TSTP Solution File: SET155+4 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET155+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 05:05:55 EDT 2022
% Result : Theorem 0.16s 0.35s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET155+4 : TPTP v8.1.0. Released v2.2.0.
% 0.09/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.30 % Computer : n026.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Sat Sep 3 03:13:08 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.10/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.31 Usage: tptp [options] [-file:]file
% 0.10/0.31 -h, -? prints this message.
% 0.10/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.31 -m, -model generate model.
% 0.10/0.31 -p, -proof generate proof.
% 0.10/0.31 -c, -core generate unsat core of named formulas.
% 0.10/0.31 -st, -statistics display statistics.
% 0.10/0.31 -t:timeout set timeout (in second).
% 0.10/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.31 -<param>:<value> configuration parameter and value.
% 0.10/0.31 -o:<output-file> file to place output in.
% 0.16/0.35 % SZS status Theorem
% 0.16/0.35 % SZS output start Proof
% 0.16/0.35 tff(member_type, type, (
% 0.16/0.35 member: ( $i * $i ) > $o)).
% 0.16/0.35 tff(difference_type, type, (
% 0.16/0.35 difference: ( $i * $i ) > $i)).
% 0.16/0.35 tff(tptp_fun_A_5_type, type, (
% 0.16/0.35 tptp_fun_A_5: $i)).
% 0.16/0.35 tff(tptp_fun_E_3_type, type, (
% 0.16/0.35 tptp_fun_E_3: $i)).
% 0.16/0.35 tff(tptp_fun_X_0_type, type, (
% 0.16/0.35 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.16/0.35 tff(union_type, type, (
% 0.16/0.35 union: ( $i * $i ) > $i)).
% 0.16/0.35 tff(tptp_fun_B_4_type, type, (
% 0.16/0.35 tptp_fun_B_4: $i)).
% 0.16/0.35 tff(intersection_type, type, (
% 0.16/0.35 intersection: ( $i * $i ) > $i)).
% 0.16/0.35 tff(subset_type, type, (
% 0.16/0.35 subset: ( $i * $i ) > $o)).
% 0.16/0.35 tff(equal_set_type, type, (
% 0.16/0.35 equal_set: ( $i * $i ) > $o)).
% 0.16/0.35 tff(1,assumption,((~((~subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4)))) | ![X: $i] : ((~member(X, intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(X, difference(E!3, union(A!5, B!4)))))) | (~(subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))) | (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4)))))))), introduced(assumption)).
% 0.16/0.35 tff(2,plain,
% 0.16/0.35 (^[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))))))))),
% 0.16/0.35 inference(bind,[status(th)],[])).
% 0.16/0.35 tff(3,plain,
% 0.16/0.35 (![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)))))))),
% 0.16/0.35 inference(quant_intro,[status(thm)],[2])).
% 0.16/0.35 tff(4,plain,
% 0.16/0.35 (^[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))))))))),
% 0.16/0.35 inference(bind,[status(th)],[])).
% 0.16/0.35 tff(5,plain,
% 0.16/0.35 (![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)))))))),
% 0.16/0.35 inference(quant_intro,[status(thm)],[4])).
% 0.16/0.35 tff(6,plain,
% 0.16/0.35 (![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)))))))),
% 0.16/0.35 inference(transitivity,[status(thm)],[5, 3])).
% 0.16/0.35 tff(7,plain,
% 0.16/0.35 (^[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)))))))))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(8,plain,
% 0.16/0.36 (![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)))))))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[7])).
% 0.16/0.36 tff(9,plain,
% 0.16/0.36 (![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)))),
% 0.16/0.36 inference(rewrite,[status(thm)],[])).
% 0.16/0.36 tff(10,plain,
% 0.16/0.36 (^[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))))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(11,plain,
% 0.16/0.36 (![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)))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[10])).
% 0.16/0.36 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')).
% 0.16/0.36 tff(13,plain,
% 0.16/0.36 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.16/0.36 tff(14,plain,
% 0.16/0.36 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.16/0.36 tff(15,plain,(
% 0.16/0.36 ![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)))))),
% 0.16/0.36 inference(skolemize,[status(sab)],[14])).
% 0.16/0.36 tff(16,plain,
% 0.16/0.36 (![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)))))))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.16/0.36 tff(17,plain,
% 0.16/0.36 (![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)))))))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[16, 6])).
% 0.16/0.36 tff(18,plain,
% 0.16/0.36 ((~![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(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4)))) | ![X: $i] : ((~member(X, intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(X, difference(E!3, union(A!5, B!4)))))) | (~(subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))) | (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4)))))))))),
% 0.16/0.36 inference(quant_inst,[status(thm)],[])).
% 0.16/0.36 tff(19,plain,
% 0.16/0.36 ($false),
% 0.16/0.36 inference(unit_resolution,[status(thm)],[18, 17, 1])).
% 0.16/0.36 tff(20,plain,(~((~((~subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4)))) | ![X: $i] : ((~member(X, intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(X, difference(E!3, union(A!5, B!4)))))) | (~(subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))) | (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4))))))))), inference(lemma,lemma(discharge,[]))).
% 0.16/0.36 tff(21,plain,
% 0.16/0.36 (((~((~subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4)))) | ![X: $i] : ((~member(X, intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(X, difference(E!3, union(A!5, B!4)))))) | (~(subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))) | (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4)))))))) | (subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))) | (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4))))))),
% 0.16/0.36 inference(tautology,[status(thm)],[])).
% 0.16/0.36 tff(22,plain,
% 0.16/0.36 (subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))) | (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4)))))),
% 0.16/0.36 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.16/0.36 tff(23,plain,
% 0.16/0.36 (^[B: $i, A: $i, E: $i] : refl((member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A)))) <=> (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A)))))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(24,plain,
% 0.16/0.36 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A)))) <=> ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[23])).
% 0.16/0.36 tff(25,plain,
% 0.16/0.36 (^[B: $i, A: $i, E: $i] : rewrite((member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A)))))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(26,plain,
% 0.16/0.36 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[25])).
% 0.16/0.36 tff(27,plain,
% 0.16/0.36 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.16/0.36 inference(rewrite,[status(thm)],[])).
% 0.16/0.36 tff(28,axiom,(![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','difference')).
% 0.16/0.36 tff(29,plain,
% 0.16/0.36 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.16/0.36 tff(30,plain,(
% 0.16/0.36 ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.16/0.36 inference(skolemize,[status(sab)],[29])).
% 0.16/0.36 tff(31,plain,
% 0.16/0.36 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.16/0.36 tff(32,plain,
% 0.16/0.36 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.16/0.36 tff(33,plain,
% 0.16/0.36 ((~![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))) | (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4))) <=> (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), union(A!5, B!4)))))),
% 0.16/0.36 inference(quant_inst,[status(thm)],[])).
% 0.16/0.36 tff(34,plain,
% 0.16/0.36 (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4))) <=> (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), union(A!5, B!4))))),
% 0.16/0.36 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.16/0.36 tff(35,assumption,(~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4))))), introduced(assumption)).
% 0.16/0.36 tff(36,plain,
% 0.16/0.36 (((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4)))) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4))))),
% 0.16/0.36 inference(tautology,[status(thm)],[])).
% 0.16/0.36 tff(37,plain,
% 0.16/0.36 (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4)))),
% 0.16/0.36 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.16/0.36 tff(38,plain,
% 0.16/0.36 ((~(member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4))) <=> (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), union(A!5, B!4)))))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4))) | ((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), union(A!5, B!4)))),
% 0.16/0.36 inference(tautology,[status(thm)],[])).
% 0.16/0.36 tff(39,plain,
% 0.16/0.36 ((~(member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4))) <=> (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), union(A!5, B!4)))))) | ((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), union(A!5, B!4)))),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.16/0.37 tff(40,plain,
% 0.16/0.37 ((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), union(A!5, B!4))),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[39, 34])).
% 0.16/0.37 tff(41,plain,
% 0.16/0.37 ((~![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))) | (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, B!4)) <=> (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4))))),
% 0.16/0.37 inference(quant_inst,[status(thm)],[])).
% 0.16/0.37 tff(42,plain,
% 0.16/0.37 (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, B!4)) <=> (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4)))),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[41, 32])).
% 0.16/0.37 tff(43,plain,
% 0.16/0.37 (^[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))))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(44,plain,
% 0.16/0.37 (![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)))))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[43])).
% 0.16/0.37 tff(45,plain,
% 0.16/0.37 (^[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))))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(46,plain,
% 0.16/0.37 (![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)))))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[45])).
% 0.16/0.37 tff(47,plain,
% 0.16/0.37 (![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)))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(48,axiom,(![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','intersection')).
% 0.16/0.37 tff(49,plain,
% 0.16/0.37 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.16/0.37 tff(50,plain,(
% 0.16/0.37 ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.16/0.37 inference(skolemize,[status(sab)],[49])).
% 0.16/0.37 tff(51,plain,
% 0.16/0.37 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.16/0.37 tff(52,plain,
% 0.16/0.37 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.16/0.37 tff(53,plain,
% 0.16/0.37 ((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4))) <=> (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, B!4))))))),
% 0.16/0.37 inference(quant_inst,[status(thm)],[])).
% 0.16/0.37 tff(54,plain,
% 0.16/0.37 (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4))) <=> (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, B!4)))))),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.16/0.37 tff(55,plain,
% 0.16/0.37 (((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4)))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))),
% 0.16/0.37 inference(tautology,[status(thm)],[])).
% 0.16/0.37 tff(56,plain,
% 0.16/0.37 (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[55, 35])).
% 0.16/0.37 tff(57,plain,
% 0.16/0.37 ((~(member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4))) <=> (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, B!4))))))) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, B!4)))))),
% 0.16/0.37 inference(tautology,[status(thm)],[])).
% 0.16/0.37 tff(58,plain,
% 0.16/0.37 ((~(member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4))) <=> (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, B!4))))))) | (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, B!4)))))),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.16/0.37 tff(59,plain,
% 0.16/0.37 (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, B!4))))),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[58, 54])).
% 0.16/0.37 tff(60,plain,
% 0.16/0.37 (((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, B!4))),
% 0.16/0.38 inference(tautology,[status(thm)],[])).
% 0.16/0.38 tff(61,plain,
% 0.16/0.38 (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, B!4))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.16/0.38 tff(62,plain,
% 0.16/0.38 ((~(member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, B!4)) <=> (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4))))) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4)))),
% 0.16/0.38 inference(tautology,[status(thm)],[])).
% 0.16/0.38 tff(63,plain,
% 0.16/0.38 ((~(member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, B!4)) <=> (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4))))) | (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4)))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.16/0.38 tff(64,plain,
% 0.16/0.38 (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[63, 42])).
% 0.16/0.38 tff(65,plain,
% 0.16/0.38 (((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)),
% 0.16/0.38 inference(tautology,[status(thm)],[])).
% 0.16/0.38 tff(66,plain,
% 0.16/0.38 (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.16/0.38 tff(67,plain,
% 0.16/0.38 ((~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), union(A!5, B!4)))) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), union(A!5, B!4))),
% 0.16/0.38 inference(tautology,[status(thm)],[])).
% 0.16/0.38 tff(68,plain,
% 0.16/0.38 (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), union(A!5, B!4))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[67, 66, 40])).
% 0.16/0.38 tff(69,plain,
% 0.16/0.38 (((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4)) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4))),
% 0.16/0.38 inference(tautology,[status(thm)],[])).
% 0.16/0.38 tff(70,plain,
% 0.16/0.38 (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4)),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[69, 64])).
% 0.16/0.38 tff(71,plain,
% 0.16/0.38 ((~![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))) | (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, A!5)) <=> (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5))))),
% 0.16/0.38 inference(quant_inst,[status(thm)],[])).
% 0.16/0.38 tff(72,plain,
% 0.16/0.38 (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, A!5)) <=> (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5)))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[71, 32])).
% 0.16/0.38 tff(73,plain,
% 0.16/0.38 (((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, A!5))),
% 0.16/0.38 inference(tautology,[status(thm)],[])).
% 0.16/0.38 tff(74,plain,
% 0.16/0.38 (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, A!5))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[73, 59])).
% 0.16/0.38 tff(75,plain,
% 0.16/0.38 ((~(member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, A!5)) <=> (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5))))) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, A!5))) | (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5)))),
% 0.16/0.38 inference(tautology,[status(thm)],[])).
% 0.16/0.38 tff(76,plain,
% 0.16/0.38 ((~(member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, A!5)) <=> (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5))))) | (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5)))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.16/0.38 tff(77,plain,
% 0.16/0.38 (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[76, 72])).
% 0.16/0.38 tff(78,plain,
% 0.16/0.38 (((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5))),
% 0.16/0.38 inference(tautology,[status(thm)],[])).
% 0.16/0.38 tff(79,plain,
% 0.16/0.38 (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5)),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.16/0.38 tff(80,plain,
% 0.16/0.38 ((~(member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5)),
% 0.16/0.38 inference(tautology,[status(thm)],[])).
% 0.16/0.38 tff(81,plain,
% 0.16/0.38 (~(member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[80, 79, 70])).
% 0.16/0.38 tff(82,assumption,(~(member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5)))), introduced(assumption)).
% 0.16/0.38 tff(83,plain,
% 0.16/0.38 (^[X: $i, A: $i, B: $i] : refl((member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> (member(X, union(A, B)) <=> (member(X, B) | member(X, A))))),
% 0.16/0.38 inference(bind,[status(th)],[])).
% 0.16/0.38 tff(84,plain,
% 0.16/0.38 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.16/0.38 inference(quant_intro,[status(thm)],[83])).
% 0.16/0.38 tff(85,plain,
% 0.16/0.38 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(86,plain,
% 0.16/0.38 (^[X: $i, A: $i, B: $i] : rewrite((member(X, union(A, B)) <=> (member(X, A) | member(X, B))) <=> (member(X, union(A, B)) <=> (member(X, B) | member(X, A))))),
% 0.16/0.38 inference(bind,[status(th)],[])).
% 0.16/0.38 tff(87,plain,
% 0.16/0.38 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.16/0.38 inference(quant_intro,[status(thm)],[86])).
% 0.16/0.38 tff(88,axiom,(![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','union')).
% 0.16/0.38 tff(89,plain,
% 0.16/0.38 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.16/0.38 tff(90,plain,
% 0.16/0.38 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.16/0.38 tff(91,plain,(
% 0.16/0.38 ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.16/0.38 inference(skolemize,[status(sab)],[90])).
% 0.16/0.38 tff(92,plain,
% 0.16/0.38 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.16/0.38 tff(93,plain,
% 0.16/0.38 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5)))),
% 0.16/0.38 inference(quant_inst,[status(thm)],[])).
% 0.16/0.38 tff(94,plain,
% 0.16/0.38 ($false),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[93, 92, 82])).
% 0.16/0.39 tff(95,plain,(member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5))), inference(lemma,lemma(discharge,[]))).
% 0.16/0.39 tff(96,plain,
% 0.16/0.39 ((~(member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5)))) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), union(A!5, B!4))) | (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5))),
% 0.16/0.39 inference(tautology,[status(thm)],[])).
% 0.16/0.39 tff(97,plain,
% 0.16/0.39 ((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), union(A!5, B!4))) | (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.16/0.39 tff(98,plain,
% 0.16/0.39 ($false),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[97, 81, 68])).
% 0.16/0.39 tff(99,plain,((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4)))), inference(lemma,lemma(discharge,[]))).
% 0.16/0.39 tff(100,plain,
% 0.16/0.39 ((~(subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))) | (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4))))))) | subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))) | (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4)))))),
% 0.16/0.39 inference(tautology,[status(thm)],[])).
% 0.16/0.39 tff(101,plain,
% 0.16/0.39 ((~(subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))) | (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4))))))) | subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4)))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.16/0.39 tff(102,plain,
% 0.16/0.39 (subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4)))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[101, 22])).
% 0.16/0.39 tff(103,plain,
% 0.16/0.39 (^[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))))))),
% 0.16/0.39 inference(bind,[status(th)],[])).
% 0.16/0.39 tff(104,plain,
% 0.16/0.39 (![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)))))),
% 0.16/0.39 inference(quant_intro,[status(thm)],[103])).
% 0.16/0.39 tff(105,plain,
% 0.16/0.39 (^[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))))))),
% 0.16/0.39 inference(bind,[status(th)],[])).
% 0.16/0.39 tff(106,plain,
% 0.16/0.39 (![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)))))),
% 0.16/0.39 inference(quant_intro,[status(thm)],[105])).
% 0.16/0.39 tff(107,plain,
% 0.16/0.39 (![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)))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(108,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')).
% 0.16/0.39 tff(109,plain,
% 0.16/0.39 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.16/0.39 tff(110,plain,(
% 0.16/0.39 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.16/0.39 inference(skolemize,[status(sab)],[109])).
% 0.16/0.39 tff(111,plain,
% 0.16/0.39 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.16/0.39 tff(112,plain,
% 0.16/0.39 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.16/0.39 tff(113,plain,
% 0.16/0.39 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))) <=> (~((~subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | (~subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4)))))))),
% 0.16/0.39 inference(quant_inst,[status(thm)],[])).
% 0.16/0.39 tff(114,plain,
% 0.16/0.39 (equal_set(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))) <=> (~((~subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | (~subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))))))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.16/0.39 tff(115,plain,
% 0.16/0.39 ((~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | equal_set(difference(E, union(A, B)), intersection(difference(E, A), difference(E, B))))) <=> (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | equal_set(difference(E, union(A, B)), intersection(difference(E, A), difference(E, B)))))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(116,plain,
% 0.16/0.39 ((~![A: $i, B: $i, E: $i] : ((subset(A, E) & subset(B, E)) => equal_set(difference(E, union(A, B)), intersection(difference(E, A), difference(E, B))))) <=> (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | equal_set(difference(E, union(A, B)), intersection(difference(E, A), difference(E, B)))))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(117,axiom,(~![A: $i, B: $i, E: $i] : ((subset(A, E) & subset(B, E)) => equal_set(difference(E, union(A, B)), intersection(difference(E, A), difference(E, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thI26')).
% 0.16/0.39 tff(118,plain,
% 0.16/0.39 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | equal_set(difference(E, union(A, B)), intersection(difference(E, A), difference(E, B))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.16/0.39 tff(119,plain,
% 0.16/0.39 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | equal_set(difference(E, union(A, B)), intersection(difference(E, A), difference(E, B))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[118, 115])).
% 0.16/0.39 tff(120,plain,
% 0.16/0.39 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | equal_set(difference(E, union(A, B)), intersection(difference(E, A), difference(E, B))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.16/0.39 tff(121,plain,
% 0.16/0.39 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | equal_set(difference(E, union(A, B)), intersection(difference(E, A), difference(E, B))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[120, 115])).
% 0.16/0.39 tff(122,plain,
% 0.16/0.39 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | equal_set(difference(E, union(A, B)), intersection(difference(E, A), difference(E, B))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[121, 115])).
% 0.16/0.39 tff(123,plain,
% 0.16/0.39 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | equal_set(difference(E, union(A, B)), intersection(difference(E, A), difference(E, B))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[122, 115])).
% 0.16/0.39 tff(124,plain,
% 0.16/0.39 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | equal_set(difference(E, union(A, B)), intersection(difference(E, A), difference(E, B))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[123, 115])).
% 0.16/0.39 tff(125,plain,(
% 0.16/0.39 ~((~(subset(A!5, E!3) & subset(B!4, E!3))) | equal_set(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))))),
% 0.16/0.39 inference(skolemize,[status(sab)],[124])).
% 0.16/0.39 tff(126,plain,
% 0.16/0.39 (~equal_set(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))),
% 0.16/0.39 inference(or_elim,[status(thm)],[125])).
% 0.16/0.39 tff(127,plain,
% 0.16/0.39 ((~(equal_set(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))) <=> (~((~subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | (~subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4)))))))) | equal_set(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))) | ((~subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | (~subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4)))))),
% 0.16/0.39 inference(tautology,[status(thm)],[])).
% 0.16/0.39 tff(128,plain,
% 0.16/0.39 ((~(equal_set(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))) <=> (~((~subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | (~subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4)))))))) | ((~subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | (~subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4)))))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.16/0.39 tff(129,plain,
% 0.16/0.39 ((~subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | (~subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[128, 114])).
% 0.16/0.39 tff(130,plain,
% 0.16/0.39 ((~((~subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | (~subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4)))))) | (~subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | (~subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))))),
% 0.16/0.39 inference(tautology,[status(thm)],[])).
% 0.16/0.39 tff(131,plain,
% 0.16/0.39 ((~subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | (~subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.16/0.39 tff(132,plain,
% 0.16/0.39 (~subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[131, 102])).
% 0.16/0.39 tff(133,assumption,((~((~subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | ![X: $i] : ((~member(X, difference(E!3, union(A!5, B!4)))) | member(X, intersection(difference(E!3, A!5), difference(E!3, B!4)))))) | (~(subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4)))) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))))))), introduced(assumption)).
% 0.16/0.40 tff(134,plain,
% 0.16/0.40 ((~![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(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | ![X: $i] : ((~member(X, difference(E!3, union(A!5, B!4)))) | member(X, intersection(difference(E!3, A!5), difference(E!3, B!4)))))) | (~(subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4)))) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))))))))),
% 0.16/0.40 inference(quant_inst,[status(thm)],[])).
% 0.16/0.40 tff(135,plain,
% 0.16/0.40 ($false),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[134, 17, 133])).
% 0.16/0.40 tff(136,plain,(~((~((~subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | ![X: $i] : ((~member(X, difference(E!3, union(A!5, B!4)))) | member(X, intersection(difference(E!3, A!5), difference(E!3, B!4)))))) | (~(subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4)))) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4))))))))), inference(lemma,lemma(discharge,[]))).
% 0.16/0.40 tff(137,plain,
% 0.16/0.40 (((~((~subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | ![X: $i] : ((~member(X, difference(E!3, union(A!5, B!4)))) | member(X, intersection(difference(E!3, A!5), difference(E!3, B!4)))))) | (~(subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4)))) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))))))) | (subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4)))) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4))))))),
% 0.16/0.40 inference(tautology,[status(thm)],[])).
% 0.16/0.40 tff(138,plain,
% 0.16/0.40 (subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4)))) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))))),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.16/0.40 tff(139,plain,
% 0.16/0.40 ((~(subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4)))) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4))))))) | subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4)))) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))))),
% 0.16/0.40 inference(tautology,[status(thm)],[])).
% 0.16/0.40 tff(140,plain,
% 0.16/0.40 (subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4)))) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))))),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.16/0.40 tff(141,plain,
% 0.16/0.40 (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4)))) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4))))),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[140, 132])).
% 0.16/0.40 tff(142,plain,
% 0.16/0.40 (((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4)))) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4))))),
% 0.16/0.40 inference(tautology,[status(thm)],[])).
% 0.16/0.40 tff(143,plain,
% 0.16/0.40 (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[142, 141])).
% 0.16/0.40 tff(144,assumption,(~(member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4))) <=> (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, B!4))))))), introduced(assumption)).
% 0.16/0.40 tff(145,plain,
% 0.16/0.40 ((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4))) <=> (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, B!4))))))),
% 0.16/0.40 inference(quant_inst,[status(thm)],[])).
% 0.16/0.40 tff(146,plain,
% 0.16/0.40 ($false),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[145, 52, 144])).
% 0.16/0.40 tff(147,plain,(member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4))) <=> (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, B!4)))))), inference(lemma,lemma(discharge,[]))).
% 0.16/0.41 tff(148,plain,
% 0.16/0.41 ((~(member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4))) <=> (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, B!4))))))) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4))) | ((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, B!4))))),
% 0.16/0.41 inference(tautology,[status(thm)],[])).
% 0.16/0.41 tff(149,plain,
% 0.16/0.41 (member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4))) | ((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, B!4))))),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.16/0.41 tff(150,plain,
% 0.16/0.41 ((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, B!4)))),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[149, 143])).
% 0.16/0.41 tff(151,plain,
% 0.16/0.41 (((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4)))) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4)))),
% 0.16/0.41 inference(tautology,[status(thm)],[])).
% 0.16/0.41 tff(152,plain,
% 0.16/0.41 (member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4)))),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[151, 141])).
% 0.16/0.41 tff(153,assumption,(~(member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4))) <=> (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4)))))), introduced(assumption)).
% 0.16/0.41 tff(154,plain,
% 0.16/0.41 ((~![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))) | (member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4))) <=> (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4)))))),
% 0.16/0.41 inference(quant_inst,[status(thm)],[])).
% 0.16/0.41 tff(155,plain,
% 0.16/0.41 ($false),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[154, 32, 153])).
% 0.16/0.41 tff(156,plain,(member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4))) <=> (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4))))), inference(lemma,lemma(discharge,[]))).
% 0.16/0.41 tff(157,plain,
% 0.16/0.41 ((~(member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4))) <=> (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4)))))) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4)))) | (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4))))),
% 0.16/0.41 inference(tautology,[status(thm)],[])).
% 0.16/0.41 tff(158,plain,
% 0.16/0.41 ((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4)))) | (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4))))),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[157, 156])).
% 0.16/0.41 tff(159,plain,
% 0.16/0.41 (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4)))),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[158, 152])).
% 0.16/0.41 tff(160,assumption,((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4)), introduced(assumption)).
% 0.16/0.41 tff(161,assumption,(~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4)))), introduced(assumption)).
% 0.16/0.41 tff(162,plain,
% 0.16/0.41 (((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4))) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)),
% 0.16/0.41 inference(tautology,[status(thm)],[])).
% 0.16/0.41 tff(163,plain,
% 0.16/0.41 (member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[162, 161])).
% 0.16/0.41 tff(164,plain,
% 0.16/0.41 ((~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4))) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4)),
% 0.16/0.41 inference(tautology,[status(thm)],[])).
% 0.16/0.41 tff(165,plain,
% 0.16/0.41 (member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4)),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[164, 163, 160])).
% 0.16/0.41 tff(166,assumption,(~(member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5)))), introduced(assumption)).
% 0.16/0.41 tff(167,plain,
% 0.16/0.41 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5)))),
% 0.16/0.41 inference(quant_inst,[status(thm)],[])).
% 0.16/0.41 tff(168,plain,
% 0.16/0.41 ($false),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[167, 92, 166])).
% 0.16/0.41 tff(169,plain,(member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5))), inference(lemma,lemma(discharge,[]))).
% 0.16/0.41 tff(170,plain,
% 0.16/0.41 (((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4))) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4)))),
% 0.16/0.41 inference(tautology,[status(thm)],[])).
% 0.16/0.41 tff(171,plain,
% 0.16/0.41 (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4))),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[170, 161])).
% 0.16/0.41 tff(172,plain,
% 0.16/0.41 ((~(member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5)))) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4)) | (~(member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5)))),
% 0.16/0.41 inference(tautology,[status(thm)],[])).
% 0.16/0.41 tff(173,plain,
% 0.16/0.41 (~(member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5))),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[172, 171, 169])).
% 0.16/0.41 tff(174,plain,
% 0.16/0.41 ((member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5)) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4))),
% 0.16/0.41 inference(tautology,[status(thm)],[])).
% 0.16/0.41 tff(175,plain,
% 0.16/0.41 ($false),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[174, 173, 165])).
% 0.16/0.41 tff(176,plain,(((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4))) | (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4)))), inference(lemma,lemma(discharge,[]))).
% 0.16/0.42 tff(177,plain,
% 0.16/0.42 (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4))),
% 0.16/0.42 inference(unit_resolution,[status(thm)],[176, 159])).
% 0.16/0.42 tff(178,assumption,(~(member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, B!4)) <=> (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4))))), introduced(assumption)).
% 0.16/0.42 tff(179,plain,
% 0.16/0.42 ((~![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))) | (member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, B!4)) <=> (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4))))),
% 0.16/0.42 inference(quant_inst,[status(thm)],[])).
% 0.16/0.42 tff(180,plain,
% 0.16/0.42 ($false),
% 0.16/0.42 inference(unit_resolution,[status(thm)],[179, 32, 178])).
% 0.16/0.42 tff(181,plain,(member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, B!4)) <=> (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4)))), inference(lemma,lemma(discharge,[]))).
% 0.16/0.42 tff(182,plain,
% 0.16/0.42 ((~(member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, B!4)) <=> (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4))))) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, B!4)) | ((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4))),
% 0.16/0.42 inference(tautology,[status(thm)],[])).
% 0.16/0.42 tff(183,plain,
% 0.16/0.42 (member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, B!4)) | ((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4))),
% 0.16/0.42 inference(unit_resolution,[status(thm)],[182, 181])).
% 0.16/0.42 tff(184,plain,
% 0.16/0.42 (member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, B!4))),
% 0.16/0.42 inference(unit_resolution,[status(thm)],[183, 177])).
% 0.16/0.42 tff(185,plain,
% 0.16/0.42 ((~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, B!4))))) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, B!4)))),
% 0.16/0.42 inference(tautology,[status(thm)],[])).
% 0.16/0.42 tff(186,plain,
% 0.16/0.42 (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, A!5))),
% 0.16/0.42 inference(unit_resolution,[status(thm)],[185, 184, 150])).
% 0.16/0.42 tff(187,plain,
% 0.16/0.42 (member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)),
% 0.16/0.42 inference(unit_resolution,[status(thm)],[162, 159])).
% 0.16/0.42 tff(188,plain,
% 0.16/0.42 (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4))),
% 0.16/0.42 inference(unit_resolution,[status(thm)],[170, 159])).
% 0.16/0.42 tff(189,plain,
% 0.16/0.42 (member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4)) | (~(member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5)))),
% 0.16/0.42 inference(unit_resolution,[status(thm)],[172, 169])).
% 0.16/0.42 tff(190,plain,
% 0.16/0.42 (~(member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5))),
% 0.16/0.42 inference(unit_resolution,[status(thm)],[189, 188])).
% 0.16/0.42 tff(191,plain,
% 0.16/0.42 ((member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5)) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5))),
% 0.16/0.42 inference(tautology,[status(thm)],[])).
% 0.16/0.42 tff(192,plain,
% 0.16/0.42 (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5)),
% 0.16/0.42 inference(unit_resolution,[status(thm)],[191, 190])).
% 0.16/0.42 tff(193,plain,
% 0.16/0.42 ((~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5))) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5)),
% 0.16/0.42 inference(tautology,[status(thm)],[])).
% 0.16/0.42 tff(194,plain,
% 0.16/0.42 (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5))),
% 0.16/0.42 inference(unit_resolution,[status(thm)],[193, 192, 187])).
% 0.16/0.42 tff(195,assumption,(~(member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, A!5)) <=> (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5))))), introduced(assumption)).
% 0.16/0.42 tff(196,plain,
% 0.16/0.42 ((~![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))) | (member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, A!5)) <=> (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5))))),
% 0.16/0.42 inference(quant_inst,[status(thm)],[])).
% 0.16/0.42 tff(197,plain,
% 0.16/0.42 ($false),
% 0.16/0.42 inference(unit_resolution,[status(thm)],[196, 32, 195])).
% 0.16/0.43 tff(198,plain,(member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, A!5)) <=> (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5)))), inference(lemma,lemma(discharge,[]))).
% 0.16/0.43 tff(199,plain,
% 0.16/0.43 ((~(member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, A!5)) <=> (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5))))) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, A!5)) | ((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5))),
% 0.16/0.43 inference(tautology,[status(thm)],[])).
% 0.16/0.43 tff(200,plain,
% 0.16/0.43 (member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, A!5)) | ((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5))),
% 0.16/0.43 inference(unit_resolution,[status(thm)],[199, 198])).
% 0.16/0.43 tff(201,plain,
% 0.16/0.43 ($false),
% 0.16/0.43 inference(unit_resolution,[status(thm)],[200, 194, 186])).
% 0.16/0.43 % SZS output end Proof
%------------------------------------------------------------------------------