TSTP Solution File: SET764+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET764+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 05:07:55 EDT 2022
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET764+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n006.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 07:47:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(member_type, type, (
% 0.20/0.41 member: ( $i * $i ) > $o)).
% 0.20/0.41 tff(empty_set_type, type, (
% 0.20/0.41 empty_set: $i)).
% 0.20/0.41 tff(tptp_fun_X_0_type, type, (
% 0.20/0.41 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.20/0.41 tff(inverse_image2_type, type, (
% 0.20/0.41 inverse_image2: ( $i * $i ) > $i)).
% 0.20/0.41 tff(tptp_fun_F_41_type, type, (
% 0.20/0.41 tptp_fun_F_41: $i)).
% 0.20/0.41 tff(subset_type, type, (
% 0.20/0.41 subset: ( $i * $i ) > $o)).
% 0.20/0.41 tff(apply_type, type, (
% 0.20/0.41 apply: ( $i * $i * $i ) > $o)).
% 0.20/0.41 tff(tptp_fun_Y_25_type, type, (
% 0.20/0.41 tptp_fun_Y_25: ( $i * $i * $i ) > $i)).
% 0.20/0.41 tff(equal_set_type, type, (
% 0.20/0.41 equal_set: ( $i * $i ) > $o)).
% 0.20/0.41 tff(maps_type, type, (
% 0.20/0.41 maps: ( $i * $i * $i ) > $o)).
% 0.20/0.41 tff(tptp_fun_B_39_type, type, (
% 0.20/0.41 tptp_fun_B_39: $i)).
% 0.20/0.41 tff(tptp_fun_A_40_type, type, (
% 0.20/0.41 tptp_fun_A_40: $i)).
% 0.20/0.41 tff(1,plain,
% 0.20/0.41 (^[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))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 (![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)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 (^[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))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(4,plain,
% 0.20/0.41 (![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)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 (![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)))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[4, 2])).
% 0.20/0.41 tff(6,plain,
% 0.20/0.41 (^[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)))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(7,plain,
% 0.20/0.42 (![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)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.42 tff(8,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(9,plain,
% 0.20/0.42 (^[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))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(10,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[9])).
% 0.20/0.42 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')).
% 0.20/0.42 tff(12,plain,
% 0.20/0.42 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.20/0.42 tff(14,plain,(
% 0.20/0.42 ![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)))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[13])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 (![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)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 (![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)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 ((~![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(empty_set, inverse_image2(F!41, empty_set))) | ![X: $i] : ((~member(X, empty_set)) | member(X, inverse_image2(F!41, empty_set))))) | (~(subset(empty_set, inverse_image2(F!41, empty_set)) | (~((~member(tptp_fun_X_0(inverse_image2(F!41, empty_set), empty_set), empty_set)) | member(tptp_fun_X_0(inverse_image2(F!41, empty_set), empty_set), inverse_image2(F!41, empty_set))))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 (~((~((~subset(empty_set, inverse_image2(F!41, empty_set))) | ![X: $i] : ((~member(X, empty_set)) | member(X, inverse_image2(F!41, empty_set))))) | (~(subset(empty_set, inverse_image2(F!41, empty_set)) | (~((~member(tptp_fun_X_0(inverse_image2(F!41, empty_set), empty_set), empty_set)) | member(tptp_fun_X_0(inverse_image2(F!41, empty_set), empty_set), inverse_image2(F!41, empty_set)))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 (((~((~subset(empty_set, inverse_image2(F!41, empty_set))) | ![X: $i] : ((~member(X, empty_set)) | member(X, inverse_image2(F!41, empty_set))))) | (~(subset(empty_set, inverse_image2(F!41, empty_set)) | (~((~member(tptp_fun_X_0(inverse_image2(F!41, empty_set), empty_set), empty_set)) | member(tptp_fun_X_0(inverse_image2(F!41, empty_set), empty_set), inverse_image2(F!41, empty_set))))))) | (subset(empty_set, inverse_image2(F!41, empty_set)) | (~((~member(tptp_fun_X_0(inverse_image2(F!41, empty_set), empty_set), empty_set)) | member(tptp_fun_X_0(inverse_image2(F!41, empty_set), empty_set), inverse_image2(F!41, empty_set)))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (subset(empty_set, inverse_image2(F!41, empty_set)) | (~((~member(tptp_fun_X_0(inverse_image2(F!41, empty_set), empty_set), empty_set)) | member(tptp_fun_X_0(inverse_image2(F!41, empty_set), empty_set), inverse_image2(F!41, empty_set))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.20/0.42 tff(21,assumption,((~((~subset(inverse_image2(F!41, empty_set), empty_set)) | ![X: $i] : ((~member(X, inverse_image2(F!41, empty_set))) | member(X, empty_set)))) | (~(subset(inverse_image2(F!41, empty_set), empty_set) | (~((~member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), inverse_image2(F!41, empty_set))) | member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set)))))), introduced(assumption)).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 ((~![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(inverse_image2(F!41, empty_set), empty_set)) | ![X: $i] : ((~member(X, inverse_image2(F!41, empty_set))) | member(X, empty_set)))) | (~(subset(inverse_image2(F!41, empty_set), empty_set) | (~((~member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), inverse_image2(F!41, empty_set))) | member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set)))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[22, 16, 21])).
% 0.20/0.42 tff(24,plain,(~((~((~subset(inverse_image2(F!41, empty_set), empty_set)) | ![X: $i] : ((~member(X, inverse_image2(F!41, empty_set))) | member(X, empty_set)))) | (~(subset(inverse_image2(F!41, empty_set), empty_set) | (~((~member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), inverse_image2(F!41, empty_set))) | member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (((~((~subset(inverse_image2(F!41, empty_set), empty_set)) | ![X: $i] : ((~member(X, inverse_image2(F!41, empty_set))) | member(X, empty_set)))) | (~(subset(inverse_image2(F!41, empty_set), empty_set) | (~((~member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), inverse_image2(F!41, empty_set))) | member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set)))))) | (subset(inverse_image2(F!41, empty_set), empty_set) | (~((~member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), inverse_image2(F!41, empty_set))) | member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 (subset(inverse_image2(F!41, empty_set), empty_set) | (~((~member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), inverse_image2(F!41, empty_set))) | member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.20/0.42 tff(27,assumption,((~((~member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), inverse_image2(F!41, empty_set))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set, F!41), empty_set)) | (~apply(F!41, tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), tptp_fun_Y_25(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set, F!41))))))) | (~(member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), inverse_image2(F!41, empty_set)) | ![Y: $i] : ((~member(Y, empty_set)) | (~apply(F!41, tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), Y)))))), introduced(assumption)).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (^[F: $i, B: $i, X: $i] : refl((~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 (![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> ![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 (^[F: $i, B: $i, X: $i] : rewrite((~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 (![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> ![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[30])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 (![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> ![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[31, 29])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 (^[F: $i, B: $i, X: $i] : trans(monotonicity(rewrite(((~member(X, inverse_image2(F, B))) | (member(tptp_fun_Y_25(X, B, F), B) & apply(F, X, tptp_fun_Y_25(X, B, F)))) <=> ((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))), rewrite((member(X, inverse_image2(F, B)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))) <=> (member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))), ((((~member(X, inverse_image2(F, B))) | (member(tptp_fun_Y_25(X, B, F), B) & apply(F, X, tptp_fun_Y_25(X, B, F)))) & (member(X, inverse_image2(F, B)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))) <=> (((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F)))))) & (member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))), rewrite((((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F)))))) & (member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))) <=> (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))), ((((~member(X, inverse_image2(F, B))) | (member(tptp_fun_Y_25(X, B, F), B) & apply(F, X, tptp_fun_Y_25(X, B, F)))) & (member(X, inverse_image2(F, B)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))) <=> (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (![F: $i, B: $i, X: $i] : (((~member(X, inverse_image2(F, B))) | (member(tptp_fun_Y_25(X, B, F), B) & apply(F, X, tptp_fun_Y_25(X, B, F)))) & (member(X, inverse_image2(F, B)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))) <=> ![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[33])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 (![F: $i, B: $i, X: $i] : (member(X, inverse_image2(F, B)) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) <=> ![F: $i, B: $i, X: $i] : (member(X, inverse_image2(F, B)) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(36,axiom,(![F: $i, B: $i, X: $i] : (member(X, inverse_image2(F, B)) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','inverse_image2')).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (![F: $i, B: $i, X: $i] : (member(X, inverse_image2(F, B)) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.42 tff(38,plain,(
% 0.20/0.42 ![F: $i, B: $i, X: $i] : (((~member(X, inverse_image2(F, B))) | (member(tptp_fun_Y_25(X, B, F), B) & apply(F, X, tptp_fun_Y_25(X, B, F)))) & (member(X, inverse_image2(F, B)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[37])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 (![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 (![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 ((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), inverse_image2(F!41, empty_set))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set, F!41), empty_set)) | (~apply(F!41, tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), tptp_fun_Y_25(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set, F!41))))))) | (~(member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), inverse_image2(F!41, empty_set)) | ![Y: $i] : ((~member(Y, empty_set)) | (~apply(F!41, tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), Y)))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[41, 40, 27])).
% 0.20/0.42 tff(43,plain,(~((~((~member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), inverse_image2(F!41, empty_set))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set, F!41), empty_set)) | (~apply(F!41, tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), tptp_fun_Y_25(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set, F!41))))))) | (~(member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), inverse_image2(F!41, empty_set)) | ![Y: $i] : ((~member(Y, empty_set)) | (~apply(F!41, tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 (((~((~member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), inverse_image2(F!41, empty_set))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set, F!41), empty_set)) | (~apply(F!41, tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), tptp_fun_Y_25(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set, F!41))))))) | (~(member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), inverse_image2(F!41, empty_set)) | ![Y: $i] : ((~member(Y, empty_set)) | (~apply(F!41, tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), Y)))))) | ((~member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), inverse_image2(F!41, empty_set))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set, F!41), empty_set)) | (~apply(F!41, tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), tptp_fun_Y_25(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set, F!41))))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(45,plain,
% 0.20/0.43 ((~member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), inverse_image2(F!41, empty_set))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set, F!41), empty_set)) | (~apply(F!41, tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), tptp_fun_Y_25(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set, F!41)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.20/0.43 tff(46,assumption,(member(tptp_fun_Y_25(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set, F!41), empty_set)), introduced(assumption)).
% 0.20/0.43 tff(47,plain,
% 0.20/0.43 (^[X: $i] : refl((~member(X, empty_set)) <=> (~member(X, empty_set)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(48,plain,
% 0.20/0.43 (![X: $i] : (~member(X, empty_set)) <=> ![X: $i] : (~member(X, empty_set))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[47])).
% 0.20/0.43 tff(49,plain,
% 0.20/0.43 (![X: $i] : (~member(X, empty_set)) <=> ![X: $i] : (~member(X, empty_set))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(50,axiom,(![X: $i] : (~member(X, empty_set))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','empty_set')).
% 0.20/0.43 tff(51,plain,
% 0.20/0.43 (![X: $i] : (~member(X, empty_set))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.43 tff(52,plain,(
% 0.20/0.43 ![X: $i] : (~member(X, empty_set))),
% 0.20/0.43 inference(skolemize,[status(sab)],[51])).
% 0.20/0.43 tff(53,plain,
% 0.20/0.43 (![X: $i] : (~member(X, empty_set))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.20/0.43 tff(54,plain,
% 0.20/0.43 ((~![X: $i] : (~member(X, empty_set))) | (~member(tptp_fun_Y_25(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set, F!41), empty_set))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(55,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[54, 53, 46])).
% 0.20/0.43 tff(56,plain,(~member(tptp_fun_Y_25(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set, F!41), empty_set)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(57,plain,
% 0.20/0.43 (((~member(tptp_fun_Y_25(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set, F!41), empty_set)) | (~apply(F!41, tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), tptp_fun_Y_25(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set, F!41)))) | member(tptp_fun_Y_25(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set, F!41), empty_set)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(58,plain,
% 0.20/0.43 ((~member(tptp_fun_Y_25(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set, F!41), empty_set)) | (~apply(F!41, tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), tptp_fun_Y_25(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set, F!41)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.20/0.43 tff(59,plain,
% 0.20/0.43 ((~((~member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), inverse_image2(F!41, empty_set))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set, F!41), empty_set)) | (~apply(F!41, tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), tptp_fun_Y_25(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set, F!41))))))) | (~member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), inverse_image2(F!41, empty_set))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set, F!41), empty_set)) | (~apply(F!41, tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), tptp_fun_Y_25(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set, F!41)))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(60,plain,
% 0.20/0.43 ((~((~member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), inverse_image2(F!41, empty_set))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set, F!41), empty_set)) | (~apply(F!41, tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), tptp_fun_Y_25(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set, F!41))))))) | (~member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), inverse_image2(F!41, empty_set)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.20/0.43 tff(61,plain,
% 0.20/0.43 (~member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), inverse_image2(F!41, empty_set))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[60, 45])).
% 0.20/0.43 tff(62,plain,
% 0.20/0.43 (((~member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), inverse_image2(F!41, empty_set))) | member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set)) | member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), inverse_image2(F!41, empty_set))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(63,plain,
% 0.20/0.43 ((~member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), inverse_image2(F!41, empty_set))) | member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.20/0.43 tff(64,plain,
% 0.20/0.43 ((~(subset(inverse_image2(F!41, empty_set), empty_set) | (~((~member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), inverse_image2(F!41, empty_set))) | member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set))))) | subset(inverse_image2(F!41, empty_set), empty_set) | (~((~member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), inverse_image2(F!41, empty_set))) | member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 ((~(subset(inverse_image2(F!41, empty_set), empty_set) | (~((~member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), inverse_image2(F!41, empty_set))) | member(tptp_fun_X_0(empty_set, inverse_image2(F!41, empty_set)), empty_set))))) | subset(inverse_image2(F!41, empty_set), empty_set)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.20/0.43 tff(66,plain,
% 0.20/0.43 (subset(inverse_image2(F!41, empty_set), empty_set)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[65, 26])).
% 0.20/0.43 tff(67,plain,
% 0.20/0.43 (^[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))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(68,plain,
% 0.20/0.43 (![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)))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[67])).
% 0.20/0.43 tff(69,plain,
% 0.20/0.43 (^[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))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 (![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)))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[69])).
% 0.20/0.43 tff(71,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(72,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')).
% 0.20/0.43 tff(73,plain,
% 0.20/0.43 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.43 tff(74,plain,(
% 0.20/0.43 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[73])).
% 0.20/0.43 tff(75,plain,
% 0.20/0.43 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.20/0.43 tff(76,plain,
% 0.20/0.43 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.20/0.43 tff(77,plain,
% 0.20/0.43 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(inverse_image2(F!41, empty_set), empty_set) <=> (~((~subset(inverse_image2(F!41, empty_set), empty_set)) | (~subset(empty_set, inverse_image2(F!41, empty_set))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(78,plain,
% 0.20/0.43 (equal_set(inverse_image2(F!41, empty_set), empty_set) <=> (~((~subset(inverse_image2(F!41, empty_set), empty_set)) | (~subset(empty_set, inverse_image2(F!41, empty_set)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.20/0.43 tff(79,plain,
% 0.20/0.43 ((~![F: $i, A: $i, B: $i] : ((~maps(F, A, B)) | equal_set(inverse_image2(F, empty_set), empty_set))) <=> (~![F: $i, A: $i, B: $i] : ((~maps(F, A, B)) | equal_set(inverse_image2(F, empty_set), empty_set)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(80,plain,
% 0.20/0.43 ((~![F: $i, A: $i, B: $i] : (maps(F, A, B) => equal_set(inverse_image2(F, empty_set), empty_set))) <=> (~![F: $i, A: $i, B: $i] : ((~maps(F, A, B)) | equal_set(inverse_image2(F, empty_set), empty_set)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(81,axiom,(~![F: $i, A: $i, B: $i] : (maps(F, A, B) => equal_set(inverse_image2(F, empty_set), empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thIIa14')).
% 0.20/0.43 tff(82,plain,
% 0.20/0.43 (~![F: $i, A: $i, B: $i] : ((~maps(F, A, B)) | equal_set(inverse_image2(F, empty_set), empty_set))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.20/0.43 tff(83,plain,
% 0.20/0.43 (~![F: $i, A: $i, B: $i] : ((~maps(F, A, B)) | equal_set(inverse_image2(F, empty_set), empty_set))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[82, 79])).
% 0.20/0.43 tff(84,plain,
% 0.20/0.43 (~![F: $i, A: $i, B: $i] : ((~maps(F, A, B)) | equal_set(inverse_image2(F, empty_set), empty_set))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.20/0.43 tff(85,plain,
% 0.20/0.43 (~![F: $i, A: $i, B: $i] : ((~maps(F, A, B)) | equal_set(inverse_image2(F, empty_set), empty_set))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[84, 79])).
% 0.20/0.43 tff(86,plain,
% 0.20/0.43 (~![F: $i, A: $i, B: $i] : ((~maps(F, A, B)) | equal_set(inverse_image2(F, empty_set), empty_set))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[85, 79])).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 (~![F: $i, A: $i, B: $i] : ((~maps(F, A, B)) | equal_set(inverse_image2(F, empty_set), empty_set))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.20/0.43 tff(88,plain,
% 0.20/0.43 (~![F: $i, A: $i, B: $i] : ((~maps(F, A, B)) | equal_set(inverse_image2(F, empty_set), empty_set))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[87, 79])).
% 0.20/0.43 tff(89,plain,(
% 0.20/0.43 ~((~maps(F!41, A!40, B!39)) | equal_set(inverse_image2(F!41, empty_set), empty_set))),
% 0.20/0.43 inference(skolemize,[status(sab)],[88])).
% 0.20/0.43 tff(90,plain,
% 0.20/0.43 (~equal_set(inverse_image2(F!41, empty_set), empty_set)),
% 0.20/0.43 inference(or_elim,[status(thm)],[89])).
% 0.20/0.43 tff(91,plain,
% 0.20/0.43 ((~(equal_set(inverse_image2(F!41, empty_set), empty_set) <=> (~((~subset(inverse_image2(F!41, empty_set), empty_set)) | (~subset(empty_set, inverse_image2(F!41, empty_set))))))) | equal_set(inverse_image2(F!41, empty_set), empty_set) | ((~subset(inverse_image2(F!41, empty_set), empty_set)) | (~subset(empty_set, inverse_image2(F!41, empty_set))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(92,plain,
% 0.20/0.43 ((~(equal_set(inverse_image2(F!41, empty_set), empty_set) <=> (~((~subset(inverse_image2(F!41, empty_set), empty_set)) | (~subset(empty_set, inverse_image2(F!41, empty_set))))))) | ((~subset(inverse_image2(F!41, empty_set), empty_set)) | (~subset(empty_set, inverse_image2(F!41, empty_set))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.20/0.44 tff(93,plain,
% 0.20/0.44 ((~subset(inverse_image2(F!41, empty_set), empty_set)) | (~subset(empty_set, inverse_image2(F!41, empty_set)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[92, 78])).
% 0.20/0.44 tff(94,plain,
% 0.20/0.44 ((~((~subset(inverse_image2(F!41, empty_set), empty_set)) | (~subset(empty_set, inverse_image2(F!41, empty_set))))) | (~subset(inverse_image2(F!41, empty_set), empty_set)) | (~subset(empty_set, inverse_image2(F!41, empty_set)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(95,plain,
% 0.20/0.44 ((~subset(inverse_image2(F!41, empty_set), empty_set)) | (~subset(empty_set, inverse_image2(F!41, empty_set)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.20/0.44 tff(96,plain,
% 0.20/0.44 (~subset(empty_set, inverse_image2(F!41, empty_set))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[95, 66])).
% 0.20/0.44 tff(97,plain,
% 0.20/0.44 ((~(subset(empty_set, inverse_image2(F!41, empty_set)) | (~((~member(tptp_fun_X_0(inverse_image2(F!41, empty_set), empty_set), empty_set)) | member(tptp_fun_X_0(inverse_image2(F!41, empty_set), empty_set), inverse_image2(F!41, empty_set)))))) | subset(empty_set, inverse_image2(F!41, empty_set)) | (~((~member(tptp_fun_X_0(inverse_image2(F!41, empty_set), empty_set), empty_set)) | member(tptp_fun_X_0(inverse_image2(F!41, empty_set), empty_set), inverse_image2(F!41, empty_set))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(98,plain,
% 0.20/0.44 ((~(subset(empty_set, inverse_image2(F!41, empty_set)) | (~((~member(tptp_fun_X_0(inverse_image2(F!41, empty_set), empty_set), empty_set)) | member(tptp_fun_X_0(inverse_image2(F!41, empty_set), empty_set), inverse_image2(F!41, empty_set)))))) | (~((~member(tptp_fun_X_0(inverse_image2(F!41, empty_set), empty_set), empty_set)) | member(tptp_fun_X_0(inverse_image2(F!41, empty_set), empty_set), inverse_image2(F!41, empty_set))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.20/0.44 tff(99,plain,
% 0.20/0.44 (~((~member(tptp_fun_X_0(inverse_image2(F!41, empty_set), empty_set), empty_set)) | member(tptp_fun_X_0(inverse_image2(F!41, empty_set), empty_set), inverse_image2(F!41, empty_set)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[98, 20])).
% 0.20/0.44 tff(100,plain,
% 0.20/0.44 (((~member(tptp_fun_X_0(inverse_image2(F!41, empty_set), empty_set), empty_set)) | member(tptp_fun_X_0(inverse_image2(F!41, empty_set), empty_set), inverse_image2(F!41, empty_set))) | member(tptp_fun_X_0(inverse_image2(F!41, empty_set), empty_set), empty_set)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(101,plain,
% 0.20/0.44 (member(tptp_fun_X_0(inverse_image2(F!41, empty_set), empty_set), empty_set)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.20/0.44 tff(102,plain,
% 0.20/0.44 ((~![X: $i] : (~member(X, empty_set))) | (~member(tptp_fun_X_0(inverse_image2(F!41, empty_set), empty_set), empty_set))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(103,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[102, 53, 101])).
% 0.20/0.44 % SZS output end Proof
%------------------------------------------------------------------------------