~![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(B!1, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_F_11(C, C!2, B!1)), B!1)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), F), B!1)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, B!1)), C!2))))))))) | (~((~(C = k5_relat_1(B!1, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, B!1), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), B!1))))))))))))) | (~v1_relat_1(k5_relat_1(B!1, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(B!1, C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, B!1), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(B!1, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), B!1))))))))),
% 5.35/3.71 inference(rewrite,[status(thm)],[])).
% 5.35/3.71 tff(342,plain,
% 5.35/3.71 (((~v1_relat_1(k5_relat_1(B!1, C!2))) | (~((~((k5_relat_1(B!1, C!2) = k5_relat_1(B!1, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(B!1, C!2), C!2, B!1), tptp_fun_E_9(k5_relat_1(B!1, C!2), C!2, B!1)), k5_relat_1(B!1, C!2)) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(B!1, C!2), C!2, B!1), tptp_fun_F_11(k5_relat_1(B!1, C!2), C!2, B!1)), B!1)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(k5_relat_1(B!1, C!2), C!2, B!1), tptp_fun_E_9(k5_relat_1(B!1, C!2), C!2, B!1)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(B!1, C!2), C!2, B!1), tptp_fun_E_9(k5_relat_1(B!1, C!2), C!2, B!1)), k5_relat_1(B!1, C!2))) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(B!1, C!2), C!2, B!1), F), B!1)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(k5_relat_1(B!1, C!2), C!2, B!1)), C!2))))))))) | (~((~(k5_relat_1(B!1, C!2) = k5_relat_1(B!1, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(B!1, C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, B!1), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(B!1, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), B!1)))))))))))) <=> ((~v1_relat_1(k5_relat_1(B!1, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(B!1, C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, B!1), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(B!1, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), B!1))))))))),
% 5.35/3.71 inference(rewrite,[status(thm)],[])).
% 5.35/3.71 tff(343,plain,
% 5.35/3.71 (((~![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(B!1, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_F_11(C, C!2, B!1)), B!1)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), F), B!1)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, B!1)), C!2))))))))) | (~((~(C = k5_relat_1(B!1, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, B!1), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), B!1))))))))))))) | ((~v1_relat_1(k5_relat_1(B!1, C!2))) | (~((~((k5_relat_1(B!1, C!2) = k5_relat_1(B!1, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(B!1, C!2), C!2, B!1), tptp_fun_E_9(k5_relat_1(B!1, C!2), C!2, B!1)), k5_relat_1(B!1, C!2)) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(B!1, C!2), C!2, B!1), tptp_fun_F_11(k5_relat_1(B!1, C!2), C!2, B!1)), B!1)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(k5_relat_1(B!1, C!2), C!2, B!1), tptp_fun_E_9(k5_relat_1(B!1, C!2), C!2, B!1)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(B!1, C!2), C!2, B!1), tptp_fun_E_9(k5_relat_1(B!1, C!2), C!2, B!1)), k5_relat_1(B!1, C!2))) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(B!1, C!2), C!2, B!1), F), B!1)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(k5_relat_1(B!1, C!2), C!2, B!1)), C!2))))))))) | (~((~(k5_relat_1(B!1, C!2) = k5_relat_1(B!1, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(B!1, C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, B!1), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(B!1, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), B!1))))))))))))) <=> ((~![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(B!1, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_F_11(C, C!2, B!1)), B!1)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), F), B!1)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, B!1)), C!2))))))))) | (~((~(C = k5_relat_1(B!1, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, B!1), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), B!1))))))))))))) | ((~v1_relat_1(k5_relat_1(B!1, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(B!1, C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, B!1), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(B!1, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), B!1)))))))))),
% 5.35/3.71 inference(monotonicity,[status(thm)],[342])).
% 5.35/3.71 tff(344,plain,
% 5.35/3.71 (((~![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(B!1, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_F_11(C, C!2, B!1)), B!1)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), F), B!1)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, B!1)), C!2))))))))) | (~((~(C = k5_relat_1(B!1, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, B!1), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), B!1))))))))))))) | ((~v1_relat_1(k5_relat_1(B!1, C!2))) | (~((~((k5_relat_1(B!1, C!2) = k5_relat_1(B!1, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(B!1, C!2), C!2, B!1), tptp_fun_E_9(k5_relat_1(B!1, C!2), C!2, B!1)), k5_relat_1(B!1, C!2)) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(B!1, C!2), C!2, B!1), tptp_fun_F_11(k5_relat_1(B!1, C!2), C!2, B!1)), B!1)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(k5_relat_1(B!1, C!2), C!2, B!1), tptp_fun_E_9(k5_relat_1(B!1, C!2), C!2, B!1)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(B!1, C!2), C!2, B!1), tptp_fun_E_9(k5_relat_1(B!1, C!2), C!2, B!1)), k5_relat_1(B!1, C!2))) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(B!1, C!2), C!2, B!1), F), B!1)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(k5_relat_1(B!1, C!2), C!2, B!1)), C!2))))))))) | (~((~(k5_relat_1(B!1, C!2) = k5_relat_1(B!1, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(B!1, C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, B!1), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(B!1, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), B!1))))))))))))) <=> ((~![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(B!1, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_F_11(C, C!2, B!1)), B!1)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), F), B!1)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, B!1)), C!2))))))))) | (~((~(C = k5_relat_1(B!1, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, B!1), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), B!1))))))))))))) | (~v1_relat_1(k5_relat_1(B!1, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(B!1, C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, B!1), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(B!1, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), B!1))))))))),
% 5.35/3.71 inference(transitivity,[status(thm)],[343, 341])).
% 5.35/3.71 tff(345,plain,
% 5.35/3.71 ((~![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(B!1, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_F_11(C, C!2, B!1)), B!1)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), F), B!1)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, B!1)), C!2))))))))) | (~((~(C = k5_relat_1(B!1, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, B!1), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), B!1))))))))))))) | ((~v1_relat_1(k5_relat_1(B!1, C!2))) | (~((~((k5_relat_1(B!1, C!2) = k5_relat_1(B!1, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(B!1, C!2), C!2, B!1), tptp_fun_E_9(k5_relat_1(B!1, C!2), C!2, B!1)), k5_relat_1(B!1, C!2)) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(B!1, C!2), C!2, B!1), tptp_fun_F_11(k5_relat_1(B!1, C!2), C!2, B!1)), B!1)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(k5_relat_1(B!1, C!2), C!2, B!1), tptp_fun_E_9(k5_relat_1(B!1, C!2), C!2, B!1)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(B!1, C!2), C!2, B!1), tptp_fun_E_9(k5_relat_1(B!1, C!2), C!2, B!1)), k5_relat_1(B!1, C!2))) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(k5_relat_1(B!1, C!2), C!2, B!1), F), B!1)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(k5_relat_1(B!1, C!2), C!2, B!1)), C!2))))))))) | (~((~(k5_relat_1(B!1, C!2) = k5_relat_1(B!1, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(B!1, C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, B!1), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(B!1, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), B!1))))))))))))),
% 5.35/3.71 inference(quant_inst,[status(thm)],[])).
% 5.35/3.71 tff(346,plain,
% 5.35/3.71 ((~![C: $i] : ((~v1_relat_1(C)) | (~((~((C = k5_relat_1(B!1, C!2)) | (~((~(r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_F_11(C, C!2, B!1)), B!1)) | (~r2_hidden(k4_tarski(tptp_fun_F_11(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C!2)))))) | (~((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), tptp_fun_E_9(C, C!2, B!1)), C)) | ![F: $i] : ((~r2_hidden(k4_tarski(tptp_fun_D_10(C, C!2, B!1), F), B!1)) | (~r2_hidden(k4_tarski(F, tptp_fun_E_9(C, C!2, B!1)), C!2))))))))) | (~((~(C = k5_relat_1(B!1, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), C)) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, B!1), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), C) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), B!1))))))))))))) | (~v1_relat_1(k5_relat_1(B!1, C!2))) | ![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(B!1, C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, B!1), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(B!1, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), B!1)))))))),
% 5.35/3.71 inference(modus_ponens,[status(thm)],[345, 344])).
% 5.35/3.71 tff(347,plain,
% 5.35/3.71 (![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(B!1, C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, B!1), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(B!1, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), B!1)))))))),
% 5.35/3.71 inference(unit_resolution,[status(thm)],[346, 340, 333])).
% 5.35/3.71 tff(348,plain,
% 5.35/3.71 ((~![D: $i, E: $i] : (~((~((~r2_hidden(k4_tarski(D, E), k5_relat_1(B!1, C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(E, D, C!2, B!1), E), C!2)) | (~r2_hidden(k4_tarski(D, tptp_fun_F_8(E, D, C!2, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(D, E), k5_relat_1(B!1, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, E), C!2)) | (~r2_hidden(k4_tarski(D, F), B!1)))))))) | (~((~((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(B!1, C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, B!1), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(B!1, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), F), B!1)))))))),
% 5.35/3.71 inference(quant_inst,[status(thm)],[])).
% 5.35/3.71 tff(349,plain,
% 5.35/3.71 (~((~((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(B!1, C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, B!1), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(B!1, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), F), B!1))))))),
% 5.35/3.72 inference(unit_resolution,[status(thm)],[348, 347])).
% 5.35/3.72 tff(350,plain,
% 5.35/3.72 (((~((~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(B!1, C!2))) | (~((~r2_hidden(k4_tarski(tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, B!1), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, B!1)), B!1)))))) | (~(r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(B!1, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), F), B!1)))))) | (r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(B!1, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), F), B!1))))),
% 5.35/3.72 inference(tautology,[status(thm)],[])).
% 5.35/3.72 tff(351,plain,
% 5.35/3.72 (r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(B!1, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), F), B!1)))),
% 5.35/3.72 inference(unit_resolution,[status(thm)],[350, 349])).
% 5.35/3.72 tff(352,plain,
% 5.35/3.72 ((~(r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(B!1, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), F), B!1))))) | r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(B!1, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), F), B!1)))),
% 5.35/3.72 inference(tautology,[status(thm)],[])).
% 5.35/3.72 tff(353,plain,
% 5.35/3.72 (r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), k5_relat_1(B!1, C!2)) | ![F: $i] : ((~r2_hidden(k4_tarski(F, tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), F), B!1)))),
% 5.35/3.72 inference(unit_resolution,[status(thm)],[352, 351])).
% 5.35/3.72 tff(354,plain,
% 5.35/3.72 (![F: $i] : ((~r2_hidden(k4_tarski(F, tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), F), B!1)))),
% 5.35/3.72 inference(unit_resolution,[status(thm)],[353, 322])).
% 5.35/3.72 tff(355,plain,
% 5.35/3.72 (((~![F: $i] : ((~r2_hidden(k4_tarski(F, tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), F), B!1)))) | ((~r2_hidden(k4_tarski(tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1)))) <=> ((~![F: $i] : ((~r2_hidden(k4_tarski(F, tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), F), B!1)))) | (~r2_hidden(k4_tarski(tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1)))),
% 5.39/3.73 inference(rewrite,[status(thm)],[])).
% 5.39/3.73 tff(356,plain,
% 5.39/3.73 ((~![F: $i] : ((~r2_hidden(k4_tarski(F, tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), F), B!1)))) | ((~r2_hidden(k4_tarski(tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1)))),
% 5.39/3.73 inference(quant_inst,[status(thm)],[])).
% 5.39/3.73 tff(357,plain,
% 5.39/3.73 ((~![F: $i] : ((~r2_hidden(k4_tarski(F, tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), F), B!1)))) | (~r2_hidden(k4_tarski(tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0)), tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2)))), C!2)) | (~r2_hidden(k4_tarski(tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_F_8(tptp_fun_D_3(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), tptp_fun_C_4(tptp_fun_C_6(k3_xboole_0(k5_relat_1(A!0, C!2), k5_relat_1(B!1, C!2)), k5_relat_1(k3_xboole_0(A!0, B!1), C!2))), C!2, k3_xboole_0(B!1, A!0))), B!1))),
% 5.39/3.73 inference(modus_ponens,[status(thm)],[356, 355])).
% 5.39/3.73 tff(358,plain,
% 5.39/3.73 ($false),
% 5.39/3.73 inference(unit_resolution,[status(thm)],[357, 354, 235, 233])).
% 5.39/3.73 % SZS output end Proof
%------------------------------------------------------------------------------