TSTP Solution File: SET697+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET697+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 0.63s 0.69s
% Output : Proof 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET697+4 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 07:22:24 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.
% 0.63/0.69 % SZS status Theorem
% 0.63/0.69 % SZS output start Proof
% 0.63/0.69 tff(member_type, type, (
% 0.63/0.69 member: ( $i * $i ) > $o)).
% 0.63/0.69 tff(tptp_fun_B_4_type, type, (
% 0.63/0.69 tptp_fun_B_4: $i)).
% 0.63/0.69 tff(tptp_fun_X_0_type, type, (
% 0.63/0.69 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.63/0.69 tff(tptp_fun_A_5_type, type, (
% 0.63/0.69 tptp_fun_A_5: $i)).
% 0.63/0.69 tff(tptp_fun_E_3_type, type, (
% 0.63/0.69 tptp_fun_E_3: $i)).
% 0.63/0.69 tff(difference_type, type, (
% 0.63/0.69 difference: ( $i * $i ) > $i)).
% 0.63/0.69 tff(subset_type, type, (
% 0.63/0.69 subset: ( $i * $i ) > $o)).
% 0.63/0.69 tff(equal_set_type, type, (
% 0.63/0.69 equal_set: ( $i * $i ) > $o)).
% 0.63/0.69 tff(empty_set_type, type, (
% 0.63/0.69 empty_set: $i)).
% 0.63/0.69 tff(intersection_type, type, (
% 0.63/0.69 intersection: ( $i * $i ) > $i)).
% 0.63/0.69 tff(1,plain,
% 0.63/0.69 (^[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))))))),
% 0.63/0.69 inference(bind,[status(th)],[])).
% 0.63/0.69 tff(2,plain,
% 0.63/0.69 (![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)))))),
% 0.63/0.69 inference(quant_intro,[status(thm)],[1])).
% 0.63/0.69 tff(3,plain,
% 0.63/0.69 (^[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))))))),
% 0.63/0.69 inference(bind,[status(th)],[])).
% 0.63/0.69 tff(4,plain,
% 0.63/0.69 (![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)))))),
% 0.63/0.69 inference(quant_intro,[status(thm)],[3])).
% 0.63/0.69 tff(5,plain,
% 0.63/0.69 (![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)))),
% 0.63/0.69 inference(rewrite,[status(thm)],[])).
% 0.63/0.69 tff(6,axiom,(![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','intersection')).
% 0.63/0.69 tff(7,plain,
% 0.63/0.69 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.63/0.69 tff(8,plain,(
% 0.63/0.69 ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.63/0.69 inference(skolemize,[status(sab)],[7])).
% 0.63/0.69 tff(9,plain,
% 0.63/0.69 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.63/0.69 tff(10,plain,
% 0.63/0.69 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.63/0.69 tff(11,plain,
% 0.63/0.69 ((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4))) <=> (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))))))),
% 0.63/0.69 inference(quant_inst,[status(thm)],[])).
% 0.63/0.69 tff(12,plain,
% 0.63/0.69 (member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4))) <=> (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.63/0.69 tff(13,plain,
% 0.63/0.69 (^[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))))))))),
% 0.63/0.69 inference(bind,[status(th)],[])).
% 0.63/0.69 tff(14,plain,
% 0.63/0.69 (![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)))))))),
% 0.63/0.69 inference(quant_intro,[status(thm)],[13])).
% 0.63/0.69 tff(15,plain,
% 0.63/0.69 (^[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))))))))),
% 0.63/0.69 inference(bind,[status(th)],[])).
% 0.63/0.69 tff(16,plain,
% 0.63/0.69 (![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)))))))),
% 0.63/0.69 inference(quant_intro,[status(thm)],[15])).
% 0.63/0.69 tff(17,plain,
% 0.63/0.69 (![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)))))))),
% 0.63/0.69 inference(transitivity,[status(thm)],[16, 14])).
% 0.63/0.69 tff(18,plain,
% 0.63/0.69 (^[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)))))))))),
% 0.63/0.69 inference(bind,[status(th)],[])).
% 0.63/0.69 tff(19,plain,
% 0.63/0.69 (![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)))))))),
% 0.63/0.69 inference(quant_intro,[status(thm)],[18])).
% 0.63/0.69 tff(20,plain,
% 0.63/0.69 (![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)))),
% 0.63/0.69 inference(rewrite,[status(thm)],[])).
% 0.63/0.69 tff(21,plain,
% 0.63/0.69 (^[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))))),
% 0.63/0.69 inference(bind,[status(th)],[])).
% 0.63/0.69 tff(22,plain,
% 0.63/0.69 (![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)))),
% 0.63/0.69 inference(quant_intro,[status(thm)],[21])).
% 0.63/0.69 tff(23,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')).
% 0.63/0.69 tff(24,plain,
% 0.63/0.69 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.63/0.69 tff(25,plain,
% 0.63/0.69 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.63/0.69 tff(26,plain,(
% 0.63/0.69 ![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)))))),
% 0.63/0.69 inference(skolemize,[status(sab)],[25])).
% 0.63/0.69 tff(27,plain,
% 0.63/0.69 (![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)))))))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.63/0.69 tff(28,plain,
% 0.63/0.69 (![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)))))))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.63/0.69 tff(29,plain,
% 0.63/0.69 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, empty_set)))) | (~(subset(intersection(A!5, difference(E!3, B!4)), empty_set) | (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), empty_set)))))))),
% 0.63/0.69 inference(quant_inst,[status(thm)],[])).
% 0.63/0.69 tff(30,plain,
% 0.63/0.69 (~((~((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, empty_set)))) | (~(subset(intersection(A!5, difference(E!3, B!4)), empty_set) | (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), empty_set))))))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.63/0.69 tff(31,plain,
% 0.63/0.69 (((~((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, empty_set)))) | (~(subset(intersection(A!5, difference(E!3, B!4)), empty_set) | (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), empty_set)))))) | (subset(intersection(A!5, difference(E!3, B!4)), empty_set) | (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), empty_set))))),
% 0.63/0.69 inference(tautology,[status(thm)],[])).
% 0.63/0.69 tff(32,plain,
% 0.63/0.69 (subset(intersection(A!5, difference(E!3, B!4)), empty_set) | (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), empty_set)))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.63/0.69 tff(33,assumption,(~equal_set(intersection(A!5, difference(E!3, B!4)), empty_set)), introduced(assumption)).
% 0.63/0.69 tff(34,plain,
% 0.63/0.69 (^[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))))))),
% 0.63/0.69 inference(bind,[status(th)],[])).
% 0.63/0.69 tff(35,plain,
% 0.63/0.69 (![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)))))),
% 0.63/0.69 inference(quant_intro,[status(thm)],[34])).
% 0.63/0.69 tff(36,plain,
% 0.63/0.69 (^[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))))))),
% 0.63/0.69 inference(bind,[status(th)],[])).
% 0.63/0.69 tff(37,plain,
% 0.63/0.69 (![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)))))),
% 0.63/0.69 inference(quant_intro,[status(thm)],[36])).
% 0.63/0.69 tff(38,plain,
% 0.63/0.69 (![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)))),
% 0.63/0.69 inference(rewrite,[status(thm)],[])).
% 0.63/0.69 tff(39,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')).
% 0.63/0.69 tff(40,plain,
% 0.63/0.69 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.63/0.69 tff(41,plain,(
% 0.63/0.69 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.63/0.69 inference(skolemize,[status(sab)],[40])).
% 0.63/0.69 tff(42,plain,
% 0.63/0.69 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.63/0.69 tff(43,plain,
% 0.63/0.69 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.63/0.69 tff(44,plain,
% 0.63/0.69 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(intersection(A!5, difference(E!3, B!4)), empty_set) <=> (~((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | (~subset(empty_set, intersection(A!5, difference(E!3, B!4)))))))),
% 0.63/0.69 inference(quant_inst,[status(thm)],[])).
% 0.63/0.69 tff(45,plain,
% 0.63/0.69 (equal_set(intersection(A!5, difference(E!3, B!4)), empty_set) <=> (~((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | (~subset(empty_set, intersection(A!5, difference(E!3, B!4))))))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.63/0.69 tff(46,plain,
% 0.63/0.69 ((~(equal_set(intersection(A!5, difference(E!3, B!4)), empty_set) <=> (~((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | (~subset(empty_set, intersection(A!5, difference(E!3, B!4)))))))) | equal_set(intersection(A!5, difference(E!3, B!4)), empty_set) | ((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | (~subset(empty_set, intersection(A!5, difference(E!3, B!4)))))),
% 0.63/0.69 inference(tautology,[status(thm)],[])).
% 0.63/0.69 tff(47,plain,
% 0.63/0.69 (equal_set(intersection(A!5, difference(E!3, B!4)), empty_set) | ((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | (~subset(empty_set, intersection(A!5, difference(E!3, B!4)))))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.63/0.69 tff(48,plain,
% 0.63/0.69 ((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | (~subset(empty_set, intersection(A!5, difference(E!3, B!4))))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[47, 33])).
% 0.63/0.69 tff(49,assumption,((~((~subset(empty_set, intersection(A!5, difference(E!3, B!4)))) | ![X: $i] : ((~member(X, empty_set)) | member(X, intersection(A!5, difference(E!3, B!4)))))) | (~(subset(empty_set, intersection(A!5, difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), empty_set)) | member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), intersection(A!5, difference(E!3, B!4)))))))), introduced(assumption)).
% 0.63/0.69 tff(50,plain,
% 0.63/0.69 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(empty_set, intersection(A!5, difference(E!3, B!4)))) | ![X: $i] : ((~member(X, empty_set)) | member(X, intersection(A!5, difference(E!3, B!4)))))) | (~(subset(empty_set, intersection(A!5, difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), empty_set)) | member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), intersection(A!5, difference(E!3, B!4)))))))))),
% 0.63/0.70 inference(quant_inst,[status(thm)],[])).
% 0.63/0.70 tff(51,plain,
% 0.63/0.70 ($false),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[50, 28, 49])).
% 0.63/0.70 tff(52,plain,(~((~((~subset(empty_set, intersection(A!5, difference(E!3, B!4)))) | ![X: $i] : ((~member(X, empty_set)) | member(X, intersection(A!5, difference(E!3, B!4)))))) | (~(subset(empty_set, intersection(A!5, difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), empty_set)) | member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), intersection(A!5, difference(E!3, B!4))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.70 tff(53,plain,
% 0.63/0.70 (((~((~subset(empty_set, intersection(A!5, difference(E!3, B!4)))) | ![X: $i] : ((~member(X, empty_set)) | member(X, intersection(A!5, difference(E!3, B!4)))))) | (~(subset(empty_set, intersection(A!5, difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), empty_set)) | member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), intersection(A!5, difference(E!3, B!4)))))))) | (subset(empty_set, intersection(A!5, difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), empty_set)) | member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), intersection(A!5, difference(E!3, B!4))))))),
% 0.63/0.70 inference(tautology,[status(thm)],[])).
% 0.63/0.70 tff(54,plain,
% 0.63/0.70 (subset(empty_set, intersection(A!5, difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), empty_set)) | member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), intersection(A!5, difference(E!3, B!4)))))),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.63/0.70 tff(55,assumption,(member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), empty_set)), introduced(assumption)).
% 0.63/0.70 tff(56,plain,
% 0.63/0.70 (^[X: $i] : refl((~member(X, empty_set)) <=> (~member(X, empty_set)))),
% 0.63/0.70 inference(bind,[status(th)],[])).
% 0.63/0.70 tff(57,plain,
% 0.63/0.70 (![X: $i] : (~member(X, empty_set)) <=> ![X: $i] : (~member(X, empty_set))),
% 0.63/0.70 inference(quant_intro,[status(thm)],[56])).
% 0.63/0.70 tff(58,plain,
% 0.63/0.70 (![X: $i] : (~member(X, empty_set)) <=> ![X: $i] : (~member(X, empty_set))),
% 0.63/0.70 inference(rewrite,[status(thm)],[])).
% 0.63/0.70 tff(59,axiom,(![X: $i] : (~member(X, empty_set))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','empty_set')).
% 0.63/0.70 tff(60,plain,
% 0.63/0.70 (![X: $i] : (~member(X, empty_set))),
% 0.63/0.70 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.63/0.70 tff(61,plain,(
% 0.63/0.70 ![X: $i] : (~member(X, empty_set))),
% 0.63/0.70 inference(skolemize,[status(sab)],[60])).
% 0.63/0.70 tff(62,plain,
% 0.63/0.70 (![X: $i] : (~member(X, empty_set))),
% 0.63/0.70 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.63/0.70 tff(63,plain,
% 0.63/0.70 ((~![X: $i] : (~member(X, empty_set))) | (~member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), empty_set))),
% 0.63/0.70 inference(quant_inst,[status(thm)],[])).
% 0.63/0.70 tff(64,plain,
% 0.63/0.70 ($false),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[63, 62, 55])).
% 0.63/0.70 tff(65,plain,(~member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), empty_set)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.70 tff(66,plain,
% 0.63/0.70 (((~member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), empty_set)) | member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), empty_set)),
% 0.63/0.70 inference(tautology,[status(thm)],[])).
% 0.63/0.70 tff(67,plain,
% 0.63/0.70 ((~member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), empty_set)) | member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), intersection(A!5, difference(E!3, B!4)))),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.63/0.70 tff(68,plain,
% 0.63/0.70 ((~(subset(empty_set, intersection(A!5, difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), empty_set)) | member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), intersection(A!5, difference(E!3, B!4))))))) | subset(empty_set, intersection(A!5, difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), empty_set)) | member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), intersection(A!5, difference(E!3, B!4)))))),
% 0.63/0.70 inference(tautology,[status(thm)],[])).
% 0.63/0.70 tff(69,plain,
% 0.63/0.70 ((~(subset(empty_set, intersection(A!5, difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), empty_set)) | member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), intersection(A!5, difference(E!3, B!4))))))) | subset(empty_set, intersection(A!5, difference(E!3, B!4)))),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.63/0.70 tff(70,plain,
% 0.63/0.70 (subset(empty_set, intersection(A!5, difference(E!3, B!4)))),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[69, 54])).
% 0.63/0.70 tff(71,plain,
% 0.63/0.70 ((~((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | (~subset(empty_set, intersection(A!5, difference(E!3, B!4)))))) | (~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | (~subset(empty_set, intersection(A!5, difference(E!3, B!4))))),
% 0.63/0.70 inference(tautology,[status(thm)],[])).
% 0.63/0.70 tff(72,plain,
% 0.63/0.70 ((~((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | (~subset(empty_set, intersection(A!5, difference(E!3, B!4)))))) | (~subset(intersection(A!5, difference(E!3, B!4)), empty_set))),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.63/0.70 tff(73,plain,
% 0.63/0.70 (~subset(intersection(A!5, difference(E!3, B!4)), empty_set)),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[72, 48])).
% 0.63/0.70 tff(74,plain,
% 0.63/0.70 ((~(subset(intersection(A!5, difference(E!3, B!4)), empty_set) | (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), empty_set))))) | subset(intersection(A!5, difference(E!3, B!4)), empty_set) | (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), empty_set)))),
% 0.63/0.70 inference(tautology,[status(thm)],[])).
% 0.63/0.70 tff(75,plain,
% 0.63/0.70 ((~(subset(intersection(A!5, difference(E!3, B!4)), empty_set) | (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), empty_set))))) | (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), empty_set)))),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.63/0.70 tff(76,plain,
% 0.63/0.70 (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), empty_set))),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[75, 32])).
% 0.63/0.70 tff(77,plain,
% 0.63/0.70 (((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), empty_set)) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))),
% 0.63/0.70 inference(tautology,[status(thm)],[])).
% 0.63/0.70 tff(78,plain,
% 0.63/0.70 (member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.63/0.70 tff(79,plain,
% 0.63/0.70 ((~(member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4))) <=> (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))))))) | (~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))))),
% 0.63/0.70 inference(tautology,[status(thm)],[])).
% 0.63/0.70 tff(80,plain,
% 0.63/0.70 ((~(member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4))) <=> (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))))))) | (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))))),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.63/0.70 tff(81,plain,
% 0.63/0.70 (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))))),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[80, 12])).
% 0.63/0.70 tff(82,plain,
% 0.63/0.70 (((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), A!5)),
% 0.63/0.70 inference(tautology,[status(thm)],[])).
% 0.63/0.70 tff(83,plain,
% 0.63/0.70 (member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), A!5)),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.63/0.70 tff(84,plain,
% 0.63/0.70 ((~(subset(A!5, B!4) <=> equal_set(intersection(A!5, difference(E!3, B!4)), empty_set))) <=> ((~subset(A!5, B!4)) <=> equal_set(intersection(A!5, difference(E!3, B!4)), empty_set))),
% 0.63/0.70 inference(rewrite,[status(thm)],[])).
% 0.63/0.70 tff(85,plain,
% 0.63/0.70 ((~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(intersection(A, difference(E, B)), empty_set)))) <=> (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(intersection(A, difference(E, B)), empty_set))))),
% 0.63/0.70 inference(rewrite,[status(thm)],[])).
% 0.63/0.70 tff(86,plain,
% 0.63/0.70 ((~![A: $i, B: $i, E: $i] : ((subset(A, E) & subset(B, E)) => (subset(A, B) <=> equal_set(intersection(A, difference(E, B)), empty_set)))) <=> (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(intersection(A, difference(E, B)), empty_set))))),
% 0.63/0.70 inference(rewrite,[status(thm)],[])).
% 0.63/0.70 tff(87,axiom,(~![A: $i, B: $i, E: $i] : ((subset(A, E) & subset(B, E)) => (subset(A, B) <=> equal_set(intersection(A, difference(E, B)), empty_set)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thI31')).
% 0.63/0.70 tff(88,plain,
% 0.63/0.70 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(intersection(A, difference(E, B)), empty_set)))),
% 0.63/0.70 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.63/0.70 tff(89,plain,
% 0.63/0.70 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(intersection(A, difference(E, B)), empty_set)))),
% 0.63/0.70 inference(modus_ponens,[status(thm)],[88, 85])).
% 0.63/0.70 tff(90,plain,
% 0.63/0.70 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(intersection(A, difference(E, B)), empty_set)))),
% 0.63/0.70 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.63/0.70 tff(91,plain,
% 0.63/0.70 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(intersection(A, difference(E, B)), empty_set)))),
% 0.63/0.70 inference(modus_ponens,[status(thm)],[90, 85])).
% 0.63/0.70 tff(92,plain,
% 0.63/0.70 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(intersection(A, difference(E, B)), empty_set)))),
% 0.63/0.70 inference(modus_ponens,[status(thm)],[91, 85])).
% 0.63/0.70 tff(93,plain,
% 0.63/0.70 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(intersection(A, difference(E, B)), empty_set)))),
% 0.63/0.70 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.63/0.70 tff(94,plain,
% 0.63/0.70 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(intersection(A, difference(E, B)), empty_set)))),
% 0.63/0.70 inference(modus_ponens,[status(thm)],[93, 85])).
% 0.63/0.70 tff(95,plain,(
% 0.63/0.70 ~((~(subset(A!5, E!3) & subset(B!4, E!3))) | (subset(A!5, B!4) <=> equal_set(intersection(A!5, difference(E!3, B!4)), empty_set)))),
% 0.63/0.70 inference(skolemize,[status(sab)],[94])).
% 0.63/0.70 tff(96,plain,
% 0.63/0.70 (~(subset(A!5, B!4) <=> equal_set(intersection(A!5, difference(E!3, B!4)), empty_set))),
% 0.63/0.70 inference(or_elim,[status(thm)],[95])).
% 0.63/0.70 tff(97,plain,
% 0.63/0.70 ((~subset(A!5, B!4)) <=> equal_set(intersection(A!5, difference(E!3, B!4)), empty_set)),
% 0.63/0.70 inference(modus_ponens,[status(thm)],[96, 84])).
% 0.63/0.70 tff(98,plain,
% 0.63/0.70 (subset(A!5, B!4) | equal_set(intersection(A!5, difference(E!3, B!4)), empty_set) | (~((~subset(A!5, B!4)) <=> equal_set(intersection(A!5, difference(E!3, B!4)), empty_set)))),
% 0.63/0.70 inference(tautology,[status(thm)],[])).
% 0.63/0.70 tff(99,plain,
% 0.63/0.70 (subset(A!5, B!4) | equal_set(intersection(A!5, difference(E!3, B!4)), empty_set)),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.63/0.70 tff(100,plain,
% 0.63/0.70 (subset(A!5, B!4)),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[99, 33])).
% 0.63/0.70 tff(101,plain,
% 0.63/0.70 ((~![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)))))))),
% 0.63/0.70 inference(quant_inst,[status(thm)],[])).
% 0.63/0.70 tff(102,plain,
% 0.63/0.70 (~((~((~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))))))),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[101, 28])).
% 0.63/0.70 tff(103,plain,
% 0.63/0.70 (((~((~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)))),
% 0.63/0.70 inference(tautology,[status(thm)],[])).
% 0.63/0.70 tff(104,plain,
% 0.63/0.70 ((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.63/0.70 tff(105,plain,
% 0.63/0.70 ((~((~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))),
% 0.63/0.70 inference(tautology,[status(thm)],[])).
% 0.63/0.70 tff(106,plain,
% 0.63/0.70 ((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.63/0.70 tff(107,plain,
% 0.63/0.70 (![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[106, 100])).
% 0.63/0.70 tff(108,plain,
% 0.63/0.70 (((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | ((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), A!5)) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), B!4))) <=> ((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | (~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), A!5)) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), B!4))),
% 0.63/0.70 inference(rewrite,[status(thm)],[])).
% 0.63/0.70 tff(109,plain,
% 0.63/0.70 ((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | ((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), A!5)) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), B!4))),
% 0.63/0.70 inference(quant_inst,[status(thm)],[])).
% 0.63/0.70 tff(110,plain,
% 0.63/0.70 ((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | (~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), A!5)) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), B!4)),
% 0.63/0.70 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.63/0.70 tff(111,plain,
% 0.63/0.70 (member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), B!4)),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[110, 107, 83])).
% 0.63/0.70 tff(112,plain,
% 0.63/0.70 (^[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)))))),
% 0.63/0.70 inference(bind,[status(th)],[])).
% 0.63/0.70 tff(113,plain,
% 0.63/0.70 (![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))))),
% 0.63/0.70 inference(quant_intro,[status(thm)],[112])).
% 0.63/0.70 tff(114,plain,
% 0.63/0.70 (^[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)))))),
% 0.63/0.70 inference(bind,[status(th)],[])).
% 0.63/0.70 tff(115,plain,
% 0.63/0.70 (![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))))),
% 0.63/0.70 inference(quant_intro,[status(thm)],[114])).
% 0.63/0.70 tff(116,plain,
% 0.63/0.70 (![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))))),
% 0.63/0.70 inference(rewrite,[status(thm)],[])).
% 0.63/0.70 tff(117,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')).
% 0.63/0.70 tff(118,plain,
% 0.63/0.70 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.63/0.70 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.63/0.70 tff(119,plain,(
% 0.63/0.70 ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.63/0.70 inference(skolemize,[status(sab)],[118])).
% 0.63/0.70 tff(120,plain,
% 0.63/0.70 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))),
% 0.63/0.70 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.63/0.70 tff(121,plain,
% 0.63/0.70 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))),
% 0.63/0.70 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.63/0.70 tff(122,plain,
% 0.63/0.70 ((~![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))) | (member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)) <=> (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), B!4))))),
% 0.63/0.70 inference(quant_inst,[status(thm)],[])).
% 0.63/0.70 tff(123,plain,
% 0.63/0.70 (member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)) <=> (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), B!4)))),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.63/0.70 tff(124,plain,
% 0.63/0.70 (((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))),
% 0.63/0.70 inference(tautology,[status(thm)],[])).
% 0.63/0.70 tff(125,plain,
% 0.63/0.70 (member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[124, 81])).
% 0.63/0.70 tff(126,plain,
% 0.63/0.70 ((~(member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)) <=> (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), B!4))))) | (~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), B!4)))),
% 0.63/0.70 inference(tautology,[status(thm)],[])).
% 0.63/0.70 tff(127,plain,
% 0.63/0.70 ((~(member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)) <=> (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), B!4))))) | (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), B!4)))),
% 0.63/0.71 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.63/0.71 tff(128,plain,
% 0.63/0.71 (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), B!4))),
% 0.63/0.71 inference(unit_resolution,[status(thm)],[127, 123])).
% 0.63/0.71 tff(129,plain,
% 0.63/0.71 (((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), B!4)) | (~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), B!4))),
% 0.63/0.71 inference(tautology,[status(thm)],[])).
% 0.63/0.71 tff(130,plain,
% 0.63/0.71 ($false),
% 0.63/0.71 inference(unit_resolution,[status(thm)],[129, 128, 111])).
% 0.63/0.71 tff(131,plain,(equal_set(intersection(A!5, difference(E!3, B!4)), empty_set)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.71 tff(132,plain,
% 0.63/0.71 ((~subset(A!5, B!4)) | (~equal_set(intersection(A!5, difference(E!3, B!4)), empty_set)) | (~((~subset(A!5, B!4)) <=> equal_set(intersection(A!5, difference(E!3, B!4)), empty_set)))),
% 0.63/0.71 inference(tautology,[status(thm)],[])).
% 0.63/0.71 tff(133,plain,
% 0.63/0.71 ((~subset(A!5, B!4)) | (~equal_set(intersection(A!5, difference(E!3, B!4)), empty_set))),
% 0.63/0.71 inference(unit_resolution,[status(thm)],[132, 97])).
% 0.63/0.71 tff(134,plain,
% 0.63/0.71 (~subset(A!5, B!4)),
% 0.63/0.71 inference(unit_resolution,[status(thm)],[133, 131])).
% 0.63/0.71 tff(135,plain,
% 0.63/0.71 (((~((~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))))),
% 0.63/0.71 inference(tautology,[status(thm)],[])).
% 0.63/0.71 tff(136,plain,
% 0.63/0.71 (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)))),
% 0.63/0.71 inference(unit_resolution,[status(thm)],[135, 102])).
% 0.63/0.71 tff(137,plain,
% 0.63/0.71 ((~(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)))),
% 0.63/0.71 inference(tautology,[status(thm)],[])).
% 0.63/0.71 tff(138,plain,
% 0.63/0.71 (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)))),
% 0.63/0.71 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.63/0.71 tff(139,plain,
% 0.63/0.71 (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4))),
% 0.63/0.71 inference(unit_resolution,[status(thm)],[138, 134])).
% 0.63/0.71 tff(140,plain,
% 0.63/0.71 (((~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)),
% 0.63/0.71 inference(tautology,[status(thm)],[])).
% 0.63/0.71 tff(141,plain,
% 0.63/0.71 (member(tptp_fun_X_0(B!4, A!5), A!5)),
% 0.63/0.71 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.63/0.71 tff(142,plain,
% 0.63/0.71 ((~![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)))))))),
% 0.63/0.71 inference(quant_inst,[status(thm)],[])).
% 0.63/0.71 tff(143,plain,
% 0.63/0.71 (~((~((~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))))))),
% 0.63/0.71 inference(unit_resolution,[status(thm)],[142, 28])).
% 0.63/0.71 tff(144,plain,
% 0.63/0.71 (((~((~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)))),
% 0.63/0.71 inference(tautology,[status(thm)],[])).
% 0.63/0.71 tff(145,plain,
% 0.63/0.71 ((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3))),
% 0.63/0.71 inference(unit_resolution,[status(thm)],[144, 143])).
% 0.63/0.71 tff(146,plain,
% 0.63/0.71 (subset(A!5, E!3) & subset(B!4, E!3)),
% 0.63/0.71 inference(or_elim,[status(thm)],[95])).
% 0.63/0.71 tff(147,plain,
% 0.63/0.71 (subset(A!5, E!3)),
% 0.63/0.71 inference(and_elim,[status(thm)],[146])).
% 0.63/0.71 tff(148,plain,
% 0.63/0.71 ((~((~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))),
% 0.63/0.71 inference(tautology,[status(thm)],[])).
% 0.63/0.71 tff(149,plain,
% 0.63/0.71 ((~((~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))),
% 0.63/0.71 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.63/0.71 tff(150,plain,
% 0.63/0.71 (![X: $i] : ((~member(X, A!5)) | member(X, E!3))),
% 0.63/0.71 inference(unit_resolution,[status(thm)],[149, 145])).
% 0.63/0.71 tff(151,plain,
% 0.63/0.71 (((~![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))),
% 0.63/0.71 inference(rewrite,[status(thm)],[])).
% 0.63/0.71 tff(152,plain,
% 0.63/0.71 ((~![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))),
% 0.63/0.71 inference(quant_inst,[status(thm)],[])).
% 0.63/0.71 tff(153,plain,
% 0.63/0.71 ((~![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)),
% 0.63/0.71 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.63/0.71 tff(154,plain,
% 0.63/0.71 (member(tptp_fun_X_0(B!4, A!5), E!3)),
% 0.63/0.71 inference(unit_resolution,[status(thm)],[153, 150, 141])).
% 0.63/0.71 tff(155,plain,
% 0.63/0.71 (((~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))),
% 0.63/0.71 inference(tautology,[status(thm)],[])).
% 0.63/0.71 tff(156,plain,
% 0.63/0.71 (~member(tptp_fun_X_0(B!4, A!5), B!4)),
% 0.63/0.71 inference(unit_resolution,[status(thm)],[155, 139])).
% 0.63/0.71 tff(157,plain,
% 0.63/0.71 ((~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4))) | (~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4)),
% 0.63/0.71 inference(tautology,[status(thm)],[])).
% 0.63/0.71 tff(158,plain,
% 0.63/0.71 (~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4))),
% 0.63/0.71 inference(unit_resolution,[status(thm)],[157, 156, 154])).
% 0.63/0.71 tff(159,plain,
% 0.63/0.71 ((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4))) <=> (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))))))),
% 0.63/0.71 inference(quant_inst,[status(thm)],[])).
% 0.63/0.71 tff(160,plain,
% 0.63/0.71 (member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4))) <=> (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)))))),
% 0.63/0.71 inference(unit_resolution,[status(thm)],[159, 10])).
% 0.63/0.71 tff(161,assumption,(member(tptp_fun_X_0(B!4, A!5), empty_set)), introduced(assumption)).
% 0.63/0.71 tff(162,plain,
% 0.63/0.71 ((~![X: $i] : (~member(X, empty_set))) | (~member(tptp_fun_X_0(B!4, A!5), empty_set))),
% 0.63/0.71 inference(quant_inst,[status(thm)],[])).
% 0.63/0.71 tff(163,plain,
% 0.63/0.71 ($false),
% 0.63/0.71 inference(unit_resolution,[status(thm)],[162, 62, 161])).
% 0.63/0.71 tff(164,plain,(~member(tptp_fun_X_0(B!4, A!5), empty_set)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.71 tff(165,plain,
% 0.63/0.71 (((~((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, empty_set)))) | (~(subset(intersection(A!5, difference(E!3, B!4)), empty_set) | (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), empty_set)))))) | ((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, empty_set)))),
% 0.63/0.71 inference(tautology,[status(thm)],[])).
% 0.63/0.71 tff(166,plain,
% 0.63/0.71 ((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, empty_set))),
% 0.63/0.71 inference(unit_resolution,[status(thm)],[165, 30])).
% 0.63/0.71 tff(167,plain,
% 0.63/0.71 ((~(equal_set(intersection(A!5, difference(E!3, B!4)), empty_set) <=> (~((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | (~subset(empty_set, intersection(A!5, difference(E!3, B!4)))))))) | (~equal_set(intersection(A!5, difference(E!3, B!4)), empty_set)) | (~((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | (~subset(empty_set, intersection(A!5, difference(E!3, B!4))))))),
% 0.63/0.71 inference(tautology,[status(thm)],[])).
% 0.63/0.71 tff(168,plain,
% 0.63/0.71 ((~equal_set(intersection(A!5, difference(E!3, B!4)), empty_set)) | (~((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | (~subset(empty_set, intersection(A!5, difference(E!3, B!4))))))),
% 0.63/0.71 inference(unit_resolution,[status(thm)],[167, 45])).
% 0.63/0.71 tff(169,plain,
% 0.63/0.71 (~((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | (~subset(empty_set, intersection(A!5, difference(E!3, B!4)))))),
% 0.63/0.71 inference(unit_resolution,[status(thm)],[168, 131])).
% 0.63/0.71 tff(170,plain,
% 0.63/0.71 (((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | (~subset(empty_set, intersection(A!5, difference(E!3, B!4))))) | subset(intersection(A!5, difference(E!3, B!4)), empty_set)),
% 0.63/0.71 inference(tautology,[status(thm)],[])).
% 0.63/0.71 tff(171,plain,
% 0.63/0.71 (subset(intersection(A!5, difference(E!3, B!4)), empty_set)),
% 0.63/0.71 inference(unit_resolution,[status(thm)],[170, 169])).
% 0.63/0.71 tff(172,plain,
% 0.63/0.71 ((~((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, empty_set)))) | (~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, empty_set))),
% 0.63/0.71 inference(tautology,[status(thm)],[])).
% 0.63/0.71 tff(173,plain,
% 0.63/0.71 ((~((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, empty_set)))) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, empty_set))),
% 0.63/0.71 inference(unit_resolution,[status(thm)],[172, 171])).
% 0.63/0.71 tff(174,plain,
% 0.63/0.71 (![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, empty_set))),
% 0.63/0.71 inference(unit_resolution,[status(thm)],[173, 166])).
% 0.63/0.71 tff(175,plain,
% 0.63/0.71 (((~![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, empty_set))) | ((~member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, A!5), empty_set))) <=> ((~![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, empty_set))) | (~member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, A!5), empty_set))),
% 0.63/0.71 inference(rewrite,[status(thm)],[])).
% 0.63/0.71 tff(176,plain,
% 0.63/0.71 ((~![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, empty_set))) | ((~member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, A!5), empty_set))),
% 0.63/0.71 inference(quant_inst,[status(thm)],[])).
% 0.63/0.71 tff(177,plain,
% 0.63/0.71 ((~![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, empty_set))) | (~member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, A!5), empty_set)),
% 0.63/0.71 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.63/0.71 tff(178,plain,
% 0.63/0.71 (~member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4)))),
% 0.63/0.71 inference(unit_resolution,[status(thm)],[177, 174, 164])).
% 0.63/0.71 tff(179,plain,
% 0.63/0.71 ((~(member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4))) <=> (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))))))) | member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4))) | ((~member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))))),
% 0.75/0.71 inference(tautology,[status(thm)],[])).
% 0.75/0.71 tff(180,plain,
% 0.75/0.71 ((~(member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4))) <=> (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))))))) | ((~member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))))),
% 0.75/0.71 inference(unit_resolution,[status(thm)],[179, 178])).
% 0.75/0.71 tff(181,plain,
% 0.75/0.71 ((~member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)))),
% 0.75/0.71 inference(unit_resolution,[status(thm)],[180, 160])).
% 0.75/0.71 tff(182,plain,
% 0.75/0.71 ((~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))))) | (~member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)))),
% 0.75/0.71 inference(tautology,[status(thm)],[])).
% 0.75/0.71 tff(183,plain,
% 0.75/0.71 ((~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))))) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)))),
% 0.75/0.71 inference(unit_resolution,[status(thm)],[182, 141])).
% 0.75/0.71 tff(184,plain,
% 0.75/0.71 (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))),
% 0.75/0.71 inference(unit_resolution,[status(thm)],[183, 181])).
% 0.75/0.71 tff(185,plain,
% 0.75/0.71 ((~(member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)) <=> (~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4))))) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)) | ((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4))),
% 0.75/0.71 inference(tautology,[status(thm)],[])).
% 0.75/0.71 tff(186,plain,
% 0.75/0.71 (~(member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)) <=> (~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4))))),
% 0.75/0.71 inference(unit_resolution,[status(thm)],[185, 184, 158])).
% 0.75/0.71 tff(187,plain,
% 0.75/0.71 ((~![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))) | (member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)) <=> (~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4))))),
% 0.75/0.71 inference(quant_inst,[status(thm)],[])).
% 0.75/0.71 tff(188,plain,
% 0.75/0.71 ($false),
% 0.75/0.71 inference(unit_resolution,[status(thm)],[187, 121, 186])).
% 0.75/0.71 % SZS output end Proof
%------------------------------------------------------------------------------