TSTP Solution File: SET194+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET194+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 05:06:05 EDT 2022
% Result : Theorem 0.15s 0.34s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SET194+3 : TPTP v8.1.0. Released v2.2.0.
% 0.02/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.30 % Computer : n008.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Sat Sep 3 03:22:40 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.09/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.30 Usage: tptp [options] [-file:]file
% 0.09/0.30 -h, -? prints this message.
% 0.09/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.30 -m, -model generate model.
% 0.09/0.30 -p, -proof generate proof.
% 0.09/0.30 -c, -core generate unsat core of named formulas.
% 0.09/0.30 -st, -statistics display statistics.
% 0.09/0.30 -t:timeout set timeout (in second).
% 0.09/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.30 -<param>:<value> configuration parameter and value.
% 0.09/0.30 -o:<output-file> file to place output in.
% 0.15/0.34 % SZS status Theorem
% 0.15/0.34 % SZS output start Proof
% 0.15/0.34 tff(member_type, type, (
% 0.15/0.34 member: ( $i * $i ) > $o)).
% 0.15/0.34 tff(tptp_fun_C_2_type, type, (
% 0.15/0.34 tptp_fun_C_2: $i)).
% 0.15/0.34 tff(tptp_fun_D_0_type, type, (
% 0.15/0.34 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.15/0.34 tff(tptp_fun_B_3_type, type, (
% 0.15/0.34 tptp_fun_B_3: $i)).
% 0.15/0.34 tff(union_type, type, (
% 0.15/0.34 union: ( $i * $i ) > $i)).
% 0.15/0.34 tff(subset_type, type, (
% 0.15/0.34 subset: ( $i * $i ) > $o)).
% 0.15/0.34 tff(1,plain,
% 0.15/0.34 (^[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))))))))),
% 0.15/0.34 inference(bind,[status(th)],[])).
% 0.15/0.34 tff(2,plain,
% 0.15/0.34 (![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)))))))),
% 0.15/0.34 inference(quant_intro,[status(thm)],[1])).
% 0.15/0.34 tff(3,plain,
% 0.15/0.34 (^[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))))))))),
% 0.15/0.34 inference(bind,[status(th)],[])).
% 0.15/0.34 tff(4,plain,
% 0.15/0.34 (![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)))))))),
% 0.15/0.34 inference(quant_intro,[status(thm)],[3])).
% 0.15/0.34 tff(5,plain,
% 0.15/0.34 (![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)))))))),
% 0.15/0.34 inference(transitivity,[status(thm)],[4, 2])).
% 0.15/0.34 tff(6,plain,
% 0.15/0.34 (^[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)))))))))),
% 0.15/0.34 inference(bind,[status(th)],[])).
% 0.15/0.34 tff(7,plain,
% 0.15/0.34 (![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)))))))),
% 0.15/0.35 inference(quant_intro,[status(thm)],[6])).
% 0.15/0.35 tff(8,plain,
% 0.15/0.35 (![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)))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(9,plain,
% 0.15/0.35 (^[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))))),
% 0.15/0.35 inference(bind,[status(th)],[])).
% 0.15/0.35 tff(10,plain,
% 0.15/0.35 (![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)))),
% 0.15/0.35 inference(quant_intro,[status(thm)],[9])).
% 0.15/0.35 tff(11,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')).
% 0.15/0.35 tff(12,plain,
% 0.15/0.35 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.15/0.35 tff(13,plain,
% 0.15/0.35 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.15/0.35 tff(14,plain,(
% 0.15/0.35 ![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)))))),
% 0.15/0.35 inference(skolemize,[status(sab)],[13])).
% 0.15/0.35 tff(15,plain,
% 0.15/0.35 (![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)))))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.15/0.35 tff(16,plain,
% 0.15/0.35 (![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)))))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.15/0.35 tff(17,plain,
% 0.15/0.35 ((~![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, union(B!3, C!2))) | ![D: $i] : ((~member(D, B!3)) | member(D, union(B!3, C!2))))) | (~(subset(B!3, union(B!3, C!2)) | (~((~member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2))))))))),
% 0.15/0.35 inference(quant_inst,[status(thm)],[])).
% 0.15/0.35 tff(18,plain,
% 0.15/0.35 (~((~((~subset(B!3, union(B!3, C!2))) | ![D: $i] : ((~member(D, B!3)) | member(D, union(B!3, C!2))))) | (~(subset(B!3, union(B!3, C!2)) | (~((~member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)))))))),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.15/0.35 tff(19,plain,
% 0.15/0.35 (((~((~subset(B!3, union(B!3, C!2))) | ![D: $i] : ((~member(D, B!3)) | member(D, union(B!3, C!2))))) | (~(subset(B!3, union(B!3, C!2)) | (~((~member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2))))))) | (subset(B!3, union(B!3, C!2)) | (~((~member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)))))),
% 0.15/0.35 inference(tautology,[status(thm)],[])).
% 0.15/0.35 tff(20,plain,
% 0.15/0.35 (subset(B!3, union(B!3, C!2)) | (~((~member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2))))),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.15/0.35 tff(21,plain,
% 0.15/0.35 ((~![B: $i, C: $i] : subset(B, union(B, C))) <=> (~![B: $i, C: $i] : subset(B, union(B, C)))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(22,axiom,(~![B: $i, C: $i] : subset(B, union(B, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_subset_of_union')).
% 0.15/0.35 tff(23,plain,
% 0.15/0.35 (~![B: $i, C: $i] : subset(B, union(B, C))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.15/0.35 tff(24,plain,
% 0.15/0.35 (~![B: $i, C: $i] : subset(B, union(B, C))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[23, 21])).
% 0.15/0.35 tff(25,plain,
% 0.15/0.35 (~![B: $i, C: $i] : subset(B, union(B, C))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.15/0.35 tff(26,plain,
% 0.15/0.35 (~![B: $i, C: $i] : subset(B, union(B, C))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.15/0.35 tff(27,plain,
% 0.15/0.35 (~![B: $i, C: $i] : subset(B, union(B, C))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.15/0.35 tff(28,plain,
% 0.15/0.35 (~![B: $i, C: $i] : subset(B, union(B, C))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[27, 21])).
% 0.15/0.35 tff(29,plain,
% 0.15/0.35 (~![B: $i, C: $i] : subset(B, union(B, C))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.15/0.35 tff(30,plain,(
% 0.15/0.35 ~subset(B!3, union(B!3, C!2))),
% 0.15/0.35 inference(skolemize,[status(sab)],[29])).
% 0.15/0.35 tff(31,plain,
% 0.15/0.35 ((~(subset(B!3, union(B!3, C!2)) | (~((~member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)))))) | subset(B!3, union(B!3, C!2)) | (~((~member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2))))),
% 0.15/0.35 inference(tautology,[status(thm)],[])).
% 0.15/0.35 tff(32,plain,
% 0.15/0.35 ((~(subset(B!3, union(B!3, C!2)) | (~((~member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)))))) | (~((~member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2))))),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.15/0.35 tff(33,plain,
% 0.15/0.35 (~((~member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)))),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[32, 20])).
% 0.15/0.35 tff(34,plain,
% 0.15/0.35 (((~member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2))) | member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)),
% 0.15/0.35 inference(tautology,[status(thm)],[])).
% 0.15/0.35 tff(35,plain,
% 0.15/0.35 (member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.15/0.35 tff(36,plain,
% 0.15/0.35 ((member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3) | member(tptp_fun_D_0(union(B!3, C!2), B!3), C!2)) | (~member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3))),
% 0.15/0.35 inference(tautology,[status(thm)],[])).
% 0.15/0.35 tff(37,plain,
% 0.15/0.35 (member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3) | member(tptp_fun_D_0(union(B!3, C!2), B!3), C!2)),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.15/0.35 tff(38,plain,
% 0.15/0.35 (((~member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2))) | (~member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)))),
% 0.15/0.35 inference(tautology,[status(thm)],[])).
% 0.15/0.35 tff(39,plain,
% 0.15/0.35 (~member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2))),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[38, 33])).
% 0.15/0.35 tff(40,plain,
% 0.15/0.35 ((~(member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)) <=> (member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3) | member(tptp_fun_D_0(union(B!3, C!2), B!3), C!2)))) | member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)) | (~(member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3) | member(tptp_fun_D_0(union(B!3, C!2), B!3), C!2)))),
% 0.15/0.35 inference(tautology,[status(thm)],[])).
% 0.15/0.35 tff(41,plain,
% 0.15/0.35 (~(member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)) <=> (member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3) | member(tptp_fun_D_0(union(B!3, C!2), B!3), C!2)))),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[40, 39, 37])).
% 0.15/0.35 tff(42,plain,
% 0.15/0.35 (^[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))))),
% 0.15/0.35 inference(bind,[status(th)],[])).
% 0.15/0.35 tff(43,plain,
% 0.15/0.35 (![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)))),
% 0.15/0.35 inference(quant_intro,[status(thm)],[42])).
% 0.15/0.35 tff(44,plain,
% 0.15/0.35 (![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)))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(45,plain,
% 0.15/0.35 (^[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))))),
% 0.15/0.35 inference(bind,[status(th)],[])).
% 0.15/0.35 tff(46,plain,
% 0.15/0.35 (![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)))),
% 0.15/0.35 inference(quant_intro,[status(thm)],[45])).
% 0.15/0.35 tff(47,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')).
% 0.15/0.35 tff(48,plain,
% 0.15/0.35 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.15/0.35 tff(49,plain,
% 0.15/0.35 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.15/0.35 tff(50,plain,(
% 0.15/0.35 ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.15/0.35 inference(skolemize,[status(sab)],[49])).
% 0.15/0.35 tff(51,plain,
% 0.15/0.35 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.15/0.35 tff(52,plain,
% 0.15/0.35 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)) <=> (member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3) | member(tptp_fun_D_0(union(B!3, C!2), B!3), C!2)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)) <=> (member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3) | member(tptp_fun_D_0(union(B!3, C!2), B!3), C!2))))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(53,plain,
% 0.15/0.35 ((member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)) <=> (member(tptp_fun_D_0(union(B!3, C!2), B!3), C!2) | member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3))) <=> (member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)) <=> (member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3) | member(tptp_fun_D_0(union(B!3, C!2), B!3), C!2)))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(54,plain,
% 0.15/0.35 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)) <=> (member(tptp_fun_D_0(union(B!3, C!2), B!3), C!2) | member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)) <=> (member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3) | member(tptp_fun_D_0(union(B!3, C!2), B!3), C!2))))),
% 0.15/0.35 inference(monotonicity,[status(thm)],[53])).
% 0.15/0.35 tff(55,plain,
% 0.15/0.35 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)) <=> (member(tptp_fun_D_0(union(B!3, C!2), B!3), C!2) | member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)) <=> (member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3) | member(tptp_fun_D_0(union(B!3, C!2), B!3), C!2))))),
% 0.15/0.35 inference(transitivity,[status(thm)],[54, 52])).
% 0.15/0.35 tff(56,plain,
% 0.15/0.35 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)) <=> (member(tptp_fun_D_0(union(B!3, C!2), B!3), C!2) | member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3)))),
% 0.15/0.35 inference(quant_inst,[status(thm)],[])).
% 0.15/0.35 tff(57,plain,
% 0.15/0.35 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(B!3, C!2), B!3), union(B!3, C!2)) <=> (member(tptp_fun_D_0(union(B!3, C!2), B!3), B!3) | member(tptp_fun_D_0(union(B!3, C!2), B!3), C!2)))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.15/0.36 tff(58,plain,
% 0.15/0.36 ($false),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[57, 51, 41])).
% 0.15/0.36 % SZS output end Proof
%------------------------------------------------------------------------------