TSTP Solution File: SET767+4 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET767+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 05:07:56 EDT 2022
% Result : Theorem 0.22s 0.42s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET767+4 : TPTP v8.1.0. Released v2.2.0.
% 0.08/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Sep 3 07:49:55 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.22/0.42 % SZS status Theorem
% 0.22/0.42 % SZS output start Proof
% 0.22/0.42 tff(apply_type, type, (
% 0.22/0.42 apply: ( $i * $i * $i ) > $o)).
% 0.22/0.42 tff(tptp_fun_X_0_type, type, (
% 0.22/0.42 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.22/0.42 tff(equivalence_class_type, type, (
% 0.22/0.42 equivalence_class: ( $i * $i * $i ) > $i)).
% 0.22/0.42 tff(tptp_fun_R_21_type, type, (
% 0.22/0.42 tptp_fun_R_21: $i)).
% 0.22/0.42 tff(tptp_fun_E_22_type, type, (
% 0.22/0.42 tptp_fun_E_22: $i)).
% 0.22/0.42 tff(tptp_fun_A_20_type, type, (
% 0.22/0.42 tptp_fun_A_20: $i)).
% 0.22/0.42 tff(member_type, type, (
% 0.22/0.42 member: ( $i * $i ) > $o)).
% 0.22/0.42 tff(subset_type, type, (
% 0.22/0.42 subset: ( $i * $i ) > $o)).
% 0.22/0.42 tff(equivalence_type, type, (
% 0.22/0.42 equivalence: ( $i * $i ) > $o)).
% 0.22/0.42 tff(1,plain,
% 0.22/0.42 (^[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))))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(2,plain,
% 0.22/0.42 (![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)))))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.42 tff(3,plain,
% 0.22/0.42 (^[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))))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(4,plain,
% 0.22/0.42 (![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)))))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[3])).
% 0.22/0.42 tff(5,plain,
% 0.22/0.42 (![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)))))))),
% 0.22/0.42 inference(transitivity,[status(thm)],[4, 2])).
% 0.22/0.42 tff(6,plain,
% 0.22/0.42 (^[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)))))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(7,plain,
% 0.22/0.42 (![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)))))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[6])).
% 0.22/0.42 tff(8,plain,
% 0.22/0.42 (![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)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(9,plain,
% 0.22/0.42 (^[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))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(10,plain,
% 0.22/0.42 (![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)))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[9])).
% 0.22/0.42 tff(11,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')).
% 0.22/0.42 tff(12,plain,
% 0.22/0.42 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.22/0.42 tff(13,plain,
% 0.22/0.42 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.22/0.42 tff(14,plain,(
% 0.22/0.42 ![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)))))),
% 0.22/0.42 inference(skolemize,[status(sab)],[13])).
% 0.22/0.42 tff(15,plain,
% 0.22/0.42 (![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)))))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.22/0.42 tff(16,plain,
% 0.22/0.42 (![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)))))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.22/0.42 tff(17,plain,
% 0.22/0.42 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(equivalence_class(A!20, E!22, R!21), E!22)) | ![X: $i] : ((~member(X, equivalence_class(A!20, E!22, R!21))) | member(X, E!22)))) | (~(subset(equivalence_class(A!20, E!22, R!21), E!22) | (~((~member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), equivalence_class(A!20, E!22, R!21))) | member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), E!22)))))))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(18,plain,
% 0.22/0.42 (~((~((~subset(equivalence_class(A!20, E!22, R!21), E!22)) | ![X: $i] : ((~member(X, equivalence_class(A!20, E!22, R!21))) | member(X, E!22)))) | (~(subset(equivalence_class(A!20, E!22, R!21), E!22) | (~((~member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), equivalence_class(A!20, E!22, R!21))) | member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), E!22))))))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.22/0.42 tff(19,plain,
% 0.22/0.42 (((~((~subset(equivalence_class(A!20, E!22, R!21), E!22)) | ![X: $i] : ((~member(X, equivalence_class(A!20, E!22, R!21))) | member(X, E!22)))) | (~(subset(equivalence_class(A!20, E!22, R!21), E!22) | (~((~member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), equivalence_class(A!20, E!22, R!21))) | member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), E!22)))))) | (subset(equivalence_class(A!20, E!22, R!21), E!22) | (~((~member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), equivalence_class(A!20, E!22, R!21))) | member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), E!22))))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(20,plain,
% 0.22/0.42 (subset(equivalence_class(A!20, E!22, R!21), E!22) | (~((~member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), equivalence_class(A!20, E!22, R!21))) | member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), E!22)))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.22/0.42 tff(21,plain,
% 0.22/0.42 ((~![E: $i, R: $i, A: $i] : ((~equivalence(R, E)) | subset(equivalence_class(A, E, R), E))) <=> (~![E: $i, R: $i, A: $i] : ((~equivalence(R, E)) | subset(equivalence_class(A, E, R), E)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(22,plain,
% 0.22/0.42 ((~![E: $i, R: $i, A: $i] : (equivalence(R, E) => subset(equivalence_class(A, E, R), E))) <=> (~![E: $i, R: $i, A: $i] : ((~equivalence(R, E)) | subset(equivalence_class(A, E, R), E)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(23,axiom,(~![E: $i, R: $i, A: $i] : (equivalence(R, E) => subset(equivalence_class(A, E, R), E))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thIII03')).
% 0.22/0.42 tff(24,plain,
% 0.22/0.42 (~![E: $i, R: $i, A: $i] : ((~equivalence(R, E)) | subset(equivalence_class(A, E, R), E))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.22/0.42 tff(25,plain,
% 0.22/0.42 (~![E: $i, R: $i, A: $i] : ((~equivalence(R, E)) | subset(equivalence_class(A, E, R), E))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.22/0.42 tff(26,plain,
% 0.22/0.42 (~![E: $i, R: $i, A: $i] : ((~equivalence(R, E)) | subset(equivalence_class(A, E, R), E))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.22/0.42 tff(27,plain,
% 0.22/0.42 (~![E: $i, R: $i, A: $i] : ((~equivalence(R, E)) | subset(equivalence_class(A, E, R), E))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.22/0.42 tff(28,plain,
% 0.22/0.42 (~![E: $i, R: $i, A: $i] : ((~equivalence(R, E)) | subset(equivalence_class(A, E, R), E))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[27, 21])).
% 0.22/0.42 tff(29,plain,
% 0.22/0.42 (~![E: $i, R: $i, A: $i] : ((~equivalence(R, E)) | subset(equivalence_class(A, E, R), E))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.22/0.42 tff(30,plain,
% 0.22/0.42 (~![E: $i, R: $i, A: $i] : ((~equivalence(R, E)) | subset(equivalence_class(A, E, R), E))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[29, 21])).
% 0.22/0.42 tff(31,plain,(
% 0.22/0.42 ~((~equivalence(R!21, E!22)) | subset(equivalence_class(A!20, E!22, R!21), E!22))),
% 0.22/0.42 inference(skolemize,[status(sab)],[30])).
% 0.22/0.42 tff(32,plain,
% 0.22/0.42 (~subset(equivalence_class(A!20, E!22, R!21), E!22)),
% 0.22/0.42 inference(or_elim,[status(thm)],[31])).
% 0.22/0.42 tff(33,plain,
% 0.22/0.42 ((~(subset(equivalence_class(A!20, E!22, R!21), E!22) | (~((~member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), equivalence_class(A!20, E!22, R!21))) | member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), E!22))))) | subset(equivalence_class(A!20, E!22, R!21), E!22) | (~((~member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), equivalence_class(A!20, E!22, R!21))) | member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), E!22)))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(34,plain,
% 0.22/0.42 ((~(subset(equivalence_class(A!20, E!22, R!21), E!22) | (~((~member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), equivalence_class(A!20, E!22, R!21))) | member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), E!22))))) | (~((~member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), equivalence_class(A!20, E!22, R!21))) | member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), E!22)))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.22/0.42 tff(35,plain,
% 0.22/0.42 (~((~member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), equivalence_class(A!20, E!22, R!21))) | member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), E!22))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[34, 20])).
% 0.22/0.42 tff(36,plain,
% 0.22/0.42 (((~member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), equivalence_class(A!20, E!22, R!21))) | member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), E!22)) | (~member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), E!22))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(37,plain,
% 0.22/0.42 (~member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), E!22)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.22/0.43 tff(38,plain,
% 0.22/0.43 (((~member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), E!22)) | (~apply(R!21, A!20, tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21))))) | member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), E!22)),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(39,plain,
% 0.22/0.43 ((~member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), E!22)) | (~apply(R!21, A!20, tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21))))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.22/0.43 tff(40,plain,
% 0.22/0.43 (((~member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), equivalence_class(A!20, E!22, R!21))) | member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), E!22)) | member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), equivalence_class(A!20, E!22, R!21))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(41,plain,
% 0.22/0.43 (member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), equivalence_class(A!20, E!22, R!21))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[40, 35])).
% 0.22/0.43 tff(42,plain,
% 0.22/0.43 ((~(member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), equivalence_class(A!20, E!22, R!21)) <=> (~((~member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), E!22)) | (~apply(R!21, A!20, tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)))))))) | (~member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), equivalence_class(A!20, E!22, R!21))) | (~((~member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), E!22)) | (~apply(R!21, A!20, tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21))))))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(43,plain,
% 0.22/0.43 (~(member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), equivalence_class(A!20, E!22, R!21)) <=> (~((~member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), E!22)) | (~apply(R!21, A!20, tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)))))))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[42, 41, 39])).
% 0.22/0.43 tff(44,plain,
% 0.22/0.43 (^[R: $i, E: $i, A: $i, X: $i] : refl((member(X, equivalence_class(A, E, R)) <=> (~((~member(X, E)) | (~apply(R, A, X))))) <=> (member(X, equivalence_class(A, E, R)) <=> (~((~member(X, E)) | (~apply(R, A, X))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(45,plain,
% 0.22/0.43 (![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (~((~member(X, E)) | (~apply(R, A, X))))) <=> ![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (~((~member(X, E)) | (~apply(R, A, X)))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[44])).
% 0.22/0.43 tff(46,plain,
% 0.22/0.43 (^[R: $i, E: $i, A: $i, X: $i] : rewrite((member(X, equivalence_class(A, E, R)) <=> (member(X, E) & apply(R, A, X))) <=> (member(X, equivalence_class(A, E, R)) <=> (~((~member(X, E)) | (~apply(R, A, X))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(47,plain,
% 0.22/0.43 (![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (member(X, E) & apply(R, A, X))) <=> ![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (~((~member(X, E)) | (~apply(R, A, X)))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[46])).
% 0.22/0.43 tff(48,plain,
% 0.22/0.43 (![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (member(X, E) & apply(R, A, X))) <=> ![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (member(X, E) & apply(R, A, X)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(49,axiom,(![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (member(X, E) & apply(R, A, X)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax','equivalence_class')).
% 0.22/0.43 tff(50,plain,
% 0.22/0.43 (![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (member(X, E) & apply(R, A, X)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.22/0.43 tff(51,plain,(
% 0.22/0.43 ![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (member(X, E) & apply(R, A, X)))),
% 0.22/0.43 inference(skolemize,[status(sab)],[50])).
% 0.22/0.43 tff(52,plain,
% 0.22/0.43 (![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (~((~member(X, E)) | (~apply(R, A, X)))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.22/0.43 tff(53,plain,
% 0.22/0.43 (![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (~((~member(X, E)) | (~apply(R, A, X)))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.22/0.43 tff(54,plain,
% 0.22/0.43 ((~![R: $i, E: $i, A: $i, X: $i] : (member(X, equivalence_class(A, E, R)) <=> (~((~member(X, E)) | (~apply(R, A, X)))))) | (member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), equivalence_class(A!20, E!22, R!21)) <=> (~((~member(tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)), E!22)) | (~apply(R!21, A!20, tptp_fun_X_0(E!22, equivalence_class(A!20, E!22, R!21)))))))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(55,plain,
% 0.22/0.43 ($false),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[54, 53, 43])).
% 0.22/0.43 % SZS output end Proof
%------------------------------------------------------------------------------