TSTP Solution File: SET027+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET027+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 05:04:58 EDT 2022
% Result : Theorem 0.13s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET027+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 : n018.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Sep 3 01:27:14 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.41 % SZS status Theorem
% 0.13/0.41 % SZS output start Proof
% 0.13/0.41 tff(member_type, type, (
% 0.13/0.41 member: ( $i * $i ) > $o)).
% 0.13/0.41 tff(tptp_fun_C_2_type, type, (
% 0.13/0.41 tptp_fun_C_2: $i)).
% 0.13/0.41 tff(tptp_fun_D_0_type, type, (
% 0.13/0.41 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.13/0.41 tff(tptp_fun_B_3_type, type, (
% 0.13/0.41 tptp_fun_B_3: $i)).
% 0.13/0.41 tff(tptp_fun_D_1_type, type, (
% 0.13/0.41 tptp_fun_D_1: $i)).
% 0.13/0.41 tff(subset_type, type, (
% 0.13/0.41 subset: ( $i * $i ) > $o)).
% 0.13/0.41 tff(1,plain,
% 0.13/0.41 (^[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))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(2,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))))))) <=> ![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)))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.41 tff(3,plain,
% 0.13/0.41 (^[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))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(4,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))))))) <=> ![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)))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.41 tff(5,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))))))) <=> ![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)))))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[4, 2])).
% 0.13/0.41 tff(6,plain,
% 0.13/0.41 (^[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)))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(7,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))))) <=> ![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)))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[6])).
% 0.13/0.41 tff(8,plain,
% 0.13/0.41 (![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)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(9,plain,
% 0.13/0.41 (^[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))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(10,plain,
% 0.13/0.41 (![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)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[9])).
% 0.13/0.41 tff(11,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')).
% 0.13/0.41 tff(12,plain,
% 0.13/0.41 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.13/0.41 tff(13,plain,
% 0.13/0.41 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.13/0.41 tff(14,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)))))),
% 0.13/0.41 inference(skolemize,[status(sab)],[13])).
% 0.13/0.41 tff(15,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)))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.13/0.41 tff(16,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)))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.13/0.41 tff(17,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!3, D!1)) | ![D: $i] : ((~member(D, B!3)) | member(D, D!1)))) | (~(subset(B!3, D!1) | (~((~member(tptp_fun_D_0(D!1, B!3), B!3)) | member(tptp_fun_D_0(D!1, B!3), D!1)))))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(18,plain,
% 0.13/0.41 (~((~((~subset(B!3, D!1)) | ![D: $i] : ((~member(D, B!3)) | member(D, D!1)))) | (~(subset(B!3, D!1) | (~((~member(tptp_fun_D_0(D!1, B!3), B!3)) | member(tptp_fun_D_0(D!1, B!3), D!1))))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.13/0.41 tff(19,plain,
% 0.13/0.41 (((~((~subset(B!3, D!1)) | ![D: $i] : ((~member(D, B!3)) | member(D, D!1)))) | (~(subset(B!3, D!1) | (~((~member(tptp_fun_D_0(D!1, B!3), B!3)) | member(tptp_fun_D_0(D!1, B!3), D!1)))))) | (subset(B!3, D!1) | (~((~member(tptp_fun_D_0(D!1, B!3), B!3)) | member(tptp_fun_D_0(D!1, B!3), D!1))))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(20,plain,
% 0.13/0.41 (subset(B!3, D!1) | (~((~member(tptp_fun_D_0(D!1, B!3), B!3)) | member(tptp_fun_D_0(D!1, B!3), D!1)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.13/0.41 tff(21,plain,
% 0.13/0.41 ((~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(C, D))) | subset(B, D))) <=> (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(C, D))) | subset(B, D)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(22,plain,
% 0.13/0.41 ((~![B: $i, C: $i, D: $i] : ((subset(B, C) & subset(C, D)) => subset(B, D))) <=> (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(C, D))) | subset(B, D)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(23,axiom,(~![B: $i, C: $i, D: $i] : ((subset(B, C) & subset(C, D)) => subset(B, D))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_transitivity_of_subset')).
% 0.13/0.41 tff(24,plain,
% 0.13/0.41 (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(C, D))) | subset(B, D))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(C, D))) | subset(B, D))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(C, D))) | subset(B, D))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(C, D))) | subset(B, D))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(C, D))) | subset(B, D))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[27, 21])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(C, D))) | subset(B, D))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(C, D))) | subset(B, D))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[29, 21])).
% 0.20/0.42 tff(31,plain,(
% 0.20/0.42 ~((~(subset(B!3, C!2) & subset(C!2, D!1))) | subset(B!3, D!1))),
% 0.20/0.42 inference(skolemize,[status(sab)],[30])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 (~subset(B!3, D!1)),
% 0.20/0.42 inference(or_elim,[status(thm)],[31])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 ((~(subset(B!3, D!1) | (~((~member(tptp_fun_D_0(D!1, B!3), B!3)) | member(tptp_fun_D_0(D!1, B!3), D!1))))) | subset(B!3, D!1) | (~((~member(tptp_fun_D_0(D!1, B!3), B!3)) | member(tptp_fun_D_0(D!1, B!3), D!1)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 ((~(subset(B!3, D!1) | (~((~member(tptp_fun_D_0(D!1, B!3), B!3)) | member(tptp_fun_D_0(D!1, B!3), D!1))))) | (~((~member(tptp_fun_D_0(D!1, B!3), B!3)) | member(tptp_fun_D_0(D!1, B!3), D!1)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 (~((~member(tptp_fun_D_0(D!1, B!3), B!3)) | member(tptp_fun_D_0(D!1, B!3), D!1))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[34, 20])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (((~member(tptp_fun_D_0(D!1, B!3), B!3)) | member(tptp_fun_D_0(D!1, B!3), D!1)) | member(tptp_fun_D_0(D!1, B!3), B!3)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (member(tptp_fun_D_0(D!1, B!3), B!3)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 ((~![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(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2)))) | (~(subset(B!3, C!2) | (~((~member(tptp_fun_D_0(C!2, B!3), B!3)) | member(tptp_fun_D_0(C!2, B!3), C!2)))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 (~((~((~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2)))) | (~(subset(B!3, C!2) | (~((~member(tptp_fun_D_0(C!2, B!3), B!3)) | member(tptp_fun_D_0(C!2, B!3), C!2))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[38, 16])).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 (((~((~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2)))) | (~(subset(B!3, C!2) | (~((~member(tptp_fun_D_0(C!2, B!3), B!3)) | member(tptp_fun_D_0(C!2, B!3), C!2)))))) | ((~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 ((~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 (subset(B!3, C!2) & subset(C!2, D!1)),
% 0.20/0.42 inference(or_elim,[status(thm)],[31])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 (subset(B!3, C!2)),
% 0.20/0.42 inference(and_elim,[status(thm)],[42])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 ((~((~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2)))) | (~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 ((~((~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2)))) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 (![D: $i] : ((~member(D, B!3)) | member(D, C!2))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[45, 41])).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 (((~![D: $i] : ((~member(D, B!3)) | member(D, C!2))) | ((~member(tptp_fun_D_0(D!1, B!3), B!3)) | member(tptp_fun_D_0(D!1, B!3), C!2))) <=> ((~![D: $i] : ((~member(D, B!3)) | member(D, C!2))) | (~member(tptp_fun_D_0(D!1, B!3), B!3)) | member(tptp_fun_D_0(D!1, B!3), C!2))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 ((~![D: $i] : ((~member(D, B!3)) | member(D, C!2))) | ((~member(tptp_fun_D_0(D!1, B!3), B!3)) | member(tptp_fun_D_0(D!1, B!3), C!2))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 ((~![D: $i] : ((~member(D, B!3)) | member(D, C!2))) | (~member(tptp_fun_D_0(D!1, B!3), B!3)) | member(tptp_fun_D_0(D!1, B!3), C!2)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.20/0.42 tff(50,plain,
% 0.20/0.42 (member(tptp_fun_D_0(D!1, B!3), C!2)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[49, 46, 37])).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 (((~member(tptp_fun_D_0(D!1, B!3), B!3)) | member(tptp_fun_D_0(D!1, B!3), D!1)) | (~member(tptp_fun_D_0(D!1, B!3), D!1))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 (~member(tptp_fun_D_0(D!1, B!3), D!1)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[51, 35])).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 ((~![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(C!2, D!1)) | ![D: $i] : ((~member(D, C!2)) | member(D, D!1)))) | (~(subset(C!2, D!1) | (~((~member(tptp_fun_D_0(D!1, C!2), C!2)) | member(tptp_fun_D_0(D!1, C!2), D!1)))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(54,plain,
% 0.20/0.42 (~((~((~subset(C!2, D!1)) | ![D: $i] : ((~member(D, C!2)) | member(D, D!1)))) | (~(subset(C!2, D!1) | (~((~member(tptp_fun_D_0(D!1, C!2), C!2)) | member(tptp_fun_D_0(D!1, C!2), D!1))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[53, 16])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 (((~((~subset(C!2, D!1)) | ![D: $i] : ((~member(D, C!2)) | member(D, D!1)))) | (~(subset(C!2, D!1) | (~((~member(tptp_fun_D_0(D!1, C!2), C!2)) | member(tptp_fun_D_0(D!1, C!2), D!1)))))) | ((~subset(C!2, D!1)) | ![D: $i] : ((~member(D, C!2)) | member(D, D!1)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 ((~subset(C!2, D!1)) | ![D: $i] : ((~member(D, C!2)) | member(D, D!1))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.20/0.42 tff(57,plain,
% 0.20/0.42 (subset(C!2, D!1)),
% 0.20/0.42 inference(and_elim,[status(thm)],[42])).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 ((~((~subset(C!2, D!1)) | ![D: $i] : ((~member(D, C!2)) | member(D, D!1)))) | (~subset(C!2, D!1)) | ![D: $i] : ((~member(D, C!2)) | member(D, D!1))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 ((~((~subset(C!2, D!1)) | ![D: $i] : ((~member(D, C!2)) | member(D, D!1)))) | ![D: $i] : ((~member(D, C!2)) | member(D, D!1))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 (![D: $i] : ((~member(D, C!2)) | member(D, D!1))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[59, 56])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 (((~![D: $i] : ((~member(D, C!2)) | member(D, D!1))) | ((~member(tptp_fun_D_0(D!1, B!3), C!2)) | member(tptp_fun_D_0(D!1, B!3), D!1))) <=> ((~![D: $i] : ((~member(D, C!2)) | member(D, D!1))) | (~member(tptp_fun_D_0(D!1, B!3), C!2)) | member(tptp_fun_D_0(D!1, B!3), D!1))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 ((~![D: $i] : ((~member(D, C!2)) | member(D, D!1))) | ((~member(tptp_fun_D_0(D!1, B!3), C!2)) | member(tptp_fun_D_0(D!1, B!3), D!1))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 ((~![D: $i] : ((~member(D, C!2)) | member(D, D!1))) | (~member(tptp_fun_D_0(D!1, B!3), C!2)) | member(tptp_fun_D_0(D!1, B!3), D!1)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[63, 60, 52, 50])).
% 0.20/0.42 % SZS output end Proof
%------------------------------------------------------------------------------