TSTP Solution File: SET600+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET600+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 05:07:13 EDT 2022
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET600+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 06:51:40 EDT 2022
% 0.12/0.34 % 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.
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(member_type, type, (
% 0.19/0.39 member: ( $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_B_4_type, type, (
% 0.19/0.39 tptp_fun_B_4: $i)).
% 0.19/0.39 tff(tptp_fun_D_2_type, type, (
% 0.19/0.39 tptp_fun_D_2: ( $i * $i ) > $i)).
% 0.19/0.39 tff(union_type, type, (
% 0.19/0.39 union: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_C_3_type, type, (
% 0.19/0.39 tptp_fun_C_3: $i)).
% 0.19/0.39 tff(empty_set_type, type, (
% 0.19/0.39 empty_set: $i)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (^[B: $i, C: $i] : refl((union(B, C) = union(C, B)) <=> (union(B, C) = union(C, B)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(4,axiom,(![B: $i, C: $i] : (union(B, C) = union(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_of_union')).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.39 tff(6,plain,(
% 0.19/0.39 ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.19/0.39 inference(skolemize,[status(sab)],[5])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(B!4, C!3) = union(C!3, B!4))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (union(B!4, C!3) = union(C!3, B!4)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.39 tff(10,assumption,(~(union(B!4, C!3) = empty_set)), introduced(assumption)).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 (((~(union(B!4, C!3) = empty_set)) <=> (~((~(B!4 = empty_set)) | (~(C!3 = empty_set))))) <=> ((union(B!4, C!3) = empty_set) <=> ((~(B!4 = empty_set)) | (~(C!3 = empty_set))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (((B!4 = empty_set) & (C!3 = empty_set)) <=> (~((~(B!4 = empty_set)) | (~(C!3 = empty_set))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (((~(union(B!4, C!3) = empty_set)) <=> ((B!4 = empty_set) & (C!3 = empty_set))) <=> ((~(union(B!4, C!3) = empty_set)) <=> (~((~(B!4 = empty_set)) | (~(C!3 = empty_set)))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[12])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (((~(union(B!4, C!3) = empty_set)) <=> ((B!4 = empty_set) & (C!3 = empty_set))) <=> ((union(B!4, C!3) = empty_set) <=> ((~(B!4 = empty_set)) | (~(C!3 = empty_set))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[13, 11])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 ((~((union(B!4, C!3) = empty_set) <=> ((B!4 = empty_set) & (C!3 = empty_set)))) <=> ((~(union(B!4, C!3) = empty_set)) <=> ((B!4 = empty_set) & (C!3 = empty_set)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 ((~![B: $i, C: $i] : ((union(B, C) = empty_set) <=> ((B = empty_set) & (C = empty_set)))) <=> (~![B: $i, C: $i] : ((union(B, C) = empty_set) <=> ((B = empty_set) & (C = empty_set))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(17,axiom,(~![B: $i, C: $i] : ((union(B, C) = empty_set) <=> ((B = empty_set) & (C = empty_set)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_th59')).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (~![B: $i, C: $i] : ((union(B, C) = empty_set) <=> ((B = empty_set) & (C = empty_set)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (~![B: $i, C: $i] : ((union(B, C) = empty_set) <=> ((B = empty_set) & (C = empty_set)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[18, 16])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (~![B: $i, C: $i] : ((union(B, C) = empty_set) <=> ((B = empty_set) & (C = empty_set)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[19, 16])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (~![B: $i, C: $i] : ((union(B, C) = empty_set) <=> ((B = empty_set) & (C = empty_set)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (~![B: $i, C: $i] : ((union(B, C) = empty_set) <=> ((B = empty_set) & (C = empty_set)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[21, 16])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (~![B: $i, C: $i] : ((union(B, C) = empty_set) <=> ((B = empty_set) & (C = empty_set)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[22, 16])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 (~![B: $i, C: $i] : ((union(B, C) = empty_set) <=> ((B = empty_set) & (C = empty_set)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.19/0.40 tff(25,plain,(
% 0.19/0.40 ~((union(B!4, C!3) = empty_set) <=> ((B!4 = empty_set) & (C!3 = empty_set)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[24])).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 ((~(union(B!4, C!3) = empty_set)) <=> ((B!4 = empty_set) & (C!3 = empty_set))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[25, 15])).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 ((union(B!4, C!3) = empty_set) <=> ((~(B!4 = empty_set)) | (~(C!3 = empty_set)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[26, 14])).
% 0.19/0.40 tff(28,plain,
% 0.19/0.40 ((union(B!4, C!3) = empty_set) | (~((~(B!4 = empty_set)) | (~(C!3 = empty_set)))) | (~((union(B!4, C!3) = empty_set) <=> ((~(B!4 = empty_set)) | (~(C!3 = empty_set)))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 ((union(B!4, C!3) = empty_set) | (~((~(B!4 = empty_set)) | (~(C!3 = empty_set))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 (~((~(B!4 = empty_set)) | (~(C!3 = empty_set)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[29, 10])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 (((~(B!4 = empty_set)) | (~(C!3 = empty_set))) | (C!3 = empty_set)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 (C!3 = empty_set),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (empty_set = C!3),
% 0.19/0.40 inference(symmetry,[status(thm)],[32])).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 (((~(B!4 = empty_set)) | (~(C!3 = empty_set))) | (B!4 = empty_set)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 (B!4 = empty_set),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[34, 30])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 (empty_set = B!4),
% 0.19/0.40 inference(symmetry,[status(thm)],[35])).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 (union(empty_set, empty_set) = union(B!4, C!3)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[36, 33])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 (union(empty_set, empty_set) = union(C!3, B!4)),
% 0.19/0.40 inference(transitivity,[status(thm)],[37, 9])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 (member(tptp_fun_D_2(union(C!3, B!4), empty_set), union(empty_set, empty_set)) <=> member(tptp_fun_D_2(union(C!3, B!4), empty_set), union(C!3, B!4))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[38])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (member(tptp_fun_D_2(union(C!3, B!4), empty_set), union(C!3, B!4)) <=> member(tptp_fun_D_2(union(C!3, B!4), empty_set), union(empty_set, empty_set))),
% 0.19/0.40 inference(symmetry,[status(thm)],[39])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 ((empty_set = union(B!4, C!3)) <=> (union(B!4, C!3) = empty_set)),
% 0.19/0.40 inference(commutativity,[status(thm)],[])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 (union(C!3, B!4) = union(B!4, C!3)),
% 0.19/0.40 inference(symmetry,[status(thm)],[9])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 ((empty_set = union(C!3, B!4)) <=> (empty_set = union(B!4, C!3))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[42])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 ((empty_set = union(C!3, B!4)) <=> (union(B!4, C!3) = empty_set)),
% 0.19/0.40 inference(transitivity,[status(thm)],[43, 41])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 ((union(B!4, C!3) = empty_set) <=> (empty_set = union(C!3, B!4))),
% 0.19/0.40 inference(symmetry,[status(thm)],[44])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 ((~(union(B!4, C!3) = empty_set)) <=> (~(empty_set = union(C!3, B!4)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[45])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (~(empty_set = union(C!3, B!4))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[10, 46])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (^[B: $i, C: $i, D: $i] : refl((~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))) <=> (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[48])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))),
% 0.19/0.40 inference(pull_quant,[status(thm)],[])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 (^[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_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))) <=> (?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))), pull_quant((?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))) <=> (~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))))), pull_quant((~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))) <=> ![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[51])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[52, 50])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[53, 49])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 (^[B: $i, C: $i] : rewrite((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[55])).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[56, 54])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 (^[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_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))), rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 (^[B: $i, C: $i] : rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))) <=> ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[60])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(63,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')).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.19/0.40 tff(65,plain,(
% 0.19/0.40 ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[64])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[67, 57])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))) | (~((~((~(empty_set = union(C!3, B!4))) | (member(union(C!3, B!4), empty_set) <=> member(union(C!3, B!4), union(C!3, B!4))))) | (~((empty_set = union(C!3, B!4)) | ((~member(tptp_fun_D_2(union(C!3, B!4), empty_set), empty_set)) <=> member(tptp_fun_D_2(union(C!3, B!4), empty_set), union(C!3, B!4)))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (~((~((~(empty_set = union(C!3, B!4))) | (member(union(C!3, B!4), empty_set) <=> member(union(C!3, B!4), union(C!3, B!4))))) | (~((empty_set = union(C!3, B!4)) | ((~member(tptp_fun_D_2(union(C!3, B!4), empty_set), empty_set)) <=> member(tptp_fun_D_2(union(C!3, B!4), empty_set), union(C!3, B!4))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (((~((~(empty_set = union(C!3, B!4))) | (member(union(C!3, B!4), empty_set) <=> member(union(C!3, B!4), union(C!3, B!4))))) | (~((empty_set = union(C!3, B!4)) | ((~member(tptp_fun_D_2(union(C!3, B!4), empty_set), empty_set)) <=> member(tptp_fun_D_2(union(C!3, B!4), empty_set), union(C!3, B!4)))))) | ((empty_set = union(C!3, B!4)) | ((~member(tptp_fun_D_2(union(C!3, B!4), empty_set), empty_set)) <=> member(tptp_fun_D_2(union(C!3, B!4), empty_set), union(C!3, B!4))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 ((empty_set = union(C!3, B!4)) | ((~member(tptp_fun_D_2(union(C!3, B!4), empty_set), empty_set)) <=> member(tptp_fun_D_2(union(C!3, B!4), empty_set), union(C!3, B!4)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 ((~((empty_set = union(C!3, B!4)) | ((~member(tptp_fun_D_2(union(C!3, B!4), empty_set), empty_set)) <=> member(tptp_fun_D_2(union(C!3, B!4), empty_set), union(C!3, B!4))))) | (empty_set = union(C!3, B!4)) | ((~member(tptp_fun_D_2(union(C!3, B!4), empty_set), empty_set)) <=> member(tptp_fun_D_2(union(C!3, B!4), empty_set), union(C!3, B!4)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 ((empty_set = union(C!3, B!4)) | ((~member(tptp_fun_D_2(union(C!3, B!4), empty_set), empty_set)) <=> member(tptp_fun_D_2(union(C!3, B!4), empty_set), union(C!3, B!4)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 ((~member(tptp_fun_D_2(union(C!3, B!4), empty_set), empty_set)) <=> member(tptp_fun_D_2(union(C!3, B!4), empty_set), union(C!3, B!4))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[74, 47])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 (^[B: $i] : refl((~member(B, empty_set)) <=> (~member(B, empty_set)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[76])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(79,axiom,(![B: $i] : (~member(B, empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','empty_set_defn')).
% 0.19/0.41 tff(80,plain,
% 0.19/0.41 (![B: $i] : (~member(B, empty_set))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.19/0.41 tff(81,plain,(
% 0.19/0.41 ![B: $i] : (~member(B, empty_set))),
% 0.19/0.41 inference(skolemize,[status(sab)],[80])).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (![B: $i] : (~member(B, empty_set))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 ((~![B: $i] : (~member(B, empty_set))) | (~member(tptp_fun_D_2(union(C!3, B!4), empty_set), empty_set))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 (~member(tptp_fun_D_2(union(C!3, B!4), empty_set), empty_set)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 ((~((~member(tptp_fun_D_2(union(C!3, B!4), empty_set), empty_set)) <=> member(tptp_fun_D_2(union(C!3, B!4), empty_set), union(C!3, B!4)))) | member(tptp_fun_D_2(union(C!3, B!4), empty_set), empty_set) | member(tptp_fun_D_2(union(C!3, B!4), empty_set), union(C!3, B!4))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 (member(tptp_fun_D_2(union(C!3, B!4), empty_set), union(C!3, B!4))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[85, 84, 75])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 (member(tptp_fun_D_2(union(C!3, B!4), empty_set), union(empty_set, empty_set))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[86, 40])).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[88])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[91])).
% 0.19/0.41 tff(93,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')).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.19/0.41 tff(95,plain,
% 0.19/0.41 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.19/0.41 tff(96,plain,(
% 0.19/0.41 ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[95])).
% 0.19/0.41 tff(97,plain,
% 0.19/0.41 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[96, 89])).
% 0.19/0.41 tff(98,plain,
% 0.19/0.41 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_2(union(C!3, B!4), empty_set), union(empty_set, empty_set)) <=> member(tptp_fun_D_2(union(C!3, B!4), empty_set), empty_set))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_2(union(C!3, B!4), empty_set), union(empty_set, empty_set)) <=> member(tptp_fun_D_2(union(C!3, B!4), empty_set), empty_set)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 ((member(tptp_fun_D_2(union(C!3, B!4), empty_set), union(empty_set, empty_set)) <=> (member(tptp_fun_D_2(union(C!3, B!4), empty_set), empty_set) | member(tptp_fun_D_2(union(C!3, B!4), empty_set), empty_set))) <=> (member(tptp_fun_D_2(union(C!3, B!4), empty_set), union(empty_set, empty_set)) <=> member(tptp_fun_D_2(union(C!3, B!4), empty_set), empty_set))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_2(union(C!3, B!4), empty_set), union(empty_set, empty_set)) <=> (member(tptp_fun_D_2(union(C!3, B!4), empty_set), empty_set) | member(tptp_fun_D_2(union(C!3, B!4), empty_set), empty_set)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_2(union(C!3, B!4), empty_set), union(empty_set, empty_set)) <=> member(tptp_fun_D_2(union(C!3, B!4), empty_set), empty_set)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[99])).
% 0.19/0.41 tff(101,plain,
% 0.19/0.41 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_2(union(C!3, B!4), empty_set), union(empty_set, empty_set)) <=> (member(tptp_fun_D_2(union(C!3, B!4), empty_set), empty_set) | member(tptp_fun_D_2(union(C!3, B!4), empty_set), empty_set)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_2(union(C!3, B!4), empty_set), union(empty_set, empty_set)) <=> member(tptp_fun_D_2(union(C!3, B!4), empty_set), empty_set)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[100, 98])).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_2(union(C!3, B!4), empty_set), union(empty_set, empty_set)) <=> (member(tptp_fun_D_2(union(C!3, B!4), empty_set), empty_set) | member(tptp_fun_D_2(union(C!3, B!4), empty_set), empty_set)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_2(union(C!3, B!4), empty_set), union(empty_set, empty_set)) <=> member(tptp_fun_D_2(union(C!3, B!4), empty_set), empty_set))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.19/0.41 tff(104,plain,
% 0.19/0.41 (member(tptp_fun_D_2(union(C!3, B!4), empty_set), union(empty_set, empty_set)) <=> member(tptp_fun_D_2(union(C!3, B!4), empty_set), empty_set)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[103, 97])).
% 0.19/0.41 tff(105,plain,
% 0.19/0.41 ((~(member(tptp_fun_D_2(union(C!3, B!4), empty_set), union(empty_set, empty_set)) <=> member(tptp_fun_D_2(union(C!3, B!4), empty_set), empty_set))) | (~member(tptp_fun_D_2(union(C!3, B!4), empty_set), union(empty_set, empty_set))) | member(tptp_fun_D_2(union(C!3, B!4), empty_set), empty_set)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 (~member(tptp_fun_D_2(union(C!3, B!4), empty_set), union(empty_set, empty_set))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[105, 84, 104])).
% 0.19/0.41 tff(107,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[106, 87])).
% 0.19/0.41 tff(108,plain,(union(B!4, C!3) = empty_set), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 (union(C!3, B!4) = empty_set),
% 0.19/0.41 inference(transitivity,[status(thm)],[42, 108])).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 ((B!4 = union(C!3, B!4)) <=> (B!4 = empty_set)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[109])).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 ((B!4 = empty_set) <=> (B!4 = union(C!3, B!4))),
% 0.19/0.41 inference(symmetry,[status(thm)],[110])).
% 0.19/0.41 tff(112,plain,
% 0.19/0.41 ((~(B!4 = empty_set)) <=> (~(B!4 = union(C!3, B!4)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[111])).
% 0.19/0.41 tff(113,plain,
% 0.19/0.41 ((C!3 = union(C!3, B!4)) <=> (C!3 = empty_set)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[109])).
% 0.19/0.41 tff(114,assumption,((~member(tptp_fun_D_2(union(C!3, B!4), C!3), C!3)) <=> member(tptp_fun_D_2(union(C!3, B!4), C!3), union(C!3, B!4))), introduced(assumption)).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 (empty_set = union(B!4, C!3)),
% 0.19/0.41 inference(symmetry,[status(thm)],[108])).
% 0.19/0.41 tff(116,plain,
% 0.19/0.41 (empty_set = union(C!3, B!4)),
% 0.19/0.41 inference(transitivity,[status(thm)],[115, 9])).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 (member(tptp_fun_D_2(union(C!3, B!4), C!3), empty_set) <=> member(tptp_fun_D_2(union(C!3, B!4), C!3), union(C!3, B!4))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[116])).
% 0.19/0.41 tff(118,plain,
% 0.19/0.41 ((~member(tptp_fun_D_2(union(C!3, B!4), C!3), empty_set)) <=> (~member(tptp_fun_D_2(union(C!3, B!4), C!3), union(C!3, B!4)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[117])).
% 0.19/0.42 tff(119,plain,
% 0.19/0.42 ((~![B: $i] : (~member(B, empty_set))) | (~member(tptp_fun_D_2(union(C!3, B!4), C!3), empty_set))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(120,plain,
% 0.19/0.42 (~member(tptp_fun_D_2(union(C!3, B!4), C!3), empty_set)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[119, 82])).
% 0.19/0.42 tff(121,plain,
% 0.19/0.42 (~member(tptp_fun_D_2(union(C!3, B!4), C!3), union(C!3, B!4))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[120, 118])).
% 0.19/0.42 tff(122,plain,
% 0.19/0.42 ((~((~member(tptp_fun_D_2(union(C!3, B!4), C!3), C!3)) <=> member(tptp_fun_D_2(union(C!3, B!4), C!3), union(C!3, B!4)))) | member(tptp_fun_D_2(union(C!3, B!4), C!3), C!3) | member(tptp_fun_D_2(union(C!3, B!4), C!3), union(C!3, B!4))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(123,plain,
% 0.19/0.42 (member(tptp_fun_D_2(union(C!3, B!4), C!3), C!3)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[122, 121, 114])).
% 0.19/0.42 tff(124,plain,
% 0.19/0.42 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_2(union(C!3, B!4), C!3), union(C!3, B!4)) <=> (member(tptp_fun_D_2(union(C!3, B!4), C!3), B!4) | member(tptp_fun_D_2(union(C!3, B!4), C!3), C!3)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(125,plain,
% 0.19/0.42 (member(tptp_fun_D_2(union(C!3, B!4), C!3), union(C!3, B!4)) <=> (member(tptp_fun_D_2(union(C!3, B!4), C!3), B!4) | member(tptp_fun_D_2(union(C!3, B!4), C!3), C!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[124, 97])).
% 0.19/0.42 tff(126,plain,
% 0.19/0.42 ((~(member(tptp_fun_D_2(union(C!3, B!4), C!3), union(C!3, B!4)) <=> (member(tptp_fun_D_2(union(C!3, B!4), C!3), B!4) | member(tptp_fun_D_2(union(C!3, B!4), C!3), C!3)))) | member(tptp_fun_D_2(union(C!3, B!4), C!3), union(C!3, B!4)) | (~(member(tptp_fun_D_2(union(C!3, B!4), C!3), B!4) | member(tptp_fun_D_2(union(C!3, B!4), C!3), C!3)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(127,plain,
% 0.19/0.42 (~(member(tptp_fun_D_2(union(C!3, B!4), C!3), B!4) | member(tptp_fun_D_2(union(C!3, B!4), C!3), C!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[126, 121, 125])).
% 0.19/0.42 tff(128,plain,
% 0.19/0.42 ((member(tptp_fun_D_2(union(C!3, B!4), C!3), B!4) | member(tptp_fun_D_2(union(C!3, B!4), C!3), C!3)) | (~member(tptp_fun_D_2(union(C!3, B!4), C!3), C!3))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(129,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[128, 127, 123])).
% 0.19/0.42 tff(130,plain,(~((~member(tptp_fun_D_2(union(C!3, B!4), C!3), C!3)) <=> member(tptp_fun_D_2(union(C!3, B!4), C!3), union(C!3, B!4)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(131,plain,
% 0.19/0.42 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))) | (~((~((~(C!3 = union(C!3, B!4))) | (member(union(C!3, B!4), C!3) <=> member(union(C!3, B!4), union(C!3, B!4))))) | (~((C!3 = union(C!3, B!4)) | ((~member(tptp_fun_D_2(union(C!3, B!4), C!3), C!3)) <=> member(tptp_fun_D_2(union(C!3, B!4), C!3), union(C!3, B!4)))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(132,plain,
% 0.19/0.42 (~((~((~(C!3 = union(C!3, B!4))) | (member(union(C!3, B!4), C!3) <=> member(union(C!3, B!4), union(C!3, B!4))))) | (~((C!3 = union(C!3, B!4)) | ((~member(tptp_fun_D_2(union(C!3, B!4), C!3), C!3)) <=> member(tptp_fun_D_2(union(C!3, B!4), C!3), union(C!3, B!4))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[131, 68])).
% 0.19/0.42 tff(133,plain,
% 0.19/0.42 (((~((~(C!3 = union(C!3, B!4))) | (member(union(C!3, B!4), C!3) <=> member(union(C!3, B!4), union(C!3, B!4))))) | (~((C!3 = union(C!3, B!4)) | ((~member(tptp_fun_D_2(union(C!3, B!4), C!3), C!3)) <=> member(tptp_fun_D_2(union(C!3, B!4), C!3), union(C!3, B!4)))))) | ((C!3 = union(C!3, B!4)) | ((~member(tptp_fun_D_2(union(C!3, B!4), C!3), C!3)) <=> member(tptp_fun_D_2(union(C!3, B!4), C!3), union(C!3, B!4))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(134,plain,
% 0.19/0.42 ((C!3 = union(C!3, B!4)) | ((~member(tptp_fun_D_2(union(C!3, B!4), C!3), C!3)) <=> member(tptp_fun_D_2(union(C!3, B!4), C!3), union(C!3, B!4)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.19/0.42 tff(135,plain,
% 0.19/0.42 ((~((C!3 = union(C!3, B!4)) | ((~member(tptp_fun_D_2(union(C!3, B!4), C!3), C!3)) <=> member(tptp_fun_D_2(union(C!3, B!4), C!3), union(C!3, B!4))))) | (C!3 = union(C!3, B!4)) | ((~member(tptp_fun_D_2(union(C!3, B!4), C!3), C!3)) <=> member(tptp_fun_D_2(union(C!3, B!4), C!3), union(C!3, B!4)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(136,plain,
% 0.19/0.42 ((C!3 = union(C!3, B!4)) | ((~member(tptp_fun_D_2(union(C!3, B!4), C!3), C!3)) <=> member(tptp_fun_D_2(union(C!3, B!4), C!3), union(C!3, B!4)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.19/0.42 tff(137,plain,
% 0.19/0.42 (C!3 = union(C!3, B!4)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[136, 130])).
% 0.19/0.42 tff(138,plain,
% 0.19/0.42 (C!3 = empty_set),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[137, 113])).
% 0.19/0.42 tff(139,plain,
% 0.19/0.42 ((~(union(B!4, C!3) = empty_set)) | ((~(B!4 = empty_set)) | (~(C!3 = empty_set))) | (~((union(B!4, C!3) = empty_set) <=> ((~(B!4 = empty_set)) | (~(C!3 = empty_set)))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(140,plain,
% 0.19/0.42 ((~(union(B!4, C!3) = empty_set)) | ((~(B!4 = empty_set)) | (~(C!3 = empty_set)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[139, 27])).
% 0.19/0.42 tff(141,plain,
% 0.19/0.42 ((~(B!4 = empty_set)) | (~(C!3 = empty_set))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[140, 108])).
% 0.19/0.42 tff(142,plain,
% 0.19/0.42 ((~((~(B!4 = empty_set)) | (~(C!3 = empty_set)))) | (~(B!4 = empty_set)) | (~(C!3 = empty_set))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(143,plain,
% 0.19/0.42 ((~(B!4 = empty_set)) | (~(C!3 = empty_set))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[142, 141])).
% 0.19/0.42 tff(144,plain,
% 0.19/0.42 (~(B!4 = empty_set)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[143, 138])).
% 0.19/0.42 tff(145,plain,
% 0.19/0.42 (~(B!4 = union(C!3, B!4))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[144, 112])).
% 0.19/0.42 tff(146,plain,
% 0.19/0.42 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))) | (~((~((~(B!4 = union(C!3, B!4))) | (member(union(C!3, B!4), B!4) <=> member(union(C!3, B!4), union(C!3, B!4))))) | (~((B!4 = union(C!3, B!4)) | ((~member(tptp_fun_D_2(union(C!3, B!4), B!4), B!4)) <=> member(tptp_fun_D_2(union(C!3, B!4), B!4), union(C!3, B!4)))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(147,plain,
% 0.19/0.42 (~((~((~(B!4 = union(C!3, B!4))) | (member(union(C!3, B!4), B!4) <=> member(union(C!3, B!4), union(C!3, B!4))))) | (~((B!4 = union(C!3, B!4)) | ((~member(tptp_fun_D_2(union(C!3, B!4), B!4), B!4)) <=> member(tptp_fun_D_2(union(C!3, B!4), B!4), union(C!3, B!4))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[146, 68])).
% 0.19/0.42 tff(148,plain,
% 0.19/0.42 (((~((~(B!4 = union(C!3, B!4))) | (member(union(C!3, B!4), B!4) <=> member(union(C!3, B!4), union(C!3, B!4))))) | (~((B!4 = union(C!3, B!4)) | ((~member(tptp_fun_D_2(union(C!3, B!4), B!4), B!4)) <=> member(tptp_fun_D_2(union(C!3, B!4), B!4), union(C!3, B!4)))))) | ((B!4 = union(C!3, B!4)) | ((~member(tptp_fun_D_2(union(C!3, B!4), B!4), B!4)) <=> member(tptp_fun_D_2(union(C!3, B!4), B!4), union(C!3, B!4))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(149,plain,
% 0.19/0.42 ((B!4 = union(C!3, B!4)) | ((~member(tptp_fun_D_2(union(C!3, B!4), B!4), B!4)) <=> member(tptp_fun_D_2(union(C!3, B!4), B!4), union(C!3, B!4)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.19/0.42 tff(150,plain,
% 0.19/0.42 ((~((B!4 = union(C!3, B!4)) | ((~member(tptp_fun_D_2(union(C!3, B!4), B!4), B!4)) <=> member(tptp_fun_D_2(union(C!3, B!4), B!4), union(C!3, B!4))))) | (B!4 = union(C!3, B!4)) | ((~member(tptp_fun_D_2(union(C!3, B!4), B!4), B!4)) <=> member(tptp_fun_D_2(union(C!3, B!4), B!4), union(C!3, B!4)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(151,plain,
% 0.19/0.42 ((B!4 = union(C!3, B!4)) | ((~member(tptp_fun_D_2(union(C!3, B!4), B!4), B!4)) <=> member(tptp_fun_D_2(union(C!3, B!4), B!4), union(C!3, B!4)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.19/0.42 tff(152,plain,
% 0.19/0.42 ((~member(tptp_fun_D_2(union(C!3, B!4), B!4), B!4)) <=> member(tptp_fun_D_2(union(C!3, B!4), B!4), union(C!3, B!4))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[151, 145])).
% 0.19/0.42 tff(153,plain,
% 0.19/0.42 (member(tptp_fun_D_2(union(C!3, B!4), B!4), empty_set) <=> member(tptp_fun_D_2(union(C!3, B!4), B!4), union(C!3, B!4))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[116])).
% 0.19/0.42 tff(154,plain,
% 0.19/0.42 ((~member(tptp_fun_D_2(union(C!3, B!4), B!4), empty_set)) <=> (~member(tptp_fun_D_2(union(C!3, B!4), B!4), union(C!3, B!4)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[153])).
% 0.19/0.42 tff(155,plain,
% 0.19/0.42 ((~![B: $i] : (~member(B, empty_set))) | (~member(tptp_fun_D_2(union(C!3, B!4), B!4), empty_set))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(156,plain,
% 0.19/0.42 (~member(tptp_fun_D_2(union(C!3, B!4), B!4), empty_set)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[155, 82])).
% 0.19/0.42 tff(157,plain,
% 0.19/0.42 (~member(tptp_fun_D_2(union(C!3, B!4), B!4), union(C!3, B!4))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[156, 154])).
% 0.19/0.42 tff(158,plain,
% 0.19/0.42 ((~((~member(tptp_fun_D_2(union(C!3, B!4), B!4), B!4)) <=> member(tptp_fun_D_2(union(C!3, B!4), B!4), union(C!3, B!4)))) | member(tptp_fun_D_2(union(C!3, B!4), B!4), B!4) | member(tptp_fun_D_2(union(C!3, B!4), B!4), union(C!3, B!4))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(159,plain,
% 0.19/0.42 (member(tptp_fun_D_2(union(C!3, B!4), B!4), B!4)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[158, 157, 152])).
% 0.19/0.42 tff(160,plain,
% 0.19/0.42 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_2(union(C!3, B!4), B!4), union(B!4, union(C!3, B!4))) <=> (member(tptp_fun_D_2(union(C!3, B!4), B!4), B!4) | member(tptp_fun_D_2(union(C!3, B!4), B!4), union(C!3, B!4))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_2(union(C!3, B!4), B!4), union(B!4, union(C!3, B!4))) <=> (member(tptp_fun_D_2(union(C!3, B!4), B!4), B!4) | member(tptp_fun_D_2(union(C!3, B!4), B!4), union(C!3, B!4)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(161,plain,
% 0.19/0.42 ((member(tptp_fun_D_2(union(C!3, B!4), B!4), union(B!4, union(C!3, B!4))) <=> (member(tptp_fun_D_2(union(C!3, B!4), B!4), union(C!3, B!4)) | member(tptp_fun_D_2(union(C!3, B!4), B!4), B!4))) <=> (member(tptp_fun_D_2(union(C!3, B!4), B!4), union(B!4, union(C!3, B!4))) <=> (member(tptp_fun_D_2(union(C!3, B!4), B!4), B!4) | member(tptp_fun_D_2(union(C!3, B!4), B!4), union(C!3, B!4))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(162,plain,
% 0.19/0.42 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_2(union(C!3, B!4), B!4), union(B!4, union(C!3, B!4))) <=> (member(tptp_fun_D_2(union(C!3, B!4), B!4), union(C!3, B!4)) | member(tptp_fun_D_2(union(C!3, B!4), B!4), B!4)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_2(union(C!3, B!4), B!4), union(B!4, union(C!3, B!4))) <=> (member(tptp_fun_D_2(union(C!3, B!4), B!4), B!4) | member(tptp_fun_D_2(union(C!3, B!4), B!4), union(C!3, B!4)))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[161])).
% 0.19/0.42 tff(163,plain,
% 0.19/0.42 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_2(union(C!3, B!4), B!4), union(B!4, union(C!3, B!4))) <=> (member(tptp_fun_D_2(union(C!3, B!4), B!4), union(C!3, B!4)) | member(tptp_fun_D_2(union(C!3, B!4), B!4), B!4)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_2(union(C!3, B!4), B!4), union(B!4, union(C!3, B!4))) <=> (member(tptp_fun_D_2(union(C!3, B!4), B!4), B!4) | member(tptp_fun_D_2(union(C!3, B!4), B!4), union(C!3, B!4)))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[162, 160])).
% 0.19/0.42 tff(164,plain,
% 0.19/0.42 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_2(union(C!3, B!4), B!4), union(B!4, union(C!3, B!4))) <=> (member(tptp_fun_D_2(union(C!3, B!4), B!4), union(C!3, B!4)) | member(tptp_fun_D_2(union(C!3, B!4), B!4), B!4)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(165,plain,
% 0.19/0.42 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_2(union(C!3, B!4), B!4), union(B!4, union(C!3, B!4))) <=> (member(tptp_fun_D_2(union(C!3, B!4), B!4), B!4) | member(tptp_fun_D_2(union(C!3, B!4), B!4), union(C!3, B!4))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.19/0.43 tff(166,plain,
% 0.19/0.43 (member(tptp_fun_D_2(union(C!3, B!4), B!4), union(B!4, union(C!3, B!4))) <=> (member(tptp_fun_D_2(union(C!3, B!4), B!4), B!4) | member(tptp_fun_D_2(union(C!3, B!4), B!4), union(C!3, B!4)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[165, 97])).
% 0.19/0.43 tff(167,plain,
% 0.19/0.43 (union(C!3, B!4) = C!3),
% 0.19/0.43 inference(symmetry,[status(thm)],[137])).
% 0.19/0.43 tff(168,plain,
% 0.19/0.43 (union(B!4, union(C!3, B!4)) = union(B!4, C!3)),
% 0.19/0.43 inference(monotonicity,[status(thm)],[167])).
% 0.19/0.43 tff(169,plain,
% 0.19/0.43 (union(B!4, union(C!3, B!4)) = union(C!3, B!4)),
% 0.19/0.43 inference(transitivity,[status(thm)],[168, 9])).
% 0.19/0.43 tff(170,plain,
% 0.19/0.43 (member(tptp_fun_D_2(union(C!3, B!4), B!4), union(B!4, union(C!3, B!4))) <=> member(tptp_fun_D_2(union(C!3, B!4), B!4), union(C!3, B!4))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[169])).
% 0.19/0.43 tff(171,plain,
% 0.19/0.43 (member(tptp_fun_D_2(union(C!3, B!4), B!4), union(C!3, B!4)) <=> member(tptp_fun_D_2(union(C!3, B!4), B!4), union(B!4, union(C!3, B!4)))),
% 0.19/0.43 inference(symmetry,[status(thm)],[170])).
% 0.19/0.43 tff(172,plain,
% 0.19/0.43 (member(tptp_fun_D_2(union(C!3, B!4), B!4), empty_set) <=> member(tptp_fun_D_2(union(C!3, B!4), B!4), union(B!4, union(C!3, B!4)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[153, 171])).
% 0.19/0.43 tff(173,plain,
% 0.19/0.43 ((~member(tptp_fun_D_2(union(C!3, B!4), B!4), empty_set)) <=> (~member(tptp_fun_D_2(union(C!3, B!4), B!4), union(B!4, union(C!3, B!4))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[172])).
% 0.19/0.43 tff(174,plain,
% 0.19/0.43 (~member(tptp_fun_D_2(union(C!3, B!4), B!4), union(B!4, union(C!3, B!4)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[156, 173])).
% 0.19/0.43 tff(175,plain,
% 0.19/0.43 ((~(member(tptp_fun_D_2(union(C!3, B!4), B!4), union(B!4, union(C!3, B!4))) <=> (member(tptp_fun_D_2(union(C!3, B!4), B!4), B!4) | member(tptp_fun_D_2(union(C!3, B!4), B!4), union(C!3, B!4))))) | member(tptp_fun_D_2(union(C!3, B!4), B!4), union(B!4, union(C!3, B!4))) | (~(member(tptp_fun_D_2(union(C!3, B!4), B!4), B!4) | member(tptp_fun_D_2(union(C!3, B!4), B!4), union(C!3, B!4))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(176,plain,
% 0.19/0.43 (~(member(tptp_fun_D_2(union(C!3, B!4), B!4), B!4) | member(tptp_fun_D_2(union(C!3, B!4), B!4), union(C!3, B!4)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[175, 174, 166])).
% 0.19/0.43 tff(177,plain,
% 0.19/0.43 ((member(tptp_fun_D_2(union(C!3, B!4), B!4), B!4) | member(tptp_fun_D_2(union(C!3, B!4), B!4), union(C!3, B!4))) | (~member(tptp_fun_D_2(union(C!3, B!4), B!4), B!4))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(178,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[177, 176, 159])).
% 0.19/0.43 % SZS output end Proof
%------------------------------------------------------------------------------