TSTP Solution File: SET769+4 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET769+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 0.21s 0.47s
% Output : Proof 0.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET769+4 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Sep 3 07:50:25 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 0.21/0.47 % SZS status Theorem
% 0.21/0.47 % SZS output start Proof
% 0.21/0.47 tff(member_type, type, (
% 0.21/0.47 member: ( $i * $i ) > $o)).
% 0.21/0.47 tff(equivalence_class_type, type, (
% 0.21/0.47 equivalence_class: ( $i * $i * $i ) > $i)).
% 0.21/0.47 tff(tptp_fun_R_22_type, type, (
% 0.21/0.47 tptp_fun_R_22: $i)).
% 0.21/0.47 tff(tptp_fun_E_23_type, type, (
% 0.21/0.47 tptp_fun_E_23: $i)).
% 0.21/0.47 tff(tptp_fun_A_21_type, type, (
% 0.21/0.47 tptp_fun_A_21: $i)).
% 0.21/0.47 tff(tptp_fun_B_20_type, type, (
% 0.21/0.47 tptp_fun_B_20: $i)).
% 0.21/0.47 tff(apply_type, type, (
% 0.21/0.47 apply: ( $i * $i * $i ) > $o)).
% 0.21/0.47 tff(equivalence_type, type, (
% 0.21/0.47 equivalence: ( $i * $i ) > $o)).
% 0.21/0.47 tff(tptp_fun_Z_13_type, type, (
% 0.21/0.47 tptp_fun_Z_13: ( $i * $i ) > $i)).
% 0.21/0.47 tff(tptp_fun_Y_14_type, type, (
% 0.21/0.47 tptp_fun_Y_14: ( $i * $i ) > $i)).
% 0.21/0.47 tff(tptp_fun_X_15_type, type, (
% 0.21/0.47 tptp_fun_X_15: ( $i * $i ) > $i)).
% 0.21/0.47 tff(tptp_fun_Y_11_type, type, (
% 0.21/0.47 tptp_fun_Y_11: ( $i * $i ) > $i)).
% 0.21/0.47 tff(tptp_fun_X_12_type, type, (
% 0.21/0.47 tptp_fun_X_12: ( $i * $i ) > $i)).
% 0.21/0.47 tff(tptp_fun_X_10_type, type, (
% 0.21/0.47 tptp_fun_X_10: ( $i * $i ) > $i)).
% 0.21/0.47 tff(disjoint_type, type, (
% 0.21/0.47 disjoint: ( $i * $i ) > $o)).
% 0.21/0.47 tff(equal_set_type, type, (
% 0.21/0.47 equal_set: ( $i * $i ) > $o)).
% 0.21/0.47 tff(subset_type, type, (
% 0.21/0.47 subset: ( $i * $i ) > $o)).
% 0.21/0.47 tff(tptp_fun_X_0_type, type, (
% 0.21/0.47 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.21/0.47 tff(tptp_fun_X_3_type, type, (
% 0.21/0.47 tptp_fun_X_3: ( $i * $i ) > $i)).
% 0.21/0.47 tff(1,plain,
% 0.21/0.47 (^[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))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(2,plain,
% 0.21/0.47 (![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)))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.47 tff(3,plain,
% 0.21/0.47 (^[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))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(4,plain,
% 0.21/0.47 (![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)))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.47 tff(5,plain,
% 0.21/0.47 (![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)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(6,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/sandbox2/benchmark/Axioms/SET006+2.ax','equivalence_class')).
% 0.21/0.47 tff(7,plain,
% 0.21/0.47 (![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (member(X, E) & apply(R, A, X)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.21/0.47 tff(8,plain,(
% 0.21/0.47 ![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (member(X, E) & apply(R, A, X)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[7])).
% 0.21/0.47 tff(9,plain,
% 0.21/0.47 (![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (~((~member(X, E)) | (~apply(R, A, X)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.21/0.47 tff(10,plain,
% 0.21/0.47 (![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (~((~member(X, E)) | (~apply(R, A, X)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.21/0.47 tff(11,plain,
% 0.21/0.47 ((~![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (~((~member(X, E)) | (~apply(R, A, X)))))) | (member(B!20, equivalence_class(B!20, E!23, R!22)) <=> (~((~member(B!20, E!23)) | (~apply(R!22, B!20, B!20)))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(12,plain,
% 0.21/0.47 (member(B!20, equivalence_class(B!20, E!23, R!22)) <=> (~((~member(B!20, E!23)) | (~apply(R!22, B!20, B!20))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.21/0.47 tff(13,plain,
% 0.21/0.47 (^[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)))))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(14,plain,
% 0.21/0.47 (![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))))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.47 tff(15,plain,
% 0.21/0.47 (^[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)))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(16,plain,
% 0.21/0.47 (![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))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[15])).
% 0.21/0.47 tff(17,plain,
% 0.21/0.47 (^[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)))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(18,plain,
% 0.21/0.47 (![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))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[17])).
% 0.21/0.47 tff(19,plain,
% 0.21/0.47 (![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))))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[18, 16])).
% 0.21/0.47 tff(20,plain,
% 0.21/0.47 (^[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))))))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(21,plain,
% 0.21/0.48 (![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))))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[20])).
% 0.21/0.48 tff(22,plain,
% 0.21/0.48 (^[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))))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(23,plain,
% 0.21/0.48 (![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)))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[22])).
% 0.21/0.48 tff(24,plain,
% 0.21/0.48 (![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))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(25,plain,
% 0.21/0.48 (^[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)))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(26,plain,
% 0.21/0.48 (![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))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[25])).
% 0.21/0.48 tff(27,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/sandbox2/benchmark/Axioms/SET006+2.ax','equivalence')).
% 0.21/0.48 tff(28,plain,
% 0.21/0.48 (![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))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.21/0.48 tff(29,plain,
% 0.21/0.48 (![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))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.21/0.48 tff(30,plain,(
% 0.21/0.48 ![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))))))))),
% 0.21/0.48 inference(skolemize,[status(sab)],[29])).
% 0.21/0.48 tff(31,plain,
% 0.21/0.48 (![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)))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.21/0.48 tff(32,plain,
% 0.21/0.48 (![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))))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.21/0.48 tff(33,plain,
% 0.21/0.48 (![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))))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[32, 19])).
% 0.21/0.48 tff(34,plain,
% 0.21/0.48 (![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))))))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[33, 14])).
% 0.21/0.48 tff(35,plain,
% 0.21/0.48 (((~![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!22, E!23) | (~((~member(tptp_fun_X_10(R!22, E!23), E!23)) | apply(R!22, tptp_fun_X_10(R!22, E!23), tptp_fun_X_10(R!22, E!23)))) | (~(apply(R!22, tptp_fun_Y_11(R!22, E!23), tptp_fun_X_12(R!22, E!23)) | (~apply(R!22, tptp_fun_X_12(R!22, E!23), tptp_fun_Y_11(R!22, E!23))) | (~member(tptp_fun_X_12(R!22, E!23), E!23)) | (~member(tptp_fun_Y_11(R!22, E!23), E!23)))) | (~(apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Z_13(R!22, E!23)) | (~apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Y_14(R!22, E!23))) | (~apply(R!22, tptp_fun_Y_14(R!22, E!23), tptp_fun_Z_13(R!22, E!23))) | (~member(tptp_fun_X_15(R!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R!22, E!23), E!23)) | (~member(tptp_fun_Z_13(R!22, E!23), E!23)))))) | (~((~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23))))))))))) <=> ((~![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!22, E!23) | (~((~member(tptp_fun_X_10(R!22, E!23), E!23)) | apply(R!22, tptp_fun_X_10(R!22, E!23), tptp_fun_X_10(R!22, E!23)))) | (~(apply(R!22, tptp_fun_Y_11(R!22, E!23), tptp_fun_X_12(R!22, E!23)) | (~apply(R!22, tptp_fun_X_12(R!22, E!23), tptp_fun_Y_11(R!22, E!23))) | (~member(tptp_fun_X_12(R!22, E!23), E!23)) | (~member(tptp_fun_Y_11(R!22, E!23), E!23)))) | (~(apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Z_13(R!22, E!23)) | (~apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Y_14(R!22, E!23))) | (~apply(R!22, tptp_fun_Y_14(R!22, E!23), tptp_fun_Z_13(R!22, E!23))) | (~member(tptp_fun_X_15(R!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R!22, E!23), E!23)) | (~member(tptp_fun_Z_13(R!22, E!23), E!23)))))) | (~((~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))))))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(36,plain,
% 0.21/0.49 ((~((~(equivalence(R!22, E!23) | (~((~member(tptp_fun_X_10(R!22, E!23), E!23)) | apply(R!22, tptp_fun_X_10(R!22, E!23), tptp_fun_X_10(R!22, E!23)))) | (~(apply(R!22, tptp_fun_Y_11(R!22, E!23), tptp_fun_X_12(R!22, E!23)) | (~apply(R!22, tptp_fun_X_12(R!22, E!23), tptp_fun_Y_11(R!22, E!23))) | (~member(tptp_fun_X_12(R!22, E!23), E!23)) | (~member(tptp_fun_Y_11(R!22, E!23), E!23)))) | (~(apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Z_13(R!22, E!23)) | (~apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Y_14(R!22, E!23))) | (~apply(R!22, tptp_fun_Y_14(R!22, E!23), tptp_fun_Z_13(R!22, E!23))) | (~member(tptp_fun_X_15(R!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R!22, E!23), E!23)) | (~member(tptp_fun_Z_13(R!22, E!23), E!23)))))) | (~((~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : (apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))))))))) <=> (~((~(equivalence(R!22, E!23) | (~((~member(tptp_fun_X_10(R!22, E!23), E!23)) | apply(R!22, tptp_fun_X_10(R!22, E!23), tptp_fun_X_10(R!22, E!23)))) | (~(apply(R!22, tptp_fun_Y_11(R!22, E!23), tptp_fun_X_12(R!22, E!23)) | (~apply(R!22, tptp_fun_X_12(R!22, E!23), tptp_fun_Y_11(R!22, E!23))) | (~member(tptp_fun_X_12(R!22, E!23), E!23)) | (~member(tptp_fun_Y_11(R!22, E!23), E!23)))) | (~(apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Z_13(R!22, E!23)) | (~apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Y_14(R!22, E!23))) | (~apply(R!22, tptp_fun_Y_14(R!22, E!23), tptp_fun_Z_13(R!22, E!23))) | (~member(tptp_fun_X_15(R!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R!22, E!23), E!23)) | (~member(tptp_fun_Z_13(R!22, E!23), E!23)))))) | (~((~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23))))))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(37,plain,
% 0.21/0.49 (((~![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!22, E!23) | (~((~member(tptp_fun_X_10(R!22, E!23), E!23)) | apply(R!22, tptp_fun_X_10(R!22, E!23), tptp_fun_X_10(R!22, E!23)))) | (~(apply(R!22, tptp_fun_Y_11(R!22, E!23), tptp_fun_X_12(R!22, E!23)) | (~apply(R!22, tptp_fun_X_12(R!22, E!23), tptp_fun_Y_11(R!22, E!23))) | (~member(tptp_fun_X_12(R!22, E!23), E!23)) | (~member(tptp_fun_Y_11(R!22, E!23), E!23)))) | (~(apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Z_13(R!22, E!23)) | (~apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Y_14(R!22, E!23))) | (~apply(R!22, tptp_fun_Y_14(R!22, E!23), tptp_fun_Z_13(R!22, E!23))) | (~member(tptp_fun_X_15(R!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R!22, E!23), E!23)) | (~member(tptp_fun_Z_13(R!22, E!23), E!23)))))) | (~((~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : (apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23))))))))))) <=> ((~![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!22, E!23) | (~((~member(tptp_fun_X_10(R!22, E!23), E!23)) | apply(R!22, tptp_fun_X_10(R!22, E!23), tptp_fun_X_10(R!22, E!23)))) | (~(apply(R!22, tptp_fun_Y_11(R!22, E!23), tptp_fun_X_12(R!22, E!23)) | (~apply(R!22, tptp_fun_X_12(R!22, E!23), tptp_fun_Y_11(R!22, E!23))) | (~member(tptp_fun_X_12(R!22, E!23), E!23)) | (~member(tptp_fun_Y_11(R!22, E!23), E!23)))) | (~(apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Z_13(R!22, E!23)) | (~apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Y_14(R!22, E!23))) | (~apply(R!22, tptp_fun_Y_14(R!22, E!23), tptp_fun_Z_13(R!22, E!23))) | (~member(tptp_fun_X_15(R!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R!22, E!23), E!23)) | (~member(tptp_fun_Z_13(R!22, E!23), E!23)))))) | (~((~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))))))))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[36])).
% 0.21/0.49 tff(38,plain,
% 0.21/0.49 (((~![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!22, E!23) | (~((~member(tptp_fun_X_10(R!22, E!23), E!23)) | apply(R!22, tptp_fun_X_10(R!22, E!23), tptp_fun_X_10(R!22, E!23)))) | (~(apply(R!22, tptp_fun_Y_11(R!22, E!23), tptp_fun_X_12(R!22, E!23)) | (~apply(R!22, tptp_fun_X_12(R!22, E!23), tptp_fun_Y_11(R!22, E!23))) | (~member(tptp_fun_X_12(R!22, E!23), E!23)) | (~member(tptp_fun_Y_11(R!22, E!23), E!23)))) | (~(apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Z_13(R!22, E!23)) | (~apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Y_14(R!22, E!23))) | (~apply(R!22, tptp_fun_Y_14(R!22, E!23), tptp_fun_Z_13(R!22, E!23))) | (~member(tptp_fun_X_15(R!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R!22, E!23), E!23)) | (~member(tptp_fun_Z_13(R!22, E!23), E!23)))))) | (~((~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : (apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23))))))))))) <=> ((~![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!22, E!23) | (~((~member(tptp_fun_X_10(R!22, E!23), E!23)) | apply(R!22, tptp_fun_X_10(R!22, E!23), tptp_fun_X_10(R!22, E!23)))) | (~(apply(R!22, tptp_fun_Y_11(R!22, E!23), tptp_fun_X_12(R!22, E!23)) | (~apply(R!22, tptp_fun_X_12(R!22, E!23), tptp_fun_Y_11(R!22, E!23))) | (~member(tptp_fun_X_12(R!22, E!23), E!23)) | (~member(tptp_fun_Y_11(R!22, E!23), E!23)))) | (~(apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Z_13(R!22, E!23)) | (~apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Y_14(R!22, E!23))) | (~apply(R!22, tptp_fun_Y_14(R!22, E!23), tptp_fun_Z_13(R!22, E!23))) | (~member(tptp_fun_X_15(R!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R!22, E!23), E!23)) | (~member(tptp_fun_Z_13(R!22, E!23), E!23)))))) | (~((~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))))))))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[37, 35])).
% 0.21/0.49 tff(39,plain,
% 0.21/0.49 ((~![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!22, E!23) | (~((~member(tptp_fun_X_10(R!22, E!23), E!23)) | apply(R!22, tptp_fun_X_10(R!22, E!23), tptp_fun_X_10(R!22, E!23)))) | (~(apply(R!22, tptp_fun_Y_11(R!22, E!23), tptp_fun_X_12(R!22, E!23)) | (~apply(R!22, tptp_fun_X_12(R!22, E!23), tptp_fun_Y_11(R!22, E!23))) | (~member(tptp_fun_X_12(R!22, E!23), E!23)) | (~member(tptp_fun_Y_11(R!22, E!23), E!23)))) | (~(apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Z_13(R!22, E!23)) | (~apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Y_14(R!22, E!23))) | (~apply(R!22, tptp_fun_Y_14(R!22, E!23), tptp_fun_Z_13(R!22, E!23))) | (~member(tptp_fun_X_15(R!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R!22, E!23), E!23)) | (~member(tptp_fun_Z_13(R!22, E!23), E!23)))))) | (~((~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : (apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~apply(R!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23))))))))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(40,plain,
% 0.21/0.50 ((~![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!22, E!23) | (~((~member(tptp_fun_X_10(R!22, E!23), E!23)) | apply(R!22, tptp_fun_X_10(R!22, E!23), tptp_fun_X_10(R!22, E!23)))) | (~(apply(R!22, tptp_fun_Y_11(R!22, E!23), tptp_fun_X_12(R!22, E!23)) | (~apply(R!22, tptp_fun_X_12(R!22, E!23), tptp_fun_Y_11(R!22, E!23))) | (~member(tptp_fun_X_12(R!22, E!23), E!23)) | (~member(tptp_fun_Y_11(R!22, E!23), E!23)))) | (~(apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Z_13(R!22, E!23)) | (~apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Y_14(R!22, E!23))) | (~apply(R!22, tptp_fun_Y_14(R!22, E!23), tptp_fun_Z_13(R!22, E!23))) | (~member(tptp_fun_X_15(R!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R!22, E!23), E!23)) | (~member(tptp_fun_Z_13(R!22, E!23), E!23)))))) | (~((~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23))))))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.21/0.50 tff(41,plain,
% 0.21/0.50 (~((~(equivalence(R!22, E!23) | (~((~member(tptp_fun_X_10(R!22, E!23), E!23)) | apply(R!22, tptp_fun_X_10(R!22, E!23), tptp_fun_X_10(R!22, E!23)))) | (~(apply(R!22, tptp_fun_Y_11(R!22, E!23), tptp_fun_X_12(R!22, E!23)) | (~apply(R!22, tptp_fun_X_12(R!22, E!23), tptp_fun_Y_11(R!22, E!23))) | (~member(tptp_fun_X_12(R!22, E!23), E!23)) | (~member(tptp_fun_Y_11(R!22, E!23), E!23)))) | (~(apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Z_13(R!22, E!23)) | (~apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Y_14(R!22, E!23))) | (~apply(R!22, tptp_fun_Y_14(R!22, E!23), tptp_fun_Z_13(R!22, E!23))) | (~member(tptp_fun_X_15(R!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R!22, E!23), E!23)) | (~member(tptp_fun_Z_13(R!22, E!23), E!23)))))) | (~((~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[40, 34])).
% 0.21/0.50 tff(42,plain,
% 0.21/0.50 (((~(equivalence(R!22, E!23) | (~((~member(tptp_fun_X_10(R!22, E!23), E!23)) | apply(R!22, tptp_fun_X_10(R!22, E!23), tptp_fun_X_10(R!22, E!23)))) | (~(apply(R!22, tptp_fun_Y_11(R!22, E!23), tptp_fun_X_12(R!22, E!23)) | (~apply(R!22, tptp_fun_X_12(R!22, E!23), tptp_fun_Y_11(R!22, E!23))) | (~member(tptp_fun_X_12(R!22, E!23), E!23)) | (~member(tptp_fun_Y_11(R!22, E!23), E!23)))) | (~(apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Z_13(R!22, E!23)) | (~apply(R!22, tptp_fun_X_15(R!22, E!23), tptp_fun_Y_14(R!22, E!23))) | (~apply(R!22, tptp_fun_Y_14(R!22, E!23), tptp_fun_Z_13(R!22, E!23))) | (~member(tptp_fun_X_15(R!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R!22, E!23), E!23)) | (~member(tptp_fun_Z_13(R!22, E!23), E!23)))))) | (~((~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23))))))))) | ((~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(43,plain,
% 0.21/0.50 ((~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.21/0.50 tff(44,plain,
% 0.21/0.50 ((~![E: $i, R: $i, A: $i, B: $i] : ((~(equivalence(R, E) & member(A, E) & member(B, E))) | (equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)) <=> (~disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)))))) <=> (~![E: $i, R: $i, A: $i, B: $i] : ((~(equivalence(R, E) & member(A, E) & member(B, E))) | (equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)) <=> (~disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(45,plain,
% 0.21/0.50 ((~![E: $i, R: $i, A: $i, B: $i] : (((equivalence(R, E) & member(A, E)) & member(B, E)) => (equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)) <=> (~disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)))))) <=> (~![E: $i, R: $i, A: $i, B: $i] : ((~(equivalence(R, E) & member(A, E) & member(B, E))) | (equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)) <=> (~disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(46,axiom,(~![E: $i, R: $i, A: $i, B: $i] : (((equivalence(R, E) & member(A, E)) & member(B, E)) => (equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)) <=> (~disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thIII05')).
% 0.21/0.50 tff(47,plain,
% 0.21/0.50 (~![E: $i, R: $i, A: $i, B: $i] : ((~(equivalence(R, E) & member(A, E) & member(B, E))) | (equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)) <=> (~disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.21/0.50 tff(48,plain,
% 0.21/0.50 (~![E: $i, R: $i, A: $i, B: $i] : ((~(equivalence(R, E) & member(A, E) & member(B, E))) | (equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)) <=> (~disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[47, 44])).
% 0.21/0.50 tff(49,plain,
% 0.21/0.50 (~![E: $i, R: $i, A: $i, B: $i] : ((~(equivalence(R, E) & member(A, E) & member(B, E))) | (equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)) <=> (~disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.21/0.50 tff(50,plain,
% 0.21/0.50 (~![E: $i, R: $i, A: $i, B: $i] : ((~(equivalence(R, E) & member(A, E) & member(B, E))) | (equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)) <=> (~disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[49, 44])).
% 0.21/0.50 tff(51,plain,
% 0.21/0.50 (~![E: $i, R: $i, A: $i, B: $i] : ((~(equivalence(R, E) & member(A, E) & member(B, E))) | (equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)) <=> (~disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[50, 44])).
% 0.21/0.50 tff(52,plain,
% 0.21/0.50 (~![E: $i, R: $i, A: $i, B: $i] : ((~(equivalence(R, E) & member(A, E) & member(B, E))) | (equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)) <=> (~disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.21/0.50 tff(53,plain,
% 0.21/0.50 (~![E: $i, R: $i, A: $i, B: $i] : ((~(equivalence(R, E) & member(A, E) & member(B, E))) | (equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)) <=> (~disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[52, 44])).
% 0.21/0.50 tff(54,plain,(
% 0.21/0.50 ~((~(equivalence(R!22, E!23) & member(A!21, E!23) & member(B!20, E!23))) | (equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) <=> (~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))),
% 0.21/0.50 inference(skolemize,[status(sab)],[53])).
% 0.21/0.50 tff(55,plain,
% 0.21/0.50 (equivalence(R!22, E!23) & member(A!21, E!23) & member(B!20, E!23)),
% 0.21/0.50 inference(or_elim,[status(thm)],[54])).
% 0.21/0.50 tff(56,plain,
% 0.21/0.50 (equivalence(R!22, E!23)),
% 0.21/0.50 inference(and_elim,[status(thm)],[55])).
% 0.21/0.50 tff(57,plain,
% 0.21/0.50 ((~((~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))))))) | (~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23))))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(58,plain,
% 0.21/0.50 ((~((~equivalence(R!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))))))) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.21/0.50 tff(59,plain,
% 0.21/0.50 (~((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[58, 43])).
% 0.21/0.50 tff(60,plain,
% 0.21/0.50 (((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23))))) | ![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(61,plain,
% 0.21/0.50 (![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.21/0.50 tff(62,plain,
% 0.21/0.50 (member(B!20, E!23)),
% 0.21/0.50 inference(and_elim,[status(thm)],[55])).
% 0.21/0.50 tff(63,plain,
% 0.21/0.50 (((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | ((~member(B!20, E!23)) | apply(R!22, B!20, B!20))) <=> ((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~member(B!20, E!23)) | apply(R!22, B!20, B!20))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(64,plain,
% 0.21/0.50 ((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | ((~member(B!20, E!23)) | apply(R!22, B!20, B!20))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(65,plain,
% 0.21/0.50 ((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~member(B!20, E!23)) | apply(R!22, B!20, B!20)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.21/0.50 tff(66,plain,
% 0.21/0.50 (apply(R!22, B!20, B!20)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[65, 62, 61])).
% 0.21/0.50 tff(67,plain,
% 0.21/0.50 ((~((~member(B!20, E!23)) | (~apply(R!22, B!20, B!20)))) | (~member(B!20, E!23)) | (~apply(R!22, B!20, B!20))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(68,plain,
% 0.21/0.50 (~((~member(B!20, E!23)) | (~apply(R!22, B!20, B!20)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[67, 62, 66])).
% 0.21/0.50 tff(69,plain,
% 0.21/0.50 ((~(member(B!20, equivalence_class(B!20, E!23, R!22)) <=> (~((~member(B!20, E!23)) | (~apply(R!22, B!20, B!20)))))) | member(B!20, equivalence_class(B!20, E!23, R!22)) | ((~member(B!20, E!23)) | (~apply(R!22, B!20, B!20)))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(70,plain,
% 0.21/0.50 ((~(member(B!20, equivalence_class(B!20, E!23, R!22)) <=> (~((~member(B!20, E!23)) | (~apply(R!22, B!20, B!20)))))) | member(B!20, equivalence_class(B!20, E!23, R!22))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.21/0.50 tff(71,plain,
% 0.21/0.50 (member(B!20, equivalence_class(B!20, E!23, R!22))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[70, 12])).
% 0.21/0.50 tff(72,plain,
% 0.21/0.50 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(73,plain,
% 0.21/0.50 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[72])).
% 0.21/0.50 tff(74,plain,
% 0.21/0.50 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(75,plain,
% 0.21/0.50 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[74])).
% 0.21/0.50 tff(76,plain,
% 0.21/0.50 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[75, 73])).
% 0.21/0.50 tff(77,plain,
% 0.21/0.50 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(78,plain,
% 0.21/0.50 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[77])).
% 0.21/0.50 tff(79,plain,
% 0.21/0.50 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(80,plain,
% 0.21/0.50 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(81,plain,
% 0.21/0.50 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[80])).
% 0.21/0.50 tff(82,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','subset')).
% 0.21/0.50 tff(83,plain,
% 0.21/0.50 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.21/0.50 tff(84,plain,
% 0.21/0.50 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.21/0.50 tff(85,plain,(
% 0.21/0.50 ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.21/0.50 inference(skolemize,[status(sab)],[84])).
% 0.21/0.50 tff(86,plain,
% 0.21/0.50 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.21/0.51 tff(87,plain,
% 0.21/0.51 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[86, 76])).
% 0.21/0.51 tff(88,plain,
% 0.21/0.51 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(B!20, E!23, R!22))) | member(X, equivalence_class(A!21, E!23, R!22))))) | (~(subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22))))))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(89,plain,
% 0.21/0.51 (~((~((~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(B!20, E!23, R!22))) | member(X, equivalence_class(A!21, E!23, R!22))))) | (~(subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22)))))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.21/0.51 tff(90,plain,
% 0.21/0.51 (((~((~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(B!20, E!23, R!22))) | member(X, equivalence_class(A!21, E!23, R!22))))) | (~(subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22))))))) | ((~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(B!20, E!23, R!22))) | member(X, equivalence_class(A!21, E!23, R!22))))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(91,plain,
% 0.21/0.51 ((~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(B!20, E!23, R!22))) | member(X, equivalence_class(A!21, E!23, R!22)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.21/0.51 tff(92,plain,
% 0.21/0.51 ((~![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (~((~member(X, E)) | (~apply(R, A, X)))))) | (member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22)) <=> (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(93,plain,
% 0.21/0.51 (member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22)) <=> (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[92, 10])).
% 0.21/0.51 tff(94,plain,
% 0.21/0.51 (((~((~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(B!20, E!23, R!22))) | member(X, equivalence_class(A!21, E!23, R!22))))) | (~(subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22))))))) | (subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22)))))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(95,plain,
% 0.21/0.51 (subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[94, 89])).
% 0.21/0.51 tff(96,assumption,(~equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))), introduced(assumption)).
% 0.21/0.51 tff(97,plain,
% 0.21/0.51 (^[A: $i, B: $i] : refl((equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(98,plain,
% 0.21/0.51 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[97])).
% 0.21/0.51 tff(99,plain,
% 0.21/0.51 (^[A: $i, B: $i] : rewrite((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(100,plain,
% 0.21/0.51 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[99])).
% 0.21/0.51 tff(101,plain,
% 0.21/0.51 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(102,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','equal_set')).
% 0.21/0.51 tff(103,plain,
% 0.21/0.51 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.21/0.51 tff(104,plain,(
% 0.21/0.51 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.21/0.51 inference(skolemize,[status(sab)],[103])).
% 0.21/0.51 tff(105,plain,
% 0.21/0.51 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.21/0.51 tff(106,plain,
% 0.21/0.51 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.21/0.51 tff(107,plain,
% 0.21/0.51 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) <=> (~((~subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(108,plain,
% 0.21/0.51 (equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) <=> (~((~subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.21/0.51 tff(109,plain,
% 0.21/0.51 ((~(equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) <=> (~((~subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))))) | equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | ((~subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(110,plain,
% 0.21/0.51 (equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | ((~subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.21/0.51 tff(111,plain,
% 0.21/0.51 ((~subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[110, 96])).
% 0.21/0.51 tff(112,assumption,((~((~subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | member(X, equivalence_class(B!20, E!23, R!22))))) | (~(subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))))), introduced(assumption)).
% 0.21/0.51 tff(113,plain,
% 0.21/0.51 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | member(X, equivalence_class(B!20, E!23, R!22))))) | (~(subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(114,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[113, 87, 112])).
% 0.21/0.51 tff(115,plain,(~((~((~subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | member(X, equivalence_class(B!20, E!23, R!22))))) | (~(subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(116,plain,
% 0.21/0.51 (((~((~subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | member(X, equivalence_class(B!20, E!23, R!22))))) | (~(subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))))) | (subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(117,plain,
% 0.21/0.51 (subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.21/0.51 tff(118,plain,
% 0.21/0.51 ((~![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (~((~member(X, E)) | (~apply(R, A, X)))))) | (member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)) <=> (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(119,plain,
% 0.21/0.51 (member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)) <=> (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[118, 10])).
% 0.21/0.51 tff(120,plain,
% 0.21/0.51 ((~(equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) <=> (~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))) <=> (equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) <=> disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(121,plain,
% 0.21/0.51 (~(equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) <=> (~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))),
% 0.21/0.51 inference(or_elim,[status(thm)],[54])).
% 0.21/0.51 tff(122,plain,
% 0.21/0.51 (equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) <=> disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.21/0.51 tff(123,plain,
% 0.21/0.51 (equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~(equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) <=> disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(124,plain,
% 0.21/0.51 (equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.21/0.51 tff(125,plain,
% 0.21/0.51 (~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[124, 96])).
% 0.21/0.51 tff(126,plain,
% 0.21/0.51 (^[A: $i, B: $i] : refl((~((~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))) | (~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))))) <=> (~((~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))) | (~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(127,plain,
% 0.21/0.51 (![A: $i, B: $i] : (~((~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))) | (~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))))) <=> ![A: $i, B: $i] : (~((~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))) | (~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B))))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[126])).
% 0.21/0.51 tff(128,plain,
% 0.21/0.51 (^[A: $i, B: $i] : rewrite((~((~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))) | (~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))))) <=> (~((~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))) | (~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(129,plain,
% 0.21/0.51 (![A: $i, B: $i] : (~((~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))) | (~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))))) <=> ![A: $i, B: $i] : (~((~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))) | (~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B))))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[128])).
% 0.21/0.51 tff(130,plain,
% 0.21/0.51 (![A: $i, B: $i] : (~((~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))) | (~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))))) <=> ![A: $i, B: $i] : (~((~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))) | (~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B))))))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[129, 127])).
% 0.21/0.51 tff(131,plain,
% 0.21/0.51 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~disjoint(A, B)) | ![X: $i] : (~(member(X, A) & member(X, B)))) <=> ((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))), trans(monotonicity(rewrite((member(tptp_fun_X_3(B, A), A) & member(tptp_fun_X_3(B, A), B)) <=> (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B))))), ((disjoint(A, B) | (member(tptp_fun_X_3(B, A), A) & member(tptp_fun_X_3(B, A), B))) <=> (disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B))))))), rewrite((disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B))))) <=> (disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))), ((disjoint(A, B) | (member(tptp_fun_X_3(B, A), A) & member(tptp_fun_X_3(B, A), B))) <=> (disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B))))))), ((((~disjoint(A, B)) | ![X: $i] : (~(member(X, A) & member(X, B)))) & (disjoint(A, B) | (member(tptp_fun_X_3(B, A), A) & member(tptp_fun_X_3(B, A), B)))) <=> (((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))) & (disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))))), rewrite((((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B)))) & (disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B)))))) <=> (~((~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))) | (~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B))))))))), ((((~disjoint(A, B)) | ![X: $i] : (~(member(X, A) & member(X, B)))) & (disjoint(A, B) | (member(tptp_fun_X_3(B, A), A) & member(tptp_fun_X_3(B, A), B)))) <=> (~((~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))) | (~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B))))))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(132,plain,
% 0.21/0.51 (![A: $i, B: $i] : (((~disjoint(A, B)) | ![X: $i] : (~(member(X, A) & member(X, B)))) & (disjoint(A, B) | (member(tptp_fun_X_3(B, A), A) & member(tptp_fun_X_3(B, A), B)))) <=> ![A: $i, B: $i] : (~((~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))) | (~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B))))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[131])).
% 0.21/0.51 tff(133,plain,
% 0.21/0.51 (![A: $i, B: $i] : (disjoint(A, B) <=> (~?[X: $i] : (member(X, A) & member(X, B)))) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (~?[X: $i] : (member(X, A) & member(X, B))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(134,axiom,(![A: $i, B: $i] : (disjoint(A, B) <=> (~?[X: $i] : (member(X, A) & member(X, B))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax','disjoint')).
% 0.21/0.52 tff(135,plain,
% 0.21/0.52 (![A: $i, B: $i] : (disjoint(A, B) <=> (~?[X: $i] : (member(X, A) & member(X, B))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.21/0.52 tff(136,plain,(
% 0.21/0.52 ![A: $i, B: $i] : (((~disjoint(A, B)) | ![X: $i] : (~(member(X, A) & member(X, B)))) & (disjoint(A, B) | (member(tptp_fun_X_3(B, A), A) & member(tptp_fun_X_3(B, A), B))))),
% 0.21/0.52 inference(skolemize,[status(sab)],[135])).
% 0.21/0.52 tff(137,plain,
% 0.21/0.52 (![A: $i, B: $i] : (~((~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))) | (~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B))))))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.21/0.52 tff(138,plain,
% 0.21/0.52 (![A: $i, B: $i] : (~((~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))) | (~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B))))))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[137, 130])).
% 0.21/0.52 tff(139,plain,
% 0.21/0.52 ((~![A: $i, B: $i] : (~((~((~disjoint(A, B)) | ![X: $i] : ((~member(X, A)) | (~member(X, B))))) | (~(disjoint(A, B) | (~((~member(tptp_fun_X_3(B, A), A)) | (~member(tptp_fun_X_3(B, A), B))))))))) | (~((~((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22)))))) | (~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))))))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(140,plain,
% 0.21/0.52 (~((~((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22)))))) | (~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.21/0.52 tff(141,plain,
% 0.21/0.52 (((~((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22)))))) | (~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))))))) | (disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(142,plain,
% 0.21/0.52 (disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.21/0.52 tff(143,plain,
% 0.21/0.52 ((~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))))) | disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(144,plain,
% 0.21/0.52 (disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.21/0.52 tff(145,plain,
% 0.21/0.52 (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[144, 125])).
% 0.21/0.52 tff(146,plain,
% 0.21/0.52 (((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))) | member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(147,plain,
% 0.21/0.52 (member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.21/0.52 tff(148,plain,
% 0.21/0.52 ((~(member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)) <=> (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(149,plain,
% 0.21/0.52 ((~(member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)) <=> (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))))) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.21/0.52 tff(150,plain,
% 0.21/0.52 (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[149, 119])).
% 0.21/0.52 tff(151,plain,
% 0.21/0.52 (((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) | member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(152,plain,
% 0.21/0.52 (member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.21/0.52 tff(153,plain,
% 0.21/0.52 (((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) | apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(154,plain,
% 0.21/0.52 (apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[153, 150])).
% 0.21/0.52 tff(155,plain,
% 0.21/0.52 ((~![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (~((~member(X, E)) | (~apply(R, A, X)))))) | (member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22)) <=> (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(156,plain,
% 0.21/0.52 (member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22)) <=> (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[155, 10])).
% 0.21/0.52 tff(157,plain,
% 0.21/0.52 (((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))) | member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(158,plain,
% 0.21/0.52 (member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[157, 145])).
% 0.21/0.52 tff(159,plain,
% 0.21/0.52 ((~(member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22)) <=> (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(160,plain,
% 0.21/0.52 ((~(member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22)) <=> (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))))) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.41/0.52 tff(161,plain,
% 0.41/0.52 (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))),
% 0.41/0.52 inference(unit_resolution,[status(thm)],[160, 156])).
% 0.41/0.52 tff(162,plain,
% 0.41/0.52 (((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) | apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))),
% 0.41/0.52 inference(tautology,[status(thm)],[])).
% 0.41/0.52 tff(163,plain,
% 0.41/0.52 (apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))),
% 0.41/0.52 inference(unit_resolution,[status(thm)],[162, 161])).
% 0.41/0.52 tff(164,plain,
% 0.41/0.52 (((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23))))) | ![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))),
% 0.41/0.52 inference(tautology,[status(thm)],[])).
% 0.41/0.52 tff(165,plain,
% 0.41/0.52 (![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))),
% 0.41/0.52 inference(unit_resolution,[status(thm)],[164, 59])).
% 0.41/0.52 tff(166,plain,
% 0.41/0.52 (member(A!21, E!23)),
% 0.41/0.52 inference(and_elim,[status(thm)],[55])).
% 0.41/0.52 tff(167,plain,
% 0.41/0.52 (((~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | ((~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21))) <=> ((~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21))),
% 0.41/0.52 inference(rewrite,[status(thm)],[])).
% 0.41/0.52 tff(168,plain,
% 0.41/0.52 (((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(A!21, E!23))) <=> ((~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21))),
% 0.41/0.52 inference(rewrite,[status(thm)],[])).
% 0.41/0.52 tff(169,plain,
% 0.41/0.52 (((~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | ((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(A!21, E!23)))) <=> ((~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | ((~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)))),
% 0.41/0.53 inference(monotonicity,[status(thm)],[168])).
% 0.41/0.53 tff(170,plain,
% 0.41/0.53 (((~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | ((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(A!21, E!23)))) <=> ((~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21))),
% 0.41/0.53 inference(transitivity,[status(thm)],[169, 167])).
% 0.41/0.53 tff(171,plain,
% 0.41/0.53 ((~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | ((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(A!21, E!23)))),
% 0.41/0.53 inference(quant_inst,[status(thm)],[])).
% 0.41/0.53 tff(172,plain,
% 0.41/0.53 ((~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)),
% 0.41/0.53 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.41/0.53 tff(173,plain,
% 0.41/0.53 (apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)),
% 0.41/0.53 inference(unit_resolution,[status(thm)],[172, 166, 165, 152, 163])).
% 0.41/0.53 tff(174,plain,
% 0.41/0.53 ((~![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (~((~member(X, E)) | (~apply(R, A, X)))))) | (member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)) <=> (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))))),
% 0.41/0.53 inference(quant_inst,[status(thm)],[])).
% 0.41/0.53 tff(175,plain,
% 0.41/0.53 (member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)) <=> (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))))),
% 0.41/0.53 inference(unit_resolution,[status(thm)],[174, 10])).
% 0.41/0.53 tff(176,assumption,(~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))), introduced(assumption)).
% 0.41/0.53 tff(177,plain,
% 0.41/0.53 (((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))),
% 0.41/0.53 inference(tautology,[status(thm)],[])).
% 0.41/0.53 tff(178,plain,
% 0.41/0.53 (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))),
% 0.41/0.53 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.41/0.53 tff(179,plain,
% 0.41/0.53 ((~(member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)) <=> (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)) | ((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))),
% 0.41/0.53 inference(tautology,[status(thm)],[])).
% 0.41/0.53 tff(180,plain,
% 0.41/0.53 ((~(member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)) <=> (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))))) | ((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))),
% 0.41/0.53 inference(unit_resolution,[status(thm)],[179, 178])).
% 0.41/0.53 tff(181,plain,
% 0.41/0.53 ((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))),
% 0.41/0.53 inference(unit_resolution,[status(thm)],[180, 175])).
% 0.41/0.53 tff(182,plain,
% 0.41/0.53 ((~![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (~((~member(X, E)) | (~apply(R, A, X)))))) | (member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22)) <=> (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))))),
% 0.41/0.53 inference(quant_inst,[status(thm)],[])).
% 0.41/0.53 tff(183,plain,
% 0.41/0.53 (member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22)) <=> (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))))),
% 0.41/0.53 inference(unit_resolution,[status(thm)],[182, 10])).
% 0.41/0.53 tff(184,plain,
% 0.41/0.53 (((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))),
% 0.41/0.53 inference(tautology,[status(thm)],[])).
% 0.41/0.53 tff(185,plain,
% 0.41/0.53 (member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))),
% 0.41/0.53 inference(unit_resolution,[status(thm)],[184, 176])).
% 0.41/0.53 tff(186,plain,
% 0.41/0.53 ((~(member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22)) <=> (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))))) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))))),
% 0.41/0.53 inference(tautology,[status(thm)],[])).
% 0.41/0.53 tff(187,plain,
% 0.41/0.53 ((~(member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22)) <=> (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))))) | (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))))),
% 0.41/0.53 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.41/0.53 tff(188,plain,
% 0.41/0.53 (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))),
% 0.41/0.53 inference(unit_resolution,[status(thm)],[187, 183])).
% 0.41/0.53 tff(189,plain,
% 0.41/0.53 (((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)),
% 0.41/0.53 inference(tautology,[status(thm)],[])).
% 0.41/0.53 tff(190,plain,
% 0.41/0.53 (member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)),
% 0.41/0.53 inference(unit_resolution,[status(thm)],[189, 188])).
% 0.41/0.53 tff(191,plain,
% 0.41/0.53 ((~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))),
% 0.41/0.53 inference(tautology,[status(thm)],[])).
% 0.41/0.53 tff(192,plain,
% 0.41/0.53 (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))),
% 0.41/0.53 inference(unit_resolution,[status(thm)],[191, 190, 181])).
% 0.41/0.53 tff(193,assumption,(apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))), introduced(assumption)).
% 0.41/0.53 tff(194,assumption,(member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)), introduced(assumption)).
% 0.41/0.53 tff(195,plain,
% 0.41/0.53 (((~![X: $i] : ((~member(X, E!23)) | apply(R!22, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23))))) | ![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))),
% 0.41/0.53 inference(tautology,[status(thm)],[])).
% 0.41/0.53 tff(196,plain,
% 0.41/0.53 (![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))),
% 0.41/0.53 inference(unit_resolution,[status(thm)],[195, 59])).
% 0.41/0.53 tff(197,plain,
% 0.41/0.53 (((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | ((~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))),
% 0.41/0.53 inference(rewrite,[status(thm)],[])).
% 0.41/0.53 tff(198,plain,
% 0.41/0.53 (((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23))) <=> ((~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))),
% 0.41/0.53 inference(rewrite,[status(thm)],[])).
% 0.41/0.53 tff(199,plain,
% 0.41/0.53 (((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | ((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | ((~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))))),
% 0.41/0.54 inference(monotonicity,[status(thm)],[198])).
% 0.41/0.54 tff(200,plain,
% 0.41/0.54 (((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | ((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))),
% 0.41/0.54 inference(transitivity,[status(thm)],[199, 197])).
% 0.41/0.54 tff(201,plain,
% 0.41/0.54 ((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | ((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)))),
% 0.41/0.54 inference(quant_inst,[status(thm)],[])).
% 0.41/0.54 tff(202,plain,
% 0.41/0.54 ((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, B!20, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))),
% 0.41/0.54 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.41/0.54 tff(203,plain,
% 0.41/0.54 (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))),
% 0.41/0.54 inference(unit_resolution,[status(thm)],[202, 62, 196, 194, 193, 190, 192])).
% 0.41/0.54 tff(204,plain,
% 0.41/0.54 (((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) | apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))),
% 0.41/0.54 inference(tautology,[status(thm)],[])).
% 0.41/0.54 tff(205,plain,
% 0.41/0.54 (apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))),
% 0.41/0.54 inference(unit_resolution,[status(thm)],[204, 188])).
% 0.41/0.54 tff(206,assumption,(apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)), introduced(assumption)).
% 0.41/0.54 tff(207,plain,
% 0.41/0.54 (((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | ((~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)))),
% 0.41/0.54 inference(rewrite,[status(thm)],[])).
% 0.41/0.54 tff(208,plain,
% 0.41/0.54 (((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(A!21, E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23))) <=> ((~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)))),
% 0.41/0.54 inference(rewrite,[status(thm)],[])).
% 0.41/0.54 tff(209,plain,
% 0.41/0.54 (((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | ((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(A!21, E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | ((~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21))))),
% 0.41/0.54 inference(monotonicity,[status(thm)],[208])).
% 0.41/0.54 tff(210,plain,
% 0.41/0.54 (((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | ((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(A!21, E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)))),
% 0.41/0.54 inference(transitivity,[status(thm)],[209, 207])).
% 0.41/0.54 tff(211,plain,
% 0.41/0.54 ((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | ((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(A!21, E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)))),
% 0.41/0.54 inference(quant_inst,[status(thm)],[])).
% 0.41/0.54 tff(212,plain,
% 0.41/0.54 ((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21))),
% 0.44/0.54 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.44/0.54 tff(213,plain,
% 0.44/0.54 ($false),
% 0.44/0.54 inference(unit_resolution,[status(thm)],[212, 166, 196, 194, 206, 190, 205, 203])).
% 0.44/0.54 tff(214,plain,(((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.54 tff(215,plain,
% 0.44/0.54 ((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))),
% 0.44/0.54 inference(unit_resolution,[status(thm)],[214, 173, 154, 152])).
% 0.44/0.54 tff(216,plain,
% 0.44/0.54 ((~(subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))))) | subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))),
% 0.44/0.54 inference(tautology,[status(thm)],[])).
% 0.44/0.54 tff(217,plain,
% 0.44/0.54 (subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))),
% 0.44/0.54 inference(unit_resolution,[status(thm)],[216, 215, 117])).
% 0.44/0.54 tff(218,plain,
% 0.44/0.54 ((~((~subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))) | (~subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))),
% 0.44/0.54 inference(tautology,[status(thm)],[])).
% 0.44/0.54 tff(219,plain,
% 0.44/0.54 (~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))),
% 0.44/0.54 inference(unit_resolution,[status(thm)],[218, 217, 111])).
% 0.44/0.54 tff(220,plain,
% 0.44/0.54 ((~(subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22)))))) | subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22))))),
% 0.44/0.55 inference(tautology,[status(thm)],[])).
% 0.44/0.55 tff(221,plain,
% 0.44/0.55 ((~(subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22)))))) | (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22))))),
% 0.44/0.55 inference(unit_resolution,[status(thm)],[220, 219])).
% 0.44/0.55 tff(222,plain,
% 0.44/0.55 (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22)))),
% 0.44/0.55 inference(unit_resolution,[status(thm)],[221, 95])).
% 0.44/0.55 tff(223,plain,
% 0.44/0.55 (((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22)))),
% 0.44/0.55 inference(tautology,[status(thm)],[])).
% 0.44/0.55 tff(224,plain,
% 0.44/0.55 (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22))),
% 0.44/0.55 inference(unit_resolution,[status(thm)],[223, 222])).
% 0.44/0.55 tff(225,plain,
% 0.44/0.55 ((~(member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22)) <=> (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))))) | member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22)) | ((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))),
% 0.44/0.55 inference(tautology,[status(thm)],[])).
% 0.44/0.55 tff(226,plain,
% 0.44/0.55 ((~(member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22)) <=> (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))))) | ((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))),
% 0.44/0.55 inference(unit_resolution,[status(thm)],[225, 224])).
% 0.44/0.55 tff(227,plain,
% 0.44/0.55 ((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))),
% 0.44/0.55 inference(unit_resolution,[status(thm)],[226, 93])).
% 0.44/0.55 tff(228,plain,
% 0.44/0.55 ((~![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (~((~member(X, E)) | (~apply(R, A, X)))))) | (member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22)) <=> (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))))),
% 0.44/0.55 inference(quant_inst,[status(thm)],[])).
% 0.44/0.55 tff(229,plain,
% 0.44/0.55 (member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22)) <=> (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))))),
% 0.44/0.55 inference(unit_resolution,[status(thm)],[228, 10])).
% 0.44/0.55 tff(230,plain,
% 0.44/0.55 (((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22))),
% 0.44/0.55 inference(tautology,[status(thm)],[])).
% 0.44/0.55 tff(231,plain,
% 0.44/0.55 (member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22))),
% 0.44/0.55 inference(unit_resolution,[status(thm)],[230, 222])).
% 0.44/0.55 tff(232,plain,
% 0.44/0.55 ((~(member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22)) <=> (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))))) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22))) | (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))))),
% 0.44/0.55 inference(tautology,[status(thm)],[])).
% 0.44/0.55 tff(233,plain,
% 0.44/0.55 ((~(member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), equivalence_class(B!20, E!23, R!22)) <=> (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))))) | (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))))),
% 0.44/0.55 inference(unit_resolution,[status(thm)],[232, 231])).
% 0.44/0.55 tff(234,plain,
% 0.44/0.55 (~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))),
% 0.44/0.55 inference(unit_resolution,[status(thm)],[233, 229])).
% 0.44/0.55 tff(235,plain,
% 0.44/0.55 (((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))) | member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)),
% 0.44/0.55 inference(tautology,[status(thm)],[])).
% 0.44/0.55 tff(236,plain,
% 0.44/0.55 (member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)),
% 0.44/0.55 inference(unit_resolution,[status(thm)],[235, 234])).
% 0.44/0.55 tff(237,plain,
% 0.44/0.55 ((~((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))),
% 0.44/0.55 inference(tautology,[status(thm)],[])).
% 0.44/0.55 tff(238,plain,
% 0.44/0.55 (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))),
% 0.44/0.55 inference(unit_resolution,[status(thm)],[237, 236, 227])).
% 0.44/0.55 tff(239,plain,
% 0.44/0.55 (((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | ((~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))),
% 0.44/0.55 inference(rewrite,[status(thm)],[])).
% 0.44/0.55 tff(240,plain,
% 0.44/0.55 (((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(A!21, E!23))) <=> ((~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))),
% 0.44/0.55 inference(rewrite,[status(thm)],[])).
% 0.44/0.55 tff(241,plain,
% 0.44/0.55 (((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | ((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(A!21, E!23)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | ((~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))))),
% 0.44/0.55 inference(monotonicity,[status(thm)],[240])).
% 0.44/0.55 tff(242,plain,
% 0.44/0.55 (((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | ((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(A!21, E!23)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))))),
% 0.44/0.55 inference(transitivity,[status(thm)],[241, 239])).
% 0.44/0.55 tff(243,plain,
% 0.44/0.55 ((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | ((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(A!21, E!23)))),
% 0.44/0.55 inference(quant_inst,[status(thm)],[])).
% 0.44/0.55 tff(244,plain,
% 0.44/0.55 ((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~member(A!21, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, A!21, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))),
% 0.44/0.56 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.44/0.56 tff(245,plain,
% 0.44/0.56 (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))),
% 0.44/0.56 inference(unit_resolution,[status(thm)],[244, 166, 196, 152, 163, 236, 238])).
% 0.44/0.56 tff(246,plain,
% 0.44/0.56 (((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))) | apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))),
% 0.44/0.56 inference(tautology,[status(thm)],[])).
% 0.44/0.56 tff(247,plain,
% 0.44/0.56 (apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))),
% 0.44/0.56 inference(unit_resolution,[status(thm)],[246, 234])).
% 0.44/0.56 tff(248,plain,
% 0.44/0.56 (((~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | ((~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20))) <=> ((~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20))),
% 0.44/0.56 inference(rewrite,[status(thm)],[])).
% 0.44/0.56 tff(249,plain,
% 0.44/0.56 (((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23))) <=> ((~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20))),
% 0.44/0.56 inference(rewrite,[status(thm)],[])).
% 0.44/0.56 tff(250,plain,
% 0.44/0.56 (((~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | ((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)))) <=> ((~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | ((~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)))),
% 0.44/0.56 inference(monotonicity,[status(thm)],[249])).
% 0.44/0.56 tff(251,plain,
% 0.44/0.56 (((~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | ((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)))) <=> ((~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20))),
% 0.44/0.56 inference(transitivity,[status(thm)],[250, 248])).
% 0.44/0.56 tff(252,plain,
% 0.44/0.56 ((~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | ((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, E!23)))),
% 0.44/0.56 inference(quant_inst,[status(thm)],[])).
% 0.44/0.56 tff(253,plain,
% 0.44/0.56 ((~![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)),
% 0.44/0.56 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.44/0.56 tff(254,plain,
% 0.44/0.56 (apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)),
% 0.44/0.56 inference(unit_resolution,[status(thm)],[253, 62, 165, 152, 154])).
% 0.44/0.56 tff(255,plain,
% 0.44/0.56 (((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | ((~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)))),
% 0.44/0.56 inference(rewrite,[status(thm)],[])).
% 0.44/0.56 tff(256,plain,
% 0.44/0.56 (((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | (~member(B!20, E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23))) <=> ((~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)))),
% 0.44/0.56 inference(rewrite,[status(thm)],[])).
% 0.44/0.56 tff(257,plain,
% 0.44/0.56 (((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | ((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | (~member(B!20, E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | ((~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20))))),
% 0.44/0.56 inference(monotonicity,[status(thm)],[256])).
% 0.44/0.56 tff(258,plain,
% 0.44/0.56 (((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | ((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | (~member(B!20, E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)))),
% 0.44/0.56 inference(transitivity,[status(thm)],[257, 255])).
% 0.44/0.56 tff(259,plain,
% 0.44/0.56 ((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | ((~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | (~member(B!20, E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)))),
% 0.44/0.56 inference(quant_inst,[status(thm)],[])).
% 0.44/0.56 tff(260,plain,
% 0.44/0.56 ((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~member(B!20, E!23)) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20))),
% 0.44/0.56 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.44/0.56 tff(261,plain,
% 0.44/0.56 ($false),
% 0.44/0.56 inference(unit_resolution,[status(thm)],[260, 62, 196, 152, 254, 236, 247, 245])).
% 0.44/0.56 tff(262,plain,(equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.56 tff(263,plain,
% 0.44/0.56 ((~(equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) <=> (~((~subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))))) | (~equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~((~subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))),
% 0.44/0.56 inference(tautology,[status(thm)],[])).
% 0.44/0.56 tff(264,plain,
% 0.44/0.56 ((~equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~((~subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))))),
% 0.44/0.56 inference(unit_resolution,[status(thm)],[263, 108])).
% 0.44/0.56 tff(265,plain,
% 0.44/0.56 (~((~subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))))),
% 0.44/0.56 inference(unit_resolution,[status(thm)],[264, 262])).
% 0.44/0.56 tff(266,plain,
% 0.44/0.56 (((~subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))),
% 0.44/0.56 inference(tautology,[status(thm)],[])).
% 0.44/0.56 tff(267,plain,
% 0.44/0.56 (subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))),
% 0.44/0.56 inference(unit_resolution,[status(thm)],[266, 265])).
% 0.44/0.56 tff(268,plain,
% 0.44/0.56 ((~((~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(B!20, E!23, R!22))) | member(X, equivalence_class(A!21, E!23, R!22))))) | (~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(B!20, E!23, R!22))) | member(X, equivalence_class(A!21, E!23, R!22)))),
% 0.44/0.57 inference(tautology,[status(thm)],[])).
% 0.44/0.57 tff(269,plain,
% 0.44/0.57 ((~((~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(B!20, E!23, R!22))) | member(X, equivalence_class(A!21, E!23, R!22))))) | ![X: $i] : ((~member(X, equivalence_class(B!20, E!23, R!22))) | member(X, equivalence_class(A!21, E!23, R!22)))),
% 0.44/0.57 inference(unit_resolution,[status(thm)],[268, 267])).
% 0.44/0.57 tff(270,plain,
% 0.44/0.57 (![X: $i] : ((~member(X, equivalence_class(B!20, E!23, R!22))) | member(X, equivalence_class(A!21, E!23, R!22)))),
% 0.44/0.57 inference(unit_resolution,[status(thm)],[269, 91])).
% 0.44/0.57 tff(271,plain,
% 0.44/0.57 (((~![X: $i] : ((~member(X, equivalence_class(B!20, E!23, R!22))) | member(X, equivalence_class(A!21, E!23, R!22)))) | ((~member(B!20, equivalence_class(B!20, E!23, R!22))) | member(B!20, equivalence_class(A!21, E!23, R!22)))) <=> ((~![X: $i] : ((~member(X, equivalence_class(B!20, E!23, R!22))) | member(X, equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, equivalence_class(B!20, E!23, R!22))) | member(B!20, equivalence_class(A!21, E!23, R!22)))),
% 0.44/0.57 inference(rewrite,[status(thm)],[])).
% 0.44/0.57 tff(272,plain,
% 0.44/0.57 ((~![X: $i] : ((~member(X, equivalence_class(B!20, E!23, R!22))) | member(X, equivalence_class(A!21, E!23, R!22)))) | ((~member(B!20, equivalence_class(B!20, E!23, R!22))) | member(B!20, equivalence_class(A!21, E!23, R!22)))),
% 0.44/0.57 inference(quant_inst,[status(thm)],[])).
% 0.44/0.57 tff(273,plain,
% 0.44/0.57 ((~![X: $i] : ((~member(X, equivalence_class(B!20, E!23, R!22))) | member(X, equivalence_class(A!21, E!23, R!22)))) | (~member(B!20, equivalence_class(B!20, E!23, R!22))) | member(B!20, equivalence_class(A!21, E!23, R!22))),
% 0.44/0.57 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.44/0.57 tff(274,plain,
% 0.44/0.57 (member(B!20, equivalence_class(A!21, E!23, R!22))),
% 0.44/0.57 inference(unit_resolution,[status(thm)],[273, 270, 71])).
% 0.44/0.57 tff(275,plain,
% 0.44/0.57 ((~equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~(equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) <=> disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))))),
% 0.44/0.57 inference(tautology,[status(thm)],[])).
% 0.44/0.57 tff(276,plain,
% 0.44/0.57 ((~equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))),
% 0.44/0.57 inference(unit_resolution,[status(thm)],[275, 122])).
% 0.44/0.57 tff(277,plain,
% 0.44/0.57 (disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))),
% 0.44/0.57 inference(unit_resolution,[status(thm)],[276, 262])).
% 0.44/0.57 tff(278,plain,
% 0.44/0.57 (((~((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22)))))) | (~(disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22)))))))) | ((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22)))))),
% 0.44/0.57 inference(tautology,[status(thm)],[])).
% 0.44/0.57 tff(279,plain,
% 0.44/0.57 ((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22))))),
% 0.44/0.57 inference(unit_resolution,[status(thm)],[278, 140])).
% 0.44/0.57 tff(280,plain,
% 0.44/0.57 ((~((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22)))))) | (~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22))))),
% 0.44/0.57 inference(tautology,[status(thm)],[])).
% 0.44/0.57 tff(281,plain,
% 0.44/0.57 ((~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | ![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22))))),
% 0.44/0.57 inference(unit_resolution,[status(thm)],[280, 279])).
% 0.44/0.57 tff(282,plain,
% 0.44/0.57 (![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22))))),
% 0.44/0.57 inference(unit_resolution,[status(thm)],[281, 277])).
% 0.44/0.57 tff(283,plain,
% 0.44/0.57 (((~![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22))))) | ((~member(B!20, equivalence_class(A!21, E!23, R!22))) | (~member(B!20, equivalence_class(B!20, E!23, R!22))))) <=> ((~![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22))))) | (~member(B!20, equivalence_class(A!21, E!23, R!22))) | (~member(B!20, equivalence_class(B!20, E!23, R!22))))),
% 0.44/0.57 inference(rewrite,[status(thm)],[])).
% 0.44/0.57 tff(284,plain,
% 0.44/0.57 ((~![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22))))) | ((~member(B!20, equivalence_class(A!21, E!23, R!22))) | (~member(B!20, equivalence_class(B!20, E!23, R!22))))),
% 0.44/0.57 inference(quant_inst,[status(thm)],[])).
% 0.44/0.57 tff(285,plain,
% 0.44/0.57 ((~![X: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | (~member(X, equivalence_class(B!20, E!23, R!22))))) | (~member(B!20, equivalence_class(A!21, E!23, R!22))) | (~member(B!20, equivalence_class(B!20, E!23, R!22)))),
% 0.44/0.57 inference(modus_ponens,[status(thm)],[284, 283])).
% 0.44/0.57 tff(286,plain,
% 0.44/0.57 ($false),
% 0.44/0.57 inference(unit_resolution,[status(thm)],[285, 282, 71, 274])).
% 0.44/0.57 % SZS output end Proof
%------------------------------------------------------------------------------