TSTP Solution File: SET770+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET770+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 05:07:57 EDT 2022
% Result : Theorem 0.18s 0.39s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET770+4 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.33 % Computer : n019.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sat Sep 3 07:53:20 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 0.18/0.39 % SZS status Theorem
% 0.18/0.39 % SZS output start Proof
% 0.18/0.39 tff(apply_type, type, (
% 0.18/0.39 apply: ( $i * $i * $i ) > $o)).
% 0.18/0.39 tff(tptp_fun_X_0_type, type, (
% 0.18/0.39 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.18/0.39 tff(equivalence_class_type, type, (
% 0.18/0.39 equivalence_class: ( $i * $i * $i ) > $i)).
% 0.18/0.39 tff(tptp_fun_R_22_type, type, (
% 0.18/0.39 tptp_fun_R_22: $i)).
% 0.18/0.39 tff(tptp_fun_E_23_type, type, (
% 0.18/0.39 tptp_fun_E_23: $i)).
% 0.18/0.39 tff(tptp_fun_B_20_type, type, (
% 0.18/0.39 tptp_fun_B_20: $i)).
% 0.18/0.39 tff(tptp_fun_A_21_type, type, (
% 0.18/0.39 tptp_fun_A_21: $i)).
% 0.18/0.39 tff(tptp_fun_X_3_type, type, (
% 0.18/0.39 tptp_fun_X_3: ( $i * $i ) > $i)).
% 0.18/0.39 tff(member_type, type, (
% 0.18/0.39 member: ( $i * $i ) > $o)).
% 0.18/0.39 tff(subset_type, type, (
% 0.18/0.39 subset: ( $i * $i ) > $o)).
% 0.18/0.39 tff(disjoint_type, type, (
% 0.18/0.39 disjoint: ( $i * $i ) > $o)).
% 0.18/0.39 tff(equivalence_type, type, (
% 0.18/0.39 equivalence: ( $i * $i ) > $o)).
% 0.18/0.39 tff(equal_set_type, type, (
% 0.18/0.39 equal_set: ( $i * $i ) > $o)).
% 0.18/0.39 tff(tptp_fun_Z_13_type, type, (
% 0.18/0.39 tptp_fun_Z_13: ( $i * $i ) > $i)).
% 0.18/0.39 tff(tptp_fun_Y_14_type, type, (
% 0.18/0.39 tptp_fun_Y_14: ( $i * $i ) > $i)).
% 0.18/0.39 tff(tptp_fun_X_15_type, type, (
% 0.18/0.39 tptp_fun_X_15: ( $i * $i ) > $i)).
% 0.18/0.39 tff(tptp_fun_Y_11_type, type, (
% 0.18/0.39 tptp_fun_Y_11: ( $i * $i ) > $i)).
% 0.18/0.39 tff(tptp_fun_X_12_type, type, (
% 0.18/0.39 tptp_fun_X_12: ( $i * $i ) > $i)).
% 0.18/0.39 tff(tptp_fun_X_10_type, type, (
% 0.18/0.39 tptp_fun_X_10: ( $i * $i ) > $i)).
% 0.18/0.39 tff(1,plain,
% 0.18/0.39 (^[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))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(2,plain,
% 0.18/0.39 (![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)))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.39 tff(3,plain,
% 0.18/0.39 (^[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))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(4,plain,
% 0.18/0.39 (![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)))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.18/0.39 tff(5,plain,
% 0.18/0.39 (![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)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 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/sandbox/benchmark/Axioms/SET006+2.ax','equivalence_class')).
% 0.18/0.39 tff(7,plain,
% 0.18/0.39 (![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (member(X, E) & apply(R, A, X)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.18/0.39 tff(8,plain,(
% 0.18/0.39 ![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (member(X, E) & apply(R, A, X)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[7])).
% 0.18/0.39 tff(9,plain,
% 0.18/0.39 (![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (~((~member(X, E)) | (~apply(R, A, X)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.18/0.39 tff(10,plain,
% 0.18/0.39 (![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (~((~member(X, E)) | (~apply(R, A, X)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.18/0.39 tff(11,plain,
% 0.18/0.39 ((~![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)))))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(12,plain,
% 0.18/0.39 (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))))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.18/0.39 tff(13,plain,
% 0.18/0.39 (^[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))))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(14,plain,
% 0.18/0.39 (![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)))))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[13])).
% 0.18/0.39 tff(15,plain,
% 0.18/0.39 (^[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))))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(16,plain,
% 0.18/0.39 (![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)))))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[15])).
% 0.18/0.39 tff(17,plain,
% 0.18/0.39 (![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)))))))),
% 0.18/0.39 inference(transitivity,[status(thm)],[16, 14])).
% 0.18/0.39 tff(18,plain,
% 0.18/0.39 (^[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)))))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(19,plain,
% 0.18/0.39 (![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)))))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[18])).
% 0.18/0.39 tff(20,plain,
% 0.18/0.39 (![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)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(21,plain,
% 0.18/0.39 (^[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))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(22,plain,
% 0.18/0.39 (![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)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[21])).
% 0.18/0.39 tff(23,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','subset')).
% 0.18/0.39 tff(24,plain,
% 0.18/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.18/0.39 tff(25,plain,
% 0.18/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.18/0.39 tff(26,plain,(
% 0.18/0.39 ![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)))))),
% 0.18/0.39 inference(skolemize,[status(sab)],[25])).
% 0.18/0.39 tff(27,plain,
% 0.18/0.39 (![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)))))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.18/0.39 tff(28,plain,
% 0.18/0.39 (![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)))))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.18/0.39 tff(29,plain,
% 0.18/0.39 ((~![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))))))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(30,plain,
% 0.18/0.39 (~((~((~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)))))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.18/0.39 tff(31,plain,
% 0.18/0.39 (((~((~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)))))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(32,plain,
% 0.18/0.40 (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))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.18/0.40 tff(33,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)).
% 0.18/0.40 tff(34,plain,
% 0.18/0.40 ((~![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: $i] : ((~member(X, equivalence_class(A!21, E!23, R!22))) | member(X, equivalence_class(B!20, E!23, R!22))))) | (~(subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)) | (~((~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(A!21, E!23, R!22))) | member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), equivalence_class(B!20, E!23, R!22))))))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(35,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[34, 28, 33])).
% 0.18/0.40 tff(36,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,[]))).
% 0.18/0.40 tff(37,plain,
% 0.18/0.40 (((~((~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)))))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(38,plain,
% 0.18/0.40 (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))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.18/0.40 tff(39,plain,
% 0.18/0.40 ((~![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)))))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(40,plain,
% 0.18/0.40 (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))))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[39, 10])).
% 0.18/0.40 tff(41,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)).
% 0.18/0.40 tff(42,plain,
% 0.18/0.40 (((~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)))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(43,plain,
% 0.18/0.40 (~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))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.18/0.40 tff(44,plain,
% 0.18/0.40 ((~(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)))))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(45,plain,
% 0.18/0.40 ((~(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)))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.18/0.40 tff(46,plain,
% 0.18/0.40 ((~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))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[45, 40])).
% 0.18/0.40 tff(47,plain,
% 0.18/0.40 ((~![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)))))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(48,plain,
% 0.18/0.40 (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))))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[47, 10])).
% 0.18/0.41 tff(49,plain,
% 0.18/0.41 (((~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))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(50,plain,
% 0.18/0.41 (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))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[49, 41])).
% 0.18/0.41 tff(51,plain,
% 0.18/0.41 ((~(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))))))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(52,plain,
% 0.18/0.41 ((~(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))))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.18/0.41 tff(53,plain,
% 0.18/0.41 (~((~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)))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[52, 48])).
% 0.18/0.41 tff(54,plain,
% 0.18/0.41 (((~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)),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(55,plain,
% 0.18/0.41 (member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.18/0.41 tff(56,plain,
% 0.18/0.41 ((~((~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))))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(57,plain,
% 0.18/0.41 (~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)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[56, 55, 46])).
% 0.18/0.41 tff(58,plain,
% 0.18/0.41 ((~![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)))))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(59,plain,
% 0.18/0.41 (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))))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[58, 10])).
% 0.18/0.41 tff(60,plain,
% 0.18/0.41 (^[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)))))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(61,plain,
% 0.18/0.41 (![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))))))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[60])).
% 0.18/0.41 tff(62,plain,
% 0.18/0.41 (^[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)))))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(63,plain,
% 0.18/0.41 (![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))))))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[62])).
% 0.18/0.41 tff(64,plain,
% 0.18/0.41 (![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))))))))),
% 0.18/0.41 inference(transitivity,[status(thm)],[63, 61])).
% 0.18/0.41 tff(65,plain,
% 0.18/0.41 (^[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))))))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(66,plain,
% 0.18/0.41 (![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))))))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[65])).
% 0.18/0.41 tff(67,plain,
% 0.18/0.41 (![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))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(68,axiom,(![A: $i, B: $i] : (disjoint(A, B) <=> (~?[X: $i] : (member(X, A) & member(X, B))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+2.ax','disjoint')).
% 0.18/0.41 tff(69,plain,
% 0.18/0.41 (![A: $i, B: $i] : (disjoint(A, B) <=> (~?[X: $i] : (member(X, A) & member(X, B))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.18/0.41 tff(70,plain,(
% 0.18/0.41 ![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))))),
% 0.18/0.41 inference(skolemize,[status(sab)],[69])).
% 0.18/0.41 tff(71,plain,
% 0.18/0.41 (![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))))))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.18/0.41 tff(72,plain,
% 0.18/0.41 (![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))))))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.18/0.41 tff(73,plain,
% 0.18/0.41 ((~![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)))))))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(74,plain,
% 0.18/0.41 (~((~((~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))))))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.18/0.41 tff(75,plain,
% 0.18/0.41 (((~((~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))))))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(76,plain,
% 0.18/0.41 (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)))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.18/0.41 tff(77,plain,
% 0.18/0.41 ((~(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)) | (~(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)) | (~(equivalence(R!22, E!23) & member(A!21, E!23) & member(B!20, E!23)))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(78,plain,
% 0.18/0.41 ((~![E: $i, R: $i, A: $i, B: $i] : (equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)) | disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)) | (~(equivalence(R, E) & member(A, E) & member(B, E))))) <=> (~![E: $i, R: $i, A: $i, B: $i] : (equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)) | disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)) | (~(equivalence(R, E) & member(A, E) & member(B, E)))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(79,plain,
% 0.18/0.41 ((~![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] : (equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)) | disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)) | (~(equivalence(R, E) & member(A, E) & member(B, E)))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(80,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/sandbox/benchmark/theBenchmark.p','thIII06')).
% 0.18/0.42 tff(81,plain,
% 0.18/0.42 (~![E: $i, R: $i, A: $i, B: $i] : (equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)) | disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)) | (~(equivalence(R, E) & member(A, E) & member(B, E))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.18/0.42 tff(82,plain,
% 0.18/0.42 (~![E: $i, R: $i, A: $i, B: $i] : (equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)) | disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)) | (~(equivalence(R, E) & member(A, E) & member(B, E))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[81, 78])).
% 0.18/0.42 tff(83,plain,
% 0.18/0.42 (~![E: $i, R: $i, A: $i, B: $i] : (equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)) | disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)) | (~(equivalence(R, E) & member(A, E) & member(B, E))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.18/0.42 tff(84,plain,
% 0.18/0.42 (~![E: $i, R: $i, A: $i, B: $i] : (equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)) | disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)) | (~(equivalence(R, E) & member(A, E) & member(B, E))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[83, 78])).
% 0.18/0.42 tff(85,plain,
% 0.18/0.42 (~![E: $i, R: $i, A: $i, B: $i] : (equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)) | disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)) | (~(equivalence(R, E) & member(A, E) & member(B, E))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[84, 78])).
% 0.18/0.42 tff(86,plain,
% 0.18/0.42 (~![E: $i, R: $i, A: $i, B: $i] : (equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)) | disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)) | (~(equivalence(R, E) & member(A, E) & member(B, E))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.18/0.42 tff(87,plain,
% 0.18/0.42 (~![E: $i, R: $i, A: $i, B: $i] : (equal_set(equivalence_class(A, E, R), equivalence_class(B, E, R)) | disjoint(equivalence_class(A, E, R), equivalence_class(B, E, R)) | (~(equivalence(R, E) & member(A, E) & member(B, E))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[86, 78])).
% 0.18/0.42 tff(88,plain,(
% 0.18/0.42 ~(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)) | (~(equivalence(R!22, E!23) & member(A!21, E!23) & member(B!20, E!23))))),
% 0.18/0.42 inference(skolemize,[status(sab)],[87])).
% 0.18/0.42 tff(89,plain,
% 0.18/0.42 (~(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)) | (~(equivalence(R!22, E!23) & member(A!21, E!23) & member(B!20, E!23))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[88, 77])).
% 0.18/0.42 tff(90,plain,
% 0.18/0.42 (~disjoint(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))),
% 0.18/0.42 inference(or_elim,[status(thm)],[89])).
% 0.18/0.42 tff(91,plain,
% 0.18/0.42 ((~(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)))))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(92,plain,
% 0.18/0.42 ((~(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))))))) | (~((~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)))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.18/0.42 tff(93,plain,
% 0.18/0.42 (~((~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))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[92, 76])).
% 0.18/0.42 tff(94,plain,
% 0.18/0.42 (((~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))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(95,plain,
% 0.18/0.42 (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))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.18/0.42 tff(96,plain,
% 0.18/0.42 ((~(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))))))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(97,plain,
% 0.18/0.42 ((~(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))))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.18/0.42 tff(98,plain,
% 0.18/0.42 (~((~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)))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[97, 59])).
% 0.18/0.42 tff(99,plain,
% 0.18/0.42 (((~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)))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(100,plain,
% 0.18/0.42 (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)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.18/0.42 tff(101,plain,
% 0.18/0.42 (((~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)),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(102,plain,
% 0.18/0.42 (member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[101, 98])).
% 0.18/0.42 tff(103,plain,
% 0.18/0.42 (^[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)))))))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(104,plain,
% 0.18/0.42 (![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))))))))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[103])).
% 0.18/0.42 tff(105,plain,
% 0.18/0.42 (^[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)))))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(106,plain,
% 0.18/0.42 (![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))))))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[105])).
% 0.18/0.42 tff(107,plain,
% 0.18/0.42 (^[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)))))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(108,plain,
% 0.18/0.42 (![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))))))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[107])).
% 0.18/0.42 tff(109,plain,
% 0.18/0.42 (![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))))))))),
% 0.18/0.43 inference(transitivity,[status(thm)],[108, 106])).
% 0.18/0.43 tff(110,plain,
% 0.18/0.43 (^[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))))))))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(111,plain,
% 0.18/0.43 (![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))))))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[110])).
% 0.18/0.43 tff(112,plain,
% 0.18/0.43 (^[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))))))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(113,plain,
% 0.18/0.43 (![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)))))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[112])).
% 0.18/0.43 tff(114,plain,
% 0.18/0.43 (![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))))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(115,plain,
% 0.18/0.43 (^[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)))))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(116,plain,
% 0.18/0.43 (![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))))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[115])).
% 0.18/0.43 tff(117,axiom,(![A: $i, R: $i] : (equivalence(R, A) <=> ((![X: $i] : (member(X, A) => apply(R, X, X)) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, A)) => (apply(R, X, Y) => apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (((member(X, A) & member(Y, A)) & member(Z, A)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z)))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+2.ax','equivalence')).
% 0.18/0.43 tff(118,plain,
% 0.18/0.43 (![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))))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.18/0.43 tff(119,plain,
% 0.18/0.43 (![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))))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.18/0.43 tff(120,plain,(
% 0.18/0.43 ![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))))))))),
% 0.18/0.43 inference(skolemize,[status(sab)],[119])).
% 0.18/0.43 tff(121,plain,
% 0.18/0.43 (![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)))))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.18/0.43 tff(122,plain,
% 0.18/0.43 (![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))))))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[121, 111])).
% 0.18/0.43 tff(123,plain,
% 0.18/0.43 (![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))))))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[122, 109])).
% 0.18/0.44 tff(124,plain,
% 0.18/0.44 (![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))))))))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[123, 104])).
% 0.18/0.44 tff(125,plain,
% 0.18/0.44 (((~![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)))))))))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(126,plain,
% 0.18/0.44 ((~((~(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))))))))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(127,plain,
% 0.18/0.44 (((~![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)))))))))))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[126])).
% 0.18/0.44 tff(128,plain,
% 0.18/0.44 (((~![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)))))))))))),
% 0.18/0.45 inference(transitivity,[status(thm)],[127, 125])).
% 0.18/0.45 tff(129,plain,
% 0.18/0.45 ((~![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))))))))))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(130,plain,
% 0.18/0.45 ((~![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))))))))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.18/0.45 tff(131,plain,
% 0.18/0.45 (~((~(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)))))))))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[130, 124])).
% 0.18/0.45 tff(132,plain,
% 0.18/0.45 (((~(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)))))))),
% 0.18/0.45 inference(tautology,[status(thm)],[])).
% 0.18/0.45 tff(133,plain,
% 0.18/0.45 ((~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))))))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.18/0.45 tff(134,plain,
% 0.18/0.45 (equivalence(R!22, E!23) & member(A!21, E!23) & member(B!20, E!23)),
% 0.18/0.45 inference(or_elim,[status(thm)],[89])).
% 0.18/0.45 tff(135,plain,
% 0.18/0.45 (equivalence(R!22, E!23)),
% 0.18/0.45 inference(and_elim,[status(thm)],[134])).
% 0.18/0.45 tff(136,plain,
% 0.18/0.45 ((~((~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))))))),
% 0.18/0.45 inference(tautology,[status(thm)],[])).
% 0.18/0.45 tff(137,plain,
% 0.18/0.45 ((~((~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))))))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.18/0.46 tff(138,plain,
% 0.18/0.46 (~((~![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)))))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[137, 133])).
% 0.18/0.46 tff(139,plain,
% 0.18/0.46 (((~![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)))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(140,plain,
% 0.18/0.46 (![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)))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.18/0.46 tff(141,plain,
% 0.18/0.46 (member(B!20, E!23)),
% 0.18/0.46 inference(and_elim,[status(thm)],[134])).
% 0.18/0.46 tff(142,plain,
% 0.18/0.46 (((~![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_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(B!20, 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, 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(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(B!20, 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, 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)))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(143,plain,
% 0.18/0.46 (((~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(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(B!20, 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, 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)))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(144,plain,
% 0.18/0.46 (((~![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(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(B!20, 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, 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))))))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[143])).
% 0.18/0.46 tff(145,plain,
% 0.18/0.46 (((~![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(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(B!20, 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, 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)))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[144, 142])).
% 0.18/0.47 tff(146,plain,
% 0.18/0.47 ((~![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)))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(147,plain,
% 0.18/0.47 ((~![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_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(B!20, 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, 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))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.18/0.47 tff(148,plain,
% 0.18/0.47 (~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)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[147, 141, 140, 102, 100, 55, 57])).
% 0.18/0.47 tff(149,plain,
% 0.18/0.47 (((~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)))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(150,plain,
% 0.18/0.47 (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)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[149, 53])).
% 0.18/0.47 tff(151,plain,
% 0.18/0.47 ((~![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (~((~member(X, E)) | (~apply(R, A, X)))))) | (member(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)))))))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(152,plain,
% 0.18/0.47 (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))))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[151, 10])).
% 0.18/0.47 tff(153,plain,
% 0.18/0.47 (((~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))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(154,plain,
% 0.18/0.47 (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))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[153, 93])).
% 0.18/0.47 tff(155,plain,
% 0.18/0.47 ((~(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))))))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(156,plain,
% 0.18/0.47 ((~(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))))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[155, 154])).
% 0.18/0.47 tff(157,plain,
% 0.18/0.47 (~((~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)))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[156, 152])).
% 0.18/0.47 tff(158,plain,
% 0.18/0.47 (((~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)))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(159,plain,
% 0.18/0.47 (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)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[158, 157])).
% 0.18/0.47 tff(160,plain,
% 0.18/0.47 (((~![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)))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(161,plain,
% 0.18/0.47 (![X: $i, Y: $i] : ((~member(Y, E!23)) | apply(R!22, Y, X) | (~apply(R!22, X, Y)) | (~member(X, E!23)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[160, 138])).
% 0.18/0.47 tff(162,plain,
% 0.18/0.47 (member(A!21, E!23)),
% 0.18/0.47 inference(and_elim,[status(thm)],[134])).
% 0.18/0.47 tff(163,plain,
% 0.18/0.47 (((~![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, 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)) | 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(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(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)), A!21))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(164,plain,
% 0.18/0.48 (((~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(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(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)), A!21))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(165,plain,
% 0.18/0.48 (((~![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(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(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)), A!21)))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[164])).
% 0.18/0.48 tff(166,plain,
% 0.18/0.48 (((~![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(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(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)), A!21))),
% 0.18/0.48 inference(transitivity,[status(thm)],[165, 163])).
% 0.18/0.48 tff(167,plain,
% 0.18/0.48 ((~![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)))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(168,plain,
% 0.18/0.48 ((~![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, 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)) | 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)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.18/0.48 tff(169,plain,
% 0.18/0.48 (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)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[168, 162, 161, 102, 159])).
% 0.18/0.48 tff(170,plain,
% 0.18/0.48 (((~![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_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_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(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_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)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(171,plain,
% 0.18/0.48 (((~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(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_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)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(172,plain,
% 0.18/0.48 (((~![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(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_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))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[171])).
% 0.18/0.49 tff(173,plain,
% 0.18/0.49 (((~![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(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_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)))),
% 0.18/0.49 inference(transitivity,[status(thm)],[172, 170])).
% 0.18/0.49 tff(174,plain,
% 0.18/0.49 ((~![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)))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(175,plain,
% 0.18/0.49 ((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(A!21, E!23)) | (~member(tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~apply(R!22, A!21, tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)))) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), A!21))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.18/0.49 tff(176,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[175, 162, 140, 102, 169, 55, 150, 148])).
% 0.18/0.49 tff(177,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))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.49 tff(178,plain,
% 0.18/0.49 ((~(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))))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(179,plain,
% 0.18/0.49 ((~(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))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[178, 177])).
% 0.18/0.49 tff(180,plain,
% 0.18/0.49 (subset(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[179, 38])).
% 0.18/0.49 tff(181,plain,
% 0.18/0.49 (^[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))))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(182,plain,
% 0.18/0.49 (![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)))))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[181])).
% 0.18/0.49 tff(183,plain,
% 0.18/0.49 (^[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))))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(184,plain,
% 0.18/0.49 (![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)))))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[183])).
% 0.18/0.49 tff(185,plain,
% 0.18/0.49 (![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)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(186,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','equal_set')).
% 0.18/0.49 tff(187,plain,
% 0.18/0.49 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.18/0.49 tff(188,plain,(
% 0.18/0.49 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.18/0.49 inference(skolemize,[status(sab)],[187])).
% 0.18/0.49 tff(189,plain,
% 0.18/0.49 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[188, 184])).
% 0.18/0.49 tff(190,plain,
% 0.18/0.49 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[189, 182])).
% 0.18/0.49 tff(191,plain,
% 0.18/0.49 ((~![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))))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(192,plain,
% 0.18/0.49 (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)))))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[191, 190])).
% 0.18/0.49 tff(193,plain,
% 0.18/0.49 (~equal_set(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))),
% 0.18/0.49 inference(or_elim,[status(thm)],[89])).
% 0.18/0.49 tff(194,plain,
% 0.18/0.49 ((~(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))))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(195,plain,
% 0.18/0.49 ((~(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))))))) | ((~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))))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[194, 193])).
% 0.18/0.49 tff(196,plain,
% 0.18/0.49 ((~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)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[195, 192])).
% 0.18/0.49 tff(197,plain,
% 0.18/0.49 ((~((~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)))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(198,plain,
% 0.18/0.49 ((~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)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[197, 196])).
% 0.18/0.49 tff(199,plain,
% 0.18/0.49 (~subset(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[198, 180])).
% 0.18/0.49 tff(200,plain,
% 0.18/0.49 ((~(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))))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(201,plain,
% 0.18/0.49 ((~(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))))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[200, 199])).
% 0.18/0.50 tff(202,plain,
% 0.18/0.50 (~((~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)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[201, 32])).
% 0.18/0.50 tff(203,plain,
% 0.18/0.50 (((~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)))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(204,plain,
% 0.18/0.50 (~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))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[203, 202])).
% 0.18/0.50 tff(205,plain,
% 0.18/0.50 ((~(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)))))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(206,plain,
% 0.18/0.50 ((~(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)))))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[205, 204])).
% 0.18/0.50 tff(207,plain,
% 0.18/0.50 ((~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))))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[206, 12])).
% 0.18/0.50 tff(208,plain,
% 0.18/0.50 ((~![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)))))))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(209,plain,
% 0.18/0.50 (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))))))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[208, 10])).
% 0.18/0.50 tff(210,plain,
% 0.18/0.50 (((~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))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(211,plain,
% 0.18/0.50 (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))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[210, 202])).
% 0.18/0.50 tff(212,plain,
% 0.18/0.50 ((~(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))))))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(213,plain,
% 0.18/0.50 ((~(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))))))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[212, 211])).
% 0.18/0.50 tff(214,plain,
% 0.18/0.50 (~((~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)))))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[213, 209])).
% 0.18/0.50 tff(215,plain,
% 0.18/0.50 (((~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)),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(216,plain,
% 0.18/0.50 (member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[215, 214])).
% 0.18/0.50 tff(217,plain,
% 0.18/0.50 ((~((~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))))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(218,plain,
% 0.18/0.50 (~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)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[217, 216, 207])).
% 0.18/0.50 tff(219,plain,
% 0.18/0.50 (((~![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_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(A!21, 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, 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(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(A!21, 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, 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)))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(220,plain,
% 0.18/0.51 (((~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(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(A!21, 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, 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)))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(221,plain,
% 0.18/0.51 (((~![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(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(A!21, 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, 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))))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[220])).
% 0.18/0.51 tff(222,plain,
% 0.18/0.51 (((~![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(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(A!21, 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, 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)))))),
% 0.18/0.51 inference(transitivity,[status(thm)],[221, 219])).
% 0.18/0.51 tff(223,plain,
% 0.18/0.51 ((~![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)))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(224,plain,
% 0.18/0.51 ((~![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_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(A!21, 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, 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))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.18/0.51 tff(225,plain,
% 0.18/0.51 (~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)))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[224, 162, 140, 102, 159, 216, 218])).
% 0.18/0.51 tff(226,plain,
% 0.18/0.51 (((~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)))),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(227,plain,
% 0.18/0.51 (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)))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[226, 214])).
% 0.18/0.51 tff(228,plain,
% 0.18/0.51 (((~![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, 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)) | 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(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(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)), B!20))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(229,plain,
% 0.18/0.51 (((~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(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(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)), B!20))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(230,plain,
% 0.18/0.51 (((~![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(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(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)), B!20)))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[229])).
% 0.18/0.51 tff(231,plain,
% 0.18/0.51 (((~![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(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(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)), B!20))),
% 0.18/0.52 inference(transitivity,[status(thm)],[230, 228])).
% 0.18/0.52 tff(232,plain,
% 0.18/0.52 ((~![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)), 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)))),
% 0.18/0.52 inference(quant_inst,[status(thm)],[])).
% 0.18/0.52 tff(233,plain,
% 0.18/0.52 ((~![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, 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)) | 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)),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.18/0.52 tff(234,plain,
% 0.18/0.52 (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)),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[233, 141, 161, 102, 100])).
% 0.18/0.52 tff(235,plain,
% 0.18/0.52 (((~![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_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(B!20, 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(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)) | (~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)))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(236,plain,
% 0.18/0.52 (((~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(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)) | (~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)))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(237,plain,
% 0.18/0.52 (((~![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(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)) | (~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))))),
% 0.18/0.52 inference(monotonicity,[status(thm)],[236])).
% 0.18/0.52 tff(238,plain,
% 0.18/0.52 (((~![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(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)) | (~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)))),
% 0.18/0.52 inference(transitivity,[status(thm)],[237, 235])).
% 0.18/0.52 tff(239,plain,
% 0.18/0.52 ((~![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)))),
% 0.18/0.53 inference(quant_inst,[status(thm)],[])).
% 0.18/0.53 tff(240,plain,
% 0.18/0.53 ((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!23)) | (~apply(R!22, Y, Z)) | (~member(Y, E!23)) | apply(R!22, X, Z) | (~apply(R!22, X, Y)) | (~member(X, E!23)))) | (~member(tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), E!23)) | (~member(B!20, E!23)) | (~apply(R!22, B!20, tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)))) | (~member(tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22)), E!23)) | apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), tptp_fun_X_0(equivalence_class(A!21, E!23, R!22), equivalence_class(B!20, E!23, R!22))) | (~apply(R!22, tptp_fun_X_3(equivalence_class(B!20, E!23, R!22), equivalence_class(A!21, E!23, R!22)), B!20))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.18/0.53 tff(241,plain,
% 0.18/0.53 ($false),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[240, 141, 140, 102, 234, 216, 227, 225])).
% 0.18/0.53 % SZS output end Proof
%------------------------------------------------------------------------------