TSTP Solution File: SET691+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET691+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 05:07:38 EDT 2022
% Result : Theorem 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET691+4 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Sep 3 07:23:44 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.
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % SZS output start Proof
% 0.13/0.38 tff(subset_type, type, (
% 0.13/0.38 subset: ( $i * $i ) > $o)).
% 0.13/0.38 tff(empty_set_type, type, (
% 0.13/0.38 empty_set: $i)).
% 0.13/0.38 tff(tptp_fun_A_3_type, type, (
% 0.13/0.38 tptp_fun_A_3: $i)).
% 0.13/0.38 tff(equal_set_type, type, (
% 0.13/0.38 equal_set: ( $i * $i ) > $o)).
% 0.13/0.38 tff(member_type, type, (
% 0.13/0.38 member: ( $i * $i ) > $o)).
% 0.13/0.38 tff(tptp_fun_X_0_type, type, (
% 0.13/0.38 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.13/0.38 tff(1,assumption,((~((~subset(empty_set, A!3)) | ![X: $i] : ((~member(X, empty_set)) | member(X, A!3)))) | (~(subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3)))))), introduced(assumption)).
% 0.13/0.38 tff(2,plain,
% 0.13/0.38 (^[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))))))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(3,plain,
% 0.13/0.38 (![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)))))))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.13/0.38 tff(4,plain,
% 0.13/0.38 (^[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))))))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(5,plain,
% 0.13/0.38 (![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)))))))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[4])).
% 0.13/0.38 tff(6,plain,
% 0.13/0.38 (![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)))))))),
% 0.13/0.38 inference(transitivity,[status(thm)],[5, 3])).
% 0.13/0.38 tff(7,plain,
% 0.13/0.38 (^[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)))))))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(8,plain,
% 0.13/0.38 (![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)))))))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[7])).
% 0.13/0.38 tff(9,plain,
% 0.13/0.38 (![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)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(10,plain,
% 0.13/0.38 (^[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))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(11,plain,
% 0.13/0.38 (![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)))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[10])).
% 0.13/0.38 tff(12,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','subset')).
% 0.13/0.38 tff(13,plain,
% 0.13/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.13/0.38 tff(14,plain,
% 0.13/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.13/0.38 tff(15,plain,(
% 0.13/0.38 ![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)))))),
% 0.13/0.38 inference(skolemize,[status(sab)],[14])).
% 0.13/0.38 tff(16,plain,
% 0.13/0.38 (![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)))))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.13/0.38 tff(17,plain,
% 0.13/0.38 (![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)))))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[16, 6])).
% 0.13/0.38 tff(18,plain,
% 0.13/0.38 ((~![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, A!3)) | ![X: $i] : ((~member(X, empty_set)) | member(X, A!3)))) | (~(subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3)))))))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(19,plain,
% 0.13/0.38 ($false),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[18, 17, 1])).
% 0.13/0.38 tff(20,plain,(~((~((~subset(empty_set, A!3)) | ![X: $i] : ((~member(X, empty_set)) | member(X, A!3)))) | (~(subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3))))))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.38 tff(21,plain,
% 0.13/0.38 (((~((~subset(empty_set, A!3)) | ![X: $i] : ((~member(X, empty_set)) | member(X, A!3)))) | (~(subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3)))))) | (subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3))))),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(22,plain,
% 0.13/0.38 (subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3)))),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.13/0.38 tff(23,assumption,(member(tptp_fun_X_0(A!3, empty_set), empty_set)), introduced(assumption)).
% 0.13/0.38 tff(24,plain,
% 0.13/0.38 (^[X: $i] : refl((~member(X, empty_set)) <=> (~member(X, empty_set)))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(25,plain,
% 0.13/0.38 (![X: $i] : (~member(X, empty_set)) <=> ![X: $i] : (~member(X, empty_set))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[24])).
% 0.13/0.38 tff(26,plain,
% 0.13/0.38 (![X: $i] : (~member(X, empty_set)) <=> ![X: $i] : (~member(X, empty_set))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(27,axiom,(![X: $i] : (~member(X, empty_set))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','empty_set')).
% 0.13/0.38 tff(28,plain,
% 0.13/0.38 (![X: $i] : (~member(X, empty_set))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.13/0.38 tff(29,plain,(
% 0.13/0.38 ![X: $i] : (~member(X, empty_set))),
% 0.13/0.38 inference(skolemize,[status(sab)],[28])).
% 0.13/0.38 tff(30,plain,
% 0.13/0.38 (![X: $i] : (~member(X, empty_set))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.13/0.38 tff(31,plain,
% 0.13/0.38 ((~![X: $i] : (~member(X, empty_set))) | (~member(tptp_fun_X_0(A!3, empty_set), empty_set))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(32,plain,
% 0.13/0.38 ($false),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[31, 30, 23])).
% 0.13/0.38 tff(33,plain,(~member(tptp_fun_X_0(A!3, empty_set), empty_set)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.38 tff(34,plain,
% 0.13/0.38 (((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3)) | member(tptp_fun_X_0(A!3, empty_set), empty_set)),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(35,plain,
% 0.13/0.38 ((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.13/0.38 tff(36,plain,
% 0.13/0.38 ((~(subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3))))) | subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3)))),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(37,plain,
% 0.13/0.38 ((~(subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3))))) | subset(empty_set, A!3)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.13/0.38 tff(38,plain,
% 0.13/0.38 (subset(empty_set, A!3)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[37, 22])).
% 0.13/0.38 tff(39,assumption,(~equal_set(A!3, empty_set)), introduced(assumption)).
% 0.13/0.38 tff(40,plain,
% 0.13/0.38 ((~(subset(A!3, empty_set) <=> equal_set(A!3, empty_set))) <=> ((~subset(A!3, empty_set)) <=> equal_set(A!3, empty_set))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(41,plain,
% 0.13/0.38 ((~![A: $i] : (subset(A, empty_set) <=> equal_set(A, empty_set))) <=> (~![A: $i] : (subset(A, empty_set) <=> equal_set(A, empty_set)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(42,axiom,(~![A: $i] : (subset(A, empty_set) <=> equal_set(A, empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thI16')).
% 0.13/0.38 tff(43,plain,
% 0.13/0.38 (~![A: $i] : (subset(A, empty_set) <=> equal_set(A, empty_set))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.13/0.38 tff(44,plain,
% 0.13/0.38 (~![A: $i] : (subset(A, empty_set) <=> equal_set(A, empty_set))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[43, 41])).
% 0.13/0.38 tff(45,plain,
% 0.13/0.38 (~![A: $i] : (subset(A, empty_set) <=> equal_set(A, empty_set))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[44, 41])).
% 0.13/0.38 tff(46,plain,
% 0.13/0.38 (~![A: $i] : (subset(A, empty_set) <=> equal_set(A, empty_set))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.13/0.38 tff(47,plain,
% 0.13/0.38 (~![A: $i] : (subset(A, empty_set) <=> equal_set(A, empty_set))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[46, 41])).
% 0.13/0.38 tff(48,plain,
% 0.13/0.38 (~![A: $i] : (subset(A, empty_set) <=> equal_set(A, empty_set))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[47, 41])).
% 0.13/0.38 tff(49,plain,
% 0.13/0.38 (~![A: $i] : (subset(A, empty_set) <=> equal_set(A, empty_set))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.13/0.38 tff(50,plain,(
% 0.13/0.38 ~(subset(A!3, empty_set) <=> equal_set(A!3, empty_set))),
% 0.13/0.38 inference(skolemize,[status(sab)],[49])).
% 0.13/0.38 tff(51,plain,
% 0.13/0.38 ((~subset(A!3, empty_set)) <=> equal_set(A!3, empty_set)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[50, 40])).
% 0.13/0.38 tff(52,plain,
% 0.13/0.38 (subset(A!3, empty_set) | equal_set(A!3, empty_set) | (~((~subset(A!3, empty_set)) <=> equal_set(A!3, empty_set)))),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(53,plain,
% 0.13/0.38 (subset(A!3, empty_set) | equal_set(A!3, empty_set)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.13/0.38 tff(54,plain,
% 0.13/0.38 (subset(A!3, empty_set)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[53, 39])).
% 0.13/0.38 tff(55,plain,
% 0.13/0.38 (^[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))))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(56,plain,
% 0.13/0.38 (![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)))))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[55])).
% 0.13/0.38 tff(57,plain,
% 0.13/0.38 (^[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))))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(58,plain,
% 0.13/0.38 (![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)))))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[57])).
% 0.13/0.38 tff(59,plain,
% 0.13/0.38 (![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)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(60,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','equal_set')).
% 0.13/0.38 tff(61,plain,
% 0.13/0.38 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.13/0.38 tff(62,plain,(
% 0.13/0.38 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.13/0.38 inference(skolemize,[status(sab)],[61])).
% 0.13/0.38 tff(63,plain,
% 0.13/0.38 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.13/0.38 tff(64,plain,
% 0.13/0.38 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.13/0.38 tff(65,plain,
% 0.13/0.38 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(A!3, empty_set) <=> (~((~subset(A!3, empty_set)) | (~subset(empty_set, A!3)))))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(66,plain,
% 0.13/0.38 (equal_set(A!3, empty_set) <=> (~((~subset(A!3, empty_set)) | (~subset(empty_set, A!3))))),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.13/0.38 tff(67,plain,
% 0.13/0.38 ((~(equal_set(A!3, empty_set) <=> (~((~subset(A!3, empty_set)) | (~subset(empty_set, A!3)))))) | equal_set(A!3, empty_set) | ((~subset(A!3, empty_set)) | (~subset(empty_set, A!3)))),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(68,plain,
% 0.13/0.38 (equal_set(A!3, empty_set) | ((~subset(A!3, empty_set)) | (~subset(empty_set, A!3)))),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.13/0.38 tff(69,plain,
% 0.13/0.38 ((~subset(A!3, empty_set)) | (~subset(empty_set, A!3))),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[68, 39])).
% 0.13/0.38 tff(70,plain,
% 0.13/0.38 ((~((~subset(A!3, empty_set)) | (~subset(empty_set, A!3)))) | (~subset(A!3, empty_set)) | (~subset(empty_set, A!3))),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(71,plain,
% 0.13/0.38 ($false),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[70, 69, 54, 38])).
% 0.13/0.38 tff(72,plain,(equal_set(A!3, empty_set)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.38 tff(73,plain,
% 0.13/0.38 ((~subset(A!3, empty_set)) | (~equal_set(A!3, empty_set)) | (~((~subset(A!3, empty_set)) <=> equal_set(A!3, empty_set)))),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(74,plain,
% 0.13/0.38 ((~subset(A!3, empty_set)) | (~equal_set(A!3, empty_set))),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[73, 51])).
% 0.13/0.38 tff(75,plain,
% 0.13/0.38 (~subset(A!3, empty_set)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[74, 72])).
% 0.13/0.38 tff(76,plain,
% 0.13/0.38 ((~(equal_set(A!3, empty_set) <=> (~((~subset(A!3, empty_set)) | (~subset(empty_set, A!3)))))) | (~equal_set(A!3, empty_set)) | (~((~subset(A!3, empty_set)) | (~subset(empty_set, A!3))))),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(77,plain,
% 0.13/0.38 ((~equal_set(A!3, empty_set)) | (~((~subset(A!3, empty_set)) | (~subset(empty_set, A!3))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[76, 66])).
% 0.13/0.39 tff(78,plain,
% 0.13/0.39 (~((~subset(A!3, empty_set)) | (~subset(empty_set, A!3)))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[77, 72])).
% 0.13/0.39 tff(79,plain,
% 0.13/0.39 (((~subset(A!3, empty_set)) | (~subset(empty_set, A!3))) | subset(A!3, empty_set)),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(80,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[79, 78, 75])).
% 0.13/0.39 % SZS output end Proof
%------------------------------------------------------------------------------