TSTP Solution File: SET185+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET185+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 05:06:03 EDT 2022
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET185+3 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 03:36:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(member_type, type, (
% 0.20/0.41 member: ( $i * $i ) > $o)).
% 0.20/0.41 tff(union_type, type, (
% 0.20/0.41 union: ( $i * $i ) > $i)).
% 0.20/0.41 tff(tptp_fun_B_3_type, type, (
% 0.20/0.41 tptp_fun_B_3: $i)).
% 0.20/0.41 tff(tptp_fun_C_2_type, type, (
% 0.20/0.41 tptp_fun_C_2: $i)).
% 0.20/0.41 tff(tptp_fun_D_1_type, type, (
% 0.20/0.41 tptp_fun_D_1: ( $i * $i ) > $i)).
% 0.20/0.41 tff(subset_type, type, (
% 0.20/0.41 subset: ( $i * $i ) > $o)).
% 0.20/0.41 tff(tptp_fun_D_0_type, type, (
% 0.20/0.41 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.20/0.41 tff(1,assumption,(~member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)), introduced(assumption)).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 (^[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))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 (![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)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.41 tff(4,plain,
% 0.20/0.41 (^[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))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 (![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)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.41 tff(6,plain,
% 0.20/0.41 (![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)))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[5, 3])).
% 0.20/0.41 tff(7,plain,
% 0.20/0.41 (^[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)))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(8,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))))) <=> ![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)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[7])).
% 0.20/0.42 tff(9,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(10,plain,
% 0.20/0.42 (^[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))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(11,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.42 tff(12,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')).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.20/0.42 tff(15,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)))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[14])).
% 0.20/0.42 tff(16,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)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.20/0.42 tff(17,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)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[16, 6])).
% 0.20/0.42 tff(18,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(19,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)],[18, 17])).
% 0.20/0.42 tff(20,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(21,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)],[20, 19])).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 ((~![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))) <=> (~![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 ((~![B: $i, C: $i] : (subset(B, C) => (union(B, C) = C))) <=> (~![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(24,axiom,(~![B: $i, C: $i] : (subset(B, C) => (union(B, C) = C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_subset_union')).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (~![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 (~![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[25, 22])).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 (~![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (~![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[27, 22])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 (~![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[28, 22])).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 (~![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 (~![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[30, 22])).
% 0.20/0.42 tff(32,plain,(
% 0.20/0.42 ~((~subset(B!3, C!2)) | (union(B!3, C!2) = C!2))),
% 0.20/0.42 inference(skolemize,[status(sab)],[31])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 (subset(B!3, C!2)),
% 0.20/0.42 inference(or_elim,[status(thm)],[32])).
% 0.20/0.42 tff(34,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(35,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)],[34, 33])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (![D: $i] : ((~member(D, B!3)) | member(D, C!2))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[35, 21])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (((~![D: $i] : ((~member(D, B!3)) | member(D, C!2))) | ((~member(tptp_fun_D_1(union(C!2, B!3), C!2), B!3)) | member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2))) <=> ((~![D: $i] : ((~member(D, B!3)) | member(D, C!2))) | (~member(tptp_fun_D_1(union(C!2, B!3), C!2), B!3)) | member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 ((~![D: $i] : ((~member(D, B!3)) | member(D, C!2))) | ((~member(tptp_fun_D_1(union(C!2, B!3), C!2), B!3)) | member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 ((~![D: $i] : ((~member(D, B!3)) | member(D, C!2))) | (~member(tptp_fun_D_1(union(C!2, B!3), C!2), B!3)) | member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 ((~member(tptp_fun_D_1(union(C!2, B!3), C!2), B!3)) | member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[39, 36])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 (~member(tptp_fun_D_1(union(C!2, B!3), C!2), B!3)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[40, 1])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 (^[B: $i, C: $i, D: $i] : refl((~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[42])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 (![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.20/0.42 inference(pull_quant,[status(thm)],[])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 (^[B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) <=> ![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))), ((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) <=> (~![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))))), pull_quant((~![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))) <=> ?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C))))), ((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) <=> ?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))) <=> (?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))), pull_quant((?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> (~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))))), pull_quant((~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[46, 44])).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[47, 43])).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 (^[B: $i, C: $i] : rewrite((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(50,plain,
% 0.20/0.42 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[50, 48])).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 (^[B: $i, C: $i] : trans(monotonicity(rewrite(((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) <=> ((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))), rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.42 tff(54,plain,
% 0.20/0.42 (^[B: $i, C: $i] : rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))) <=> ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C))) <=> ![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(57,axiom,(![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','equal_member_defn')).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.20/0.42 tff(59,plain,(
% 0.20/0.42 ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[58])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.20/0.43 tff(62,plain,
% 0.20/0.43 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[61, 51])).
% 0.20/0.43 tff(63,plain,
% 0.20/0.43 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))) | (~((~((~(C!2 = union(C!2, B!3))) | (member(tptp_fun_D_1(C!2, B!3), C!2) <=> member(tptp_fun_D_1(C!2, B!3), union(C!2, B!3))))) | (~((C!2 = union(C!2, B!3)) | ((~member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)) <=> member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3)))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(64,plain,
% 0.20/0.43 (~((~((~(C!2 = union(C!2, B!3))) | (member(tptp_fun_D_1(C!2, B!3), C!2) <=> member(tptp_fun_D_1(C!2, B!3), union(C!2, B!3))))) | (~((C!2 = union(C!2, B!3)) | ((~member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)) <=> member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 (((~((~(C!2 = union(C!2, B!3))) | (member(tptp_fun_D_1(C!2, B!3), C!2) <=> member(tptp_fun_D_1(C!2, B!3), union(C!2, B!3))))) | (~((C!2 = union(C!2, B!3)) | ((~member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)) <=> member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3)))))) | ((C!2 = union(C!2, B!3)) | ((~member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)) <=> member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(66,plain,
% 0.20/0.43 ((C!2 = union(C!2, B!3)) | ((~member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)) <=> member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.20/0.43 tff(67,plain,
% 0.20/0.43 ((C!2 = union(B!3, C!2)) <=> (union(B!3, C!2) = C!2)),
% 0.20/0.43 inference(commutativity,[status(thm)],[])).
% 0.20/0.43 tff(68,plain,
% 0.20/0.43 (^[B: $i, C: $i] : refl((union(B, C) = union(C, B)) <=> (union(B, C) = union(C, B)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(69,plain,
% 0.20/0.43 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(71,axiom,(![B: $i, C: $i] : (union(B, C) = union(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_of_union')).
% 0.20/0.43 tff(72,plain,
% 0.20/0.43 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.43 tff(73,plain,(
% 0.20/0.43 ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.20/0.43 inference(skolemize,[status(sab)],[72])).
% 0.20/0.43 tff(74,plain,
% 0.20/0.43 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.20/0.43 tff(75,plain,
% 0.20/0.43 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(B!3, C!2) = union(C!2, B!3))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(76,plain,
% 0.20/0.43 (union(B!3, C!2) = union(C!2, B!3)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.20/0.43 tff(77,plain,
% 0.20/0.43 (union(C!2, B!3) = union(B!3, C!2)),
% 0.20/0.43 inference(symmetry,[status(thm)],[76])).
% 0.20/0.43 tff(78,plain,
% 0.20/0.43 ((C!2 = union(C!2, B!3)) <=> (C!2 = union(B!3, C!2))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[77])).
% 0.20/0.43 tff(79,plain,
% 0.20/0.43 ((C!2 = union(C!2, B!3)) <=> (union(B!3, C!2) = C!2)),
% 0.20/0.43 inference(transitivity,[status(thm)],[78, 67])).
% 0.20/0.43 tff(80,plain,
% 0.20/0.43 ((union(B!3, C!2) = C!2) <=> (C!2 = union(C!2, B!3))),
% 0.20/0.43 inference(symmetry,[status(thm)],[79])).
% 0.20/0.43 tff(81,plain,
% 0.20/0.43 ((~(union(B!3, C!2) = C!2)) <=> (~(C!2 = union(C!2, B!3)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[80])).
% 0.20/0.43 tff(82,plain,
% 0.20/0.43 (~(union(B!3, C!2) = C!2)),
% 0.20/0.43 inference(or_elim,[status(thm)],[32])).
% 0.20/0.43 tff(83,plain,
% 0.20/0.43 (~(C!2 = union(C!2, B!3))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.43 tff(84,plain,
% 0.20/0.43 ((~((C!2 = union(C!2, B!3)) | ((~member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)) <=> member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3))))) | (C!2 = union(C!2, B!3)) | ((~member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)) <=> member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(85,plain,
% 0.20/0.43 ((~member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)) <=> member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[84, 83, 66])).
% 0.20/0.43 tff(86,plain,
% 0.20/0.43 ((~((~member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)) <=> member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3)))) | member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) | member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 (member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2) | member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.20/0.43 tff(88,plain,
% 0.20/0.43 (member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[87, 1])).
% 0.20/0.43 tff(89,plain,
% 0.20/0.43 (^[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))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(90,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[89])).
% 0.20/0.43 tff(91,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(92,plain,
% 0.20/0.43 (^[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))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(93,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[92])).
% 0.20/0.43 tff(94,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')).
% 0.20/0.43 tff(95,plain,
% 0.20/0.43 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.43 tff(96,plain,
% 0.20/0.43 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.20/0.43 tff(97,plain,(
% 0.20/0.43 ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[96])).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3)) <=> (member(tptp_fun_D_1(union(C!2, B!3), C!2), B!3) | member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(100,plain,
% 0.20/0.43 (member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3)) <=> (member(tptp_fun_D_1(union(C!2, B!3), C!2), B!3) | member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 ((~(member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3)) <=> (member(tptp_fun_D_1(union(C!2, B!3), C!2), B!3) | member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)))) | (~member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3))) | (member(tptp_fun_D_1(union(C!2, B!3), C!2), B!3) | member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(102,plain,
% 0.20/0.43 ((~member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3))) | (member(tptp_fun_D_1(union(C!2, B!3), C!2), B!3) | member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.20/0.43 tff(103,plain,
% 0.20/0.43 (member(tptp_fun_D_1(union(C!2, B!3), C!2), B!3) | member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[102, 88])).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 ((~(member(tptp_fun_D_1(union(C!2, B!3), C!2), B!3) | member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2))) | member(tptp_fun_D_1(union(C!2, B!3), C!2), B!3) | member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(105,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[104, 103, 41, 1])).
% 0.20/0.43 tff(106,plain,(member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(107,plain,
% 0.20/0.43 ((~((~member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)) <=> member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3)))) | (~member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)) | (~member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(108,plain,
% 0.20/0.43 ((~member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)) | (~member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[107, 85])).
% 0.20/0.43 tff(109,plain,
% 0.20/0.43 (~member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[108, 106])).
% 0.20/0.43 tff(110,plain,
% 0.20/0.43 ((member(tptp_fun_D_1(union(C!2, B!3), C!2), B!3) | member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)) | (~member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(111,plain,
% 0.20/0.43 (member(tptp_fun_D_1(union(C!2, B!3), C!2), B!3) | member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[110, 106])).
% 0.20/0.43 tff(112,plain,
% 0.20/0.43 ((~(member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3)) <=> (member(tptp_fun_D_1(union(C!2, B!3), C!2), B!3) | member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)))) | member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3)) | (~(member(tptp_fun_D_1(union(C!2, B!3), C!2), B!3) | member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(113,plain,
% 0.20/0.43 (member(tptp_fun_D_1(union(C!2, B!3), C!2), union(C!2, B!3)) | (~(member(tptp_fun_D_1(union(C!2, B!3), C!2), B!3) | member(tptp_fun_D_1(union(C!2, B!3), C!2), C!2)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[112, 100])).
% 0.20/0.43 tff(114,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[113, 111, 109])).
% 0.20/0.43 % SZS output end Proof
%------------------------------------------------------------------------------