TSTP Solution File: SET766+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET766+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 05:07:56 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET766+4 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 07:34:19 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(apply_type, type, (
% 0.20/0.40 apply: ( $i * $i * $i ) > $o)).
% 0.20/0.40 tff(tptp_fun_R_21_type, type, (
% 0.20/0.40 tptp_fun_R_21: $i)).
% 0.20/0.40 tff(member_type, type, (
% 0.20/0.40 member: ( $i * $i ) > $o)).
% 0.20/0.40 tff(tptp_fun_E_22_type, type, (
% 0.20/0.40 tptp_fun_E_22: $i)).
% 0.20/0.40 tff(equivalence_type, type, (
% 0.20/0.40 equivalence: ( $i * $i ) > $o)).
% 0.20/0.40 tff(tptp_fun_Z_13_type, type, (
% 0.20/0.40 tptp_fun_Z_13: ( $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_Y_14_type, type, (
% 0.20/0.40 tptp_fun_Y_14: ( $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_X_15_type, type, (
% 0.20/0.40 tptp_fun_X_15: ( $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_Y_11_type, type, (
% 0.20/0.40 tptp_fun_Y_11: ( $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_X_12_type, type, (
% 0.20/0.40 tptp_fun_X_12: ( $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_X_10_type, type, (
% 0.20/0.40 tptp_fun_X_10: ( $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_A_20_type, type, (
% 0.20/0.40 tptp_fun_A_20: $i)).
% 0.20/0.40 tff(equivalence_class_type, type, (
% 0.20/0.40 equivalence_class: ( $i * $i * $i ) > $i)).
% 0.20/0.40 tff(1,plain,
% 0.20/0.40 (^[A: $i, R: $i] : rewrite((~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (^[A: $i, R: $i] : refl((~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (^[A: $i, R: $i] : rewrite((~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[5])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[6, 4])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (^[A: $i, R: $i] : trans(monotonicity(rewrite(((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) <=> ((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))), trans(monotonicity(rewrite((~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) <=> (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A))))), rewrite((~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))) <=> (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))), ((equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))) <=> (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))), rewrite((equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))) <=> (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))), ((equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))) <=> (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))), ((((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))))) <=> (((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))), rewrite((((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) <=> (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))), ((((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))))) <=> (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 (![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))))) <=> ![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[8])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 (^[A: $i, R: $i] : rewrite((((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | ((~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))))) <=> (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(11,plain,
% 0.20/0.41 (![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | ((~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.41 tff(12,plain,
% 0.20/0.41 (![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) <=> ![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 (^[A: $i, R: $i] : rewrite((equivalence(R, A) <=> ((![X: $i] : (member(X, A) => apply(R, X, X)) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, A)) => (apply(R, X, Y) => apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (((member(X, A) & member(Y, A)) & member(Z, A)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z))))) <=> (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 (![A: $i, R: $i] : (equivalence(R, A) <=> ((![X: $i] : (member(X, A) => apply(R, X, X)) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, A)) => (apply(R, X, Y) => apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (((member(X, A) & member(Y, A)) & member(Z, A)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z))))) <=> ![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.41 tff(15,axiom,(![A: $i, R: $i] : (equivalence(R, A) <=> ((![X: $i] : (member(X, A) => apply(R, X, X)) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, A)) => (apply(R, X, Y) => apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (((member(X, A) & member(Y, A)) & member(Z, A)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z)))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+2.ax','equivalence')).
% 0.20/0.41 tff(16,plain,
% 0.20/0.41 (![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 (![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.20/0.41 tff(18,plain,(
% 0.20/0.41 ![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | ((~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[17])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 (![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.20/0.41 tff(20,plain,
% 0.20/0.41 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[19, 9])).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[20, 7])).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 (![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[21, 2])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 (((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!21, E!22) | (~((~member(tptp_fun_X_10(R!21, E!22), E!22)) | apply(R!21, tptp_fun_X_10(R!21, E!22), tptp_fun_X_10(R!21, E!22)))) | (~(apply(R!21, tptp_fun_Y_11(R!21, E!22), tptp_fun_X_12(R!21, E!22)) | (~apply(R!21, tptp_fun_X_12(R!21, E!22), tptp_fun_Y_11(R!21, E!22))) | (~member(tptp_fun_X_12(R!21, E!22), E!22)) | (~member(tptp_fun_Y_11(R!21, E!22), E!22)))) | (~(apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Z_13(R!21, E!22)) | (~apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Y_14(R!21, E!22))) | (~apply(R!21, tptp_fun_Y_14(R!21, E!22), tptp_fun_Z_13(R!21, E!22))) | (~member(tptp_fun_X_15(R!21, E!22), E!22)) | (~member(tptp_fun_Y_14(R!21, E!22), E!22)) | (~member(tptp_fun_Z_13(R!21, E!22), E!22)))))) | (~((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22))))))))))) <=> ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!21, E!22) | (~((~member(tptp_fun_X_10(R!21, E!22), E!22)) | apply(R!21, tptp_fun_X_10(R!21, E!22), tptp_fun_X_10(R!21, E!22)))) | (~(apply(R!21, tptp_fun_Y_11(R!21, E!22), tptp_fun_X_12(R!21, E!22)) | (~apply(R!21, tptp_fun_X_12(R!21, E!22), tptp_fun_Y_11(R!21, E!22))) | (~member(tptp_fun_X_12(R!21, E!22), E!22)) | (~member(tptp_fun_Y_11(R!21, E!22), E!22)))) | (~(apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Z_13(R!21, E!22)) | (~apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Y_14(R!21, E!22))) | (~apply(R!21, tptp_fun_Y_14(R!21, E!22), tptp_fun_Z_13(R!21, E!22))) | (~member(tptp_fun_X_15(R!21, E!22), E!22)) | (~member(tptp_fun_Y_14(R!21, E!22), E!22)) | (~member(tptp_fun_Z_13(R!21, E!22), E!22)))))) | (~((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22)))))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 ((~((~(equivalence(R!21, E!22) | (~((~member(tptp_fun_X_10(R!21, E!22), E!22)) | apply(R!21, tptp_fun_X_10(R!21, E!22), tptp_fun_X_10(R!21, E!22)))) | (~(apply(R!21, tptp_fun_Y_11(R!21, E!22), tptp_fun_X_12(R!21, E!22)) | (~apply(R!21, tptp_fun_X_12(R!21, E!22), tptp_fun_Y_11(R!21, E!22))) | (~member(tptp_fun_X_12(R!21, E!22), E!22)) | (~member(tptp_fun_Y_11(R!21, E!22), E!22)))) | (~(apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Z_13(R!21, E!22)) | (~apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Y_14(R!21, E!22))) | (~apply(R!21, tptp_fun_Y_14(R!21, E!22), tptp_fun_Z_13(R!21, E!22))) | (~member(tptp_fun_X_15(R!21, E!22), E!22)) | (~member(tptp_fun_Y_14(R!21, E!22), E!22)) | (~member(tptp_fun_Z_13(R!21, E!22), E!22)))))) | (~((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : (apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22)))))))))) <=> (~((~(equivalence(R!21, E!22) | (~((~member(tptp_fun_X_10(R!21, E!22), E!22)) | apply(R!21, tptp_fun_X_10(R!21, E!22), tptp_fun_X_10(R!21, E!22)))) | (~(apply(R!21, tptp_fun_Y_11(R!21, E!22), tptp_fun_X_12(R!21, E!22)) | (~apply(R!21, tptp_fun_X_12(R!21, E!22), tptp_fun_Y_11(R!21, E!22))) | (~member(tptp_fun_X_12(R!21, E!22), E!22)) | (~member(tptp_fun_Y_11(R!21, E!22), E!22)))) | (~(apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Z_13(R!21, E!22)) | (~apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Y_14(R!21, E!22))) | (~apply(R!21, tptp_fun_Y_14(R!21, E!22), tptp_fun_Z_13(R!21, E!22))) | (~member(tptp_fun_X_15(R!21, E!22), E!22)) | (~member(tptp_fun_Y_14(R!21, E!22), E!22)) | (~member(tptp_fun_Z_13(R!21, E!22), E!22)))))) | (~((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22))))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!21, E!22) | (~((~member(tptp_fun_X_10(R!21, E!22), E!22)) | apply(R!21, tptp_fun_X_10(R!21, E!22), tptp_fun_X_10(R!21, E!22)))) | (~(apply(R!21, tptp_fun_Y_11(R!21, E!22), tptp_fun_X_12(R!21, E!22)) | (~apply(R!21, tptp_fun_X_12(R!21, E!22), tptp_fun_Y_11(R!21, E!22))) | (~member(tptp_fun_X_12(R!21, E!22), E!22)) | (~member(tptp_fun_Y_11(R!21, E!22), E!22)))) | (~(apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Z_13(R!21, E!22)) | (~apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Y_14(R!21, E!22))) | (~apply(R!21, tptp_fun_Y_14(R!21, E!22), tptp_fun_Z_13(R!21, E!22))) | (~member(tptp_fun_X_15(R!21, E!22), E!22)) | (~member(tptp_fun_Y_14(R!21, E!22), E!22)) | (~member(tptp_fun_Z_13(R!21, E!22), E!22)))))) | (~((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : (apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22))))))))))) <=> ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!21, E!22) | (~((~member(tptp_fun_X_10(R!21, E!22), E!22)) | apply(R!21, tptp_fun_X_10(R!21, E!22), tptp_fun_X_10(R!21, E!22)))) | (~(apply(R!21, tptp_fun_Y_11(R!21, E!22), tptp_fun_X_12(R!21, E!22)) | (~apply(R!21, tptp_fun_X_12(R!21, E!22), tptp_fun_Y_11(R!21, E!22))) | (~member(tptp_fun_X_12(R!21, E!22), E!22)) | (~member(tptp_fun_Y_11(R!21, E!22), E!22)))) | (~(apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Z_13(R!21, E!22)) | (~apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Y_14(R!21, E!22))) | (~apply(R!21, tptp_fun_Y_14(R!21, E!22), tptp_fun_Z_13(R!21, E!22))) | (~member(tptp_fun_X_15(R!21, E!22), E!22)) | (~member(tptp_fun_Y_14(R!21, E!22), E!22)) | (~member(tptp_fun_Z_13(R!21, E!22), E!22)))))) | (~((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22)))))))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[24])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 (((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!21, E!22) | (~((~member(tptp_fun_X_10(R!21, E!22), E!22)) | apply(R!21, tptp_fun_X_10(R!21, E!22), tptp_fun_X_10(R!21, E!22)))) | (~(apply(R!21, tptp_fun_Y_11(R!21, E!22), tptp_fun_X_12(R!21, E!22)) | (~apply(R!21, tptp_fun_X_12(R!21, E!22), tptp_fun_Y_11(R!21, E!22))) | (~member(tptp_fun_X_12(R!21, E!22), E!22)) | (~member(tptp_fun_Y_11(R!21, E!22), E!22)))) | (~(apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Z_13(R!21, E!22)) | (~apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Y_14(R!21, E!22))) | (~apply(R!21, tptp_fun_Y_14(R!21, E!22), tptp_fun_Z_13(R!21, E!22))) | (~member(tptp_fun_X_15(R!21, E!22), E!22)) | (~member(tptp_fun_Y_14(R!21, E!22), E!22)) | (~member(tptp_fun_Z_13(R!21, E!22), E!22)))))) | (~((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : (apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22))))))))))) <=> ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!21, E!22) | (~((~member(tptp_fun_X_10(R!21, E!22), E!22)) | apply(R!21, tptp_fun_X_10(R!21, E!22), tptp_fun_X_10(R!21, E!22)))) | (~(apply(R!21, tptp_fun_Y_11(R!21, E!22), tptp_fun_X_12(R!21, E!22)) | (~apply(R!21, tptp_fun_X_12(R!21, E!22), tptp_fun_Y_11(R!21, E!22))) | (~member(tptp_fun_X_12(R!21, E!22), E!22)) | (~member(tptp_fun_Y_11(R!21, E!22), E!22)))) | (~(apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Z_13(R!21, E!22)) | (~apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Y_14(R!21, E!22))) | (~apply(R!21, tptp_fun_Y_14(R!21, E!22), tptp_fun_Z_13(R!21, E!22))) | (~member(tptp_fun_X_15(R!21, E!22), E!22)) | (~member(tptp_fun_Y_14(R!21, E!22), E!22)) | (~member(tptp_fun_Z_13(R!21, E!22), E!22)))))) | (~((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22)))))))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[25, 23])).
% 0.20/0.43 tff(27,plain,
% 0.20/0.43 ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!21, E!22) | (~((~member(tptp_fun_X_10(R!21, E!22), E!22)) | apply(R!21, tptp_fun_X_10(R!21, E!22), tptp_fun_X_10(R!21, E!22)))) | (~(apply(R!21, tptp_fun_Y_11(R!21, E!22), tptp_fun_X_12(R!21, E!22)) | (~apply(R!21, tptp_fun_X_12(R!21, E!22), tptp_fun_Y_11(R!21, E!22))) | (~member(tptp_fun_X_12(R!21, E!22), E!22)) | (~member(tptp_fun_Y_11(R!21, E!22), E!22)))) | (~(apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Z_13(R!21, E!22)) | (~apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Y_14(R!21, E!22))) | (~apply(R!21, tptp_fun_Y_14(R!21, E!22), tptp_fun_Z_13(R!21, E!22))) | (~member(tptp_fun_X_15(R!21, E!22), E!22)) | (~member(tptp_fun_Y_14(R!21, E!22), E!22)) | (~member(tptp_fun_Z_13(R!21, E!22), E!22)))))) | (~((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : (apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22))))))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(28,plain,
% 0.20/0.43 ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!21, E!22) | (~((~member(tptp_fun_X_10(R!21, E!22), E!22)) | apply(R!21, tptp_fun_X_10(R!21, E!22), tptp_fun_X_10(R!21, E!22)))) | (~(apply(R!21, tptp_fun_Y_11(R!21, E!22), tptp_fun_X_12(R!21, E!22)) | (~apply(R!21, tptp_fun_X_12(R!21, E!22), tptp_fun_Y_11(R!21, E!22))) | (~member(tptp_fun_X_12(R!21, E!22), E!22)) | (~member(tptp_fun_Y_11(R!21, E!22), E!22)))) | (~(apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Z_13(R!21, E!22)) | (~apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Y_14(R!21, E!22))) | (~apply(R!21, tptp_fun_Y_14(R!21, E!22), tptp_fun_Z_13(R!21, E!22))) | (~member(tptp_fun_X_15(R!21, E!22), E!22)) | (~member(tptp_fun_Y_14(R!21, E!22), E!22)) | (~member(tptp_fun_Z_13(R!21, E!22), E!22)))))) | (~((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22))))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.43 tff(29,plain,
% 0.20/0.43 (~((~(equivalence(R!21, E!22) | (~((~member(tptp_fun_X_10(R!21, E!22), E!22)) | apply(R!21, tptp_fun_X_10(R!21, E!22), tptp_fun_X_10(R!21, E!22)))) | (~(apply(R!21, tptp_fun_Y_11(R!21, E!22), tptp_fun_X_12(R!21, E!22)) | (~apply(R!21, tptp_fun_X_12(R!21, E!22), tptp_fun_Y_11(R!21, E!22))) | (~member(tptp_fun_X_12(R!21, E!22), E!22)) | (~member(tptp_fun_Y_11(R!21, E!22), E!22)))) | (~(apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Z_13(R!21, E!22)) | (~apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Y_14(R!21, E!22))) | (~apply(R!21, tptp_fun_Y_14(R!21, E!22), tptp_fun_Z_13(R!21, E!22))) | (~member(tptp_fun_X_15(R!21, E!22), E!22)) | (~member(tptp_fun_Y_14(R!21, E!22), E!22)) | (~member(tptp_fun_Z_13(R!21, E!22), E!22)))))) | (~((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22)))))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[28, 22])).
% 0.20/0.43 tff(30,plain,
% 0.20/0.43 (((~(equivalence(R!21, E!22) | (~((~member(tptp_fun_X_10(R!21, E!22), E!22)) | apply(R!21, tptp_fun_X_10(R!21, E!22), tptp_fun_X_10(R!21, E!22)))) | (~(apply(R!21, tptp_fun_Y_11(R!21, E!22), tptp_fun_X_12(R!21, E!22)) | (~apply(R!21, tptp_fun_X_12(R!21, E!22), tptp_fun_Y_11(R!21, E!22))) | (~member(tptp_fun_X_12(R!21, E!22), E!22)) | (~member(tptp_fun_Y_11(R!21, E!22), E!22)))) | (~(apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Z_13(R!21, E!22)) | (~apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Y_14(R!21, E!22))) | (~apply(R!21, tptp_fun_Y_14(R!21, E!22), tptp_fun_Z_13(R!21, E!22))) | (~member(tptp_fun_X_15(R!21, E!22), E!22)) | (~member(tptp_fun_Y_14(R!21, E!22), E!22)) | (~member(tptp_fun_Z_13(R!21, E!22), E!22)))))) | (~((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22))))))))) | ((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22)))))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(31,plain,
% 0.20/0.43 ((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.20/0.43 tff(32,plain,
% 0.20/0.43 ((~![E: $i, R: $i, A: $i] : ((~(equivalence(R, E) & member(A, E))) | member(A, equivalence_class(A, E, R)))) <=> (~![E: $i, R: $i, A: $i] : ((~(equivalence(R, E) & member(A, E))) | member(A, equivalence_class(A, E, R))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(33,plain,
% 0.20/0.43 ((~![E: $i, R: $i, A: $i] : ((equivalence(R, E) & member(A, E)) => member(A, equivalence_class(A, E, R)))) <=> (~![E: $i, R: $i, A: $i] : ((~(equivalence(R, E) & member(A, E))) | member(A, equivalence_class(A, E, R))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(34,axiom,(~![E: $i, R: $i, A: $i] : ((equivalence(R, E) & member(A, E)) => member(A, equivalence_class(A, E, R)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thIII02')).
% 0.20/0.43 tff(35,plain,
% 0.20/0.43 (~![E: $i, R: $i, A: $i] : ((~(equivalence(R, E) & member(A, E))) | member(A, equivalence_class(A, E, R)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.43 tff(36,plain,
% 0.20/0.43 (~![E: $i, R: $i, A: $i] : ((~(equivalence(R, E) & member(A, E))) | member(A, equivalence_class(A, E, R)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[35, 32])).
% 0.20/0.43 tff(37,plain,
% 0.20/0.43 (~![E: $i, R: $i, A: $i] : ((~(equivalence(R, E) & member(A, E))) | member(A, equivalence_class(A, E, R)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.20/0.43 tff(38,plain,
% 0.20/0.43 (~![E: $i, R: $i, A: $i] : ((~(equivalence(R, E) & member(A, E))) | member(A, equivalence_class(A, E, R)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[37, 32])).
% 0.20/0.43 tff(39,plain,
% 0.20/0.43 (~![E: $i, R: $i, A: $i] : ((~(equivalence(R, E) & member(A, E))) | member(A, equivalence_class(A, E, R)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[38, 32])).
% 0.20/0.43 tff(40,plain,
% 0.20/0.43 (~![E: $i, R: $i, A: $i] : ((~(equivalence(R, E) & member(A, E))) | member(A, equivalence_class(A, E, R)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.20/0.43 tff(41,plain,
% 0.20/0.43 (~![E: $i, R: $i, A: $i] : ((~(equivalence(R, E) & member(A, E))) | member(A, equivalence_class(A, E, R)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[40, 32])).
% 0.20/0.43 tff(42,plain,(
% 0.20/0.43 ~((~(equivalence(R!21, E!22) & member(A!20, E!22))) | member(A!20, equivalence_class(A!20, E!22, R!21)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[41])).
% 0.20/0.43 tff(43,plain,
% 0.20/0.43 (equivalence(R!21, E!22) & member(A!20, E!22)),
% 0.20/0.43 inference(or_elim,[status(thm)],[42])).
% 0.20/0.43 tff(44,plain,
% 0.20/0.43 (equivalence(R!21, E!22)),
% 0.20/0.43 inference(and_elim,[status(thm)],[43])).
% 0.20/0.43 tff(45,plain,
% 0.20/0.43 ((~((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22)))))))) | (~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22))))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(46,plain,
% 0.20/0.43 ((~((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22)))))))) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.20/0.43 tff(47,plain,
% 0.20/0.43 (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[46, 31])).
% 0.20/0.43 tff(48,plain,
% 0.20/0.43 (((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22))))) | ![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(49,plain,
% 0.20/0.43 (![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.20/0.43 tff(50,plain,
% 0.20/0.44 (^[R: $i, E: $i, A: $i, X: $i] : refl((member(X, equivalence_class(A, E, R)) <=> (~((~member(X, E)) | (~apply(R, A, X))))) <=> (member(X, equivalence_class(A, E, R)) <=> (~((~member(X, E)) | (~apply(R, A, X))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(51,plain,
% 0.20/0.44 (![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (~((~member(X, E)) | (~apply(R, A, X))))) <=> ![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (~((~member(X, E)) | (~apply(R, A, X)))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.44 tff(52,plain,
% 0.20/0.44 (^[R: $i, E: $i, A: $i, X: $i] : rewrite((member(X, equivalence_class(A, E, R)) <=> (member(X, E) & apply(R, A, X))) <=> (member(X, equivalence_class(A, E, R)) <=> (~((~member(X, E)) | (~apply(R, A, X))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(53,plain,
% 0.20/0.44 (![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (member(X, E) & apply(R, A, X))) <=> ![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (~((~member(X, E)) | (~apply(R, A, X)))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.44 tff(54,plain,
% 0.20/0.44 (![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (member(X, E) & apply(R, A, X))) <=> ![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (member(X, E) & apply(R, A, X)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(55,axiom,(![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (member(X, E) & apply(R, A, X)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+2.ax','equivalence_class')).
% 0.20/0.44 tff(56,plain,
% 0.20/0.44 (![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (member(X, E) & apply(R, A, X)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.20/0.44 tff(57,plain,(
% 0.20/0.44 ![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (member(X, E) & apply(R, A, X)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[56])).
% 0.20/0.44 tff(58,plain,
% 0.20/0.44 (![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (~((~member(X, E)) | (~apply(R, A, X)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.20/0.44 tff(59,plain,
% 0.20/0.44 (![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (~((~member(X, E)) | (~apply(R, A, X)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.20/0.44 tff(60,plain,
% 0.20/0.44 ((~![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (~((~member(X, E)) | (~apply(R, A, X)))))) | (member(A!20, equivalence_class(A!20, E!22, R!21)) <=> (~((~member(A!20, E!22)) | (~apply(R!21, A!20, A!20)))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(61,plain,
% 0.20/0.44 (member(A!20, equivalence_class(A!20, E!22, R!21)) <=> (~((~member(A!20, E!22)) | (~apply(R!21, A!20, A!20))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.20/0.44 tff(62,plain,
% 0.20/0.44 (~member(A!20, equivalence_class(A!20, E!22, R!21))),
% 0.20/0.44 inference(or_elim,[status(thm)],[42])).
% 0.20/0.44 tff(63,plain,
% 0.20/0.44 ((~(member(A!20, equivalence_class(A!20, E!22, R!21)) <=> (~((~member(A!20, E!22)) | (~apply(R!21, A!20, A!20)))))) | member(A!20, equivalence_class(A!20, E!22, R!21)) | ((~member(A!20, E!22)) | (~apply(R!21, A!20, A!20)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(64,plain,
% 0.20/0.44 ((~(member(A!20, equivalence_class(A!20, E!22, R!21)) <=> (~((~member(A!20, E!22)) | (~apply(R!21, A!20, A!20)))))) | ((~member(A!20, E!22)) | (~apply(R!21, A!20, A!20)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.20/0.44 tff(65,plain,
% 0.20/0.44 ((~member(A!20, E!22)) | (~apply(R!21, A!20, A!20))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[64, 61])).
% 0.20/0.44 tff(66,plain,
% 0.20/0.44 (member(A!20, E!22)),
% 0.20/0.44 inference(and_elim,[status(thm)],[43])).
% 0.20/0.44 tff(67,plain,
% 0.20/0.44 ((~((~member(A!20, E!22)) | (~apply(R!21, A!20, A!20)))) | (~member(A!20, E!22)) | (~apply(R!21, A!20, A!20))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(68,plain,
% 0.20/0.44 ((~((~member(A!20, E!22)) | (~apply(R!21, A!20, A!20)))) | (~apply(R!21, A!20, A!20))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.20/0.44 tff(69,plain,
% 0.20/0.44 (~apply(R!21, A!20, A!20)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[68, 65])).
% 0.20/0.44 tff(70,plain,
% 0.20/0.44 (((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | ((~member(A!20, E!22)) | apply(R!21, A!20, A!20))) <=> ((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~member(A!20, E!22)) | apply(R!21, A!20, A!20))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(71,plain,
% 0.20/0.44 ((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | ((~member(A!20, E!22)) | apply(R!21, A!20, A!20))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(72,plain,
% 0.20/0.44 ((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~member(A!20, E!22)) | apply(R!21, A!20, A!20)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.44 tff(73,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[72, 66, 69, 49])).
% 0.20/0.44 % SZS output end Proof
%------------------------------------------------------------------------------