TSTP Solution File: SET698+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET698+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 05:07:39 EDT 2022
% Result : Theorem 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET698+4 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Sep 3 07:22:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(member_type, type, (
% 0.20/0.39 member: ( $i * $i ) > $o)).
% 0.20/0.39 tff(tptp_fun_A_5_type, type, (
% 0.20/0.39 tptp_fun_A_5: $i)).
% 0.20/0.39 tff(tptp_fun_X_0_type, type, (
% 0.20/0.39 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.20/0.39 tff(union_type, type, (
% 0.20/0.39 union: ( $i * $i ) > $i)).
% 0.20/0.39 tff(tptp_fun_B_4_type, type, (
% 0.20/0.39 tptp_fun_B_4: $i)).
% 0.20/0.39 tff(difference_type, type, (
% 0.20/0.39 difference: ( $i * $i ) > $i)).
% 0.20/0.39 tff(tptp_fun_E_3_type, type, (
% 0.20/0.39 tptp_fun_E_3: $i)).
% 0.20/0.39 tff(subset_type, type, (
% 0.20/0.39 subset: ( $i * $i ) > $o)).
% 0.20/0.39 tff(equal_set_type, type, (
% 0.20/0.39 equal_set: ( $i * $i ) > $o)).
% 0.20/0.39 tff(1,plain,
% 0.20/0.39 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(2,plain,
% 0.20/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.39 tff(3,plain,
% 0.20/0.39 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(4,plain,
% 0.20/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[4, 2])).
% 0.20/0.39 tff(6,plain,
% 0.20/0.39 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(7,plain,
% 0.20/0.39 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.39 tff(8,plain,
% 0.20/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(9,plain,
% 0.20/0.39 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[9])).
% 0.20/0.39 tff(11,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','subset')).
% 0.20/0.39 tff(12,plain,
% 0.20/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.39 tff(13,plain,
% 0.20/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.20/0.39 tff(14,plain,(
% 0.20/0.39 ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[13])).
% 0.20/0.39 tff(15,plain,
% 0.20/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.20/0.39 tff(16,plain,
% 0.20/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.20/0.39 tff(17,plain,
% 0.20/0.39 ((~![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(union(difference(E!3, A!5), B!4), E!3)) | ![X: $i] : ((~member(X, union(difference(E!3, A!5), B!4))) | member(X, E!3)))) | (~(subset(union(difference(E!3, A!5), B!4), E!3) | (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)))))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(18,plain,
% 0.20/0.39 (~((~((~subset(union(difference(E!3, A!5), B!4), E!3)) | ![X: $i] : ((~member(X, union(difference(E!3, A!5), B!4))) | member(X, E!3)))) | (~(subset(union(difference(E!3, A!5), B!4), E!3) | (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3))))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 (((~((~subset(union(difference(E!3, A!5), B!4), E!3)) | ![X: $i] : ((~member(X, union(difference(E!3, A!5), B!4))) | member(X, E!3)))) | (~(subset(union(difference(E!3, A!5), B!4), E!3) | (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)))))) | (subset(union(difference(E!3, A!5), B!4), E!3) | (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3))))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(20,plain,
% 0.20/0.39 (subset(union(difference(E!3, A!5), B!4), E!3) | (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.20/0.40 tff(21,assumption,(~subset(A!5, B!4)), introduced(assumption)).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 ((~![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(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))) | (~(subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 (~((~((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))) | (~(subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4))))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[22, 16])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 (((~((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))) | (~(subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))))) | (subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 ((~(subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4))))) | subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 (subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[27, 21])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 (((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)) | (~member(tptp_fun_X_0(B!4, A!5), B!4))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 (~member(tptp_fun_X_0(B!4, A!5), B!4)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 (((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)) | member(tptp_fun_X_0(B!4, A!5), A!5)),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 (member(tptp_fun_X_0(B!4, A!5), A!5)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[31, 28])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), A!5))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 ((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), A!5)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.20/0.40 tff(35,assumption,(~(member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5)) <=> (~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), A!5))))), introduced(assumption)).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 (^[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)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 (![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))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[36])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 (^[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)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 (![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))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 (![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))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(41,axiom,(![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','difference')).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.40 tff(43,plain,(
% 0.20/0.40 ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[42])).
% 0.20/0.40 tff(44,plain,
% 0.20/0.40 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.20/0.40 tff(45,plain,
% 0.20/0.40 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 ((~![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))) | (member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5)) <=> (~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), A!5))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(47,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[46, 45, 35])).
% 0.20/0.40 tff(48,plain,(member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5)) <=> (~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), A!5)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(49,plain,
% 0.20/0.40 ((~(member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5)) <=> (~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), A!5))))) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5))) | (~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), A!5)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(50,plain,
% 0.20/0.40 ((~member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5))) | (~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), A!5)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.20/0.40 tff(51,plain,
% 0.20/0.40 (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[50, 34])).
% 0.20/0.40 tff(52,plain,
% 0.20/0.40 ((~(member(tptp_fun_X_0(B!4, A!5), B!4) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5)))) | member(tptp_fun_X_0(B!4, A!5), B!4) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(53,plain,
% 0.20/0.40 (~(member(tptp_fun_X_0(B!4, A!5), B!4) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[52, 51, 30])).
% 0.20/0.40 tff(54,assumption,(~(member(tptp_fun_X_0(B!4, A!5), union(difference(E!3, A!5), B!4)) <=> (member(tptp_fun_X_0(B!4, A!5), B!4) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5))))), introduced(assumption)).
% 0.20/0.40 tff(55,plain,
% 0.20/0.40 (^[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))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(56,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[55])).
% 0.20/0.40 tff(57,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(58,plain,
% 0.20/0.40 (^[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))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[58])).
% 0.20/0.40 tff(60,axiom,(![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','union')).
% 0.20/0.40 tff(61,plain,
% 0.20/0.40 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.20/0.40 tff(63,plain,(
% 0.20/0.40 ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[62])).
% 0.20/0.40 tff(64,plain,
% 0.20/0.40 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.20/0.40 tff(65,plain,
% 0.20/0.40 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(B!4, A!5), union(difference(E!3, A!5), B!4)) <=> (member(tptp_fun_X_0(B!4, A!5), B!4) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(66,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[65, 64, 54])).
% 0.20/0.40 tff(67,plain,(member(tptp_fun_X_0(B!4, A!5), union(difference(E!3, A!5), B!4)) <=> (member(tptp_fun_X_0(B!4, A!5), B!4) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(68,plain,
% 0.20/0.40 ((~(member(tptp_fun_X_0(B!4, A!5), union(difference(E!3, A!5), B!4)) <=> (member(tptp_fun_X_0(B!4, A!5), B!4) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5))))) | (~member(tptp_fun_X_0(B!4, A!5), union(difference(E!3, A!5), B!4))) | (member(tptp_fun_X_0(B!4, A!5), B!4) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 ((~member(tptp_fun_X_0(B!4, A!5), union(difference(E!3, A!5), B!4))) | (member(tptp_fun_X_0(B!4, A!5), B!4) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 (~member(tptp_fun_X_0(B!4, A!5), union(difference(E!3, A!5), B!4))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[69, 53])).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 ((~![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(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))) | (~(subset(A!5, E!3) | (~((~member(tptp_fun_X_0(E!3, A!5), A!5)) | member(tptp_fun_X_0(E!3, A!5), E!3)))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(72,plain,
% 0.20/0.40 (~((~((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))) | (~(subset(A!5, E!3) | (~((~member(tptp_fun_X_0(E!3, A!5), A!5)) | member(tptp_fun_X_0(E!3, A!5), E!3))))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[71, 16])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 (((~((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))) | (~(subset(A!5, E!3) | (~((~member(tptp_fun_X_0(E!3, A!5), A!5)) | member(tptp_fun_X_0(E!3, A!5), E!3)))))) | ((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 ((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.20/0.40 tff(75,plain,
% 0.20/0.40 ((~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(union(difference(E, A), B), E)))) <=> (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(union(difference(E, A), B), E))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(76,plain,
% 0.20/0.40 ((~![A: $i, B: $i, E: $i] : ((subset(A, E) & subset(B, E)) => (subset(A, B) <=> equal_set(union(difference(E, A), B), E)))) <=> (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(union(difference(E, A), B), E))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(77,axiom,(~![A: $i, B: $i, E: $i] : ((subset(A, E) & subset(B, E)) => (subset(A, B) <=> equal_set(union(difference(E, A), B), E)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thI32')).
% 0.20/0.41 tff(78,plain,
% 0.20/0.41 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(union(difference(E, A), B), E)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.20/0.41 tff(79,plain,
% 0.20/0.41 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(union(difference(E, A), B), E)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[78, 75])).
% 0.20/0.41 tff(80,plain,
% 0.20/0.41 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(union(difference(E, A), B), E)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.20/0.41 tff(81,plain,
% 0.20/0.41 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(union(difference(E, A), B), E)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[80, 75])).
% 0.20/0.41 tff(82,plain,
% 0.20/0.41 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(union(difference(E, A), B), E)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[81, 75])).
% 0.20/0.41 tff(83,plain,
% 0.20/0.41 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(union(difference(E, A), B), E)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.20/0.41 tff(84,plain,
% 0.20/0.41 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(union(difference(E, A), B), E)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[83, 75])).
% 0.20/0.41 tff(85,plain,(
% 0.20/0.41 ~((~(subset(A!5, E!3) & subset(B!4, E!3))) | (subset(A!5, B!4) <=> equal_set(union(difference(E!3, A!5), B!4), E!3)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[84])).
% 0.20/0.41 tff(86,plain,
% 0.20/0.41 (subset(A!5, E!3) & subset(B!4, E!3)),
% 0.20/0.41 inference(or_elim,[status(thm)],[85])).
% 0.20/0.41 tff(87,plain,
% 0.20/0.41 (subset(A!5, E!3)),
% 0.20/0.41 inference(and_elim,[status(thm)],[86])).
% 0.20/0.41 tff(88,plain,
% 0.20/0.41 ((~((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))) | (~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(89,plain,
% 0.20/0.41 ((~((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.20/0.41 tff(90,plain,
% 0.20/0.41 (![X: $i] : ((~member(X, A!5)) | member(X, E!3))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[89, 74])).
% 0.20/0.41 tff(91,plain,
% 0.20/0.41 (((~![X: $i] : ((~member(X, A!5)) | member(X, E!3))) | ((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), E!3))) <=> ((~![X: $i] : ((~member(X, A!5)) | member(X, E!3))) | (~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), E!3))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(92,plain,
% 0.20/0.41 ((~![X: $i] : ((~member(X, A!5)) | member(X, E!3))) | ((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), E!3))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(93,plain,
% 0.20/0.41 ((~![X: $i] : ((~member(X, A!5)) | member(X, E!3))) | (~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), E!3)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.41 tff(94,plain,
% 0.20/0.41 (member(tptp_fun_X_0(B!4, A!5), E!3)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[93, 90, 32])).
% 0.20/0.41 tff(95,plain,
% 0.20/0.41 ((~(subset(A!5, B!4) <=> equal_set(union(difference(E!3, A!5), B!4), E!3))) <=> ((~subset(A!5, B!4)) <=> equal_set(union(difference(E!3, A!5), B!4), E!3))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(96,plain,
% 0.20/0.41 (~(subset(A!5, B!4) <=> equal_set(union(difference(E!3, A!5), B!4), E!3))),
% 0.20/0.41 inference(or_elim,[status(thm)],[85])).
% 0.20/0.41 tff(97,plain,
% 0.20/0.41 ((~subset(A!5, B!4)) <=> equal_set(union(difference(E!3, A!5), B!4), E!3)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.20/0.41 tff(98,plain,
% 0.20/0.41 (subset(A!5, B!4) | equal_set(union(difference(E!3, A!5), B!4), E!3) | (~((~subset(A!5, B!4)) <=> equal_set(union(difference(E!3, A!5), B!4), E!3)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(99,plain,
% 0.20/0.41 (subset(A!5, B!4) | equal_set(union(difference(E!3, A!5), B!4), E!3)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.20/0.41 tff(100,plain,
% 0.20/0.41 (equal_set(union(difference(E!3, A!5), B!4), E!3)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[99, 21])).
% 0.20/0.41 tff(101,plain,
% 0.20/0.41 (^[A: $i, B: $i] : refl((equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(102,plain,
% 0.20/0.41 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[101])).
% 0.20/0.41 tff(103,plain,
% 0.20/0.41 (^[A: $i, B: $i] : rewrite((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(104,plain,
% 0.20/0.41 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[103])).
% 0.20/0.41 tff(105,plain,
% 0.20/0.41 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(106,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','equal_set')).
% 0.20/0.41 tff(107,plain,
% 0.20/0.41 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.20/0.41 tff(108,plain,(
% 0.20/0.41 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[107])).
% 0.20/0.41 tff(109,plain,
% 0.20/0.41 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.20/0.41 tff(110,plain,
% 0.20/0.41 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.20/0.41 tff(111,plain,
% 0.20/0.41 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(union(difference(E!3, A!5), B!4), E!3) <=> (~((~subset(union(difference(E!3, A!5), B!4), E!3)) | (~subset(E!3, union(difference(E!3, A!5), B!4))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(112,plain,
% 0.20/0.41 (equal_set(union(difference(E!3, A!5), B!4), E!3) <=> (~((~subset(union(difference(E!3, A!5), B!4), E!3)) | (~subset(E!3, union(difference(E!3, A!5), B!4)))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.20/0.41 tff(113,plain,
% 0.20/0.41 ((~(equal_set(union(difference(E!3, A!5), B!4), E!3) <=> (~((~subset(union(difference(E!3, A!5), B!4), E!3)) | (~subset(E!3, union(difference(E!3, A!5), B!4))))))) | (~equal_set(union(difference(E!3, A!5), B!4), E!3)) | (~((~subset(union(difference(E!3, A!5), B!4), E!3)) | (~subset(E!3, union(difference(E!3, A!5), B!4)))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(114,plain,
% 0.20/0.41 ((~equal_set(union(difference(E!3, A!5), B!4), E!3)) | (~((~subset(union(difference(E!3, A!5), B!4), E!3)) | (~subset(E!3, union(difference(E!3, A!5), B!4)))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.20/0.41 tff(115,plain,
% 0.20/0.41 (~((~subset(union(difference(E!3, A!5), B!4), E!3)) | (~subset(E!3, union(difference(E!3, A!5), B!4))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[114, 100])).
% 0.20/0.41 tff(116,plain,
% 0.20/0.41 (((~subset(union(difference(E!3, A!5), B!4), E!3)) | (~subset(E!3, union(difference(E!3, A!5), B!4)))) | subset(E!3, union(difference(E!3, A!5), B!4))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(117,plain,
% 0.20/0.41 (subset(E!3, union(difference(E!3, A!5), B!4))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.20/0.41 tff(118,assumption,((~((~subset(E!3, union(difference(E!3, A!5), B!4))) | ![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!5), B!4))))) | (~(subset(E!3, union(difference(E!3, A!5), B!4)) | (~((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4))))))), introduced(assumption)).
% 0.20/0.41 tff(119,plain,
% 0.20/0.41 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(E!3, union(difference(E!3, A!5), B!4))) | ![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!5), B!4))))) | (~(subset(E!3, union(difference(E!3, A!5), B!4)) | (~((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4))))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(120,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[119, 16, 118])).
% 0.20/0.41 tff(121,plain,(~((~((~subset(E!3, union(difference(E!3, A!5), B!4))) | ![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!5), B!4))))) | (~(subset(E!3, union(difference(E!3, A!5), B!4)) | (~((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4)))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(122,plain,
% 0.20/0.41 (((~((~subset(E!3, union(difference(E!3, A!5), B!4))) | ![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!5), B!4))))) | (~(subset(E!3, union(difference(E!3, A!5), B!4)) | (~((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4))))))) | ((~subset(E!3, union(difference(E!3, A!5), B!4))) | ![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!5), B!4))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(123,plain,
% 0.20/0.41 ((~subset(E!3, union(difference(E!3, A!5), B!4))) | ![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!5), B!4)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.20/0.41 tff(124,plain,
% 0.20/0.41 ((~((~subset(E!3, union(difference(E!3, A!5), B!4))) | ![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!5), B!4))))) | (~subset(E!3, union(difference(E!3, A!5), B!4))) | ![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!5), B!4)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(125,plain,
% 0.20/0.41 ((~subset(E!3, union(difference(E!3, A!5), B!4))) | ![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!5), B!4)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.20/0.41 tff(126,plain,
% 0.20/0.41 (![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!5), B!4)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[125, 117])).
% 0.20/0.41 tff(127,plain,
% 0.20/0.41 (((~![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!5), B!4)))) | ((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), union(difference(E!3, A!5), B!4)))) <=> ((~![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!5), B!4)))) | (~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), union(difference(E!3, A!5), B!4)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(128,plain,
% 0.20/0.41 ((~![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!5), B!4)))) | ((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), union(difference(E!3, A!5), B!4)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(129,plain,
% 0.20/0.41 ((~![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!5), B!4)))) | (~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), union(difference(E!3, A!5), B!4))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.20/0.41 tff(130,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[129, 126, 94, 70])).
% 0.20/0.41 tff(131,plain,(subset(A!5, B!4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(132,plain,
% 0.20/0.41 ((~subset(A!5, B!4)) | (~equal_set(union(difference(E!3, A!5), B!4), E!3)) | (~((~subset(A!5, B!4)) <=> equal_set(union(difference(E!3, A!5), B!4), E!3)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(133,plain,
% 0.20/0.42 ((~subset(A!5, B!4)) | (~equal_set(union(difference(E!3, A!5), B!4), E!3))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[132, 97])).
% 0.20/0.42 tff(134,plain,
% 0.20/0.42 (~equal_set(union(difference(E!3, A!5), B!4), E!3)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[133, 131])).
% 0.20/0.42 tff(135,plain,
% 0.20/0.42 ((~(equal_set(union(difference(E!3, A!5), B!4), E!3) <=> (~((~subset(union(difference(E!3, A!5), B!4), E!3)) | (~subset(E!3, union(difference(E!3, A!5), B!4))))))) | equal_set(union(difference(E!3, A!5), B!4), E!3) | ((~subset(union(difference(E!3, A!5), B!4), E!3)) | (~subset(E!3, union(difference(E!3, A!5), B!4))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(136,plain,
% 0.20/0.42 (equal_set(union(difference(E!3, A!5), B!4), E!3) | ((~subset(union(difference(E!3, A!5), B!4), E!3)) | (~subset(E!3, union(difference(E!3, A!5), B!4))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[135, 112])).
% 0.20/0.42 tff(137,plain,
% 0.20/0.42 ((~subset(union(difference(E!3, A!5), B!4), E!3)) | (~subset(E!3, union(difference(E!3, A!5), B!4)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[136, 134])).
% 0.20/0.42 tff(138,plain,
% 0.20/0.42 (((~((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))) | (~(subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))))) | ((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(139,plain,
% 0.20/0.42 ((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[138, 23])).
% 0.20/0.42 tff(140,plain,
% 0.20/0.42 ((~((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))) | (~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(141,plain,
% 0.20/0.42 ((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.20/0.42 tff(142,plain,
% 0.20/0.42 (![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[141, 131])).
% 0.20/0.42 tff(143,plain,
% 0.20/0.42 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4)) <=> (member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), B!4) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), difference(E!3, A!5))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(144,plain,
% 0.20/0.42 (member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4)) <=> (member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), B!4) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), difference(E!3, A!5)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[143, 64])).
% 0.20/0.42 tff(145,assumption,(~((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4)))), introduced(assumption)).
% 0.20/0.42 tff(146,plain,
% 0.20/0.42 (((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4))) | (~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(147,plain,
% 0.20/0.42 (~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.20/0.42 tff(148,plain,
% 0.20/0.42 ((~(member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4)) <=> (member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), B!4) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), difference(E!3, A!5))))) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4)) | (~(member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), B!4) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), difference(E!3, A!5))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(149,plain,
% 0.20/0.42 ((~(member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4)) <=> (member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), B!4) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), difference(E!3, A!5))))) | (~(member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), B!4) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), difference(E!3, A!5))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.20/0.42 tff(150,plain,
% 0.20/0.42 (~(member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), B!4) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), difference(E!3, A!5)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[149, 144])).
% 0.20/0.42 tff(151,plain,
% 0.20/0.42 ((member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), B!4) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), difference(E!3, A!5))) | (~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), B!4))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(152,plain,
% 0.20/0.42 (~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), B!4)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.20/0.42 tff(153,assumption,(![X: $i] : ((~member(X, A!5)) | member(X, B!4))), introduced(assumption)).
% 0.20/0.42 tff(154,plain,
% 0.20/0.42 (((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | ((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), A!5)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), B!4))) <=> ((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | (~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), A!5)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), B!4))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(155,plain,
% 0.20/0.42 ((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | ((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), A!5)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), B!4))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(156,plain,
% 0.20/0.42 ((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | (~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), A!5)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), B!4)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.20/0.42 tff(157,plain,
% 0.20/0.42 (~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), A!5)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[156, 153, 152])).
% 0.20/0.42 tff(158,plain,
% 0.20/0.42 ((~![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))) | (member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), difference(E!3, A!5)) <=> (~((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), A!5))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(159,plain,
% 0.20/0.42 (member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), difference(E!3, A!5)) <=> (~((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), A!5)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[158, 45])).
% 0.20/0.42 tff(160,plain,
% 0.20/0.42 ((member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), B!4) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), difference(E!3, A!5))) | (~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), difference(E!3, A!5)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(161,plain,
% 0.20/0.42 (~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), difference(E!3, A!5))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[160, 150])).
% 0.20/0.42 tff(162,plain,
% 0.20/0.42 ((~(member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), difference(E!3, A!5)) <=> (~((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), A!5))))) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), difference(E!3, A!5)) | ((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), A!5))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(163,plain,
% 0.20/0.43 ((~(member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), difference(E!3, A!5)) <=> (~((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), A!5))))) | ((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), A!5))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[162, 161])).
% 0.20/0.43 tff(164,plain,
% 0.20/0.43 ((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), A!5)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[163, 159])).
% 0.20/0.43 tff(165,plain,
% 0.20/0.43 (((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4))) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(166,plain,
% 0.20/0.43 (member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[165, 145])).
% 0.20/0.43 tff(167,plain,
% 0.20/0.43 ((~((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), A!5))) | (~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), A!5)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(168,plain,
% 0.20/0.43 ((~((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), A!5))) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), A!5)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.20/0.43 tff(169,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[168, 164, 157])).
% 0.20/0.43 tff(170,plain,(((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4))) | (~![X: $i] : ((~member(X, A!5)) | member(X, B!4)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(171,plain,
% 0.20/0.43 ((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[170, 142])).
% 0.20/0.43 tff(172,plain,
% 0.20/0.43 (((~((~subset(E!3, union(difference(E!3, A!5), B!4))) | ![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!5), B!4))))) | (~(subset(E!3, union(difference(E!3, A!5), B!4)) | (~((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4))))))) | (subset(E!3, union(difference(E!3, A!5), B!4)) | (~((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4)))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(173,plain,
% 0.20/0.43 (subset(E!3, union(difference(E!3, A!5), B!4)) | (~((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[172, 121])).
% 0.20/0.43 tff(174,plain,
% 0.20/0.43 ((~(subset(E!3, union(difference(E!3, A!5), B!4)) | (~((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4)))))) | subset(E!3, union(difference(E!3, A!5), B!4)) | (~((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(175,plain,
% 0.20/0.43 (subset(E!3, union(difference(E!3, A!5), B!4)) | (~((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[174, 173])).
% 0.20/0.43 tff(176,plain,
% 0.20/0.43 (subset(E!3, union(difference(E!3, A!5), B!4))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[175, 171])).
% 0.20/0.43 tff(177,plain,
% 0.20/0.43 ((~((~subset(union(difference(E!3, A!5), B!4), E!3)) | (~subset(E!3, union(difference(E!3, A!5), B!4))))) | (~subset(union(difference(E!3, A!5), B!4), E!3)) | (~subset(E!3, union(difference(E!3, A!5), B!4)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(178,plain,
% 0.20/0.43 (~subset(union(difference(E!3, A!5), B!4), E!3)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[177, 176, 137])).
% 0.20/0.43 tff(179,plain,
% 0.20/0.43 ((~(subset(union(difference(E!3, A!5), B!4), E!3) | (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3))))) | subset(union(difference(E!3, A!5), B!4), E!3) | (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(180,plain,
% 0.20/0.43 ((~(subset(union(difference(E!3, A!5), B!4), E!3) | (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3))))) | (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[179, 178])).
% 0.20/0.43 tff(181,plain,
% 0.20/0.43 (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[180, 20])).
% 0.20/0.43 tff(182,plain,
% 0.20/0.43 (((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)) | (~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(183,plain,
% 0.20/0.43 (~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[182, 181])).
% 0.20/0.43 tff(184,plain,
% 0.20/0.43 (((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), A!5)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(185,plain,
% 0.20/0.43 ((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), A!5)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.20/0.43 tff(186,plain,
% 0.20/0.43 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4)) <=> (member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), B!4) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), difference(E!3, A!5))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(187,plain,
% 0.20/0.43 (member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4)) <=> (member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), B!4) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), difference(E!3, A!5)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[186, 64])).
% 0.20/0.43 tff(188,plain,
% 0.20/0.43 (((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(189,plain,
% 0.20/0.43 (member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[188, 181])).
% 0.20/0.43 tff(190,plain,
% 0.20/0.43 ((~(member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4)) <=> (member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), B!4) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), difference(E!3, A!5))))) | (~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4))) | (member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), B!4) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), difference(E!3, A!5)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(191,plain,
% 0.20/0.43 ((~(member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4)) <=> (member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), B!4) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), difference(E!3, A!5))))) | (member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), B!4) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), difference(E!3, A!5)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[190, 189])).
% 0.20/0.43 tff(192,plain,
% 0.20/0.43 (member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), B!4) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), difference(E!3, A!5))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[191, 187])).
% 0.20/0.43 tff(193,plain,
% 0.20/0.43 ((~![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(B!4, E!3)) | ![X: $i] : ((~member(X, B!4)) | member(X, E!3)))) | (~(subset(B!4, E!3) | (~((~member(tptp_fun_X_0(E!3, B!4), B!4)) | member(tptp_fun_X_0(E!3, B!4), E!3)))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(194,plain,
% 0.20/0.43 (~((~((~subset(B!4, E!3)) | ![X: $i] : ((~member(X, B!4)) | member(X, E!3)))) | (~(subset(B!4, E!3) | (~((~member(tptp_fun_X_0(E!3, B!4), B!4)) | member(tptp_fun_X_0(E!3, B!4), E!3))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[193, 16])).
% 0.20/0.43 tff(195,plain,
% 0.20/0.43 (((~((~subset(B!4, E!3)) | ![X: $i] : ((~member(X, B!4)) | member(X, E!3)))) | (~(subset(B!4, E!3) | (~((~member(tptp_fun_X_0(E!3, B!4), B!4)) | member(tptp_fun_X_0(E!3, B!4), E!3)))))) | ((~subset(B!4, E!3)) | ![X: $i] : ((~member(X, B!4)) | member(X, E!3)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(196,plain,
% 0.20/0.43 ((~subset(B!4, E!3)) | ![X: $i] : ((~member(X, B!4)) | member(X, E!3))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[195, 194])).
% 0.20/0.43 tff(197,plain,
% 0.20/0.43 (subset(B!4, E!3)),
% 0.20/0.43 inference(and_elim,[status(thm)],[86])).
% 0.20/0.43 tff(198,plain,
% 0.20/0.43 ((~((~subset(B!4, E!3)) | ![X: $i] : ((~member(X, B!4)) | member(X, E!3)))) | (~subset(B!4, E!3)) | ![X: $i] : ((~member(X, B!4)) | member(X, E!3))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(199,plain,
% 0.20/0.43 ((~((~subset(B!4, E!3)) | ![X: $i] : ((~member(X, B!4)) | member(X, E!3)))) | ![X: $i] : ((~member(X, B!4)) | member(X, E!3))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.20/0.43 tff(200,plain,
% 0.20/0.43 (![X: $i] : ((~member(X, B!4)) | member(X, E!3))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[199, 196])).
% 0.20/0.43 tff(201,plain,
% 0.20/0.43 (((~![X: $i] : ((~member(X, B!4)) | member(X, E!3))) | ((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), B!4)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3))) <=> ((~![X: $i] : ((~member(X, B!4)) | member(X, E!3))) | (~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), B!4)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(202,plain,
% 0.20/0.43 ((~![X: $i] : ((~member(X, B!4)) | member(X, E!3))) | ((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), B!4)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(203,plain,
% 0.20/0.43 ((~![X: $i] : ((~member(X, B!4)) | member(X, E!3))) | (~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), B!4)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.20/0.43 tff(204,plain,
% 0.20/0.43 (~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), B!4)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[203, 200, 183])).
% 0.20/0.43 tff(205,plain,
% 0.20/0.43 ((~(member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), B!4) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), difference(E!3, A!5)))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), B!4) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), difference(E!3, A!5))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(206,plain,
% 0.20/0.44 ((~(member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), B!4) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), difference(E!3, A!5)))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), difference(E!3, A!5))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[205, 204])).
% 0.20/0.44 tff(207,plain,
% 0.20/0.44 (member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), difference(E!3, A!5))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[206, 192])).
% 0.20/0.44 tff(208,plain,
% 0.20/0.44 ((~(member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), difference(E!3, A!5)) <=> (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), A!5))))) | (~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), difference(E!3, A!5))) | (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), A!5)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(209,plain,
% 0.20/0.44 (~(member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), difference(E!3, A!5)) <=> (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), A!5))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[208, 207, 185])).
% 0.20/0.44 tff(210,plain,
% 0.20/0.44 ((~![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))) | (member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), difference(E!3, A!5)) <=> (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), A!5))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(211,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[210, 45, 209])).
% 0.20/0.44 % SZS output end Proof
%------------------------------------------------------------------------------