TSTP Solution File: SET806+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET806+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 05:08:06 EDT 2022
% Result : Theorem 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET806+4 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 08:01:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43 % SZS output start Proof
% 0.21/0.43 tff(subset_type, type, (
% 0.21/0.43 subset: ( $i * $i ) > $o)).
% 0.21/0.43 tff(tptp_fun_X_10_type, type, (
% 0.21/0.43 tptp_fun_X_10: ( $i * $i ) > $i)).
% 0.21/0.43 tff(power_set_type, type, (
% 0.21/0.43 power_set: $i > $i)).
% 0.21/0.43 tff(tptp_fun_E_20_type, type, (
% 0.21/0.43 tptp_fun_E_20: $i)).
% 0.21/0.43 tff(equal_set_predicate_type, type, (
% 0.21/0.43 equal_set_predicate: $i)).
% 0.21/0.43 tff(equal_set_type, type, (
% 0.21/0.43 equal_set: ( $i * $i ) > $o)).
% 0.21/0.43 tff(apply_type, type, (
% 0.21/0.43 apply: ( $i * $i * $i ) > $o)).
% 0.21/0.43 tff(member_type, type, (
% 0.21/0.43 member: ( $i * $i ) > $o)).
% 0.21/0.43 tff(tptp_fun_Z_13_type, type, (
% 0.21/0.43 tptp_fun_Z_13: ( $i * $i ) > $i)).
% 0.21/0.43 tff(tptp_fun_Y_14_type, type, (
% 0.21/0.43 tptp_fun_Y_14: ( $i * $i ) > $i)).
% 0.21/0.43 tff(tptp_fun_X_15_type, type, (
% 0.21/0.43 tptp_fun_X_15: ( $i * $i ) > $i)).
% 0.21/0.43 tff(tptp_fun_X_0_type, type, (
% 0.21/0.43 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.21/0.43 tff(tptp_fun_Y_11_type, type, (
% 0.21/0.43 tptp_fun_Y_11: ( $i * $i ) > $i)).
% 0.21/0.43 tff(tptp_fun_X_12_type, type, (
% 0.21/0.43 tptp_fun_X_12: ( $i * $i ) > $i)).
% 0.21/0.43 tff(equivalence_type, type, (
% 0.21/0.43 equivalence: ( $i * $i ) > $o)).
% 0.21/0.43 tff(1,plain,
% 0.21/0.43 (^[A: $i, B: $i] : refl((equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(2,plain,
% 0.21/0.43 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.43 tff(3,plain,
% 0.21/0.43 (^[A: $i, B: $i] : rewrite((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(4,plain,
% 0.21/0.43 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.43 tff(5,plain,
% 0.21/0.43 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(6,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','equal_set')).
% 0.21/0.43 tff(7,plain,
% 0.21/0.43 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.21/0.43 tff(8,plain,(
% 0.21/0.43 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[7])).
% 0.21/0.43 tff(9,plain,
% 0.21/0.43 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.21/0.43 tff(10,plain,
% 0.21/0.43 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.21/0.43 tff(11,plain,
% 0.21/0.43 (((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) <=> ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(12,plain,
% 0.21/0.43 ((equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> (~((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))))) <=> (equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(13,plain,
% 0.21/0.43 (((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> (~((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))))) <=> ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[12])).
% 0.21/0.43 tff(14,plain,
% 0.21/0.43 (((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> (~((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))))) <=> ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[13, 11])).
% 0.21/0.43 tff(15,plain,
% 0.21/0.43 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> (~((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(16,plain,
% 0.21/0.43 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.21/0.43 tff(17,plain,
% 0.21/0.43 (equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[16, 10])).
% 0.21/0.43 tff(18,plain,
% 0.21/0.43 (^[X: $i, Y: $i] : refl((apply(equal_set_predicate, X, Y) <=> equal_set(X, Y)) <=> (apply(equal_set_predicate, X, Y) <=> equal_set(X, Y)))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(19,plain,
% 0.21/0.43 (![X: $i, Y: $i] : (apply(equal_set_predicate, X, Y) <=> equal_set(X, Y)) <=> ![X: $i, Y: $i] : (apply(equal_set_predicate, X, Y) <=> equal_set(X, Y))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[18])).
% 0.21/0.43 tff(20,plain,
% 0.21/0.43 (![X: $i, Y: $i] : (apply(equal_set_predicate, X, Y) <=> equal_set(X, Y)) <=> ![X: $i, Y: $i] : (apply(equal_set_predicate, X, Y) <=> equal_set(X, Y))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(21,axiom,(![X: $i, Y: $i] : (apply(equal_set_predicate, X, Y) <=> equal_set(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rel_equal_set')).
% 0.21/0.43 tff(22,plain,
% 0.21/0.43 (![X: $i, Y: $i] : (apply(equal_set_predicate, X, Y) <=> equal_set(X, Y))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.21/0.43 tff(23,plain,(
% 0.21/0.43 ![X: $i, Y: $i] : (apply(equal_set_predicate, X, Y) <=> equal_set(X, Y))),
% 0.21/0.43 inference(skolemize,[status(sab)],[22])).
% 0.21/0.43 tff(24,plain,
% 0.21/0.43 (![X: $i, Y: $i] : (apply(equal_set_predicate, X, Y) <=> equal_set(X, Y))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.21/0.43 tff(25,plain,
% 0.21/0.43 ((~![X: $i, Y: $i] : (apply(equal_set_predicate, X, Y) <=> equal_set(X, Y))) | (apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(26,plain,
% 0.21/0.43 (apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.21/0.43 tff(27,plain,
% 0.21/0.43 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(28,plain,
% 0.21/0.43 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[27])).
% 0.21/0.43 tff(29,plain,
% 0.21/0.43 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(30,plain,
% 0.21/0.43 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[29])).
% 0.21/0.43 tff(31,plain,
% 0.21/0.43 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[30, 28])).
% 0.21/0.43 tff(32,plain,
% 0.21/0.43 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(33,plain,
% 0.21/0.44 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[32])).
% 0.21/0.44 tff(34,plain,
% 0.21/0.44 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(35,plain,
% 0.21/0.44 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(36,plain,
% 0.21/0.44 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[35])).
% 0.21/0.44 tff(37,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','subset')).
% 0.21/0.44 tff(38,plain,
% 0.21/0.44 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.21/0.44 tff(39,plain,
% 0.21/0.44 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.21/0.44 tff(40,plain,(
% 0.21/0.44 ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[39])).
% 0.21/0.44 tff(41,plain,
% 0.21/0.44 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.21/0.44 tff(42,plain,
% 0.21/0.44 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[41, 31])).
% 0.21/0.44 tff(43,plain,
% 0.21/0.44 ((~![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(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(44,plain,
% 0.21/0.44 (~((~((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.21/0.44 tff(45,plain,
% 0.21/0.44 (((~((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))))) | (subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(46,plain,
% 0.21/0.44 (subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.21/0.44 tff(47,plain,
% 0.21/0.44 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) <=> (~((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(48,plain,
% 0.21/0.44 (equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) <=> (~((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[47, 10])).
% 0.21/0.44 tff(49,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : (apply(equal_set_predicate, X, Y) <=> equal_set(X, Y))) | (apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(50,plain,
% 0.21/0.44 (apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[49, 24])).
% 0.21/0.44 tff(51,assumption,(~(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))))), introduced(assumption)).
% 0.21/0.44 tff(52,plain,
% 0.21/0.44 ((apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(53,plain,
% 0.21/0.44 (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.21/0.44 tff(54,plain,
% 0.21/0.44 ((~(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))) | apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(55,plain,
% 0.21/0.44 ((~(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))) | (~equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.21/0.44 tff(56,plain,
% 0.21/0.44 (~equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[55, 50])).
% 0.21/0.44 tff(57,plain,
% 0.21/0.44 ((~(equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) <=> (~((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))))) | equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | ((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(58,plain,
% 0.21/0.44 ((~(equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) <=> (~((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))))) | ((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.21/0.44 tff(59,plain,
% 0.21/0.44 ((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[58, 48])).
% 0.21/0.44 tff(60,plain,
% 0.21/0.44 ((~![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(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(61,plain,
% 0.21/0.44 (~((~((~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[60, 42])).
% 0.21/0.44 tff(62,plain,
% 0.21/0.44 (((~((~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))))) | ((~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(63,plain,
% 0.21/0.44 ((~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.21/0.44 tff(64,plain,
% 0.21/0.44 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) <=> (~((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(65,plain,
% 0.21/0.45 (equal_set(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) <=> (~((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[64, 10])).
% 0.21/0.45 tff(66,plain,
% 0.21/0.45 ((~![X: $i, Y: $i] : (apply(equal_set_predicate, X, Y) <=> equal_set(X, Y))) | (apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(67,plain,
% 0.21/0.45 (apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[66, 24])).
% 0.21/0.45 tff(68,plain,
% 0.21/0.45 ((apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(69,plain,
% 0.21/0.45 (apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[68, 51])).
% 0.21/0.45 tff(70,plain,
% 0.21/0.45 ((~(apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | equal_set(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(71,plain,
% 0.21/0.45 ((~(apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))) | equal_set(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.21/0.45 tff(72,plain,
% 0.21/0.45 (equal_set(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[71, 67])).
% 0.21/0.45 tff(73,plain,
% 0.21/0.45 ((~(equal_set(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) <=> (~((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))))) | (~equal_set(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(74,plain,
% 0.21/0.45 ((~(equal_set(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) <=> (~((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))))) | (~((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.21/0.45 tff(75,plain,
% 0.21/0.45 (~((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[74, 65])).
% 0.21/0.45 tff(76,plain,
% 0.21/0.45 (((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) | subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(77,plain,
% 0.21/0.45 (subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.21/0.45 tff(78,plain,
% 0.21/0.45 ((~((~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(79,plain,
% 0.21/0.45 ((~((~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))) | ![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.21/0.45 tff(80,plain,
% 0.21/0.45 (![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[79, 63])).
% 0.21/0.45 tff(81,plain,
% 0.21/0.45 ((~![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(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(82,plain,
% 0.21/0.45 (~((~((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[81, 42])).
% 0.21/0.45 tff(83,plain,
% 0.21/0.45 (((~((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))))) | ((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(84,plain,
% 0.21/0.45 ((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.21/0.45 tff(85,plain,
% 0.21/0.45 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))) <=> (~((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(86,plain,
% 0.21/0.45 (equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))) <=> (~((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[85, 10])).
% 0.21/0.45 tff(87,plain,
% 0.21/0.45 ((~![X: $i, Y: $i] : (apply(equal_set_predicate, X, Y) <=> equal_set(X, Y))) | (apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(88,plain,
% 0.21/0.45 (apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[87, 24])).
% 0.21/0.45 tff(89,plain,
% 0.21/0.45 ((apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(90,plain,
% 0.21/0.45 (apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[89, 51])).
% 0.21/0.45 tff(91,plain,
% 0.21/0.45 ((~(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(92,plain,
% 0.21/0.45 ((~(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) | equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.21/0.45 tff(93,plain,
% 0.21/0.45 (equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[92, 88])).
% 0.21/0.45 tff(94,plain,
% 0.21/0.45 ((~(equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))) <=> (~((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))))) | (~equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(95,plain,
% 0.21/0.45 ((~(equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))) <=> (~((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))))) | (~((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.21/0.45 tff(96,plain,
% 0.21/0.45 (~((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[95, 86])).
% 0.21/0.46 tff(97,plain,
% 0.21/0.46 (((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))) | subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(98,plain,
% 0.21/0.46 (subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.21/0.46 tff(99,plain,
% 0.21/0.46 ((~((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))) | (~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(100,plain,
% 0.21/0.46 ((~((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.21/0.46 tff(101,plain,
% 0.21/0.46 (![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[100, 84])).
% 0.21/0.46 tff(102,assumption,(~((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))), introduced(assumption)).
% 0.21/0.46 tff(103,plain,
% 0.21/0.46 (((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(104,plain,
% 0.21/0.46 (~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.21/0.46 tff(105,assumption,(![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20))))), introduced(assumption)).
% 0.21/0.46 tff(106,plain,
% 0.21/0.46 (((~![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20))))) | ((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))) <=> ((~![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20))))) | (~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(107,plain,
% 0.21/0.46 ((~![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20))))) | ((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(108,plain,
% 0.21/0.46 ((~![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20))))) | (~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.21/0.46 tff(109,plain,
% 0.21/0.46 (~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[108, 105, 104])).
% 0.21/0.46 tff(110,plain,
% 0.21/0.46 (((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(111,plain,
% 0.21/0.46 (member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[110, 102])).
% 0.21/0.46 tff(112,assumption,(![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))), introduced(assumption)).
% 0.21/0.46 tff(113,plain,
% 0.21/0.46 (((~![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) | ((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) <=> ((~![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) | (~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(114,plain,
% 0.21/0.46 ((~![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) | ((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(115,plain,
% 0.21/0.46 ((~![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) | (~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.21/0.46 tff(116,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[115, 112, 111, 109])).
% 0.21/0.46 tff(117,plain,(((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | (~![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) | (~![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(118,plain,
% 0.21/0.46 ((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[117, 101, 80])).
% 0.21/0.46 tff(119,assumption,((~((~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))))), introduced(assumption)).
% 0.21/0.46 tff(120,plain,
% 0.21/0.46 ((~![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(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(121,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[120, 42, 119])).
% 0.21/0.46 tff(122,plain,(~((~((~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(123,plain,
% 0.21/0.46 (((~((~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))))) | (subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(124,plain,
% 0.21/0.46 (subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.21/0.46 tff(125,plain,
% 0.21/0.46 ((~(subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))))) | subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(126,plain,
% 0.21/0.46 (subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.21/0.47 tff(127,plain,
% 0.21/0.47 (subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[126, 118])).
% 0.21/0.47 tff(128,plain,
% 0.21/0.47 ((~((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))) | (~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(129,plain,
% 0.21/0.47 (~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[128, 127, 59])).
% 0.21/0.47 tff(130,plain,
% 0.21/0.47 ((~(subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))))) | subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(131,plain,
% 0.21/0.47 ((~(subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))))) | (~((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.21/0.47 tff(132,plain,
% 0.21/0.47 (~((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[131, 46])).
% 0.21/0.47 tff(133,plain,
% 0.21/0.47 (((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(134,plain,
% 0.21/0.47 (~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.21/0.47 tff(135,plain,
% 0.21/0.47 ((~![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(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(136,plain,
% 0.21/0.47 (~((~((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[135, 42])).
% 0.21/0.47 tff(137,plain,
% 0.21/0.47 (((~((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))))) | ((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(138,plain,
% 0.21/0.47 ((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.21/0.47 tff(139,plain,
% 0.21/0.47 (((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) | subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(140,plain,
% 0.21/0.47 (subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[139, 75])).
% 0.21/0.47 tff(141,plain,
% 0.21/0.47 ((~((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))) | (~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(142,plain,
% 0.21/0.47 ((~((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.21/0.47 tff(143,plain,
% 0.21/0.47 (![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[142, 138])).
% 0.21/0.47 tff(144,plain,
% 0.21/0.47 (((~![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))) | ((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))) <=> ((~![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))) | (~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(145,plain,
% 0.21/0.47 ((~![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))) | ((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(146,plain,
% 0.21/0.47 ((~![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))) | (~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.21/0.47 tff(147,plain,
% 0.21/0.47 (~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[146, 143, 134])).
% 0.21/0.47 tff(148,plain,
% 0.21/0.47 (((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(149,plain,
% 0.21/0.47 (member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[148, 132])).
% 0.21/0.47 tff(150,plain,
% 0.21/0.47 ((~![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(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(151,plain,
% 0.21/0.47 (~((~((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[150, 42])).
% 0.21/0.47 tff(152,plain,
% 0.21/0.47 (((~((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))))) | ((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(153,plain,
% 0.21/0.47 ((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.21/0.48 tff(154,plain,
% 0.21/0.48 (((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))) | subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(155,plain,
% 0.21/0.48 (subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[154, 96])).
% 0.21/0.48 tff(156,plain,
% 0.21/0.48 ((~((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))) | (~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(157,plain,
% 0.21/0.48 ((~((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))) | ![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.21/0.48 tff(158,plain,
% 0.21/0.48 (![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[157, 153])).
% 0.21/0.48 tff(159,plain,
% 0.21/0.48 (((~![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) | ((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) <=> ((~![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) | (~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(160,plain,
% 0.21/0.48 ((~![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) | ((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(161,plain,
% 0.21/0.48 ((~![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) | (~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.21/0.48 tff(162,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[161, 158, 149, 147])).
% 0.21/0.48 tff(163,plain,(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(164,plain,
% 0.21/0.48 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) <=> (~((~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(165,plain,
% 0.21/0.48 (equal_set(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) <=> (~((~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20))))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[164, 10])).
% 0.21/0.48 tff(166,plain,
% 0.21/0.48 ((~![X: $i, Y: $i] : (apply(equal_set_predicate, X, Y) <=> equal_set(X, Y))) | (apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(167,plain,
% 0.21/0.48 (apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[166, 24])).
% 0.21/0.48 tff(168,assumption,(~(apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))))), introduced(assumption)).
% 0.21/0.48 tff(169,plain,
% 0.21/0.48 ((apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(170,plain,
% 0.21/0.48 (~apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[169, 168])).
% 0.21/0.48 tff(171,plain,
% 0.21/0.48 ((~(apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))) | apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) | (~equal_set(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(172,plain,
% 0.21/0.48 ((~(apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))) | (~equal_set(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.21/0.48 tff(173,plain,
% 0.21/0.48 (~equal_set(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[172, 167])).
% 0.21/0.48 tff(174,plain,
% 0.21/0.48 ((~(equal_set(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) <=> (~((~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))))))) | equal_set(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) | ((~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(175,plain,
% 0.21/0.48 ((~(equal_set(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) <=> (~((~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))))))) | ((~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[174, 173])).
% 0.21/0.48 tff(176,plain,
% 0.21/0.48 ((~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[175, 165])).
% 0.21/0.48 tff(177,plain,
% 0.21/0.48 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20))) <=> (~((~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(178,plain,
% 0.21/0.48 (equal_set(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20))) <=> (~((~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[177, 10])).
% 0.21/0.48 tff(179,plain,
% 0.21/0.48 ((~![X: $i, Y: $i] : (apply(equal_set_predicate, X, Y) <=> equal_set(X, Y))) | (apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(180,plain,
% 0.21/0.48 (apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[179, 24])).
% 0.21/0.48 tff(181,plain,
% 0.21/0.48 ((apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(182,plain,
% 0.21/0.48 (apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[181, 168])).
% 0.21/0.48 tff(183,plain,
% 0.21/0.48 ((~(apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20))))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | equal_set(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(184,plain,
% 0.21/0.48 ((~(apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20))))) | equal_set(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[183, 182])).
% 0.21/0.48 tff(185,plain,
% 0.21/0.48 (equal_set(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[184, 180])).
% 0.21/0.48 tff(186,plain,
% 0.21/0.48 ((~(equal_set(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20))) <=> (~((~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))))))) | (~equal_set(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~((~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(187,plain,
% 0.21/0.48 ((~(equal_set(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20))) <=> (~((~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))))))) | (~((~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.21/0.48 tff(188,plain,
% 0.21/0.48 (~((~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[187, 178])).
% 0.21/0.48 tff(189,plain,
% 0.21/0.48 (((~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))) | subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(190,plain,
% 0.21/0.48 (subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[189, 188])).
% 0.21/0.48 tff(191,plain,
% 0.21/0.48 (((~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))) | subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(192,plain,
% 0.21/0.48 (subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[191, 188])).
% 0.21/0.48 tff(193,plain,
% 0.21/0.48 ((~((~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))))) | (~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(194,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[193, 192, 190, 176])).
% 0.21/0.48 tff(195,plain,(apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(196,plain,
% 0.21/0.48 (^[A: $i, R: $i] : rewrite((~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(197,plain,
% 0.21/0.48 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[196])).
% 0.21/0.48 tff(198,plain,
% 0.21/0.48 (^[A: $i, R: $i] : refl((~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(199,plain,
% 0.21/0.48 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[198])).
% 0.21/0.48 tff(200,plain,
% 0.21/0.48 (^[A: $i, R: $i] : rewrite((~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(201,plain,
% 0.21/0.49 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[200])).
% 0.21/0.49 tff(202,plain,
% 0.21/0.49 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[201, 199])).
% 0.21/0.49 tff(203,plain,
% 0.21/0.49 (^[A: $i, R: $i] : trans(monotonicity(rewrite(((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) <=> ((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))), trans(monotonicity(rewrite((~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) <=> (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A))))), rewrite((~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))) <=> (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))), ((equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))) <=> (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))), rewrite((equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))) <=> (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))), ((equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))) <=> (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))), ((((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))))) <=> (((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))), rewrite((((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) <=> (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))), ((((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))))) <=> (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(204,plain,
% 0.21/0.49 (![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))))) <=> ![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[203])).
% 0.21/0.49 tff(205,plain,
% 0.21/0.49 (^[A: $i, R: $i] : rewrite((((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | ((~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))))) <=> (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(206,plain,
% 0.21/0.49 (![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | ((~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[205])).
% 0.21/0.49 tff(207,plain,
% 0.21/0.49 (![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) <=> ![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(208,plain,
% 0.21/0.49 (^[A: $i, R: $i] : rewrite((equivalence(R, A) <=> ((![X: $i] : (member(X, A) => apply(R, X, X)) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, A)) => (apply(R, X, Y) => apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (((member(X, A) & member(Y, A)) & member(Z, A)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z))))) <=> (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(209,plain,
% 0.21/0.49 (![A: $i, R: $i] : (equivalence(R, A) <=> ((![X: $i] : (member(X, A) => apply(R, X, X)) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, A)) => (apply(R, X, Y) => apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (((member(X, A) & member(Y, A)) & member(Z, A)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z))))) <=> ![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[208])).
% 0.21/0.49 tff(210,axiom,(![A: $i, R: $i] : (equivalence(R, A) <=> ((![X: $i] : (member(X, A) => apply(R, X, X)) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, A)) => (apply(R, X, Y) => apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (((member(X, A) & member(Y, A)) & member(Z, A)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax','equivalence')).
% 0.21/0.49 tff(211,plain,
% 0.21/0.49 (![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.21/0.49 tff(212,plain,
% 0.21/0.49 (![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[211, 207])).
% 0.21/0.49 tff(213,plain,(
% 0.21/0.49 ![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | ((~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))))))),
% 0.21/0.49 inference(skolemize,[status(sab)],[212])).
% 0.21/0.49 tff(214,plain,
% 0.21/0.49 (![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[213, 206])).
% 0.21/0.49 tff(215,plain,
% 0.21/0.49 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[214, 204])).
% 0.21/0.49 tff(216,plain,
% 0.21/0.49 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[215, 202])).
% 0.21/0.49 tff(217,plain,
% 0.21/0.49 (![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[216, 197])).
% 0.21/0.49 tff(218,plain,
% 0.21/0.49 (((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))))))) | (~((~equivalence(equal_set_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(equal_set_predicate, X, X))) | (~![X: $i, Y: $i] : (apply(equal_set_predicate, Y, X) | (~member(Y, power_set(E!20))) | (~apply(equal_set_predicate, X, Y)) | (~member(X, power_set(E!20))))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, power_set(E!20))) | (~apply(equal_set_predicate, Y, Z)) | (~member(Y, power_set(E!20))) | apply(equal_set_predicate, X, Z) | (~apply(equal_set_predicate, X, Y)) | (~member(X, power_set(E!20)))))))))))) <=> ((~![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(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))))))) | (~((~equivalence(equal_set_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(equal_set_predicate, X, X))) | (~![X: $i, Y: $i] : (apply(equal_set_predicate, Y, X) | (~member(Y, power_set(E!20))) | (~apply(equal_set_predicate, X, Y)) | (~member(X, power_set(E!20))))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, power_set(E!20))) | (~apply(equal_set_predicate, Y, Z)) | (~member(Y, power_set(E!20))) | apply(equal_set_predicate, X, Z) | (~apply(equal_set_predicate, X, Y)) | (~member(X, power_set(E!20))))))))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(219,plain,
% 0.21/0.49 ((~((~(equivalence(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))))))) | (~((~equivalence(equal_set_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(equal_set_predicate, X, X))) | (~![X: $i, Y: $i] : (apply(equal_set_predicate, Y, X) | (~apply(equal_set_predicate, X, Y)) | (~member(X, power_set(E!20))) | (~member(Y, power_set(E!20))))) | (~![X: $i, Y: $i, Z: $i] : (apply(equal_set_predicate, X, Z) | (~apply(equal_set_predicate, X, Y)) | (~apply(equal_set_predicate, Y, Z)) | (~member(X, power_set(E!20))) | (~member(Y, power_set(E!20))) | (~member(Z, power_set(E!20))))))))))) <=> (~((~(equivalence(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))))))) | (~((~equivalence(equal_set_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(equal_set_predicate, X, X))) | (~![X: $i, Y: $i] : (apply(equal_set_predicate, Y, X) | (~member(Y, power_set(E!20))) | (~apply(equal_set_predicate, X, Y)) | (~member(X, power_set(E!20))))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, power_set(E!20))) | (~apply(equal_set_predicate, Y, Z)) | (~member(Y, power_set(E!20))) | apply(equal_set_predicate, X, Z) | (~apply(equal_set_predicate, X, Y)) | (~member(X, power_set(E!20)))))))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(220,plain,
% 0.21/0.50 (((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))))))) | (~((~equivalence(equal_set_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(equal_set_predicate, X, X))) | (~![X: $i, Y: $i] : (apply(equal_set_predicate, Y, X) | (~apply(equal_set_predicate, X, Y)) | (~member(X, power_set(E!20))) | (~member(Y, power_set(E!20))))) | (~![X: $i, Y: $i, Z: $i] : (apply(equal_set_predicate, X, Z) | (~apply(equal_set_predicate, X, Y)) | (~apply(equal_set_predicate, Y, Z)) | (~member(X, power_set(E!20))) | (~member(Y, power_set(E!20))) | (~member(Z, power_set(E!20)))))))))))) <=> ((~![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(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))))))) | (~((~equivalence(equal_set_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(equal_set_predicate, X, X))) | (~![X: $i, Y: $i] : (apply(equal_set_predicate, Y, X) | (~member(Y, power_set(E!20))) | (~apply(equal_set_predicate, X, Y)) | (~member(X, power_set(E!20))))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, power_set(E!20))) | (~apply(equal_set_predicate, Y, Z)) | (~member(Y, power_set(E!20))) | apply(equal_set_predicate, X, Z) | (~apply(equal_set_predicate, X, Y)) | (~member(X, power_set(E!20))))))))))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[219])).
% 0.21/0.50 tff(221,plain,
% 0.21/0.50 (((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))))))) | (~((~equivalence(equal_set_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(equal_set_predicate, X, X))) | (~![X: $i, Y: $i] : (apply(equal_set_predicate, Y, X) | (~apply(equal_set_predicate, X, Y)) | (~member(X, power_set(E!20))) | (~member(Y, power_set(E!20))))) | (~![X: $i, Y: $i, Z: $i] : (apply(equal_set_predicate, X, Z) | (~apply(equal_set_predicate, X, Y)) | (~apply(equal_set_predicate, Y, Z)) | (~member(X, power_set(E!20))) | (~member(Y, power_set(E!20))) | (~member(Z, power_set(E!20)))))))))))) <=> ((~![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(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))))))) | (~((~equivalence(equal_set_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(equal_set_predicate, X, X))) | (~![X: $i, Y: $i] : (apply(equal_set_predicate, Y, X) | (~member(Y, power_set(E!20))) | (~apply(equal_set_predicate, X, Y)) | (~member(X, power_set(E!20))))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, power_set(E!20))) | (~apply(equal_set_predicate, Y, Z)) | (~member(Y, power_set(E!20))) | apply(equal_set_predicate, X, Z) | (~apply(equal_set_predicate, X, Y)) | (~member(X, power_set(E!20))))))))))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[220, 218])).
% 0.21/0.50 tff(222,plain,
% 0.21/0.50 ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))))))) | (~((~equivalence(equal_set_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(equal_set_predicate, X, X))) | (~![X: $i, Y: $i] : (apply(equal_set_predicate, Y, X) | (~apply(equal_set_predicate, X, Y)) | (~member(X, power_set(E!20))) | (~member(Y, power_set(E!20))))) | (~![X: $i, Y: $i, Z: $i] : (apply(equal_set_predicate, X, Z) | (~apply(equal_set_predicate, X, Y)) | (~apply(equal_set_predicate, Y, Z)) | (~member(X, power_set(E!20))) | (~member(Y, power_set(E!20))) | (~member(Z, power_set(E!20)))))))))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(223,plain,
% 0.21/0.50 ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))))))) | (~((~equivalence(equal_set_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(equal_set_predicate, X, X))) | (~![X: $i, Y: $i] : (apply(equal_set_predicate, Y, X) | (~member(Y, power_set(E!20))) | (~apply(equal_set_predicate, X, Y)) | (~member(X, power_set(E!20))))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, power_set(E!20))) | (~apply(equal_set_predicate, Y, Z)) | (~member(Y, power_set(E!20))) | apply(equal_set_predicate, X, Z) | (~apply(equal_set_predicate, X, Y)) | (~member(X, power_set(E!20)))))))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.21/0.50 tff(224,plain,
% 0.21/0.50 (~((~(equivalence(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))))))) | (~((~equivalence(equal_set_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(equal_set_predicate, X, X))) | (~![X: $i, Y: $i] : (apply(equal_set_predicate, Y, X) | (~member(Y, power_set(E!20))) | (~apply(equal_set_predicate, X, Y)) | (~member(X, power_set(E!20))))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, power_set(E!20))) | (~apply(equal_set_predicate, Y, Z)) | (~member(Y, power_set(E!20))) | apply(equal_set_predicate, X, Z) | (~apply(equal_set_predicate, X, Y)) | (~member(X, power_set(E!20))))))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[223, 217])).
% 0.21/0.50 tff(225,plain,
% 0.21/0.50 (((~(equivalence(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))))))) | (~((~equivalence(equal_set_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(equal_set_predicate, X, X))) | (~![X: $i, Y: $i] : (apply(equal_set_predicate, Y, X) | (~member(Y, power_set(E!20))) | (~apply(equal_set_predicate, X, Y)) | (~member(X, power_set(E!20))))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, power_set(E!20))) | (~apply(equal_set_predicate, Y, Z)) | (~member(Y, power_set(E!20))) | apply(equal_set_predicate, X, Z) | (~apply(equal_set_predicate, X, Y)) | (~member(X, power_set(E!20)))))))))) | (equivalence(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(226,plain,
% 0.21/0.50 (equivalence(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20)))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[225, 224])).
% 0.21/0.51 tff(227,plain,
% 0.21/0.51 ((~![E: $i] : equivalence(equal_set_predicate, power_set(E))) <=> (~![E: $i] : equivalence(equal_set_predicate, power_set(E)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(228,axiom,(~![E: $i] : equivalence(equal_set_predicate, power_set(E))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thIII13')).
% 0.21/0.51 tff(229,plain,
% 0.21/0.51 (~![E: $i] : equivalence(equal_set_predicate, power_set(E))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.21/0.51 tff(230,plain,
% 0.21/0.51 (~![E: $i] : equivalence(equal_set_predicate, power_set(E))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[229, 227])).
% 0.21/0.51 tff(231,plain,
% 0.21/0.51 (~![E: $i] : equivalence(equal_set_predicate, power_set(E))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[230, 227])).
% 0.21/0.51 tff(232,plain,
% 0.21/0.51 (~![E: $i] : equivalence(equal_set_predicate, power_set(E))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[231, 227])).
% 0.21/0.51 tff(233,plain,
% 0.21/0.51 (~![E: $i] : equivalence(equal_set_predicate, power_set(E))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[232, 227])).
% 0.21/0.51 tff(234,plain,
% 0.21/0.51 (~![E: $i] : equivalence(equal_set_predicate, power_set(E))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[233, 227])).
% 0.21/0.51 tff(235,plain,
% 0.21/0.51 (~![E: $i] : equivalence(equal_set_predicate, power_set(E))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[234, 227])).
% 0.21/0.51 tff(236,plain,(
% 0.21/0.51 ~equivalence(equal_set_predicate, power_set(E!20))),
% 0.21/0.51 inference(skolemize,[status(sab)],[235])).
% 0.21/0.51 tff(237,plain,
% 0.21/0.51 ((~(equivalence(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))))))) | equivalence(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20)))))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(238,plain,
% 0.21/0.51 ((~(equivalence(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))))))) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20)))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[237, 236])).
% 0.21/0.51 tff(239,plain,
% 0.21/0.51 ((~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20)))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[238, 226])).
% 0.21/0.51 tff(240,plain,
% 0.21/0.51 ((~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20)))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[239, 195])).
% 0.21/0.51 tff(241,plain,
% 0.21/0.51 (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[240, 163])).
% 0.21/0.51 tff(242,plain,
% 0.21/0.51 (((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(243,plain,
% 0.21/0.51 (~apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[242, 241])).
% 0.21/0.51 tff(244,plain,
% 0.21/0.51 ((~(apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) | (~equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(245,plain,
% 0.21/0.51 ((~(apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[244, 243])).
% 0.21/0.51 tff(246,plain,
% 0.21/0.51 (~equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[245, 26])).
% 0.21/0.51 tff(247,plain,
% 0.21/0.51 ((~(equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) | (~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(248,plain,
% 0.21/0.51 ((~(equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[247, 246])).
% 0.21/0.51 tff(249,plain,
% 0.21/0.51 (~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[248, 17])).
% 0.21/0.51 tff(250,plain,
% 0.21/0.51 (((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) <=> ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(251,plain,
% 0.21/0.51 ((~(~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) <=> subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(252,plain,
% 0.21/0.51 (($false | (~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) <=> (~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(253,plain,
% 0.21/0.51 ((~(subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))))) <=> (~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(254,plain,
% 0.21/0.51 ((~$true) <=> $false),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(255,plain,
% 0.21/0.51 (((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | $true) <=> $true),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(256,plain,
% 0.21/0.51 (![X: $i] : $true <=> $true),
% 0.21/0.51 inference(elim_unused_vars,[status(thm)],[])).
% 0.21/0.51 tff(257,plain,
% 0.21/0.51 (![X: $i] : $true <=> ![X: $i] : $true),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(258,plain,
% 0.21/0.51 (![X: $i] : $true <=> $true),
% 0.21/0.51 inference(transitivity,[status(thm)],[257, 256])).
% 0.21/0.51 tff(259,plain,
% 0.21/0.51 (^[X: $i] : rewrite(((~member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) <=> $true)),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(260,plain,
% 0.21/0.51 (![X: $i] : ((~member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) <=> ![X: $i] : $true),
% 0.21/0.51 inference(quant_intro,[status(thm)],[259])).
% 0.21/0.51 tff(261,plain,
% 0.21/0.51 (![X: $i] : ((~member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) <=> $true),
% 0.21/0.51 inference(transitivity,[status(thm)],[260, 258])).
% 0.21/0.51 tff(262,plain,
% 0.21/0.51 (((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) <=> ((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | $true)),
% 0.21/0.51 inference(monotonicity,[status(thm)],[261])).
% 0.21/0.51 tff(263,plain,
% 0.21/0.51 (((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) <=> $true),
% 0.21/0.51 inference(transitivity,[status(thm)],[262, 255])).
% 0.21/0.51 tff(264,plain,
% 0.21/0.51 ((~((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))) <=> (~$true)),
% 0.21/0.51 inference(monotonicity,[status(thm)],[263])).
% 0.21/0.51 tff(265,plain,
% 0.21/0.51 ((~((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))) <=> $false),
% 0.21/0.51 inference(transitivity,[status(thm)],[264, 254])).
% 0.21/0.51 tff(266,plain,
% 0.21/0.51 (((~((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))))) <=> ($false | (~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[265, 253])).
% 0.21/0.51 tff(267,plain,
% 0.21/0.51 (((~((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))))) <=> (~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[266, 252])).
% 0.21/0.51 tff(268,plain,
% 0.21/0.51 ((~((~((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))))))) <=> (~(~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[267])).
% 0.21/0.51 tff(269,plain,
% 0.21/0.51 ((~((~((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))))))) <=> subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))),
% 0.21/0.51 inference(transitivity,[status(thm)],[268, 251])).
% 0.21/0.51 tff(270,plain,
% 0.21/0.51 (((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))))))) <=> ((~![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(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[269])).
% 0.21/0.51 tff(271,plain,
% 0.21/0.51 (((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))))))) <=> ((~![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(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))),
% 0.21/0.52 inference(transitivity,[status(thm)],[270, 250])).
% 0.21/0.52 tff(272,plain,
% 0.21/0.52 ((~![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(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(273,plain,
% 0.21/0.52 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.21/0.52 tff(274,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[273, 42, 249])).
% 0.21/0.52 % SZS output end Proof
%------------------------------------------------------------------------------