TSTP Solution File: SET159+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET159+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 05:05:56 EDT 2022
% Result : Theorem 1.71s 1.35s
% Output : Proof 1.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SET159+3 : TPTP v8.1.0. Released v2.2.0.
% 0.09/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n008.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 03:03:40 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.
% 1.71/1.35 % SZS status Theorem
% 1.71/1.35 % SZS output start Proof
% 1.71/1.35 tff(member_type, type, (
% 1.71/1.35 member: ( $i * $i ) > $o)).
% 1.71/1.35 tff(union_type, type, (
% 1.71/1.35 union: ( $i * $i ) > $i)).
% 1.71/1.35 tff(tptp_fun_B_4_type, type, (
% 1.71/1.35 tptp_fun_B_4: $i)).
% 1.71/1.35 tff(tptp_fun_C_3_type, type, (
% 1.71/1.35 tptp_fun_C_3: $i)).
% 1.71/1.35 tff(tptp_fun_D_1_type, type, (
% 1.71/1.35 tptp_fun_D_1: ( $i * $i ) > $i)).
% 1.71/1.35 tff(tptp_fun_D_2_type, type, (
% 1.71/1.35 tptp_fun_D_2: $i)).
% 1.71/1.35 tff(1,assumption,((~member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3))), introduced(assumption)).
% 1.71/1.35 tff(2,assumption,(~member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3))), introduced(assumption)).
% 1.71/1.35 tff(3,assumption,(~(member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3)) <=> member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3))), introduced(assumption)).
% 1.71/1.35 tff(4,plain,
% 1.71/1.35 (^[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))))),
% 1.71/1.35 inference(bind,[status(th)],[])).
% 1.71/1.35 tff(5,plain,
% 1.71/1.35 (![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)))),
% 1.71/1.35 inference(quant_intro,[status(thm)],[4])).
% 1.71/1.35 tff(6,plain,
% 1.71/1.35 (![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)))),
% 1.71/1.35 inference(rewrite,[status(thm)],[])).
% 1.71/1.35 tff(7,plain,
% 1.71/1.35 (^[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))))),
% 1.71/1.35 inference(bind,[status(th)],[])).
% 1.71/1.35 tff(8,plain,
% 1.71/1.35 (![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)))),
% 1.71/1.35 inference(quant_intro,[status(thm)],[7])).
% 1.71/1.35 tff(9,axiom,(![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, B) | member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','union_defn')).
% 1.71/1.35 tff(10,plain,
% 1.71/1.35 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 1.71/1.35 inference(modus_ponens,[status(thm)],[9, 8])).
% 1.71/1.35 tff(11,plain,
% 1.71/1.35 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 1.71/1.35 inference(modus_ponens,[status(thm)],[10, 6])).
% 1.71/1.35 tff(12,plain,(
% 1.71/1.35 ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 1.71/1.35 inference(skolemize,[status(sab)],[11])).
% 1.71/1.35 tff(13,plain,
% 1.71/1.35 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 1.71/1.35 inference(modus_ponens,[status(thm)],[12, 5])).
% 1.71/1.35 tff(14,plain,
% 1.71/1.35 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3)) <=> member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3)) <=> member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3)))),
% 1.71/1.35 inference(rewrite,[status(thm)],[])).
% 1.71/1.35 tff(15,plain,
% 1.71/1.35 ((member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3)) <=> (member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3) | member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3))) <=> (member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3)) <=> member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3))),
% 1.71/1.35 inference(rewrite,[status(thm)],[])).
% 1.71/1.35 tff(16,plain,
% 1.71/1.35 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3)) <=> (member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3) | member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3)) <=> member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3)))),
% 1.71/1.35 inference(monotonicity,[status(thm)],[15])).
% 1.71/1.35 tff(17,plain,
% 1.71/1.35 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3)) <=> (member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3) | member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3)) <=> member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3)))),
% 1.71/1.35 inference(transitivity,[status(thm)],[16, 14])).
% 1.71/1.35 tff(18,plain,
% 1.71/1.35 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3)) <=> (member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3) | member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3)))),
% 1.71/1.35 inference(quant_inst,[status(thm)],[])).
% 1.71/1.35 tff(19,plain,
% 1.71/1.35 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3)) <=> member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3))),
% 1.71/1.35 inference(modus_ponens,[status(thm)],[18, 17])).
% 1.71/1.35 tff(20,plain,
% 1.71/1.35 ($false),
% 1.71/1.35 inference(unit_resolution,[status(thm)],[19, 13, 3])).
% 1.71/1.35 tff(21,plain,(member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3)) <=> member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3)), inference(lemma,lemma(discharge,[]))).
% 1.71/1.35 tff(22,plain,
% 1.71/1.35 ((~(member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3)) <=> member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3))) | member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3)) | (~member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3))),
% 1.71/1.35 inference(tautology,[status(thm)],[])).
% 1.71/1.35 tff(23,plain,
% 1.71/1.35 (member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3)) | (~member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3))),
% 1.71/1.35 inference(unit_resolution,[status(thm)],[22, 21])).
% 1.71/1.35 tff(24,plain,
% 1.71/1.35 (~member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3)),
% 1.71/1.35 inference(unit_resolution,[status(thm)],[23, 2])).
% 1.71/1.35 tff(25,plain,
% 1.71/1.35 ((~((~member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3)))) | member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3) | member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3))),
% 1.71/1.35 inference(tautology,[status(thm)],[])).
% 1.71/1.35 tff(26,plain,
% 1.71/1.35 ($false),
% 1.71/1.35 inference(unit_resolution,[status(thm)],[25, 24, 2, 1])).
% 1.71/1.35 tff(27,plain,(member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3)) | (~((~member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3))))), inference(lemma,lemma(discharge,[]))).
% 1.71/1.35 tff(28,plain,
% 1.71/1.35 (member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3))),
% 1.71/1.35 inference(unit_resolution,[status(thm)],[27, 1])).
% 1.71/1.35 tff(29,plain,
% 1.71/1.35 ((~((~member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3)))) | (~member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3)))),
% 1.71/1.35 inference(tautology,[status(thm)],[])).
% 1.71/1.35 tff(30,plain,
% 1.71/1.35 (~member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3)),
% 1.71/1.35 inference(unit_resolution,[status(thm)],[29, 28, 1])).
% 1.71/1.35 tff(31,plain,
% 1.71/1.35 ((~(member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3)) <=> member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3))) | (~member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3))) | member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3)),
% 1.71/1.35 inference(tautology,[status(thm)],[])).
% 1.71/1.35 tff(32,plain,
% 1.71/1.35 ((~member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3))) | member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3)),
% 1.71/1.35 inference(unit_resolution,[status(thm)],[31, 21])).
% 1.71/1.35 tff(33,plain,
% 1.71/1.35 ($false),
% 1.71/1.35 inference(unit_resolution,[status(thm)],[32, 30, 28])).
% 1.71/1.35 tff(34,plain,(~((~member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3)))), inference(lemma,lemma(discharge,[]))).
% 1.71/1.35 tff(35,plain,
% 1.71/1.35 (^[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)))))))),
% 1.71/1.35 inference(bind,[status(th)],[])).
% 1.71/1.35 tff(36,plain,
% 1.71/1.35 (![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))))))),
% 1.71/1.35 inference(quant_intro,[status(thm)],[35])).
% 1.71/1.35 tff(37,plain,
% 1.71/1.35 (![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))))))),
% 1.71/1.35 inference(pull_quant,[status(thm)],[])).
% 1.71/1.35 tff(38,plain,
% 1.71/1.35 (^[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))))))))),
% 1.71/1.35 inference(bind,[status(th)],[])).
% 1.71/1.35 tff(39,plain,
% 1.71/1.35 (![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))))))),
% 1.71/1.35 inference(quant_intro,[status(thm)],[38])).
% 1.71/1.35 tff(40,plain,
% 1.71/1.35 (![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))))))),
% 1.71/1.35 inference(transitivity,[status(thm)],[39, 37])).
% 1.71/1.35 tff(41,plain,
% 1.71/1.35 (![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))))))),
% 1.71/1.35 inference(transitivity,[status(thm)],[40, 36])).
% 1.71/1.35 tff(42,plain,
% 1.71/1.35 (^[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)))))))),
% 1.71/1.35 inference(bind,[status(th)],[])).
% 1.71/1.35 tff(43,plain,
% 1.71/1.35 (![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))))))),
% 1.71/1.35 inference(quant_intro,[status(thm)],[42])).
% 1.71/1.35 tff(44,plain,
% 1.71/1.35 (![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))))))),
% 1.71/1.35 inference(transitivity,[status(thm)],[43, 41])).
% 1.71/1.35 tff(45,plain,
% 1.71/1.35 (^[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))))))))),
% 1.71/1.35 inference(bind,[status(th)],[])).
% 1.71/1.35 tff(46,plain,
% 1.71/1.35 (![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))))))),
% 1.71/1.35 inference(quant_intro,[status(thm)],[45])).
% 1.71/1.35 tff(47,plain,
% 1.71/1.35 (^[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)))))),
% 1.71/1.35 inference(bind,[status(th)],[])).
% 1.71/1.35 tff(48,plain,
% 1.71/1.35 (![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))))),
% 1.71/1.35 inference(quant_intro,[status(thm)],[47])).
% 1.71/1.35 tff(49,plain,
% 1.71/1.35 (![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)))),
% 1.71/1.35 inference(rewrite,[status(thm)],[])).
% 1.71/1.35 tff(50,axiom,(![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','equal_member_defn')).
% 1.71/1.35 tff(51,plain,
% 1.71/1.35 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 1.71/1.35 inference(modus_ponens,[status(thm)],[50, 49])).
% 1.71/1.35 tff(52,plain,(
% 1.71/1.35 ![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)))))),
% 1.71/1.35 inference(skolemize,[status(sab)],[51])).
% 1.71/1.35 tff(53,plain,
% 1.71/1.35 (![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))))),
% 1.71/1.35 inference(modus_ponens,[status(thm)],[52, 48])).
% 1.71/1.35 tff(54,plain,
% 1.71/1.35 (![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))))))),
% 1.71/1.35 inference(modus_ponens,[status(thm)],[53, 46])).
% 1.71/1.35 tff(55,plain,
% 1.71/1.35 (![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))))))),
% 1.71/1.35 inference(modus_ponens,[status(thm)],[54, 44])).
% 1.71/1.35 tff(56,plain,
% 1.71/1.35 ((~![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!3 = union(C!3, C!3))) | (member(tptp_fun_D_1(union(C!3, B!4), C!3), C!3) <=> member(tptp_fun_D_1(union(C!3, B!4), C!3), union(C!3, C!3))))) | (~((C!3 = union(C!3, C!3)) | ((~member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3)))))))),
% 1.71/1.35 inference(quant_inst,[status(thm)],[])).
% 1.71/1.35 tff(57,plain,
% 1.71/1.35 (~((~((~(C!3 = union(C!3, C!3))) | (member(tptp_fun_D_1(union(C!3, B!4), C!3), C!3) <=> member(tptp_fun_D_1(union(C!3, B!4), C!3), union(C!3, C!3))))) | (~((C!3 = union(C!3, C!3)) | ((~member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3))))))),
% 1.71/1.35 inference(unit_resolution,[status(thm)],[56, 55])).
% 1.71/1.35 tff(58,plain,
% 1.71/1.35 (((~((~(C!3 = union(C!3, C!3))) | (member(tptp_fun_D_1(union(C!3, B!4), C!3), C!3) <=> member(tptp_fun_D_1(union(C!3, B!4), C!3), union(C!3, C!3))))) | (~((C!3 = union(C!3, C!3)) | ((~member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3)))))) | ((C!3 = union(C!3, C!3)) | ((~member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3))))),
% 1.71/1.35 inference(tautology,[status(thm)],[])).
% 1.71/1.35 tff(59,plain,
% 1.71/1.35 ((C!3 = union(C!3, C!3)) | ((~member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3)))),
% 1.71/1.35 inference(unit_resolution,[status(thm)],[58, 57])).
% 1.71/1.35 tff(60,plain,
% 1.71/1.35 ((~((C!3 = union(C!3, C!3)) | ((~member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3))))) | (C!3 = union(C!3, C!3)) | ((~member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3)))),
% 1.71/1.35 inference(tautology,[status(thm)],[])).
% 1.71/1.35 tff(61,plain,
% 1.71/1.35 ((C!3 = union(C!3, C!3)) | ((~member(tptp_fun_D_1(union(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_1(union(C!3, C!3), C!3), union(C!3, C!3)))),
% 1.71/1.35 inference(unit_resolution,[status(thm)],[60, 59])).
% 1.71/1.35 tff(62,plain,
% 1.71/1.35 (C!3 = union(C!3, C!3)),
% 1.71/1.35 inference(unit_resolution,[status(thm)],[61, 34])).
% 1.71/1.35 tff(63,plain,
% 1.71/1.35 (union(C!3, C!3) = C!3),
% 1.71/1.35 inference(symmetry,[status(thm)],[62])).
% 1.71/1.35 tff(64,plain,
% 1.71/1.35 (union(union(C!3, C!3), B!4) = union(C!3, B!4)),
% 1.71/1.35 inference(monotonicity,[status(thm)],[63])).
% 1.71/1.35 tff(65,plain,
% 1.71/1.35 (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(union(C!3, C!3), B!4)) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(C!3, B!4))),
% 1.71/1.35 inference(monotonicity,[status(thm)],[64])).
% 1.71/1.35 tff(66,plain,
% 1.71/1.35 (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(C!3, B!4)) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(union(C!3, C!3), B!4))),
% 1.71/1.35 inference(symmetry,[status(thm)],[65])).
% 1.71/1.35 tff(67,plain,
% 1.71/1.35 ((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(C!3, B!4))) <=> (~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(union(C!3, C!3), B!4)))),
% 1.71/1.35 inference(monotonicity,[status(thm)],[66])).
% 1.71/1.35 tff(68,assumption,(member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), D!2) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(C!3, B!4)))), introduced(assumption)).
% 1.71/1.35 tff(69,plain,
% 1.71/1.35 (^[B: $i, C: $i] : refl((union(B, C) = union(C, B)) <=> (union(B, C) = union(C, B)))),
% 1.71/1.35 inference(bind,[status(th)],[])).
% 1.71/1.35 tff(70,plain,
% 1.71/1.35 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 1.71/1.35 inference(quant_intro,[status(thm)],[69])).
% 1.71/1.35 tff(71,plain,
% 1.71/1.35 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 1.71/1.35 inference(rewrite,[status(thm)],[])).
% 1.71/1.35 tff(72,axiom,(![B: $i, C: $i] : (union(B, C) = union(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_union')).
% 1.71/1.35 tff(73,plain,
% 1.71/1.35 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 1.71/1.35 inference(modus_ponens,[status(thm)],[72, 71])).
% 1.71/1.35 tff(74,plain,(
% 1.71/1.35 ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 1.71/1.35 inference(skolemize,[status(sab)],[73])).
% 1.71/1.35 tff(75,plain,
% 1.71/1.35 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 1.71/1.35 inference(modus_ponens,[status(thm)],[74, 70])).
% 1.71/1.35 tff(76,plain,
% 1.71/1.35 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(B!4, C!3) = union(C!3, B!4))),
% 1.71/1.35 inference(quant_inst,[status(thm)],[])).
% 1.71/1.35 tff(77,plain,
% 1.71/1.35 (union(B!4, C!3) = union(C!3, B!4)),
% 1.71/1.35 inference(unit_resolution,[status(thm)],[76, 75])).
% 1.71/1.35 tff(78,plain,
% 1.71/1.35 (union(C!3, B!4) = union(B!4, C!3)),
% 1.71/1.35 inference(symmetry,[status(thm)],[77])).
% 1.71/1.35 tff(79,plain,
% 1.71/1.35 (union(D!2, union(C!3, B!4)) = union(D!2, union(B!4, C!3))),
% 1.71/1.35 inference(monotonicity,[status(thm)],[78])).
% 1.71/1.35 tff(80,plain,
% 1.71/1.35 (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(C!3, B!4))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3)))),
% 1.71/1.36 inference(monotonicity,[status(thm)],[79])).
% 1.71/1.36 tff(81,plain,
% 1.71/1.36 (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(C!3, B!4)))),
% 1.71/1.36 inference(symmetry,[status(thm)],[80])).
% 1.71/1.36 tff(82,plain,
% 1.71/1.36 ((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3)))) <=> (~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(C!3, B!4))))),
% 1.71/1.36 inference(monotonicity,[status(thm)],[81])).
% 1.71/1.36 tff(83,assumption,((~((~(union(B!4, union(D!2, union(B!4, C!3))) = union(D!2, union(B!4, C!3)))) | (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(B!4, union(D!2, union(B!4, C!3)))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3)))))) | (~((union(B!4, union(D!2, union(B!4, C!3))) = union(D!2, union(B!4, C!3))) | ((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(B!4, union(D!2, union(B!4, C!3))))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3))))))), introduced(assumption)).
% 1.71/1.36 tff(84,plain,
% 1.71/1.36 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))) | (~((~((~(union(B!4, union(D!2, union(B!4, C!3))) = union(D!2, union(B!4, C!3)))) | (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(B!4, union(D!2, union(B!4, C!3)))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3)))))) | (~((union(B!4, union(D!2, union(B!4, C!3))) = union(D!2, union(B!4, C!3))) | ((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(B!4, union(D!2, union(B!4, C!3))))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3))))))))),
% 1.71/1.36 inference(quant_inst,[status(thm)],[])).
% 1.71/1.36 tff(85,plain,
% 1.71/1.36 ($false),
% 1.71/1.36 inference(unit_resolution,[status(thm)],[84, 55, 83])).
% 1.71/1.36 tff(86,plain,(~((~((~(union(B!4, union(D!2, union(B!4, C!3))) = union(D!2, union(B!4, C!3)))) | (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(B!4, union(D!2, union(B!4, C!3)))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3)))))) | (~((union(B!4, union(D!2, union(B!4, C!3))) = union(D!2, union(B!4, C!3))) | ((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(B!4, union(D!2, union(B!4, C!3))))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3)))))))), inference(lemma,lemma(discharge,[]))).
% 1.71/1.36 tff(87,plain,
% 1.71/1.36 (((~((~(union(B!4, union(D!2, union(B!4, C!3))) = union(D!2, union(B!4, C!3)))) | (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(B!4, union(D!2, union(B!4, C!3)))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3)))))) | (~((union(B!4, union(D!2, union(B!4, C!3))) = union(D!2, union(B!4, C!3))) | ((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(B!4, union(D!2, union(B!4, C!3))))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3))))))) | ((union(B!4, union(D!2, union(B!4, C!3))) = union(D!2, union(B!4, C!3))) | ((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(B!4, union(D!2, union(B!4, C!3))))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3)))))),
% 1.71/1.36 inference(tautology,[status(thm)],[])).
% 1.71/1.36 tff(88,plain,
% 1.71/1.36 ((union(B!4, union(D!2, union(B!4, C!3))) = union(D!2, union(B!4, C!3))) | ((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(B!4, union(D!2, union(B!4, C!3))))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3))))),
% 1.71/1.36 inference(unit_resolution,[status(thm)],[87, 86])).
% 1.71/1.36 tff(89,assumption,(union(B!4, union(D!2, union(B!4, C!3))) = union(D!2, union(B!4, C!3))), introduced(assumption)).
% 1.71/1.36 tff(90,plain,
% 1.71/1.36 (union(D!2, union(B!4, C!3)) = union(B!4, union(D!2, union(B!4, C!3)))),
% 1.71/1.36 inference(symmetry,[status(thm)],[89])).
% 1.71/1.36 tff(91,plain,
% 1.71/1.36 (tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)) = tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4))),
% 1.71/1.36 inference(monotonicity,[status(thm)],[90])).
% 1.71/1.36 tff(92,plain,
% 1.71/1.36 (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4))),
% 1.71/1.36 inference(monotonicity,[status(thm)],[91])).
% 1.71/1.36 tff(93,plain,
% 1.71/1.36 (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4))),
% 1.71/1.36 inference(symmetry,[status(thm)],[92])).
% 1.71/1.36 tff(94,plain,
% 1.71/1.36 (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, C!3), B!4)) <=> member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, B!4))),
% 1.71/1.36 inference(monotonicity,[status(thm)],[64])).
% 1.71/1.36 tff(95,plain,
% 1.71/1.36 (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, B!4)) <=> member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, C!3), B!4))),
% 1.71/1.36 inference(symmetry,[status(thm)],[94])).
% 1.71/1.36 tff(96,plain,
% 1.71/1.36 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, B!4), D!2)) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, B!4))))),
% 1.71/1.36 inference(quant_inst,[status(thm)],[])).
% 1.71/1.36 tff(97,plain,
% 1.71/1.36 (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, B!4), D!2)) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, B!4)))),
% 1.71/1.36 inference(unit_resolution,[status(thm)],[96, 13])).
% 1.71/1.36 tff(98,plain,
% 1.71/1.36 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(union(B!4, C!3), D!2) = union(D!2, union(B!4, C!3)))),
% 1.71/1.36 inference(quant_inst,[status(thm)],[])).
% 1.71/1.36 tff(99,plain,
% 1.71/1.36 (union(union(B!4, C!3), D!2) = union(D!2, union(B!4, C!3))),
% 1.71/1.36 inference(unit_resolution,[status(thm)],[98, 75])).
% 1.71/1.36 tff(100,plain,
% 1.71/1.36 (union(union(C!3, B!4), D!2) = union(union(B!4, C!3), D!2)),
% 1.71/1.36 inference(monotonicity,[status(thm)],[78])).
% 1.71/1.36 tff(101,plain,
% 1.71/1.36 (union(union(C!3, B!4), D!2) = union(D!2, union(B!4, C!3))),
% 1.71/1.36 inference(transitivity,[status(thm)],[100, 99])).
% 1.71/1.36 tff(102,plain,
% 1.71/1.36 (tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)) = tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4))),
% 1.71/1.36 inference(symmetry,[status(thm)],[91])).
% 1.71/1.36 tff(103,plain,
% 1.71/1.36 (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, B!4), D!2)) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3)))),
% 1.71/1.36 inference(monotonicity,[status(thm)],[102, 101])).
% 1.71/1.36 tff(104,plain,
% 1.71/1.36 (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3))) <=> member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, B!4), D!2))),
% 1.71/1.36 inference(symmetry,[status(thm)],[103])).
% 1.71/1.36 tff(105,plain,
% 1.71/1.36 ((~![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))))))) | (~((~((~(union(union(C!3, D!2), B!4) = union(D!2, union(B!4, C!3)))) | (member(tptp_fun_D_1(union(union(C!3, D!2), B!4), union(D!2, C!3)), union(union(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(union(union(C!3, D!2), B!4), union(D!2, C!3)), union(D!2, union(B!4, C!3)))))) | (~((union(union(C!3, D!2), B!4) = union(D!2, union(B!4, C!3))) | ((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3))))))))),
% 1.71/1.36 inference(quant_inst,[status(thm)],[])).
% 1.71/1.36 tff(106,plain,
% 1.71/1.36 (~((~((~(union(union(C!3, D!2), B!4) = union(D!2, union(B!4, C!3)))) | (member(tptp_fun_D_1(union(union(C!3, D!2), B!4), union(D!2, C!3)), union(union(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(union(union(C!3, D!2), B!4), union(D!2, C!3)), union(D!2, union(B!4, C!3)))))) | (~((union(union(C!3, D!2), B!4) = union(D!2, union(B!4, C!3))) | ((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3)))))))),
% 1.71/1.36 inference(unit_resolution,[status(thm)],[105, 55])).
% 1.71/1.36 tff(107,plain,
% 1.71/1.36 (((~((~(union(union(C!3, D!2), B!4) = union(D!2, union(B!4, C!3)))) | (member(tptp_fun_D_1(union(union(C!3, D!2), B!4), union(D!2, C!3)), union(union(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(union(union(C!3, D!2), B!4), union(D!2, C!3)), union(D!2, union(B!4, C!3)))))) | (~((union(union(C!3, D!2), B!4) = union(D!2, union(B!4, C!3))) | ((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3))))))) | ((union(union(C!3, D!2), B!4) = union(D!2, union(B!4, C!3))) | ((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3)))))),
% 1.71/1.36 inference(tautology,[status(thm)],[])).
% 1.71/1.36 tff(108,plain,
% 1.71/1.36 ((union(union(C!3, D!2), B!4) = union(D!2, union(B!4, C!3))) | ((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3))))),
% 1.71/1.36 inference(unit_resolution,[status(thm)],[107, 106])).
% 1.71/1.36 tff(109,plain,
% 1.71/1.36 ((union(B!4, union(C!3, D!2)) = union(union(B!4, C!3), D!2)) <=> (union(union(B!4, C!3), D!2) = union(B!4, union(C!3, D!2)))),
% 1.71/1.36 inference(commutativity,[status(thm)],[])).
% 1.71/1.36 tff(110,plain,
% 1.71/1.36 (union(D!2, union(B!4, C!3)) = union(union(B!4, C!3), D!2)),
% 1.71/1.36 inference(symmetry,[status(thm)],[99])).
% 1.71/1.36 tff(111,plain,
% 1.71/1.36 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(B!4, union(C!3, D!2)) = union(union(C!3, D!2), B!4))),
% 1.71/1.36 inference(quant_inst,[status(thm)],[])).
% 1.71/1.36 tff(112,plain,
% 1.71/1.36 (union(B!4, union(C!3, D!2)) = union(union(C!3, D!2), B!4)),
% 1.71/1.36 inference(unit_resolution,[status(thm)],[111, 75])).
% 1.71/1.36 tff(113,plain,
% 1.71/1.36 (union(union(C!3, D!2), B!4) = union(B!4, union(C!3, D!2))),
% 1.71/1.36 inference(symmetry,[status(thm)],[112])).
% 1.71/1.36 tff(114,plain,
% 1.71/1.36 ((union(union(C!3, D!2), B!4) = union(D!2, union(B!4, C!3))) <=> (union(B!4, union(C!3, D!2)) = union(union(B!4, C!3), D!2))),
% 1.71/1.36 inference(monotonicity,[status(thm)],[113, 110])).
% 1.71/1.36 tff(115,plain,
% 1.71/1.36 ((union(union(C!3, D!2), B!4) = union(D!2, union(B!4, C!3))) <=> (union(union(B!4, C!3), D!2) = union(B!4, union(C!3, D!2)))),
% 1.71/1.36 inference(transitivity,[status(thm)],[114, 109])).
% 1.71/1.36 tff(116,plain,
% 1.71/1.36 ((union(union(B!4, C!3), D!2) = union(B!4, union(C!3, D!2))) <=> (union(union(C!3, D!2), B!4) = union(D!2, union(B!4, C!3)))),
% 1.71/1.36 inference(symmetry,[status(thm)],[115])).
% 1.71/1.36 tff(117,plain,
% 1.71/1.36 ((~(union(union(B!4, C!3), D!2) = union(B!4, union(C!3, D!2)))) <=> (~(union(union(C!3, D!2), B!4) = union(D!2, union(B!4, C!3))))),
% 1.71/1.36 inference(monotonicity,[status(thm)],[116])).
% 1.71/1.36 tff(118,plain,
% 1.71/1.36 ((~![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))) <=> (~![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D))))),
% 1.71/1.36 inference(rewrite,[status(thm)],[])).
% 1.71/1.36 tff(119,axiom,(~![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_associativity_of_union')).
% 1.71/1.36 tff(120,plain,
% 1.71/1.36 (~![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))),
% 1.71/1.36 inference(modus_ponens,[status(thm)],[119, 118])).
% 1.71/1.36 tff(121,plain,
% 1.71/1.36 (~![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))),
% 1.71/1.36 inference(modus_ponens,[status(thm)],[120, 118])).
% 1.71/1.36 tff(122,plain,
% 1.71/1.36 (~![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))),
% 1.71/1.36 inference(modus_ponens,[status(thm)],[121, 118])).
% 1.71/1.36 tff(123,plain,
% 1.71/1.36 (~![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))),
% 1.71/1.36 inference(modus_ponens,[status(thm)],[122, 118])).
% 1.71/1.36 tff(124,plain,
% 1.71/1.36 (~![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))),
% 1.71/1.36 inference(modus_ponens,[status(thm)],[123, 118])).
% 1.71/1.36 tff(125,plain,
% 1.71/1.36 (~![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))),
% 1.71/1.36 inference(modus_ponens,[status(thm)],[124, 118])).
% 1.71/1.36 tff(126,plain,
% 1.71/1.36 (~![B: $i, C: $i, D: $i] : (union(union(B, C), D) = union(B, union(C, D)))),
% 1.71/1.36 inference(modus_ponens,[status(thm)],[125, 118])).
% 1.71/1.36 tff(127,plain,(
% 1.71/1.36 ~(union(union(B!4, C!3), D!2) = union(B!4, union(C!3, D!2)))),
% 1.71/1.36 inference(skolemize,[status(sab)],[126])).
% 1.71/1.36 tff(128,plain,
% 1.71/1.36 (~(union(union(C!3, D!2), B!4) = union(D!2, union(B!4, C!3)))),
% 1.71/1.36 inference(modus_ponens,[status(thm)],[127, 117])).
% 1.71/1.36 tff(129,plain,
% 1.71/1.36 ((~((union(union(C!3, D!2), B!4) = union(D!2, union(B!4, C!3))) | ((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3)))))) | (union(union(C!3, D!2), B!4) = union(D!2, union(B!4, C!3))) | ((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3))))),
% 1.71/1.36 inference(tautology,[status(thm)],[])).
% 1.71/1.36 tff(130,plain,
% 1.71/1.36 ((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3)))),
% 1.71/1.36 inference(unit_resolution,[status(thm)],[129, 128, 108])).
% 1.71/1.36 tff(131,plain,
% 1.71/1.36 ((~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4))) <=> (~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4)))),
% 1.71/1.36 inference(monotonicity,[status(thm)],[93])).
% 1.71/1.36 tff(132,assumption,(~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4))), introduced(assumption)).
% 1.71/1.36 tff(133,plain,
% 1.71/1.36 (~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4))),
% 1.71/1.36 inference(modus_ponens,[status(thm)],[132, 131])).
% 1.71/1.36 tff(134,plain,
% 1.71/1.36 ((~((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3))))) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4)) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3)))),
% 1.71/1.36 inference(tautology,[status(thm)],[])).
% 1.71/1.36 tff(135,plain,
% 1.71/1.36 (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3)))),
% 1.71/1.36 inference(unit_resolution,[status(thm)],[134, 133, 130])).
% 1.71/1.36 tff(136,plain,
% 1.71/1.36 (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, B!4), D!2))),
% 1.71/1.36 inference(modus_ponens,[status(thm)],[135, 104])).
% 1.71/1.36 tff(137,plain,
% 1.71/1.36 ((~(member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, B!4), D!2)) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, B!4))))) | (~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, B!4), D!2))) | (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, B!4)))),
% 1.71/1.37 inference(tautology,[status(thm)],[])).
% 1.71/1.37 tff(138,plain,
% 1.71/1.37 (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, B!4))),
% 1.71/1.37 inference(unit_resolution,[status(thm)],[137, 136, 97])).
% 1.71/1.37 tff(139,plain,
% 1.71/1.37 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, C!3))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, C!3))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3)))))),
% 1.71/1.37 inference(rewrite,[status(thm)],[])).
% 1.71/1.37 tff(140,plain,
% 1.71/1.37 ((member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, C!3))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3)) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, C!3))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3))))),
% 1.71/1.37 inference(rewrite,[status(thm)],[])).
% 1.71/1.37 tff(141,plain,
% 1.71/1.37 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, C!3))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3)) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, C!3))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3)))))),
% 1.71/1.37 inference(monotonicity,[status(thm)],[140])).
% 1.71/1.37 tff(142,plain,
% 1.71/1.37 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, C!3))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3)) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, C!3))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3)))))),
% 1.71/1.37 inference(transitivity,[status(thm)],[141, 139])).
% 1.71/1.37 tff(143,plain,
% 1.71/1.37 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, C!3))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3)) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2)))),
% 1.71/1.37 inference(quant_inst,[status(thm)],[])).
% 1.71/1.37 tff(144,plain,
% 1.71/1.37 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, C!3))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3))))),
% 1.71/1.37 inference(modus_ponens,[status(thm)],[143, 142])).
% 1.71/1.37 tff(145,plain,
% 1.71/1.37 (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, C!3))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3)))),
% 1.71/1.37 inference(unit_resolution,[status(thm)],[144, 13])).
% 1.71/1.37 tff(146,plain,
% 1.71/1.37 (union(D!2, union(C!3, C!3)) = union(D!2, C!3)),
% 1.71/1.37 inference(monotonicity,[status(thm)],[63])).
% 1.71/1.37 tff(147,plain,
% 1.71/1.37 (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, C!3))) <=> member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, C!3))),
% 1.71/1.37 inference(monotonicity,[status(thm)],[146])).
% 1.71/1.37 tff(148,plain,
% 1.71/1.37 (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, C!3)) <=> member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, C!3)))),
% 1.71/1.37 inference(symmetry,[status(thm)],[147])).
% 1.71/1.37 tff(149,plain,
% 1.71/1.37 ((~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, C!3))) <=> (~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, C!3))))),
% 1.71/1.37 inference(monotonicity,[status(thm)],[148])).
% 1.71/1.37 tff(150,plain,
% 1.71/1.37 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(B!4, union(D!2, C!3))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, C!3))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(B!4, union(D!2, C!3))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, C!3)))))),
% 1.71/1.37 inference(rewrite,[status(thm)],[])).
% 1.71/1.37 tff(151,plain,
% 1.71/1.37 ((member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(B!4, union(D!2, C!3))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, C!3)) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(B!4, union(D!2, C!3))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, C!3))))),
% 1.71/1.37 inference(rewrite,[status(thm)],[])).
% 1.71/1.37 tff(152,plain,
% 1.71/1.37 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(B!4, union(D!2, C!3))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, C!3)) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), 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_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(B!4, union(D!2, C!3))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, C!3)))))),
% 1.71/1.37 inference(monotonicity,[status(thm)],[151])).
% 1.71/1.37 tff(153,plain,
% 1.71/1.37 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(B!4, union(D!2, C!3))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, C!3)) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), 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_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(B!4, union(D!2, C!3))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, C!3)))))),
% 1.71/1.37 inference(transitivity,[status(thm)],[152, 150])).
% 1.71/1.37 tff(154,plain,
% 1.71/1.37 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(B!4, union(D!2, C!3))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, C!3)) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4)))),
% 1.71/1.37 inference(quant_inst,[status(thm)],[])).
% 1.71/1.37 tff(155,plain,
% 1.71/1.37 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(B!4, union(D!2, C!3))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, C!3))))),
% 1.71/1.37 inference(modus_ponens,[status(thm)],[154, 153])).
% 1.71/1.37 tff(156,plain,
% 1.71/1.37 (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(B!4, union(D!2, C!3))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, C!3)))),
% 1.71/1.37 inference(unit_resolution,[status(thm)],[155, 13])).
% 1.71/1.37 tff(157,plain,
% 1.71/1.37 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(C!3, D!2) = union(D!2, C!3))),
% 1.71/1.37 inference(quant_inst,[status(thm)],[])).
% 1.71/1.37 tff(158,plain,
% 1.71/1.37 (union(C!3, D!2) = union(D!2, C!3)),
% 1.71/1.37 inference(unit_resolution,[status(thm)],[157, 75])).
% 1.71/1.37 tff(159,plain,
% 1.71/1.37 (union(D!2, C!3) = union(C!3, D!2)),
% 1.71/1.37 inference(symmetry,[status(thm)],[158])).
% 1.71/1.37 tff(160,plain,
% 1.71/1.37 (union(B!4, union(D!2, C!3)) = union(B!4, union(C!3, D!2))),
% 1.71/1.37 inference(monotonicity,[status(thm)],[159])).
% 1.71/1.37 tff(161,plain,
% 1.71/1.37 (union(B!4, union(D!2, C!3)) = union(union(C!3, D!2), B!4)),
% 1.71/1.37 inference(transitivity,[status(thm)],[160, 112])).
% 1.71/1.37 tff(162,plain,
% 1.71/1.37 (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(B!4, union(D!2, C!3))) <=> member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4))),
% 1.71/1.37 inference(monotonicity,[status(thm)],[161])).
% 1.71/1.37 tff(163,plain,
% 1.71/1.37 (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(B!4, union(D!2, C!3)))),
% 1.71/1.37 inference(symmetry,[status(thm)],[162])).
% 1.71/1.37 tff(164,plain,
% 1.71/1.37 ((~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4))) <=> (~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(B!4, union(D!2, C!3))))),
% 1.71/1.37 inference(monotonicity,[status(thm)],[163])).
% 1.71/1.37 tff(165,plain,
% 1.71/1.37 (~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(B!4, union(D!2, C!3)))),
% 1.71/1.37 inference(modus_ponens,[status(thm)],[132, 164])).
% 1.71/1.37 tff(166,plain,
% 1.71/1.37 ((~(member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(B!4, union(D!2, C!3))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, C!3))))) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(B!4, union(D!2, C!3))) | (~(member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, C!3))))),
% 1.71/1.37 inference(tautology,[status(thm)],[])).
% 1.71/1.37 tff(167,plain,
% 1.71/1.37 (~(member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, C!3)))),
% 1.71/1.37 inference(unit_resolution,[status(thm)],[166, 165, 156])).
% 1.71/1.37 tff(168,plain,
% 1.71/1.37 ((member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, C!3))) | (~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, C!3)))),
% 1.71/1.37 inference(tautology,[status(thm)],[])).
% 1.71/1.37 tff(169,plain,
% 1.71/1.37 (~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, C!3))),
% 1.71/1.37 inference(unit_resolution,[status(thm)],[168, 167])).
% 1.71/1.37 tff(170,plain,
% 1.71/1.37 (~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, C!3)))),
% 1.71/1.37 inference(modus_ponens,[status(thm)],[169, 149])).
% 1.71/1.37 tff(171,plain,
% 1.71/1.37 ((~(member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, C!3))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3))))) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, C!3))) | (~(member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3))))),
% 1.71/1.37 inference(tautology,[status(thm)],[])).
% 1.71/1.37 tff(172,plain,
% 1.71/1.37 (~(member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3)))),
% 1.71/1.37 inference(unit_resolution,[status(thm)],[171, 170, 145])).
% 1.71/1.37 tff(173,plain,
% 1.71/1.37 ((member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3))) | (~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2))),
% 1.71/1.37 inference(tautology,[status(thm)],[])).
% 1.71/1.37 tff(174,plain,
% 1.71/1.37 (~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2)),
% 1.71/1.37 inference(unit_resolution,[status(thm)],[173, 172])).
% 1.71/1.37 tff(175,plain,
% 1.71/1.37 ((~(member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, B!4)))) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, B!4))),
% 1.71/1.37 inference(tautology,[status(thm)],[])).
% 1.71/1.37 tff(176,plain,
% 1.71/1.37 (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, B!4))),
% 1.71/1.37 inference(unit_resolution,[status(thm)],[175, 174, 138])).
% 1.71/1.37 tff(177,plain,
% 1.71/1.37 (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, C!3), B!4))),
% 1.71/1.37 inference(modus_ponens,[status(thm)],[176, 95])).
% 1.71/1.37 tff(178,plain,
% 1.71/1.37 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, C!3), B!4)) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3))))),
% 1.71/1.37 inference(quant_inst,[status(thm)],[])).
% 1.71/1.37 tff(179,plain,
% 1.71/1.37 (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, C!3), B!4)) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3)))),
% 1.71/1.37 inference(unit_resolution,[status(thm)],[178, 13])).
% 1.71/1.37 tff(180,plain,
% 1.71/1.37 ((member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3))) | (~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3)))),
% 1.71/1.37 inference(tautology,[status(thm)],[])).
% 1.71/1.37 tff(181,plain,
% 1.71/1.37 (~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3))),
% 1.71/1.37 inference(unit_resolution,[status(thm)],[180, 172])).
% 1.71/1.37 tff(182,plain,
% 1.71/1.37 ((member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, C!3))) | (~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4))),
% 1.71/1.37 inference(tautology,[status(thm)],[])).
% 1.71/1.37 tff(183,plain,
% 1.71/1.37 (~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4)),
% 1.71/1.37 inference(unit_resolution,[status(thm)],[182, 167])).
% 1.71/1.37 tff(184,plain,
% 1.71/1.37 ((~(member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3)))) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3))),
% 1.71/1.37 inference(tautology,[status(thm)],[])).
% 1.71/1.37 tff(185,plain,
% 1.71/1.37 (~(member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3)))),
% 1.71/1.37 inference(unit_resolution,[status(thm)],[184, 183, 181])).
% 1.71/1.38 tff(186,plain,
% 1.71/1.38 ((~(member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, C!3), B!4)) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3))))) | (~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, C!3), B!4))) | (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3)))),
% 1.71/1.38 inference(tautology,[status(thm)],[])).
% 1.71/1.38 tff(187,plain,
% 1.71/1.38 ((~(member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, C!3), B!4)) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3))))) | (~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, C!3), B!4)))),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[186, 185])).
% 1.71/1.38 tff(188,plain,
% 1.71/1.38 (~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, C!3), B!4))),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[187, 179])).
% 1.71/1.38 tff(189,plain,
% 1.71/1.38 ($false),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[188, 177])).
% 1.71/1.38 tff(190,plain,(member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4)) | (~(union(B!4, union(D!2, union(B!4, C!3))) = union(D!2, union(B!4, C!3))))), inference(lemma,lemma(discharge,[]))).
% 1.71/1.38 tff(191,plain,
% 1.71/1.38 (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4))),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[190, 89])).
% 1.71/1.38 tff(192,plain,
% 1.71/1.38 (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4))),
% 1.71/1.38 inference(modus_ponens,[status(thm)],[191, 93])).
% 1.71/1.38 tff(193,plain,
% 1.71/1.38 ((~![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))))))) | (~((~((~(union(union(C!3, D!2), B!4) = union(D!2, union(B!4, C!3)))) | (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3)))))) | (~((union(union(C!3, D!2), B!4) = union(D!2, union(B!4, C!3))) | ((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3))))))))),
% 1.71/1.38 inference(quant_inst,[status(thm)],[])).
% 1.71/1.38 tff(194,plain,
% 1.71/1.38 (~((~((~(union(union(C!3, D!2), B!4) = union(D!2, union(B!4, C!3)))) | (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3)))))) | (~((union(union(C!3, D!2), B!4) = union(D!2, union(B!4, C!3))) | ((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3)))))))),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[193, 55])).
% 1.71/1.38 tff(195,plain,
% 1.71/1.38 (((~((~(union(union(C!3, D!2), B!4) = union(D!2, union(B!4, C!3)))) | (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3)))))) | (~((union(union(C!3, D!2), B!4) = union(D!2, union(B!4, C!3))) | ((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3))))))) | ((union(union(C!3, D!2), B!4) = union(D!2, union(B!4, C!3))) | ((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3)))))),
% 1.71/1.38 inference(tautology,[status(thm)],[])).
% 1.71/1.38 tff(196,plain,
% 1.71/1.38 ((union(union(C!3, D!2), B!4) = union(D!2, union(B!4, C!3))) | ((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3))))),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[195, 194])).
% 1.71/1.38 tff(197,plain,
% 1.71/1.38 ((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3)))),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[129, 128, 196])).
% 1.71/1.38 tff(198,plain,
% 1.71/1.38 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(D!2, C!3), B!4)) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, C!3))))),
% 1.71/1.38 inference(quant_inst,[status(thm)],[])).
% 1.71/1.38 tff(199,plain,
% 1.71/1.38 (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(D!2, C!3), B!4)) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, C!3)))),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[198, 13])).
% 1.71/1.38 tff(200,plain,
% 1.71/1.38 (union(union(D!2, C!3), B!4) = union(union(C!3, D!2), B!4)),
% 1.71/1.38 inference(monotonicity,[status(thm)],[159])).
% 1.71/1.38 tff(201,plain,
% 1.71/1.38 (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(D!2, C!3), B!4)) <=> member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4))),
% 1.71/1.38 inference(monotonicity,[status(thm)],[200])).
% 1.71/1.38 tff(202,plain,
% 1.71/1.38 (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(D!2, C!3), B!4))),
% 1.71/1.38 inference(symmetry,[status(thm)],[201])).
% 1.71/1.38 tff(203,plain,
% 1.71/1.38 (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(D!2, C!3), B!4))),
% 1.71/1.38 inference(modus_ponens,[status(thm)],[191, 202])).
% 1.71/1.38 tff(204,plain,
% 1.71/1.38 ((~(member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(D!2, C!3), B!4)) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, C!3))))) | (~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(D!2, C!3), B!4))) | (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, C!3)))),
% 1.71/1.38 inference(tautology,[status(thm)],[])).
% 1.71/1.38 tff(205,plain,
% 1.71/1.38 (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, C!3))),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[204, 203, 199])).
% 1.71/1.38 tff(206,plain,
% 1.71/1.38 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(D!2, union(B!4, C!3)), B!4)) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3)))))),
% 1.71/1.38 inference(quant_inst,[status(thm)],[])).
% 1.71/1.38 tff(207,plain,
% 1.71/1.38 (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(D!2, union(B!4, C!3)), B!4)) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3))))),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[206, 13])).
% 1.71/1.38 tff(208,plain,
% 1.71/1.38 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(union(D!2, union(B!4, C!3)), B!4) = union(B!4, union(D!2, union(B!4, C!3))))),
% 1.71/1.38 inference(quant_inst,[status(thm)],[])).
% 1.71/1.38 tff(209,plain,
% 1.71/1.38 (union(union(D!2, union(B!4, C!3)), B!4) = union(B!4, union(D!2, union(B!4, C!3)))),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[208, 75])).
% 1.71/1.38 tff(210,plain,
% 1.71/1.38 (union(union(D!2, union(B!4, C!3)), B!4) = union(D!2, union(B!4, C!3))),
% 1.71/1.38 inference(transitivity,[status(thm)],[209, 89])).
% 1.71/1.38 tff(211,plain,
% 1.71/1.38 (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(D!2, union(B!4, C!3)), B!4)) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3)))),
% 1.71/1.38 inference(monotonicity,[status(thm)],[102, 210])).
% 1.71/1.38 tff(212,plain,
% 1.71/1.38 (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3))) <=> member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(D!2, union(B!4, C!3)), B!4))),
% 1.71/1.38 inference(symmetry,[status(thm)],[211])).
% 1.71/1.38 tff(213,plain,
% 1.71/1.38 ((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3)))) <=> (~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(D!2, union(B!4, C!3)), B!4)))),
% 1.71/1.38 inference(monotonicity,[status(thm)],[212])).
% 1.71/1.38 tff(214,assumption,(~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3)))), introduced(assumption)).
% 1.71/1.38 tff(215,plain,
% 1.71/1.38 (~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(D!2, union(B!4, C!3)), B!4))),
% 1.71/1.38 inference(modus_ponens,[status(thm)],[214, 213])).
% 1.71/1.38 tff(216,plain,
% 1.71/1.38 ((~(member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(D!2, union(B!4, C!3)), B!4)) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3)))))) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(D!2, union(B!4, C!3)), B!4)) | (~(member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3)))))),
% 1.71/1.38 inference(tautology,[status(thm)],[])).
% 1.71/1.38 tff(217,plain,
% 1.71/1.38 (~(member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3))))),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[216, 215, 207])).
% 1.71/1.38 tff(218,plain,
% 1.71/1.38 ((member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3)))) | (~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4))),
% 1.71/1.38 inference(tautology,[status(thm)],[])).
% 1.71/1.38 tff(219,plain,
% 1.71/1.38 (~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4)),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[218, 217])).
% 1.71/1.38 tff(220,plain,
% 1.71/1.38 ((~(member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, C!3)))) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, C!3))),
% 1.71/1.38 inference(tautology,[status(thm)],[])).
% 1.71/1.38 tff(221,plain,
% 1.71/1.38 (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, C!3))),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[220, 219, 205])).
% 1.71/1.38 tff(222,plain,
% 1.71/1.38 (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, C!3)))),
% 1.71/1.38 inference(modus_ponens,[status(thm)],[221, 148])).
% 1.71/1.38 tff(223,plain,
% 1.71/1.38 ((~(member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, C!3))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3))))) | (~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, C!3)))) | (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3)))),
% 1.71/1.38 inference(tautology,[status(thm)],[])).
% 1.71/1.38 tff(224,plain,
% 1.71/1.38 (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3))),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[223, 222, 145])).
% 1.71/1.38 tff(225,plain,
% 1.71/1.38 ((~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, B!4))) <=> (~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, C!3), B!4)))),
% 1.71/1.38 inference(monotonicity,[status(thm)],[95])).
% 1.71/1.38 tff(226,plain,
% 1.71/1.38 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), 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_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, B!4)))))),
% 1.71/1.38 inference(rewrite,[status(thm)],[])).
% 1.71/1.38 tff(227,plain,
% 1.71/1.38 ((member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, B!4)) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, B!4))))),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(228,plain,
% 1.71/1.39 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, B!4)) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, B!4)))))),
% 1.71/1.39 inference(monotonicity,[status(thm)],[227])).
% 1.71/1.39 tff(229,plain,
% 1.71/1.39 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, B!4)) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, B!4)))))),
% 1.71/1.39 inference(transitivity,[status(thm)],[228, 226])).
% 1.71/1.39 tff(230,plain,
% 1.71/1.39 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, B!4)) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2)))),
% 1.71/1.39 inference(quant_inst,[status(thm)],[])).
% 1.71/1.39 tff(231,plain,
% 1.71/1.39 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, B!4))))),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[230, 229])).
% 1.71/1.39 tff(232,plain,
% 1.71/1.39 (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, B!4)))),
% 1.71/1.39 inference(unit_resolution,[status(thm)],[231, 13])).
% 1.71/1.39 tff(233,plain,
% 1.71/1.39 (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, B!4))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3)))),
% 1.71/1.39 inference(monotonicity,[status(thm)],[102, 79])).
% 1.71/1.39 tff(234,plain,
% 1.71/1.39 (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3))) <=> member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, B!4)))),
% 1.71/1.39 inference(symmetry,[status(thm)],[233])).
% 1.80/1.39 tff(235,plain,
% 1.80/1.39 ((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3)))) <=> (~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, B!4))))),
% 1.80/1.39 inference(monotonicity,[status(thm)],[234])).
% 1.80/1.39 tff(236,plain,
% 1.80/1.39 (~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, B!4)))),
% 1.80/1.39 inference(modus_ponens,[status(thm)],[214, 235])).
% 1.80/1.39 tff(237,plain,
% 1.80/1.39 ((~(member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, B!4))))) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(D!2, union(C!3, B!4))) | (~(member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, B!4))))),
% 1.80/1.39 inference(tautology,[status(thm)],[])).
% 1.80/1.39 tff(238,plain,
% 1.80/1.39 (~(member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, B!4)))),
% 1.80/1.39 inference(unit_resolution,[status(thm)],[237, 236, 232])).
% 1.80/1.39 tff(239,plain,
% 1.80/1.39 ((member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, B!4)))),
% 1.80/1.39 inference(tautology,[status(thm)],[])).
% 1.80/1.39 tff(240,plain,
% 1.80/1.39 (~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, B!4))),
% 1.80/1.39 inference(unit_resolution,[status(thm)],[239, 238])).
% 1.80/1.39 tff(241,plain,
% 1.80/1.39 (~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, C!3), B!4))),
% 1.80/1.39 inference(modus_ponens,[status(thm)],[240, 225])).
% 1.80/1.39 tff(242,plain,
% 1.80/1.39 ((~(member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, C!3), B!4)) <=> (member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3))))) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(union(C!3, C!3), B!4)) | (~(member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3))))),
% 1.80/1.39 inference(tautology,[status(thm)],[])).
% 1.80/1.39 tff(243,plain,
% 1.80/1.39 (~(member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3)))),
% 1.80/1.39 inference(unit_resolution,[status(thm)],[242, 241, 179])).
% 1.80/1.39 tff(244,plain,
% 1.80/1.39 ((member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), B!4) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3))) | (~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3)))),
% 1.80/1.39 inference(tautology,[status(thm)],[])).
% 1.80/1.39 tff(245,plain,
% 1.80/1.39 (~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3))),
% 1.80/1.39 inference(unit_resolution,[status(thm)],[244, 243])).
% 1.80/1.39 tff(246,plain,
% 1.80/1.39 ((member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2))),
% 1.80/1.39 inference(tautology,[status(thm)],[])).
% 1.80/1.39 tff(247,plain,
% 1.80/1.39 (~member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2)),
% 1.80/1.39 inference(unit_resolution,[status(thm)],[246, 238])).
% 1.80/1.39 tff(248,plain,
% 1.80/1.39 ((~(member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3)))) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3))),
% 1.80/1.39 inference(tautology,[status(thm)],[])).
% 1.80/1.39 tff(249,plain,
% 1.80/1.39 ((~(member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), D!2) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3)))) | member(tptp_fun_D_1(union(B!4, union(D!2, union(B!4, C!3))), union(union(C!3, D!2), B!4)), union(C!3, C!3))),
% 1.80/1.39 inference(unit_resolution,[status(thm)],[248, 247])).
% 1.80/1.39 tff(250,plain,
% 1.80/1.39 ($false),
% 1.80/1.39 inference(unit_resolution,[status(thm)],[249, 245, 224])).
% 1.80/1.39 tff(251,plain,(member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3))) | (~(union(B!4, union(D!2, union(B!4, C!3))) = union(D!2, union(B!4, C!3))))), inference(lemma,lemma(discharge,[]))).
% 1.80/1.39 tff(252,plain,
% 1.80/1.39 (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3)))),
% 1.80/1.39 inference(unit_resolution,[status(thm)],[251, 89])).
% 1.80/1.39 tff(253,plain,
% 1.80/1.39 ((~((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3))))) | (~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4))) | (~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3))))),
% 1.80/1.39 inference(tautology,[status(thm)],[])).
% 1.80/1.39 tff(254,plain,
% 1.80/1.39 ((~((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(D!2, union(B!4, C!3))))) | (~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(union(C!3, D!2), B!4)), union(union(C!3, D!2), B!4)))),
% 1.80/1.39 inference(unit_resolution,[status(thm)],[253, 252])).
% 1.80/1.39 tff(255,plain,
% 1.80/1.39 ($false),
% 1.80/1.39 inference(unit_resolution,[status(thm)],[254, 197, 192])).
% 1.80/1.39 tff(256,plain,(~(union(B!4, union(D!2, union(B!4, C!3))) = union(D!2, union(B!4, C!3)))), inference(lemma,lemma(discharge,[]))).
% 1.80/1.39 tff(257,plain,
% 1.80/1.39 ((~((union(B!4, union(D!2, union(B!4, C!3))) = union(D!2, union(B!4, C!3))) | ((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(B!4, union(D!2, union(B!4, C!3))))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3)))))) | (union(B!4, union(D!2, union(B!4, C!3))) = union(D!2, union(B!4, C!3))) | ((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(B!4, union(D!2, union(B!4, C!3))))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3))))),
% 1.80/1.39 inference(tautology,[status(thm)],[])).
% 1.80/1.39 tff(258,plain,
% 1.80/1.39 ((~((union(B!4, union(D!2, union(B!4, C!3))) = union(D!2, union(B!4, C!3))) | ((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(B!4, union(D!2, union(B!4, C!3))))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3)))))) | ((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(B!4, union(D!2, union(B!4, C!3))))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3))))),
% 1.80/1.39 inference(unit_resolution,[status(thm)],[257, 256])).
% 1.80/1.39 tff(259,plain,
% 1.80/1.39 ((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(B!4, union(D!2, union(B!4, C!3))))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3)))),
% 1.80/1.39 inference(unit_resolution,[status(thm)],[258, 88])).
% 1.80/1.39 tff(260,assumption,((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(B!4, union(D!2, union(B!4, C!3))))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3)))), introduced(assumption)).
% 1.80/1.39 tff(261,assumption,(~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(B!4, union(D!2, union(B!4, C!3))))), introduced(assumption)).
% 1.80/1.39 tff(262,plain,
% 1.80/1.39 ((~((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(B!4, union(D!2, union(B!4, C!3))))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3))))) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(B!4, union(D!2, union(B!4, C!3)))) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3)))),
% 1.80/1.39 inference(tautology,[status(thm)],[])).
% 1.80/1.39 tff(263,plain,
% 1.80/1.39 (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3)))),
% 1.80/1.39 inference(unit_resolution,[status(thm)],[262, 261, 260])).
% 1.80/1.39 tff(264,plain,
% 1.80/1.39 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(B!4, union(D!2, union(B!4, C!3)))) <=> (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3))) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), B!4)))),
% 1.80/1.39 inference(quant_inst,[status(thm)],[])).
% 1.80/1.39 tff(265,plain,
% 1.80/1.39 (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(B!4, union(D!2, union(B!4, C!3)))) <=> (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3))) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), B!4))),
% 1.80/1.39 inference(unit_resolution,[status(thm)],[264, 13])).
% 1.80/1.39 tff(266,plain,
% 1.80/1.39 ((~(member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(B!4, union(D!2, union(B!4, C!3)))) <=> (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3))) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), B!4)))) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(B!4, union(D!2, union(B!4, C!3)))) | (~(member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3))) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), B!4)))),
% 1.80/1.39 inference(tautology,[status(thm)],[])).
% 1.80/1.39 tff(267,plain,
% 1.80/1.39 (~(member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3))) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), B!4))),
% 1.80/1.39 inference(unit_resolution,[status(thm)],[266, 261, 265])).
% 1.80/1.39 tff(268,plain,
% 1.80/1.39 ((member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3))) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), B!4)) | (~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3))))),
% 1.80/1.39 inference(tautology,[status(thm)],[])).
% 1.80/1.39 tff(269,plain,
% 1.80/1.39 ($false),
% 1.80/1.39 inference(unit_resolution,[status(thm)],[268, 267, 263])).
% 1.80/1.39 tff(270,plain,(member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(B!4, union(D!2, union(B!4, C!3)))) | (~((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(B!4, union(D!2, union(B!4, C!3))))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3)))))), inference(lemma,lemma(discharge,[]))).
% 1.80/1.39 tff(271,plain,
% 1.80/1.39 (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(B!4, union(D!2, union(B!4, C!3))))),
% 1.80/1.39 inference(unit_resolution,[status(thm)],[270, 259])).
% 1.80/1.39 tff(272,plain,
% 1.80/1.39 ((~((~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(B!4, union(D!2, union(B!4, C!3))))) <=> member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3))))) | (~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(B!4, union(D!2, union(B!4, C!3))))) | (~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3))))),
% 1.80/1.39 inference(tautology,[status(thm)],[])).
% 1.80/1.39 tff(273,plain,
% 1.80/1.39 (~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3)))),
% 1.80/1.39 inference(unit_resolution,[status(thm)],[272, 271, 259])).
% 1.80/1.39 tff(274,plain,
% 1.80/1.39 (~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(C!3, B!4)))),
% 1.80/1.39 inference(modus_ponens,[status(thm)],[273, 82])).
% 1.80/1.39 tff(275,plain,
% 1.80/1.39 ((~(member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), D!2) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(C!3, B!4))))) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(C!3, B!4))) | (~(member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), D!2) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(C!3, B!4))))),
% 1.80/1.39 inference(tautology,[status(thm)],[])).
% 1.80/1.39 tff(276,plain,
% 1.80/1.39 (~(member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), D!2) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(C!3, B!4)))),
% 1.80/1.39 inference(unit_resolution,[status(thm)],[275, 274, 68])).
% 1.80/1.39 tff(277,plain,
% 1.80/1.39 ((member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), D!2) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(C!3, B!4)))),
% 1.80/1.39 inference(tautology,[status(thm)],[])).
% 1.80/1.39 tff(278,plain,
% 1.80/1.39 (~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(C!3, B!4))),
% 1.80/1.39 inference(unit_resolution,[status(thm)],[277, 276])).
% 1.80/1.39 tff(279,plain,
% 1.80/1.39 (~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(union(C!3, C!3), B!4))),
% 1.80/1.39 inference(modus_ponens,[status(thm)],[278, 67])).
% 1.80/1.39 tff(280,plain,
% 1.80/1.39 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(union(C!3, C!3), B!4)) <=> (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), B!4) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(C!3, C!3))))),
% 1.80/1.40 inference(quant_inst,[status(thm)],[])).
% 1.80/1.40 tff(281,plain,
% 1.80/1.40 (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(union(C!3, C!3), B!4)) <=> (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), B!4) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(C!3, C!3)))),
% 1.80/1.40 inference(unit_resolution,[status(thm)],[280, 13])).
% 1.80/1.40 tff(282,plain,
% 1.80/1.40 ((~(member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(B!4, union(D!2, union(B!4, C!3)))) <=> (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3))) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), B!4)))) | (~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(B!4, union(D!2, union(B!4, C!3))))) | (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3))) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), B!4))),
% 1.80/1.40 inference(tautology,[status(thm)],[])).
% 1.80/1.40 tff(283,plain,
% 1.80/1.40 ((~(member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(B!4, union(D!2, union(B!4, C!3)))) <=> (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3))) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), B!4)))) | (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3))) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), B!4))),
% 1.80/1.40 inference(unit_resolution,[status(thm)],[282, 271])).
% 1.80/1.40 tff(284,plain,
% 1.80/1.40 (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3))) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), B!4)),
% 1.80/1.40 inference(unit_resolution,[status(thm)],[283, 265])).
% 1.80/1.40 tff(285,plain,
% 1.80/1.40 ((~(member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3))) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), B!4))) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3))) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), B!4)),
% 1.80/1.40 inference(tautology,[status(thm)],[])).
% 1.80/1.40 tff(286,plain,
% 1.80/1.40 ((~(member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(B!4, C!3))) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), B!4))) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), B!4)),
% 1.80/1.40 inference(unit_resolution,[status(thm)],[285, 273])).
% 1.80/1.40 tff(287,plain,
% 1.80/1.40 (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), B!4)),
% 1.80/1.40 inference(unit_resolution,[status(thm)],[286, 284])).
% 1.80/1.40 tff(288,plain,
% 1.80/1.40 ((member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), B!4) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(C!3, C!3))) | (~member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), B!4))),
% 1.80/1.40 inference(tautology,[status(thm)],[])).
% 1.80/1.40 tff(289,plain,
% 1.80/1.40 (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), B!4) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(C!3, C!3))),
% 1.80/1.40 inference(unit_resolution,[status(thm)],[288, 287])).
% 1.80/1.40 tff(290,plain,
% 1.80/1.40 ((~(member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(union(C!3, C!3), B!4)) <=> (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), B!4) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(C!3, C!3))))) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(union(C!3, C!3), B!4)) | (~(member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), B!4) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(C!3, C!3))))),
% 1.80/1.40 inference(tautology,[status(thm)],[])).
% 1.80/1.40 tff(291,plain,
% 1.80/1.40 ((~(member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(union(C!3, C!3), B!4)) <=> (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), B!4) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(C!3, C!3))))) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(union(C!3, C!3), B!4))),
% 1.80/1.40 inference(unit_resolution,[status(thm)],[290, 289])).
% 1.80/1.40 tff(292,plain,
% 1.80/1.40 (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(union(C!3, C!3), B!4))),
% 1.80/1.40 inference(unit_resolution,[status(thm)],[291, 281])).
% 1.80/1.40 tff(293,plain,
% 1.80/1.40 ($false),
% 1.80/1.40 inference(unit_resolution,[status(thm)],[292, 279])).
% 1.80/1.40 tff(294,plain,(~(member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), D!2) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(C!3, B!4))))), inference(lemma,lemma(discharge,[]))).
% 1.80/1.40 tff(295,plain,
% 1.80/1.40 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), D!2) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), 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_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), D!2) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(C!3, B!4)))))),
% 1.80/1.40 inference(rewrite,[status(thm)],[])).
% 1.80/1.40 tff(296,plain,
% 1.80/1.40 ((member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(C!3, B!4)) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), D!2))) <=> (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), D!2) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(C!3, B!4))))),
% 1.80/1.40 inference(rewrite,[status(thm)],[])).
% 1.80/1.40 tff(297,plain,
% 1.80/1.40 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(C!3, B!4)) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), D!2)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), D!2) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(C!3, B!4)))))),
% 1.80/1.40 inference(monotonicity,[status(thm)],[296])).
% 1.80/1.40 tff(298,plain,
% 1.80/1.40 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(C!3, B!4)) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), D!2)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), D!2) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(C!3, B!4)))))),
% 1.80/1.40 inference(transitivity,[status(thm)],[297, 295])).
% 1.80/1.40 tff(299,plain,
% 1.80/1.40 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(C!3, B!4)) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), D!2)))),
% 1.80/1.40 inference(quant_inst,[status(thm)],[])).
% 1.80/1.40 tff(300,plain,
% 1.80/1.40 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(D!2, union(C!3, B!4))) <=> (member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), D!2) | member(tptp_fun_D_1(union(D!2, union(B!4, C!3)), union(B!4, union(D!2, union(B!4, C!3)))), union(C!3, B!4))))),
% 1.80/1.40 inference(modus_ponens,[status(thm)],[299, 298])).
% 1.80/1.40 tff(301,plain,
% 1.80/1.40 ($false),
% 1.80/1.40 inference(unit_resolution,[status(thm)],[300, 13, 294])).
% 1.80/1.40 % SZS output end Proof
%------------------------------------------------------------------------------