TSTP Solution File: SET584+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET584+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 05:07:07 EDT 2022
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET584+3 : 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 : n015.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 06:59:55 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.
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(member_type, type, (
% 0.13/0.39 member: ( $i * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun_B_4_type, type, (
% 0.13/0.39 tptp_fun_B_4: $i)).
% 0.13/0.39 tff(tptp_fun_D_0_type, type, (
% 0.13/0.39 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.13/0.39 tff(union_type, type, (
% 0.13/0.39 union: ( $i * $i ) > $i)).
% 0.13/0.39 tff(tptp_fun_D_2_type, type, (
% 0.13/0.39 tptp_fun_D_2: $i)).
% 0.13/0.39 tff(tptp_fun_C_3_type, type, (
% 0.13/0.39 tptp_fun_C_3: $i)).
% 0.13/0.39 tff(subset_type, type, (
% 0.13/0.39 subset: ( $i * $i ) > $o)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 (^[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))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (^[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))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[4])).
% 0.13/0.39 tff(6,axiom,(![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, B) | member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','union_defn')).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.13/0.39 tff(9,plain,(
% 0.13/0.39 ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[8])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(B!4, D!2)) <=> (member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), D!2) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), B!4)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(B!4, D!2)) <=> (member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), D!2) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), B!4))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (^[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))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (![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)))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[13])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (^[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))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (![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)))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[15])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (![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)))))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[16, 14])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (^[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)))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (![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)))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[18])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (^[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))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[21])).
% 0.13/0.39 tff(23,axiom,(![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','subset_defn')).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.13/0.39 tff(26,plain,(
% 0.13/0.39 ![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)))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[25])).
% 0.13/0.40 tff(27,plain,
% 0.13/0.40 (![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)))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.13/0.40 tff(28,plain,
% 0.13/0.40 (![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)))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 ((~![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!4, D!2), union(C!3, D!2))) | ![D: $i] : ((~member(D, union(B!4, D!2))) | member(D, union(C!3, D!2))))) | (~(subset(union(B!4, D!2), union(C!3, D!2)) | (~((~member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(B!4, D!2))) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(C!3, D!2))))))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 (~((~((~subset(union(B!4, D!2), union(C!3, D!2))) | ![D: $i] : ((~member(D, union(B!4, D!2))) | member(D, union(C!3, D!2))))) | (~(subset(union(B!4, D!2), union(C!3, D!2)) | (~((~member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(B!4, D!2))) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(C!3, D!2)))))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 (((~((~subset(union(B!4, D!2), union(C!3, D!2))) | ![D: $i] : ((~member(D, union(B!4, D!2))) | member(D, union(C!3, D!2))))) | (~(subset(union(B!4, D!2), union(C!3, D!2)) | (~((~member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(B!4, D!2))) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(C!3, D!2))))))) | (subset(union(B!4, D!2), union(C!3, D!2)) | (~((~member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(B!4, D!2))) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(C!3, D!2)))))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 (subset(union(B!4, D!2), union(C!3, D!2)) | (~((~member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(B!4, D!2))) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(C!3, D!2))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.13/0.40 tff(33,plain,
% 0.13/0.40 ((~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(union(B, D), union(C, D)))) <=> (~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(union(B, D), union(C, D))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(34,plain,
% 0.13/0.40 ((~![B: $i, C: $i, D: $i] : (subset(B, C) => subset(union(B, D), union(C, D)))) <=> (~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(union(B, D), union(C, D))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(35,axiom,(~![B: $i, C: $i, D: $i] : (subset(B, C) => subset(union(B, D), union(C, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_th33')).
% 0.13/0.40 tff(36,plain,
% 0.13/0.40 (~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(union(B, D), union(C, D)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.13/0.40 tff(37,plain,
% 0.13/0.40 (~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(union(B, D), union(C, D)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[36, 33])).
% 0.13/0.40 tff(38,plain,
% 0.13/0.40 (~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(union(B, D), union(C, D)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.13/0.40 tff(39,plain,
% 0.13/0.40 (~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(union(B, D), union(C, D)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[38, 33])).
% 0.13/0.40 tff(40,plain,
% 0.13/0.40 (~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(union(B, D), union(C, D)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[39, 33])).
% 0.13/0.40 tff(41,plain,
% 0.13/0.40 (~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(union(B, D), union(C, D)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.13/0.40 tff(42,plain,
% 0.13/0.40 (~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(union(B, D), union(C, D)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[41, 33])).
% 0.13/0.40 tff(43,plain,(
% 0.13/0.40 ~((~subset(B!4, C!3)) | subset(union(B!4, D!2), union(C!3, D!2)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[42])).
% 0.13/0.40 tff(44,plain,
% 0.13/0.40 (~subset(union(B!4, D!2), union(C!3, D!2))),
% 0.13/0.40 inference(or_elim,[status(thm)],[43])).
% 0.13/0.40 tff(45,plain,
% 0.13/0.40 ((~(subset(union(B!4, D!2), union(C!3, D!2)) | (~((~member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(B!4, D!2))) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(C!3, D!2)))))) | subset(union(B!4, D!2), union(C!3, D!2)) | (~((~member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(B!4, D!2))) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(C!3, D!2))))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(46,plain,
% 0.13/0.40 ((~(subset(union(B!4, D!2), union(C!3, D!2)) | (~((~member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(B!4, D!2))) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(C!3, D!2)))))) | (~((~member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(B!4, D!2))) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(C!3, D!2))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.13/0.40 tff(47,plain,
% 0.13/0.40 (~((~member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(B!4, D!2))) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(C!3, D!2)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[46, 32])).
% 0.13/0.40 tff(48,plain,
% 0.13/0.40 (((~member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(B!4, D!2))) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(C!3, D!2))) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(B!4, D!2))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(49,plain,
% 0.13/0.40 (member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(B!4, D!2))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.13/0.40 tff(50,plain,
% 0.13/0.40 ((~(member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(B!4, D!2)) <=> (member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), D!2) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), B!4)))) | (~member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(B!4, D!2))) | (member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), D!2) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), B!4))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(51,plain,
% 0.13/0.40 ((~(member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(B!4, D!2)) <=> (member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), D!2) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), B!4)))) | (member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), D!2) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), B!4))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.13/0.40 tff(52,plain,
% 0.13/0.40 (member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), D!2) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), B!4)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[51, 12])).
% 0.13/0.40 tff(53,plain,
% 0.13/0.40 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(C!3, D!2)) <=> (member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), D!2) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), C!3)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(54,plain,
% 0.13/0.40 (member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(C!3, D!2)) <=> (member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), D!2) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), C!3))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[53, 10])).
% 0.13/0.40 tff(55,plain,
% 0.13/0.40 (((~member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(B!4, D!2))) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(C!3, D!2))) | (~member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(C!3, D!2)))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(56,plain,
% 0.13/0.40 (~member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(C!3, D!2))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[55, 47])).
% 0.13/0.41 tff(57,plain,
% 0.13/0.41 ((~(member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(C!3, D!2)) <=> (member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), D!2) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), C!3)))) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(C!3, D!2)) | (~(member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), D!2) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), C!3)))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(58,plain,
% 0.13/0.41 ((~(member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), union(C!3, D!2)) <=> (member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), D!2) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), C!3)))) | (~(member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), D!2) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), C!3)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.13/0.41 tff(59,plain,
% 0.13/0.41 (~(member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), D!2) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), C!3))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[58, 54])).
% 0.13/0.41 tff(60,plain,
% 0.13/0.41 ((member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), D!2) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), C!3)) | (~member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), D!2))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(61,plain,
% 0.13/0.41 (~member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), D!2)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.13/0.41 tff(62,plain,
% 0.13/0.41 ((~(member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), D!2) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), B!4))) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), D!2) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), B!4)),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(63,plain,
% 0.13/0.41 (member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), B!4)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[62, 61, 52])).
% 0.13/0.41 tff(64,plain,
% 0.13/0.41 ((member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), D!2) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), C!3)) | (~member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), C!3))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(65,plain,
% 0.13/0.41 (~member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), C!3)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[64, 59])).
% 0.13/0.41 tff(66,plain,
% 0.13/0.41 ((~![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!4, C!3)) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3)))) | (~(subset(B!4, C!3) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | member(tptp_fun_D_0(C!3, B!4), C!3)))))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(67,plain,
% 0.13/0.41 (~((~((~subset(B!4, C!3)) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3)))) | (~(subset(B!4, C!3) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | member(tptp_fun_D_0(C!3, B!4), C!3))))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[66, 28])).
% 0.13/0.41 tff(68,plain,
% 0.13/0.41 (((~((~subset(B!4, C!3)) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3)))) | (~(subset(B!4, C!3) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | member(tptp_fun_D_0(C!3, B!4), C!3)))))) | ((~subset(B!4, C!3)) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3)))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(69,plain,
% 0.13/0.41 ((~subset(B!4, C!3)) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.13/0.41 tff(70,plain,
% 0.13/0.41 (subset(B!4, C!3)),
% 0.13/0.41 inference(or_elim,[status(thm)],[43])).
% 0.13/0.41 tff(71,plain,
% 0.13/0.41 ((~((~subset(B!4, C!3)) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3)))) | (~subset(B!4, C!3)) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(72,plain,
% 0.13/0.41 ((~((~subset(B!4, C!3)) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3)))) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.13/0.41 tff(73,plain,
% 0.13/0.41 (![D: $i] : ((~member(D, B!4)) | member(D, C!3))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[72, 69])).
% 0.13/0.41 tff(74,plain,
% 0.13/0.41 (((~![D: $i] : ((~member(D, B!4)) | member(D, C!3))) | ((~member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), B!4)) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), C!3))) <=> ((~![D: $i] : ((~member(D, B!4)) | member(D, C!3))) | (~member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), B!4)) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), C!3))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(75,plain,
% 0.13/0.41 ((~![D: $i] : ((~member(D, B!4)) | member(D, C!3))) | ((~member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), B!4)) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), C!3))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(76,plain,
% 0.13/0.41 ((~![D: $i] : ((~member(D, B!4)) | member(D, C!3))) | (~member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), B!4)) | member(tptp_fun_D_0(union(C!3, D!2), union(B!4, D!2)), C!3)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.13/0.41 tff(77,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[76, 73, 65, 63])).
% 0.13/0.41 % SZS output end Proof
%------------------------------------------------------------------------------