TSTP Solution File: SET700+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET700+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 05:07:40 EDT 2022
% Result : Theorem 0.22s 0.62s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.35 % Problem : SET700+4 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.35 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.57 % Computer : n003.cluster.edu
% 0.14/0.57 % Model : x86_64 x86_64
% 0.14/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.57 % Memory : 8042.1875MB
% 0.14/0.57 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.57 % CPULimit : 300
% 0.14/0.57 % WCLimit : 300
% 0.14/0.57 % DateTime : Sat Sep 3 07:24:55 EDT 2022
% 0.14/0.57 % CPUTime :
% 0.14/0.57 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.57 Usage: tptp [options] [-file:]file
% 0.14/0.57 -h, -? prints this message.
% 0.14/0.57 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.57 -m, -model generate model.
% 0.14/0.57 -p, -proof generate proof.
% 0.14/0.57 -c, -core generate unsat core of named formulas.
% 0.14/0.57 -st, -statistics display statistics.
% 0.14/0.57 -t:timeout set timeout (in second).
% 0.14/0.57 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.57 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.57 -<param>:<value> configuration parameter and value.
% 0.14/0.57 -o:<output-file> file to place output in.
% 0.22/0.62 % SZS status Theorem
% 0.22/0.62 % SZS output start Proof
% 0.22/0.62 tff(member_type, type, (
% 0.22/0.62 member: ( $i * $i ) > $o)).
% 0.22/0.62 tff(tptp_fun_B_4_type, type, (
% 0.22/0.62 tptp_fun_B_4: $i)).
% 0.22/0.62 tff(tptp_fun_X_0_type, type, (
% 0.22/0.62 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.22/0.62 tff(tptp_fun_A_5_type, type, (
% 0.22/0.62 tptp_fun_A_5: $i)).
% 0.22/0.62 tff(tptp_fun_E_3_type, type, (
% 0.22/0.62 tptp_fun_E_3: $i)).
% 0.22/0.62 tff(difference_type, type, (
% 0.22/0.62 difference: ( $i * $i ) > $i)).
% 0.22/0.62 tff(subset_type, type, (
% 0.22/0.62 subset: ( $i * $i ) > $o)).
% 0.22/0.62 tff(intersection_type, type, (
% 0.22/0.62 intersection: ( $i * $i ) > $i)).
% 0.22/0.62 tff(1,assumption,(~(member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4))) <=> (~((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))))))), introduced(assumption)).
% 0.22/0.62 tff(2,plain,
% 0.22/0.62 (^[X: $i, A: $i, B: $i] : refl((member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))) <=> (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))))),
% 0.22/0.62 inference(bind,[status(th)],[])).
% 0.22/0.62 tff(3,plain,
% 0.22/0.62 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))) <=> ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.22/0.62 inference(quant_intro,[status(thm)],[2])).
% 0.22/0.62 tff(4,plain,
% 0.22/0.62 (^[X: $i, A: $i, B: $i] : rewrite((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))))),
% 0.22/0.62 inference(bind,[status(th)],[])).
% 0.22/0.62 tff(5,plain,
% 0.22/0.62 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.22/0.62 inference(quant_intro,[status(thm)],[4])).
% 0.22/0.62 tff(6,plain,
% 0.22/0.62 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.22/0.62 inference(rewrite,[status(thm)],[])).
% 0.22/0.62 tff(7,axiom,(![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','intersection')).
% 0.22/0.62 tff(8,plain,
% 0.22/0.62 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.22/0.62 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.22/0.62 tff(9,plain,(
% 0.22/0.62 ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.22/0.62 inference(skolemize,[status(sab)],[8])).
% 0.22/0.62 tff(10,plain,
% 0.22/0.62 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.22/0.62 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.22/0.62 tff(11,plain,
% 0.22/0.62 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.22/0.62 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.22/0.62 tff(12,plain,
% 0.22/0.62 ((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4))) <=> (~((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))))))),
% 0.22/0.62 inference(quant_inst,[status(thm)],[])).
% 0.22/0.62 tff(13,plain,
% 0.22/0.62 ($false),
% 0.22/0.62 inference(unit_resolution,[status(thm)],[12, 11, 1])).
% 0.22/0.62 tff(14,plain,(member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4))) <=> (~((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.62 tff(15,assumption,(~subset(intersection(A!5, difference(E!3, B!4)), B!4)), introduced(assumption)).
% 0.22/0.62 tff(16,plain,
% 0.22/0.62 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.22/0.62 inference(bind,[status(th)],[])).
% 0.22/0.62 tff(17,plain,
% 0.22/0.62 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.22/0.62 inference(quant_intro,[status(thm)],[16])).
% 0.22/0.62 tff(18,plain,
% 0.22/0.62 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.22/0.62 inference(bind,[status(th)],[])).
% 0.22/0.62 tff(19,plain,
% 0.22/0.62 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.22/0.62 inference(quant_intro,[status(thm)],[18])).
% 0.22/0.62 tff(20,plain,
% 0.22/0.62 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.22/0.62 inference(transitivity,[status(thm)],[19, 17])).
% 0.22/0.62 tff(21,plain,
% 0.22/0.62 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.22/0.62 inference(bind,[status(th)],[])).
% 0.22/0.62 tff(22,plain,
% 0.22/0.62 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.22/0.62 inference(quant_intro,[status(thm)],[21])).
% 0.22/0.62 tff(23,plain,
% 0.22/0.62 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.22/0.62 inference(rewrite,[status(thm)],[])).
% 0.22/0.62 tff(24,plain,
% 0.22/0.62 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.22/0.63 inference(bind,[status(th)],[])).
% 0.22/0.63 tff(25,plain,
% 0.22/0.63 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.22/0.63 inference(quant_intro,[status(thm)],[24])).
% 0.22/0.63 tff(26,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','subset')).
% 0.22/0.63 tff(27,plain,
% 0.22/0.63 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.22/0.63 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.22/0.63 tff(28,plain,
% 0.22/0.63 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.22/0.63 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.22/0.63 tff(29,plain,(
% 0.22/0.63 ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.22/0.63 inference(skolemize,[status(sab)],[28])).
% 0.22/0.63 tff(30,plain,
% 0.22/0.63 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.22/0.63 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.22/0.63 tff(31,plain,
% 0.22/0.63 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.22/0.63 inference(modus_ponens,[status(thm)],[30, 20])).
% 0.22/0.63 tff(32,plain,
% 0.22/0.63 ((~![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)), B!4)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, B!4)))) | (~(subset(intersection(A!5, difference(E!3, B!4)), B!4) | (~((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4)))))))),
% 0.22/0.63 inference(quant_inst,[status(thm)],[])).
% 0.22/0.63 tff(33,plain,
% 0.22/0.63 (~((~((~subset(intersection(A!5, difference(E!3, B!4)), B!4)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, B!4)))) | (~(subset(intersection(A!5, difference(E!3, B!4)), B!4) | (~((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4))))))),
% 0.22/0.63 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.22/0.63 tff(34,plain,
% 0.22/0.63 (((~((~subset(intersection(A!5, difference(E!3, B!4)), B!4)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, B!4)))) | (~(subset(intersection(A!5, difference(E!3, B!4)), B!4) | (~((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4)))))) | (subset(intersection(A!5, difference(E!3, B!4)), B!4) | (~((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4))))),
% 0.22/0.63 inference(tautology,[status(thm)],[])).
% 0.22/0.63 tff(35,plain,
% 0.22/0.63 (subset(intersection(A!5, difference(E!3, B!4)), B!4) | (~((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4)))),
% 0.22/0.63 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.22/0.63 tff(36,plain,
% 0.22/0.63 ((~(subset(intersection(A!5, difference(E!3, B!4)), B!4) | (~((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4))))) | subset(intersection(A!5, difference(E!3, B!4)), B!4) | (~((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4)))),
% 0.22/0.63 inference(tautology,[status(thm)],[])).
% 0.22/0.63 tff(37,plain,
% 0.22/0.63 (subset(intersection(A!5, difference(E!3, B!4)), B!4) | (~((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4)))),
% 0.22/0.63 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.22/0.63 tff(38,plain,
% 0.22/0.63 (~((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4))),
% 0.22/0.63 inference(unit_resolution,[status(thm)],[37, 15])).
% 0.22/0.63 tff(39,plain,
% 0.22/0.63 (((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4)) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))),
% 0.22/0.63 inference(tautology,[status(thm)],[])).
% 0.22/0.63 tff(40,plain,
% 0.22/0.63 (member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))),
% 0.22/0.63 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.22/0.63 tff(41,plain,
% 0.22/0.63 ((~(member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4))) <=> (~((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))))))) | (~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | (~((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))))),
% 0.22/0.63 inference(tautology,[status(thm)],[])).
% 0.22/0.63 tff(42,plain,
% 0.22/0.63 (~((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))))),
% 0.22/0.63 inference(unit_resolution,[status(thm)],[41, 40, 14])).
% 0.22/0.63 tff(43,plain,
% 0.22/0.63 (((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), A!5)),
% 0.22/0.63 inference(tautology,[status(thm)],[])).
% 0.22/0.63 tff(44,plain,
% 0.22/0.63 (member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), A!5)),
% 0.22/0.63 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.22/0.63 tff(45,plain,
% 0.22/0.63 (((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4)) | (~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4))),
% 0.22/0.63 inference(tautology,[status(thm)],[])).
% 0.22/0.63 tff(46,plain,
% 0.22/0.63 (~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4)),
% 0.22/0.63 inference(unit_resolution,[status(thm)],[45, 38])).
% 0.22/0.63 tff(47,plain,
% 0.22/0.63 ((~(subset(A!5, B!4) <=> subset(intersection(A!5, difference(E!3, B!4)), B!4))) <=> ((~subset(A!5, B!4)) <=> subset(intersection(A!5, difference(E!3, B!4)), B!4))),
% 0.22/0.63 inference(rewrite,[status(thm)],[])).
% 0.22/0.63 tff(48,plain,
% 0.22/0.63 ((~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), B)))) <=> (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), B))))),
% 0.22/0.63 inference(rewrite,[status(thm)],[])).
% 0.22/0.63 tff(49,plain,
% 0.22/0.63 ((~![A: $i, B: $i, E: $i] : ((subset(A, E) & subset(B, E)) => (subset(A, B) <=> subset(intersection(A, difference(E, B)), B)))) <=> (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), B))))),
% 0.22/0.63 inference(rewrite,[status(thm)],[])).
% 0.22/0.63 tff(50,axiom,(~![A: $i, B: $i, E: $i] : ((subset(A, E) & subset(B, E)) => (subset(A, B) <=> subset(intersection(A, difference(E, B)), B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thI34')).
% 0.22/0.63 tff(51,plain,
% 0.22/0.63 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), B)))),
% 0.22/0.63 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.22/0.63 tff(52,plain,
% 0.22/0.63 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), B)))),
% 0.22/0.63 inference(modus_ponens,[status(thm)],[51, 48])).
% 0.22/0.63 tff(53,plain,
% 0.22/0.63 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), B)))),
% 0.22/0.63 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.22/0.63 tff(54,plain,
% 0.22/0.63 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), B)))),
% 0.22/0.63 inference(modus_ponens,[status(thm)],[53, 48])).
% 0.22/0.63 tff(55,plain,
% 0.22/0.63 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), B)))),
% 0.22/0.63 inference(modus_ponens,[status(thm)],[54, 48])).
% 0.22/0.63 tff(56,plain,
% 0.22/0.63 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), B)))),
% 0.22/0.63 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.22/0.63 tff(57,plain,
% 0.22/0.63 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), B)))),
% 0.22/0.63 inference(modus_ponens,[status(thm)],[56, 48])).
% 0.22/0.63 tff(58,plain,(
% 0.22/0.63 ~((~(subset(A!5, E!3) & subset(B!4, E!3))) | (subset(A!5, B!4) <=> subset(intersection(A!5, difference(E!3, B!4)), B!4)))),
% 0.22/0.63 inference(skolemize,[status(sab)],[57])).
% 0.22/0.63 tff(59,plain,
% 0.22/0.63 (~(subset(A!5, B!4) <=> subset(intersection(A!5, difference(E!3, B!4)), B!4))),
% 0.22/0.63 inference(or_elim,[status(thm)],[58])).
% 0.22/0.63 tff(60,plain,
% 0.22/0.63 ((~subset(A!5, B!4)) <=> subset(intersection(A!5, difference(E!3, B!4)), B!4)),
% 0.22/0.63 inference(modus_ponens,[status(thm)],[59, 47])).
% 0.22/0.63 tff(61,plain,
% 0.22/0.63 (subset(A!5, B!4) | subset(intersection(A!5, difference(E!3, B!4)), B!4) | (~((~subset(A!5, B!4)) <=> subset(intersection(A!5, difference(E!3, B!4)), B!4)))),
% 0.22/0.63 inference(tautology,[status(thm)],[])).
% 0.22/0.63 tff(62,plain,
% 0.22/0.63 (subset(A!5, B!4) | subset(intersection(A!5, difference(E!3, B!4)), B!4)),
% 0.22/0.63 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.22/0.63 tff(63,plain,
% 0.22/0.63 (subset(A!5, B!4)),
% 0.22/0.63 inference(unit_resolution,[status(thm)],[62, 15])).
% 0.22/0.63 tff(64,plain,
% 0.22/0.63 ((~![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)))))))),
% 0.22/0.63 inference(quant_inst,[status(thm)],[])).
% 0.22/0.63 tff(65,plain,
% 0.22/0.63 (~((~((~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))))))),
% 0.22/0.63 inference(unit_resolution,[status(thm)],[64, 31])).
% 0.22/0.63 tff(66,plain,
% 0.22/0.63 (((~((~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)))),
% 0.22/0.63 inference(tautology,[status(thm)],[])).
% 0.22/0.63 tff(67,plain,
% 0.22/0.63 ((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 0.22/0.63 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.22/0.63 tff(68,plain,
% 0.22/0.63 ((~((~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))),
% 0.22/0.63 inference(tautology,[status(thm)],[])).
% 0.22/0.63 tff(69,plain,
% 0.22/0.63 ((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 0.22/0.63 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.22/0.64 tff(70,plain,
% 0.22/0.64 (![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 0.22/0.64 inference(unit_resolution,[status(thm)],[69, 63])).
% 0.22/0.64 tff(71,plain,
% 0.22/0.64 (((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | ((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), A!5)) | member(tptp_fun_X_0(B!4, 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(B!4, intersection(A!5, difference(E!3, B!4))), A!5)) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4))),
% 0.22/0.64 inference(rewrite,[status(thm)],[])).
% 0.22/0.64 tff(72,plain,
% 0.22/0.64 ((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | ((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), A!5)) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4))),
% 0.22/0.64 inference(quant_inst,[status(thm)],[])).
% 0.22/0.64 tff(73,plain,
% 0.22/0.64 ((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | (~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), A!5)) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4)),
% 0.22/0.64 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.22/0.64 tff(74,plain,
% 0.22/0.64 ($false),
% 0.22/0.64 inference(unit_resolution,[status(thm)],[73, 70, 46, 44])).
% 0.22/0.64 tff(75,plain,(subset(intersection(A!5, difference(E!3, B!4)), B!4)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.64 tff(76,plain,
% 0.22/0.64 ((~subset(A!5, B!4)) | (~subset(intersection(A!5, difference(E!3, B!4)), B!4)) | (~((~subset(A!5, B!4)) <=> subset(intersection(A!5, difference(E!3, B!4)), B!4)))),
% 0.22/0.64 inference(tautology,[status(thm)],[])).
% 0.22/0.64 tff(77,plain,
% 0.22/0.64 ((~subset(A!5, B!4)) | (~subset(intersection(A!5, difference(E!3, B!4)), B!4))),
% 0.22/0.64 inference(unit_resolution,[status(thm)],[76, 60])).
% 0.22/0.64 tff(78,plain,
% 0.22/0.64 (~subset(A!5, B!4)),
% 0.22/0.64 inference(unit_resolution,[status(thm)],[77, 75])).
% 0.22/0.64 tff(79,plain,
% 0.22/0.64 (((~((~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))))),
% 0.22/0.64 inference(tautology,[status(thm)],[])).
% 0.22/0.64 tff(80,plain,
% 0.22/0.64 (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)))),
% 0.22/0.64 inference(unit_resolution,[status(thm)],[79, 65])).
% 0.22/0.64 tff(81,plain,
% 0.22/0.64 ((~(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)))),
% 0.22/0.64 inference(tautology,[status(thm)],[])).
% 0.22/0.64 tff(82,plain,
% 0.22/0.64 (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)))),
% 0.22/0.64 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.22/0.64 tff(83,plain,
% 0.22/0.64 (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4))),
% 0.22/0.64 inference(unit_resolution,[status(thm)],[82, 78])).
% 0.22/0.64 tff(84,plain,
% 0.22/0.64 (((~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)),
% 0.22/0.64 inference(tautology,[status(thm)],[])).
% 0.22/0.64 tff(85,plain,
% 0.22/0.64 (member(tptp_fun_X_0(B!4, A!5), A!5)),
% 0.22/0.64 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.22/0.64 tff(86,plain,
% 0.22/0.64 ((~![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)))))))),
% 0.22/0.64 inference(quant_inst,[status(thm)],[])).
% 0.22/0.64 tff(87,plain,
% 0.22/0.64 (~((~((~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))))))),
% 0.22/0.64 inference(unit_resolution,[status(thm)],[86, 31])).
% 0.22/0.64 tff(88,plain,
% 0.22/0.64 (((~((~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)))),
% 0.22/0.64 inference(tautology,[status(thm)],[])).
% 0.22/0.64 tff(89,plain,
% 0.22/0.64 ((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3))),
% 0.22/0.64 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.22/0.64 tff(90,plain,
% 0.22/0.64 (subset(A!5, E!3) & subset(B!4, E!3)),
% 0.22/0.64 inference(or_elim,[status(thm)],[58])).
% 0.22/0.64 tff(91,plain,
% 0.22/0.64 (subset(A!5, E!3)),
% 0.22/0.64 inference(and_elim,[status(thm)],[90])).
% 0.22/0.64 tff(92,plain,
% 0.22/0.64 ((~((~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))),
% 0.22/0.64 inference(tautology,[status(thm)],[])).
% 0.22/0.64 tff(93,plain,
% 0.22/0.64 ((~((~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))),
% 0.22/0.64 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.22/0.64 tff(94,plain,
% 0.22/0.64 (![X: $i] : ((~member(X, A!5)) | member(X, E!3))),
% 0.22/0.64 inference(unit_resolution,[status(thm)],[93, 89])).
% 0.22/0.64 tff(95,plain,
% 0.22/0.64 (((~![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))),
% 0.22/0.64 inference(rewrite,[status(thm)],[])).
% 0.22/0.64 tff(96,plain,
% 0.22/0.64 ((~![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))),
% 0.22/0.64 inference(quant_inst,[status(thm)],[])).
% 0.22/0.64 tff(97,plain,
% 0.22/0.64 ((~![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)),
% 0.22/0.64 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.22/0.64 tff(98,plain,
% 0.22/0.64 (member(tptp_fun_X_0(B!4, A!5), E!3)),
% 0.22/0.64 inference(unit_resolution,[status(thm)],[97, 94, 85])).
% 0.22/0.64 tff(99,plain,
% 0.22/0.64 (((~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))),
% 0.22/0.64 inference(tautology,[status(thm)],[])).
% 0.22/0.64 tff(100,plain,
% 0.22/0.64 (~member(tptp_fun_X_0(B!4, A!5), B!4)),
% 0.22/0.64 inference(unit_resolution,[status(thm)],[99, 83])).
% 0.22/0.64 tff(101,plain,
% 0.22/0.64 ((~((~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)),
% 0.22/0.64 inference(tautology,[status(thm)],[])).
% 0.22/0.64 tff(102,plain,
% 0.22/0.64 (~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4))),
% 0.22/0.64 inference(unit_resolution,[status(thm)],[101, 100, 98])).
% 0.22/0.64 tff(103,plain,
% 0.22/0.64 ((~![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))))))),
% 0.22/0.64 inference(quant_inst,[status(thm)],[])).
% 0.22/0.64 tff(104,plain,
% 0.22/0.64 (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)))))),
% 0.22/0.64 inference(unit_resolution,[status(thm)],[103, 11])).
% 0.22/0.64 tff(105,plain,
% 0.22/0.64 (((~((~subset(intersection(A!5, difference(E!3, B!4)), B!4)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, B!4)))) | (~(subset(intersection(A!5, difference(E!3, B!4)), B!4) | (~((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4)))))) | ((~subset(intersection(A!5, difference(E!3, B!4)), B!4)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, B!4)))),
% 0.22/0.64 inference(tautology,[status(thm)],[])).
% 0.22/0.64 tff(106,plain,
% 0.22/0.64 ((~subset(intersection(A!5, difference(E!3, B!4)), B!4)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, B!4))),
% 0.22/0.64 inference(unit_resolution,[status(thm)],[105, 33])).
% 0.22/0.64 tff(107,plain,
% 0.22/0.64 ((~((~subset(intersection(A!5, difference(E!3, B!4)), B!4)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, B!4)))) | (~subset(intersection(A!5, difference(E!3, B!4)), B!4)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, B!4))),
% 0.22/0.65 inference(tautology,[status(thm)],[])).
% 0.22/0.65 tff(108,plain,
% 0.22/0.65 ((~subset(intersection(A!5, difference(E!3, B!4)), B!4)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, B!4))),
% 0.22/0.65 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.22/0.65 tff(109,plain,
% 0.22/0.65 (![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, B!4))),
% 0.22/0.65 inference(unit_resolution,[status(thm)],[108, 75])).
% 0.22/0.65 tff(110,plain,
% 0.22/0.65 (((~![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, 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), B!4))) <=> ((~![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, 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), B!4))),
% 0.22/0.65 inference(rewrite,[status(thm)],[])).
% 0.22/0.65 tff(111,plain,
% 0.22/0.65 ((~![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, 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), B!4))),
% 0.22/0.65 inference(quant_inst,[status(thm)],[])).
% 0.22/0.65 tff(112,plain,
% 0.22/0.65 ((~![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, 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), B!4)),
% 0.22/0.65 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.22/0.65 tff(113,plain,
% 0.22/0.65 (~member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4)))),
% 0.22/0.65 inference(unit_resolution,[status(thm)],[112, 100, 109])).
% 0.22/0.65 tff(114,plain,
% 0.22/0.65 ((~(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))))),
% 0.22/0.65 inference(tautology,[status(thm)],[])).
% 0.22/0.65 tff(115,plain,
% 0.22/0.65 ((~(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))))),
% 0.22/0.65 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.22/0.65 tff(116,plain,
% 0.22/0.65 ((~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)))),
% 0.22/0.65 inference(unit_resolution,[status(thm)],[115, 104])).
% 0.22/0.65 tff(117,plain,
% 0.22/0.65 ((~((~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)))),
% 0.22/0.65 inference(tautology,[status(thm)],[])).
% 0.22/0.65 tff(118,plain,
% 0.22/0.65 ((~((~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)))),
% 0.22/0.65 inference(unit_resolution,[status(thm)],[117, 85])).
% 0.22/0.65 tff(119,plain,
% 0.22/0.65 (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))),
% 0.22/0.65 inference(unit_resolution,[status(thm)],[118, 116])).
% 0.22/0.65 tff(120,plain,
% 0.22/0.65 ((~(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))),
% 0.22/0.65 inference(tautology,[status(thm)],[])).
% 0.22/0.65 tff(121,plain,
% 0.22/0.65 (~(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))))),
% 0.22/0.65 inference(unit_resolution,[status(thm)],[120, 119, 102])).
% 0.22/0.65 tff(122,plain,
% 0.22/0.65 (^[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)))))),
% 0.22/0.65 inference(bind,[status(th)],[])).
% 0.22/0.65 tff(123,plain,
% 0.22/0.65 (![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))))),
% 0.22/0.65 inference(quant_intro,[status(thm)],[122])).
% 0.22/0.65 tff(124,plain,
% 0.22/0.65 (^[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)))))),
% 0.22/0.65 inference(bind,[status(th)],[])).
% 0.22/0.65 tff(125,plain,
% 0.22/0.65 (![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))))),
% 0.22/0.65 inference(quant_intro,[status(thm)],[124])).
% 0.22/0.65 tff(126,plain,
% 0.22/0.65 (![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))))),
% 0.22/0.65 inference(rewrite,[status(thm)],[])).
% 0.22/0.65 tff(127,axiom,(![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','difference')).
% 0.22/0.65 tff(128,plain,
% 0.22/0.65 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.22/0.65 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.22/0.65 tff(129,plain,(
% 0.22/0.65 ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.22/0.65 inference(skolemize,[status(sab)],[128])).
% 0.22/0.65 tff(130,plain,
% 0.22/0.65 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))),
% 0.22/0.65 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.22/0.65 tff(131,plain,
% 0.22/0.65 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))),
% 0.22/0.65 inference(modus_ponens,[status(thm)],[130, 123])).
% 0.22/0.65 tff(132,plain,
% 0.22/0.65 ((~![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))) | (member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)) <=> (~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4))))),
% 0.22/0.65 inference(quant_inst,[status(thm)],[])).
% 0.22/0.65 tff(133,plain,
% 0.22/0.65 ($false),
% 0.22/0.65 inference(unit_resolution,[status(thm)],[132, 131, 121])).
% 0.22/0.65 % SZS output end Proof
%------------------------------------------------------------------------------