TSTP Solution File: SET812+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET812+4 : TPTP v8.1.0. Released v3.2.0.
% 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 05:08:07 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
% 0.08/0.14 % Problem : SET812+4 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.16/0.36 % Computer : n020.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sat Sep 3 08:05:14 EDT 2022
% 0.16/0.36 % CPUTime :
% 0.16/0.37 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.16/0.37 Usage: tptp [options] [-file:]file
% 0.16/0.37 -h, -? prints this message.
% 0.16/0.37 -smt2 print SMT-LIB2 benchmark.
% 0.16/0.37 -m, -model generate model.
% 0.16/0.37 -p, -proof generate proof.
% 0.16/0.37 -c, -core generate unsat core of named formulas.
% 0.16/0.37 -st, -statistics display statistics.
% 0.16/0.37 -t:timeout set timeout (in second).
% 0.16/0.37 -smt2status display status in smt2 format instead of SZS.
% 0.16/0.37 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.16/0.37 -<param>:<value> configuration parameter and value.
% 0.16/0.37 -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(member_type, type, (
% 0.22/0.42 member: ( $i * $i ) > $o)).
% 0.22/0.42 tff(power_set_type, type, (
% 0.22/0.42 power_set: $i > $i)).
% 0.22/0.42 tff(tptp_fun_A_13_type, type, (
% 0.22/0.42 tptp_fun_A_13: $i)).
% 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(intersection_type, type, (
% 0.22/0.42 intersection: ( $i * $i ) > $i)).
% 0.22/0.42 tff(subset_type, type, (
% 0.22/0.42 subset: ( $i * $i ) > $o)).
% 0.22/0.42 tff(strict_well_order_type, type, (
% 0.22/0.42 strict_well_order: ( $i * $i ) > $o)).
% 0.22/0.42 tff(member_predicate_type, type, (
% 0.22/0.42 member_predicate: $i)).
% 0.22/0.42 tff(set_type, type, (
% 0.22/0.42 set: $i > $o)).
% 0.22/0.42 tff(on_type, type, (
% 0.22/0.42 on: $i)).
% 0.22/0.42 tff(tptp_fun_X_3_type, type, (
% 0.22/0.42 tptp_fun_X_3: $i > $i)).
% 0.22/0.42 tff(equal_set_type, type, (
% 0.22/0.42 equal_set: ( $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)))))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(7,plain,
% 0.22/0.43 (![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)))))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[6])).
% 0.22/0.43 tff(8,plain,
% 0.22/0.43 (![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)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(9,plain,
% 0.22/0.43 (^[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))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(10,plain,
% 0.22/0.43 (![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)))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[9])).
% 0.22/0.43 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')).
% 0.22/0.43 tff(12,plain,
% 0.22/0.43 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.22/0.43 tff(13,plain,
% 0.22/0.43 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.22/0.43 tff(14,plain,(
% 0.22/0.43 ![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)))))),
% 0.22/0.43 inference(skolemize,[status(sab)],[13])).
% 0.22/0.43 tff(15,plain,
% 0.22/0.43 (![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)))))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.22/0.43 tff(16,plain,
% 0.22/0.43 (![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)))))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.22/0.43 tff(17,plain,
% 0.22/0.43 ((~![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)))))))) | (~((~((~subset(intersection(A!13, power_set(A!13)), A!13)) | ![X: $i] : ((~member(X, intersection(A!13, power_set(A!13)))) | member(X, A!13)))) | (~(subset(intersection(A!13, power_set(A!13)), A!13) | (~((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13)))) | member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13)))))))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(18,plain,
% 0.22/0.43 (~((~((~subset(intersection(A!13, power_set(A!13)), A!13)) | ![X: $i] : ((~member(X, intersection(A!13, power_set(A!13)))) | member(X, A!13)))) | (~(subset(intersection(A!13, power_set(A!13)), A!13) | (~((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13)))) | member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13))))))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.22/0.43 tff(19,plain,
% 0.22/0.43 (((~((~subset(intersection(A!13, power_set(A!13)), A!13)) | ![X: $i] : ((~member(X, intersection(A!13, power_set(A!13)))) | member(X, A!13)))) | (~(subset(intersection(A!13, power_set(A!13)), A!13) | (~((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13)))) | member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13)))))) | (subset(intersection(A!13, power_set(A!13)), A!13) | (~((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13)))) | member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13))))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(20,plain,
% 0.22/0.43 (subset(intersection(A!13, power_set(A!13)), A!13) | (~((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13)))) | member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13)))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.22/0.43 tff(21,assumption,((~((~subset(A!13, intersection(A!13, power_set(A!13)))) | ![X: $i] : ((~member(X, A!13)) | member(X, intersection(A!13, power_set(A!13)))))) | (~(subset(A!13, intersection(A!13, power_set(A!13))) | (~((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13)))))))), introduced(assumption)).
% 0.22/0.43 tff(22,plain,
% 0.22/0.43 ((~![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)))))))) | (~((~((~subset(A!13, intersection(A!13, power_set(A!13)))) | ![X: $i] : ((~member(X, A!13)) | member(X, intersection(A!13, power_set(A!13)))))) | (~(subset(A!13, intersection(A!13, power_set(A!13))) | (~((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13)))))))))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(23,plain,
% 0.22/0.43 ($false),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[22, 16, 21])).
% 0.22/0.43 tff(24,plain,(~((~((~subset(A!13, intersection(A!13, power_set(A!13)))) | ![X: $i] : ((~member(X, A!13)) | member(X, intersection(A!13, power_set(A!13)))))) | (~(subset(A!13, intersection(A!13, power_set(A!13))) | (~((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13))))))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.43 tff(25,plain,
% 0.22/0.43 (((~((~subset(A!13, intersection(A!13, power_set(A!13)))) | ![X: $i] : ((~member(X, A!13)) | member(X, intersection(A!13, power_set(A!13)))))) | (~(subset(A!13, intersection(A!13, power_set(A!13))) | (~((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13)))))))) | (subset(A!13, intersection(A!13, power_set(A!13))) | (~((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13))))))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(26,plain,
% 0.22/0.43 (subset(A!13, intersection(A!13, power_set(A!13))) | (~((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13)))))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.22/0.43 tff(27,plain,
% 0.22/0.43 (^[X: $i, A: $i, B: $i] : refl((member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))) <=> (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(28,plain,
% 0.22/0.43 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))) <=> ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[27])).
% 0.22/0.43 tff(29,plain,
% 0.22/0.43 (^[X: $i, A: $i, B: $i] : rewrite((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(30,plain,
% 0.22/0.43 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[29])).
% 0.22/0.43 tff(31,plain,
% 0.22/0.43 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(32,axiom,(![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','intersection')).
% 0.22/0.43 tff(33,plain,
% 0.22/0.43 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.22/0.43 tff(34,plain,(
% 0.22/0.43 ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.22/0.43 inference(skolemize,[status(sab)],[33])).
% 0.22/0.43 tff(35,plain,
% 0.22/0.43 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.22/0.43 tff(36,plain,
% 0.22/0.43 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.22/0.43 tff(37,plain,
% 0.22/0.43 ((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13))) <=> (~((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | (~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13))))))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(38,plain,
% 0.22/0.43 (member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13))) <=> (~((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | (~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13)))))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.22/0.43 tff(39,assumption,(~((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13))))), introduced(assumption)).
% 0.22/0.43 tff(40,plain,
% 0.22/0.43 (((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13)))) | (~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13))))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(41,plain,
% 0.22/0.43 (~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13)))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.22/0.43 tff(42,plain,
% 0.22/0.43 ((~(member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13))) <=> (~((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | (~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13))))))) | member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13))) | ((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | (~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13))))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(43,plain,
% 0.22/0.43 ((~(member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13))) <=> (~((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | (~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13))))))) | ((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | (~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13))))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.22/0.43 tff(44,plain,
% 0.22/0.43 ((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | (~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13)))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[43, 38])).
% 0.22/0.43 tff(45,assumption,(~(member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13)) <=> subset(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13))), introduced(assumption)).
% 0.22/0.43 tff(46,plain,
% 0.22/0.43 (^[X: $i, A: $i] : refl((member(X, power_set(A)) <=> subset(X, A)) <=> (member(X, power_set(A)) <=> subset(X, A)))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(47,plain,
% 0.22/0.43 (![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A)) <=> ![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[46])).
% 0.22/0.43 tff(48,plain,
% 0.22/0.43 (![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A)) <=> ![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(49,axiom,(![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','power_set')).
% 0.22/0.43 tff(50,plain,
% 0.22/0.43 (![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.22/0.43 tff(51,plain,(
% 0.22/0.43 ![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 0.22/0.43 inference(skolemize,[status(sab)],[50])).
% 0.22/0.43 tff(52,plain,
% 0.22/0.43 (![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.22/0.43 tff(53,plain,
% 0.22/0.43 ((~![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))) | (member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13)) <=> subset(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(54,plain,
% 0.22/0.43 ($false),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[53, 52, 45])).
% 0.22/0.43 tff(55,plain,(member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13)) <=> subset(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.43 tff(56,plain,
% 0.22/0.43 (((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13)))) | member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(57,plain,
% 0.22/0.43 (member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[56, 39])).
% 0.22/0.43 tff(58,plain,
% 0.22/0.43 (^[A: $i] : rewrite((~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))) <=> (~((~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) | (~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(59,plain,
% 0.22/0.43 (![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))) <=> ![A: $i] : (~((~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) | (~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[58])).
% 0.22/0.43 tff(60,plain,
% 0.22/0.43 (^[A: $i] : refl((~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))) <=> (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(61,plain,
% 0.22/0.44 (![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))) <=> ![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[60])).
% 0.22/0.44 tff(62,plain,
% 0.22/0.44 (^[A: $i] : rewrite((~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))) <=> (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(63,plain,
% 0.22/0.44 (![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))) <=> ![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[62])).
% 0.22/0.44 tff(64,plain,
% 0.22/0.44 (![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))) <=> ![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))))),
% 0.22/0.44 inference(transitivity,[status(thm)],[63, 61])).
% 0.22/0.44 tff(65,plain,
% 0.22/0.44 (^[A: $i] : trans(monotonicity(rewrite(((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) <=> ((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))), rewrite((member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))) <=> (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))), ((((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) <=> (((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))) & (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))), rewrite((((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))) & (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) <=> (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))))), ((((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) <=> (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(66,plain,
% 0.22/0.44 (![A: $i] : (((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) <=> ![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[65])).
% 0.22/0.44 tff(67,plain,
% 0.22/0.44 (^[A: $i] : rewrite((((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | ((~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))) <=> (((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(68,plain,
% 0.22/0.44 (![A: $i] : (((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | ((~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))) <=> ![A: $i] : (((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[67])).
% 0.22/0.44 tff(69,plain,
% 0.22/0.44 (![A: $i] : (member(A, on) <=> (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) <=> ![A: $i] : (member(A, on) <=> (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(70,plain,
% 0.22/0.44 (^[A: $i] : rewrite((member(A, on) <=> ((set(A) & strict_well_order(member_predicate, A)) & ![X: $i] : (member(X, A) => subset(X, A)))) <=> (member(A, on) <=> (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(71,plain,
% 0.22/0.44 (![A: $i] : (member(A, on) <=> ((set(A) & strict_well_order(member_predicate, A)) & ![X: $i] : (member(X, A) => subset(X, A)))) <=> ![A: $i] : (member(A, on) <=> (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[70])).
% 0.22/0.44 tff(72,axiom,(![A: $i] : (member(A, on) <=> ((set(A) & strict_well_order(member_predicate, A)) & ![X: $i] : (member(X, A) => subset(X, A))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+4.ax','ordinal_number')).
% 0.22/0.44 tff(73,plain,
% 0.22/0.44 (![A: $i] : (member(A, on) <=> (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.22/0.44 tff(74,plain,
% 0.22/0.44 (![A: $i] : (member(A, on) <=> (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.22/0.44 tff(75,plain,(
% 0.22/0.44 ![A: $i] : (((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | ((~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))),
% 0.22/0.44 inference(skolemize,[status(sab)],[74])).
% 0.22/0.44 tff(76,plain,
% 0.22/0.44 (![A: $i] : (((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.22/0.44 tff(77,plain,
% 0.22/0.44 (![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[76, 66])).
% 0.22/0.44 tff(78,plain,
% 0.22/0.44 (![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[77, 64])).
% 0.22/0.44 tff(79,plain,
% 0.22/0.44 (![A: $i] : (~((~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) | (~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[78, 59])).
% 0.22/0.44 tff(80,plain,
% 0.22/0.44 ((~![A: $i] : (~((~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) | (~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))))))) | (~((~(member(A!13, on) | (~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~((~member(tptp_fun_X_3(A!13), A!13)) | subset(tptp_fun_X_3(A!13), A!13))))) | (~((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13)))))))))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(81,plain,
% 0.22/0.44 (~((~(member(A!13, on) | (~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~((~member(tptp_fun_X_3(A!13), A!13)) | subset(tptp_fun_X_3(A!13), A!13))))) | (~((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))))))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.22/0.44 tff(82,plain,
% 0.22/0.44 (((~(member(A!13, on) | (~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~((~member(tptp_fun_X_3(A!13), A!13)) | subset(tptp_fun_X_3(A!13), A!13))))) | (~((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13)))))))) | ((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))))))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(83,plain,
% 0.22/0.44 ((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13)))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.22/0.44 tff(84,plain,
% 0.22/0.44 ((~![A: $i] : ((~member(A, on)) | equal_set(A, intersection(A, power_set(A))))) <=> (~![A: $i] : ((~member(A, on)) | equal_set(A, intersection(A, power_set(A)))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(85,plain,
% 0.22/0.44 ((~![A: $i] : (member(A, on) => equal_set(A, intersection(A, power_set(A))))) <=> (~![A: $i] : ((~member(A, on)) | equal_set(A, intersection(A, power_set(A)))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(86,axiom,(~![A: $i] : (member(A, on) => equal_set(A, intersection(A, power_set(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thV10')).
% 0.22/0.44 tff(87,plain,
% 0.22/0.44 (~![A: $i] : ((~member(A, on)) | equal_set(A, intersection(A, power_set(A))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.22/0.44 tff(88,plain,
% 0.22/0.44 (~![A: $i] : ((~member(A, on)) | equal_set(A, intersection(A, power_set(A))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[87, 84])).
% 0.22/0.44 tff(89,plain,
% 0.22/0.44 (~![A: $i] : ((~member(A, on)) | equal_set(A, intersection(A, power_set(A))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.22/0.44 tff(90,plain,
% 0.22/0.44 (~![A: $i] : ((~member(A, on)) | equal_set(A, intersection(A, power_set(A))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[89, 84])).
% 0.22/0.44 tff(91,plain,
% 0.22/0.44 (~![A: $i] : ((~member(A, on)) | equal_set(A, intersection(A, power_set(A))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[90, 84])).
% 0.22/0.44 tff(92,plain,
% 0.22/0.44 (~![A: $i] : ((~member(A, on)) | equal_set(A, intersection(A, power_set(A))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.22/0.44 tff(93,plain,
% 0.22/0.44 (~![A: $i] : ((~member(A, on)) | equal_set(A, intersection(A, power_set(A))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[92, 84])).
% 0.22/0.44 tff(94,plain,(
% 0.22/0.44 ~((~member(A!13, on)) | equal_set(A!13, intersection(A!13, power_set(A!13))))),
% 0.22/0.44 inference(skolemize,[status(sab)],[93])).
% 0.22/0.44 tff(95,plain,
% 0.22/0.44 (member(A!13, on)),
% 0.22/0.44 inference(or_elim,[status(thm)],[94])).
% 0.22/0.44 tff(96,plain,
% 0.22/0.44 ((~((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))))))) | (~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13)))))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(97,plain,
% 0.22/0.44 ((~((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))))))) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13)))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.22/0.44 tff(98,plain,
% 0.22/0.44 (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[97, 83])).
% 0.22/0.44 tff(99,plain,
% 0.22/0.44 (((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13)))) | ![X: $i] : ((~member(X, A!13)) | subset(X, A!13))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(100,plain,
% 0.22/0.44 (![X: $i] : ((~member(X, A!13)) | subset(X, A!13))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.22/0.44 tff(101,plain,
% 0.22/0.44 (((~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))) | ((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | subset(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13))) <=> ((~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))) | (~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | subset(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(102,plain,
% 0.22/0.44 ((~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))) | ((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | subset(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(103,plain,
% 0.22/0.44 ((~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))) | (~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | subset(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.22/0.44 tff(104,plain,
% 0.22/0.44 (subset(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[103, 100, 57])).
% 0.22/0.45 tff(105,plain,
% 0.22/0.45 ((~(member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13)) <=> subset(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13))) | member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13)) | (~subset(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(106,plain,
% 0.22/0.45 (member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[105, 104, 55])).
% 0.22/0.45 tff(107,plain,
% 0.22/0.45 ((~((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | (~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13))))) | (~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | (~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13)))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(108,plain,
% 0.22/0.45 ((~((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | (~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13))))) | (~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), power_set(A!13)))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[107, 57])).
% 0.22/0.45 tff(109,plain,
% 0.22/0.45 ($false),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[108, 106, 44])).
% 0.22/0.45 tff(110,plain,((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13)))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.45 tff(111,plain,
% 0.22/0.45 ((~(subset(A!13, intersection(A!13, power_set(A!13))) | (~((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13))))))) | subset(A!13, intersection(A!13, power_set(A!13))) | (~((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13)))))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(112,plain,
% 0.22/0.45 ((~(subset(A!13, intersection(A!13, power_set(A!13))) | (~((~member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), A!13)) | member(tptp_fun_X_0(intersection(A!13, power_set(A!13)), A!13), intersection(A!13, power_set(A!13))))))) | subset(A!13, intersection(A!13, power_set(A!13)))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.22/0.45 tff(113,plain,
% 0.22/0.45 (subset(A!13, intersection(A!13, power_set(A!13)))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[112, 26])).
% 0.22/0.45 tff(114,plain,
% 0.22/0.45 (^[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))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(115,plain,
% 0.22/0.45 (![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)))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[114])).
% 0.22/0.45 tff(116,plain,
% 0.22/0.45 (^[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))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(117,plain,
% 0.22/0.45 (![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)))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[116])).
% 0.22/0.45 tff(118,plain,
% 0.22/0.45 (![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)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(119,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')).
% 0.22/0.45 tff(120,plain,
% 0.22/0.45 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.22/0.45 tff(121,plain,(
% 0.22/0.45 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.22/0.45 inference(skolemize,[status(sab)],[120])).
% 0.22/0.45 tff(122,plain,
% 0.22/0.45 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[121, 117])).
% 0.22/0.45 tff(123,plain,
% 0.22/0.45 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[122, 115])).
% 0.22/0.45 tff(124,plain,
% 0.22/0.45 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(A!13, intersection(A!13, power_set(A!13))) <=> (~((~subset(A!13, intersection(A!13, power_set(A!13)))) | (~subset(intersection(A!13, power_set(A!13)), A!13)))))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(125,plain,
% 0.22/0.45 (equal_set(A!13, intersection(A!13, power_set(A!13))) <=> (~((~subset(A!13, intersection(A!13, power_set(A!13)))) | (~subset(intersection(A!13, power_set(A!13)), A!13))))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.22/0.45 tff(126,plain,
% 0.22/0.45 (~equal_set(A!13, intersection(A!13, power_set(A!13)))),
% 0.22/0.45 inference(or_elim,[status(thm)],[94])).
% 0.22/0.45 tff(127,plain,
% 0.22/0.45 ((~(equal_set(A!13, intersection(A!13, power_set(A!13))) <=> (~((~subset(A!13, intersection(A!13, power_set(A!13)))) | (~subset(intersection(A!13, power_set(A!13)), A!13)))))) | equal_set(A!13, intersection(A!13, power_set(A!13))) | ((~subset(A!13, intersection(A!13, power_set(A!13)))) | (~subset(intersection(A!13, power_set(A!13)), A!13)))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(128,plain,
% 0.22/0.45 ((~(equal_set(A!13, intersection(A!13, power_set(A!13))) <=> (~((~subset(A!13, intersection(A!13, power_set(A!13)))) | (~subset(intersection(A!13, power_set(A!13)), A!13)))))) | ((~subset(A!13, intersection(A!13, power_set(A!13)))) | (~subset(intersection(A!13, power_set(A!13)), A!13)))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.22/0.45 tff(129,plain,
% 0.22/0.45 ((~subset(A!13, intersection(A!13, power_set(A!13)))) | (~subset(intersection(A!13, power_set(A!13)), A!13))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[128, 125])).
% 0.22/0.45 tff(130,plain,
% 0.22/0.45 ((~((~subset(A!13, intersection(A!13, power_set(A!13)))) | (~subset(intersection(A!13, power_set(A!13)), A!13)))) | (~subset(A!13, intersection(A!13, power_set(A!13)))) | (~subset(intersection(A!13, power_set(A!13)), A!13))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(131,plain,
% 0.22/0.45 ((~subset(A!13, intersection(A!13, power_set(A!13)))) | (~subset(intersection(A!13, power_set(A!13)), A!13))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.22/0.45 tff(132,plain,
% 0.22/0.45 (~subset(intersection(A!13, power_set(A!13)), A!13)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[131, 113])).
% 0.22/0.45 tff(133,plain,
% 0.22/0.45 ((~(subset(intersection(A!13, power_set(A!13)), A!13) | (~((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13)))) | member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13))))) | subset(intersection(A!13, power_set(A!13)), A!13) | (~((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13)))) | member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13)))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(134,plain,
% 0.22/0.45 ((~(subset(intersection(A!13, power_set(A!13)), A!13) | (~((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13)))) | member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13))))) | (~((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13)))) | member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13)))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.22/0.45 tff(135,plain,
% 0.22/0.45 (~((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13)))) | member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[134, 20])).
% 0.22/0.45 tff(136,plain,
% 0.22/0.45 (((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13)))) | member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13)) | (~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(137,plain,
% 0.22/0.46 (~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.22/0.46 tff(138,plain,
% 0.22/0.46 (((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13)) | (~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), power_set(A!13)))) | member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13)),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(139,plain,
% 0.22/0.46 ((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13)) | (~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), power_set(A!13)))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.22/0.46 tff(140,plain,
% 0.22/0.46 (((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13)))) | member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13)) | member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13)))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(141,plain,
% 0.22/0.46 (member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13)))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[140, 135])).
% 0.22/0.46 tff(142,plain,
% 0.22/0.46 ((~(member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13))) <=> (~((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13)) | (~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), power_set(A!13))))))) | (~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13)))) | (~((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13)) | (~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), power_set(A!13)))))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(143,plain,
% 0.22/0.46 (~(member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13))) <=> (~((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13)) | (~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), power_set(A!13))))))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[142, 141, 139])).
% 0.22/0.46 tff(144,plain,
% 0.22/0.46 ((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), intersection(A!13, power_set(A!13))) <=> (~((~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), A!13)) | (~member(tptp_fun_X_0(A!13, intersection(A!13, power_set(A!13))), power_set(A!13))))))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(145,plain,
% 0.22/0.46 ($false),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[144, 36, 143])).
% 0.22/0.46 % SZS output end Proof
%------------------------------------------------------------------------------