TSTP Solution File: SET200+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET200+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 05:06:08 EDT 2022
% Result : Theorem 0.14s 0.40s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET200+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n024.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Sep 3 03:23:48 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.14/0.40 % SZS status Theorem
% 0.14/0.40 % SZS output start Proof
% 0.14/0.40 tff(member_type, type, (
% 0.14/0.40 member: ( $i * $i ) > $o)).
% 0.14/0.40 tff(tptp_fun_B_5_type, type, (
% 0.14/0.40 tptp_fun_B_5: $i)).
% 0.14/0.40 tff(tptp_fun_D_0_type, type, (
% 0.14/0.40 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.14/0.40 tff(union_type, type, (
% 0.14/0.40 union: ( $i * $i ) > $i)).
% 0.14/0.40 tff(tptp_fun_D_3_type, type, (
% 0.14/0.40 tptp_fun_D_3: $i)).
% 0.14/0.40 tff(tptp_fun_E_2_type, type, (
% 0.14/0.40 tptp_fun_E_2: $i)).
% 0.14/0.40 tff(tptp_fun_C_4_type, type, (
% 0.14/0.40 tptp_fun_C_4: $i)).
% 0.14/0.40 tff(subset_type, type, (
% 0.14/0.40 subset: ( $i * $i ) > $o)).
% 0.14/0.40 tff(1,plain,
% 0.14/0.40 (^[B: $i, C: $i, D: $i] : refl((member(D, union(B, C)) <=> (member(D, C) | member(D, B))) <=> (member(D, union(B, C)) <=> (member(D, C) | member(D, B))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(2,plain,
% 0.14/0.40 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B))) <=> ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.40 tff(3,plain,
% 0.14/0.40 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B))) <=> ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(4,plain,
% 0.14/0.40 (^[B: $i, C: $i, D: $i] : rewrite((member(D, union(B, C)) <=> (member(D, B) | member(D, C))) <=> (member(D, union(B, C)) <=> (member(D, C) | member(D, B))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(5,plain,
% 0.14/0.40 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, B) | member(D, C))) <=> ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[4])).
% 0.14/0.40 tff(6,axiom,(![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, B) | member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','union_defn')).
% 0.14/0.40 tff(7,plain,
% 0.14/0.40 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.14/0.40 tff(8,plain,
% 0.14/0.40 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.14/0.40 tff(9,plain,(
% 0.14/0.40 ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.14/0.40 inference(skolemize,[status(sab)],[8])).
% 0.14/0.40 tff(10,plain,
% 0.14/0.40 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.14/0.40 tff(11,plain,
% 0.14/0.40 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(B!5, D!3)) <=> (member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), D!3) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), B!5)))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(12,plain,
% 0.14/0.40 (member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(B!5, D!3)) <=> (member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), D!3) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), B!5))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.14/0.40 tff(13,plain,
% 0.14/0.40 (^[B: $i, C: $i] : refl((~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(14,plain,
% 0.14/0.40 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[13])).
% 0.14/0.40 tff(15,plain,
% 0.14/0.40 (^[B: $i, C: $i] : rewrite((~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(16,plain,
% 0.14/0.40 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[15])).
% 0.14/0.40 tff(17,plain,
% 0.14/0.40 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.14/0.40 inference(transitivity,[status(thm)],[16, 14])).
% 0.14/0.40 tff(18,plain,
% 0.14/0.40 (^[B: $i, C: $i] : trans(monotonicity(rewrite(((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) <=> ((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))), rewrite((subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))) <=> (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))), ((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))), rewrite((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))), ((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(19,plain,
% 0.14/0.40 (![B: $i, C: $i] : (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[18])).
% 0.14/0.40 tff(20,plain,
% 0.14/0.40 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C))) <=> ![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(21,plain,
% 0.14/0.40 (^[B: $i, C: $i] : rewrite((subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C))) <=> (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(22,plain,
% 0.14/0.40 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C))) <=> ![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[21])).
% 0.14/0.40 tff(23,axiom,(![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','subset_defn')).
% 0.14/0.40 tff(24,plain,
% 0.14/0.40 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.14/0.40 tff(25,plain,
% 0.14/0.40 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.14/0.40 tff(26,plain,(
% 0.22/0.40 ![B: $i, C: $i] : (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))),
% 0.22/0.40 inference(skolemize,[status(sab)],[25])).
% 0.22/0.40 tff(27,plain,
% 0.22/0.40 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.22/0.40 tff(28,plain,
% 0.22/0.40 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.22/0.40 tff(29,plain,
% 0.22/0.40 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(union(B!5, D!3), union(C!4, E!2))) | ![D: $i] : ((~member(D, union(B!5, D!3))) | member(D, union(C!4, E!2))))) | (~(subset(union(B!5, D!3), union(C!4, E!2)) | (~((~member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(B!5, D!3))) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(C!4, E!2))))))))),
% 0.22/0.40 inference(quant_inst,[status(thm)],[])).
% 0.22/0.40 tff(30,plain,
% 0.22/0.40 (~((~((~subset(union(B!5, D!3), union(C!4, E!2))) | ![D: $i] : ((~member(D, union(B!5, D!3))) | member(D, union(C!4, E!2))))) | (~(subset(union(B!5, D!3), union(C!4, E!2)) | (~((~member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(B!5, D!3))) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(C!4, E!2)))))))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.22/0.40 tff(31,plain,
% 0.22/0.40 (((~((~subset(union(B!5, D!3), union(C!4, E!2))) | ![D: $i] : ((~member(D, union(B!5, D!3))) | member(D, union(C!4, E!2))))) | (~(subset(union(B!5, D!3), union(C!4, E!2)) | (~((~member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(B!5, D!3))) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(C!4, E!2))))))) | (subset(union(B!5, D!3), union(C!4, E!2)) | (~((~member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(B!5, D!3))) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(C!4, E!2)))))),
% 0.22/0.40 inference(tautology,[status(thm)],[])).
% 0.22/0.40 tff(32,plain,
% 0.22/0.40 (subset(union(B!5, D!3), union(C!4, E!2)) | (~((~member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(B!5, D!3))) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(C!4, E!2))))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.22/0.40 tff(33,plain,
% 0.22/0.40 ((~![B: $i, C: $i, D: $i, E: $i] : ((~(subset(B, C) & subset(D, E))) | subset(union(B, D), union(C, E)))) <=> (~![B: $i, C: $i, D: $i, E: $i] : ((~(subset(B, C) & subset(D, E))) | subset(union(B, D), union(C, E))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(34,plain,
% 0.22/0.40 ((~![B: $i, C: $i, D: $i, E: $i] : ((subset(B, C) & subset(D, E)) => subset(union(B, D), union(C, E)))) <=> (~![B: $i, C: $i, D: $i, E: $i] : ((~(subset(B, C) & subset(D, E))) | subset(union(B, D), union(C, E))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(35,axiom,(~![B: $i, C: $i, D: $i, E: $i] : ((subset(B, C) & subset(D, E)) => subset(union(B, D), union(C, E)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_th34')).
% 0.22/0.40 tff(36,plain,
% 0.22/0.40 (~![B: $i, C: $i, D: $i, E: $i] : ((~(subset(B, C) & subset(D, E))) | subset(union(B, D), union(C, E)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.22/0.40 tff(37,plain,
% 0.22/0.40 (~![B: $i, C: $i, D: $i, E: $i] : ((~(subset(B, C) & subset(D, E))) | subset(union(B, D), union(C, E)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[36, 33])).
% 0.22/0.40 tff(38,plain,
% 0.22/0.40 (~![B: $i, C: $i, D: $i, E: $i] : ((~(subset(B, C) & subset(D, E))) | subset(union(B, D), union(C, E)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.22/0.40 tff(39,plain,
% 0.22/0.40 (~![B: $i, C: $i, D: $i, E: $i] : ((~(subset(B, C) & subset(D, E))) | subset(union(B, D), union(C, E)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[38, 33])).
% 0.22/0.40 tff(40,plain,
% 0.22/0.40 (~![B: $i, C: $i, D: $i, E: $i] : ((~(subset(B, C) & subset(D, E))) | subset(union(B, D), union(C, E)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[39, 33])).
% 0.22/0.41 tff(41,plain,
% 0.22/0.41 (~![B: $i, C: $i, D: $i, E: $i] : ((~(subset(B, C) & subset(D, E))) | subset(union(B, D), union(C, E)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.22/0.41 tff(42,plain,
% 0.22/0.41 (~![B: $i, C: $i, D: $i, E: $i] : ((~(subset(B, C) & subset(D, E))) | subset(union(B, D), union(C, E)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[41, 33])).
% 0.22/0.41 tff(43,plain,(
% 0.22/0.41 ~((~(subset(B!5, C!4) & subset(D!3, E!2))) | subset(union(B!5, D!3), union(C!4, E!2)))),
% 0.22/0.41 inference(skolemize,[status(sab)],[42])).
% 0.22/0.41 tff(44,plain,
% 0.22/0.41 (~subset(union(B!5, D!3), union(C!4, E!2))),
% 0.22/0.41 inference(or_elim,[status(thm)],[43])).
% 0.22/0.41 tff(45,plain,
% 0.22/0.41 ((~(subset(union(B!5, D!3), union(C!4, E!2)) | (~((~member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(B!5, D!3))) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(C!4, E!2)))))) | subset(union(B!5, D!3), union(C!4, E!2)) | (~((~member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(B!5, D!3))) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(C!4, E!2))))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(46,plain,
% 0.22/0.41 ((~(subset(union(B!5, D!3), union(C!4, E!2)) | (~((~member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(B!5, D!3))) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(C!4, E!2)))))) | (~((~member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(B!5, D!3))) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(C!4, E!2))))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.22/0.41 tff(47,plain,
% 0.22/0.41 (~((~member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(B!5, D!3))) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(C!4, E!2)))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[46, 32])).
% 0.22/0.41 tff(48,plain,
% 0.22/0.41 (((~member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(B!5, D!3))) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(C!4, E!2))) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(B!5, D!3))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(49,plain,
% 0.22/0.41 (member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(B!5, D!3))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.22/0.41 tff(50,plain,
% 0.22/0.41 ((~(member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(B!5, D!3)) <=> (member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), D!3) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), B!5)))) | (~member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(B!5, D!3))) | (member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), D!3) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), B!5))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(51,plain,
% 0.22/0.41 ((~(member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(B!5, D!3)) <=> (member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), D!3) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), B!5)))) | (member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), D!3) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), B!5))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.22/0.41 tff(52,plain,
% 0.22/0.41 (member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), D!3) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), B!5)),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[51, 12])).
% 0.22/0.41 tff(53,plain,
% 0.22/0.41 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(C!4, E!2)) <=> (member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), E!2) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), C!4)))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(54,plain,
% 0.22/0.41 (member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(C!4, E!2)) <=> (member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), E!2) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), C!4))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[53, 10])).
% 0.22/0.41 tff(55,plain,
% 0.22/0.41 (((~member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(B!5, D!3))) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(C!4, E!2))) | (~member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(C!4, E!2)))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(56,plain,
% 0.22/0.41 (~member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(C!4, E!2))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[55, 47])).
% 0.22/0.41 tff(57,plain,
% 0.22/0.41 ((~(member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(C!4, E!2)) <=> (member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), E!2) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), C!4)))) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(C!4, E!2)) | (~(member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), E!2) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), C!4)))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(58,plain,
% 0.22/0.41 ((~(member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), union(C!4, E!2)) <=> (member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), E!2) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), C!4)))) | (~(member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), E!2) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), C!4)))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.22/0.41 tff(59,plain,
% 0.22/0.41 (~(member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), E!2) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), C!4))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[58, 54])).
% 0.22/0.41 tff(60,plain,
% 0.22/0.41 ((member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), E!2) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), C!4)) | (~member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), C!4))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(61,plain,
% 0.22/0.41 (~member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), C!4)),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.22/0.41 tff(62,plain,
% 0.22/0.41 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(B!5, C!4)) | ![D: $i] : ((~member(D, B!5)) | member(D, C!4)))) | (~(subset(B!5, C!4) | (~((~member(tptp_fun_D_0(C!4, B!5), B!5)) | member(tptp_fun_D_0(C!4, B!5), C!4)))))))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(63,plain,
% 0.22/0.41 (~((~((~subset(B!5, C!4)) | ![D: $i] : ((~member(D, B!5)) | member(D, C!4)))) | (~(subset(B!5, C!4) | (~((~member(tptp_fun_D_0(C!4, B!5), B!5)) | member(tptp_fun_D_0(C!4, B!5), C!4))))))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[62, 28])).
% 0.22/0.41 tff(64,plain,
% 0.22/0.41 (((~((~subset(B!5, C!4)) | ![D: $i] : ((~member(D, B!5)) | member(D, C!4)))) | (~(subset(B!5, C!4) | (~((~member(tptp_fun_D_0(C!4, B!5), B!5)) | member(tptp_fun_D_0(C!4, B!5), C!4)))))) | ((~subset(B!5, C!4)) | ![D: $i] : ((~member(D, B!5)) | member(D, C!4)))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(65,plain,
% 0.22/0.41 ((~subset(B!5, C!4)) | ![D: $i] : ((~member(D, B!5)) | member(D, C!4))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.22/0.41 tff(66,plain,
% 0.22/0.41 (subset(B!5, C!4) & subset(D!3, E!2)),
% 0.22/0.41 inference(or_elim,[status(thm)],[43])).
% 0.22/0.41 tff(67,plain,
% 0.22/0.41 (subset(B!5, C!4)),
% 0.22/0.41 inference(and_elim,[status(thm)],[66])).
% 0.22/0.41 tff(68,plain,
% 0.22/0.41 ((~((~subset(B!5, C!4)) | ![D: $i] : ((~member(D, B!5)) | member(D, C!4)))) | (~subset(B!5, C!4)) | ![D: $i] : ((~member(D, B!5)) | member(D, C!4))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(69,plain,
% 0.22/0.41 ((~((~subset(B!5, C!4)) | ![D: $i] : ((~member(D, B!5)) | member(D, C!4)))) | ![D: $i] : ((~member(D, B!5)) | member(D, C!4))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.22/0.41 tff(70,plain,
% 0.22/0.41 (![D: $i] : ((~member(D, B!5)) | member(D, C!4))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[69, 65])).
% 0.22/0.41 tff(71,plain,
% 0.22/0.41 (((~![D: $i] : ((~member(D, B!5)) | member(D, C!4))) | ((~member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), B!5)) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), C!4))) <=> ((~![D: $i] : ((~member(D, B!5)) | member(D, C!4))) | (~member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), B!5)) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), C!4))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(72,plain,
% 0.22/0.42 ((~![D: $i] : ((~member(D, B!5)) | member(D, C!4))) | ((~member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), B!5)) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), C!4))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(73,plain,
% 0.22/0.42 ((~![D: $i] : ((~member(D, B!5)) | member(D, C!4))) | (~member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), B!5)) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), C!4)),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.22/0.42 tff(74,plain,
% 0.22/0.42 (~member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), B!5)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[73, 70, 61])).
% 0.22/0.42 tff(75,plain,
% 0.22/0.42 ((member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), E!2) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), C!4)) | (~member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), E!2))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(76,plain,
% 0.22/0.42 (~member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), E!2)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[75, 59])).
% 0.22/0.42 tff(77,plain,
% 0.22/0.42 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(D!3, E!2)) | ![D: $i] : ((~member(D, D!3)) | member(D, E!2)))) | (~(subset(D!3, E!2) | (~((~member(tptp_fun_D_0(E!2, D!3), D!3)) | member(tptp_fun_D_0(E!2, D!3), E!2)))))))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(78,plain,
% 0.22/0.42 (~((~((~subset(D!3, E!2)) | ![D: $i] : ((~member(D, D!3)) | member(D, E!2)))) | (~(subset(D!3, E!2) | (~((~member(tptp_fun_D_0(E!2, D!3), D!3)) | member(tptp_fun_D_0(E!2, D!3), E!2))))))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[77, 28])).
% 0.22/0.42 tff(79,plain,
% 0.22/0.42 (((~((~subset(D!3, E!2)) | ![D: $i] : ((~member(D, D!3)) | member(D, E!2)))) | (~(subset(D!3, E!2) | (~((~member(tptp_fun_D_0(E!2, D!3), D!3)) | member(tptp_fun_D_0(E!2, D!3), E!2)))))) | ((~subset(D!3, E!2)) | ![D: $i] : ((~member(D, D!3)) | member(D, E!2)))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(80,plain,
% 0.22/0.42 ((~subset(D!3, E!2)) | ![D: $i] : ((~member(D, D!3)) | member(D, E!2))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.22/0.42 tff(81,plain,
% 0.22/0.42 (subset(D!3, E!2)),
% 0.22/0.42 inference(and_elim,[status(thm)],[66])).
% 0.22/0.42 tff(82,plain,
% 0.22/0.42 ((~((~subset(D!3, E!2)) | ![D: $i] : ((~member(D, D!3)) | member(D, E!2)))) | (~subset(D!3, E!2)) | ![D: $i] : ((~member(D, D!3)) | member(D, E!2))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(83,plain,
% 0.22/0.42 ((~((~subset(D!3, E!2)) | ![D: $i] : ((~member(D, D!3)) | member(D, E!2)))) | ![D: $i] : ((~member(D, D!3)) | member(D, E!2))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.22/0.42 tff(84,plain,
% 0.22/0.42 (![D: $i] : ((~member(D, D!3)) | member(D, E!2))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[83, 80])).
% 0.22/0.42 tff(85,plain,
% 0.22/0.42 (((~![D: $i] : ((~member(D, D!3)) | member(D, E!2))) | ((~member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), D!3)) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), E!2))) <=> ((~![D: $i] : ((~member(D, D!3)) | member(D, E!2))) | (~member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), D!3)) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), E!2))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(86,plain,
% 0.22/0.42 ((~![D: $i] : ((~member(D, D!3)) | member(D, E!2))) | ((~member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), D!3)) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), E!2))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(87,plain,
% 0.22/0.42 ((~![D: $i] : ((~member(D, D!3)) | member(D, E!2))) | (~member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), D!3)) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), E!2)),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.22/0.42 tff(88,plain,
% 0.22/0.42 (~member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), D!3)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[87, 84, 76])).
% 0.22/0.42 tff(89,plain,
% 0.22/0.42 ((~(member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), D!3) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), B!5))) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), D!3) | member(tptp_fun_D_0(union(C!4, E!2), union(B!5, D!3)), B!5)),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(90,plain,
% 0.22/0.42 ($false),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[89, 88, 74, 52])).
% 0.22/0.42 % SZS output end Proof
%------------------------------------------------------------------------------