TSTP Solution File: SET171+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET171+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 05:06:00 EDT 2022
% Result : Theorem 2.30s 1.78s
% Output : Proof 2.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET171+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 02:30:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 2.30/1.78 % SZS status Theorem
% 2.30/1.78 % SZS output start Proof
% 2.30/1.78 tff(member_type, type, (
% 2.30/1.78 member: ( $i * $i ) > $o)).
% 2.30/1.78 tff(union_type, type, (
% 2.30/1.78 union: ( $i * $i ) > $i)).
% 2.30/1.78 tff(tptp_fun_D_2_type, type, (
% 2.30/1.78 tptp_fun_D_2: $i)).
% 2.30/1.78 tff(tptp_fun_D_1_type, type, (
% 2.30/1.78 tptp_fun_D_1: ( $i * $i ) > $i)).
% 2.30/1.78 tff(intersection_type, type, (
% 2.30/1.78 intersection: ( $i * $i ) > $i)).
% 2.30/1.78 tff(tptp_fun_C_3_type, type, (
% 2.30/1.78 tptp_fun_C_3: $i)).
% 2.30/1.78 tff(tptp_fun_B_4_type, type, (
% 2.30/1.78 tptp_fun_B_4: $i)).
% 2.30/1.78 tff(subset_type, type, (
% 2.30/1.78 subset: ( $i * $i ) > $o)).
% 2.30/1.78 tff(tptp_fun_D_0_type, type, (
% 2.30/1.78 tptp_fun_D_0: ( $i * $i ) > $i)).
% 2.30/1.78 tff(1,plain,
% 2.30/1.78 (^[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))))),
% 2.30/1.78 inference(bind,[status(th)],[])).
% 2.30/1.78 tff(2,plain,
% 2.30/1.78 (![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)))),
% 2.30/1.78 inference(quant_intro,[status(thm)],[1])).
% 2.30/1.78 tff(3,plain,
% 2.30/1.78 (![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)))),
% 2.30/1.78 inference(rewrite,[status(thm)],[])).
% 2.30/1.78 tff(4,plain,
% 2.30/1.78 (^[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))))),
% 2.30/1.78 inference(bind,[status(th)],[])).
% 2.30/1.78 tff(5,plain,
% 2.30/1.78 (![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)))),
% 2.30/1.78 inference(quant_intro,[status(thm)],[4])).
% 2.30/1.78 tff(6,axiom,(![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, B) | member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','union_defn')).
% 2.30/1.78 tff(7,plain,
% 2.30/1.78 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 2.30/1.78 inference(modus_ponens,[status(thm)],[6, 5])).
% 2.30/1.78 tff(8,plain,
% 2.30/1.78 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 2.30/1.78 inference(modus_ponens,[status(thm)],[7, 3])).
% 2.30/1.78 tff(9,plain,(
% 2.30/1.78 ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 2.30/1.78 inference(skolemize,[status(sab)],[8])).
% 2.30/1.78 tff(10,plain,
% 2.30/1.78 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 2.30/1.78 inference(modus_ponens,[status(thm)],[9, 2])).
% 2.30/1.78 tff(11,plain,
% 2.30/1.78 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(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(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))))))),
% 2.30/1.78 inference(rewrite,[status(thm)],[])).
% 2.30/1.78 tff(12,plain,
% 2.30/1.78 ((member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2)))))),
% 2.42/1.78 inference(rewrite,[status(thm)],[])).
% 2.42/1.78 tff(13,plain,
% 2.42/1.78 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, 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(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))))))),
% 2.42/1.78 inference(monotonicity,[status(thm)],[12])).
% 2.42/1.78 tff(14,plain,
% 2.42/1.78 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, 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(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))))))),
% 2.42/1.78 inference(transitivity,[status(thm)],[13, 11])).
% 2.42/1.78 tff(15,plain,
% 2.42/1.78 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3)))),
% 2.42/1.78 inference(quant_inst,[status(thm)],[])).
% 2.42/1.78 tff(16,plain,
% 2.42/1.78 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2)))))),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[15, 14])).
% 2.42/1.78 tff(17,plain,
% 2.42/1.78 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))))),
% 2.42/1.78 inference(unit_resolution,[status(thm)],[16, 10])).
% 2.42/1.78 tff(18,plain,
% 2.42/1.78 (^[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)))))))),
% 2.42/1.78 inference(bind,[status(th)],[])).
% 2.42/1.78 tff(19,plain,
% 2.42/1.78 (![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))))))),
% 2.42/1.78 inference(quant_intro,[status(thm)],[18])).
% 2.42/1.78 tff(20,plain,
% 2.42/1.78 (![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))))))),
% 2.42/1.78 inference(pull_quant,[status(thm)],[])).
% 2.42/1.78 tff(21,plain,
% 2.42/1.78 (^[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))))))))),
% 2.42/1.78 inference(bind,[status(th)],[])).
% 2.42/1.78 tff(22,plain,
% 2.42/1.78 (![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))))))),
% 2.42/1.78 inference(quant_intro,[status(thm)],[21])).
% 2.42/1.78 tff(23,plain,
% 2.42/1.78 (![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))))))),
% 2.42/1.78 inference(transitivity,[status(thm)],[22, 20])).
% 2.42/1.78 tff(24,plain,
% 2.42/1.78 (![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))))))),
% 2.42/1.78 inference(transitivity,[status(thm)],[23, 19])).
% 2.42/1.78 tff(25,plain,
% 2.42/1.78 (^[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)))))))),
% 2.42/1.78 inference(bind,[status(th)],[])).
% 2.42/1.78 tff(26,plain,
% 2.42/1.78 (![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))))))),
% 2.42/1.78 inference(quant_intro,[status(thm)],[25])).
% 2.42/1.78 tff(27,plain,
% 2.42/1.78 (![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))))))),
% 2.42/1.78 inference(transitivity,[status(thm)],[26, 24])).
% 2.42/1.78 tff(28,plain,
% 2.42/1.78 (^[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))))))))),
% 2.42/1.78 inference(bind,[status(th)],[])).
% 2.42/1.78 tff(29,plain,
% 2.42/1.78 (![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))))))),
% 2.42/1.78 inference(quant_intro,[status(thm)],[28])).
% 2.42/1.78 tff(30,plain,
% 2.42/1.78 (^[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)))))),
% 2.42/1.78 inference(bind,[status(th)],[])).
% 2.42/1.78 tff(31,plain,
% 2.42/1.78 (![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))))),
% 2.42/1.78 inference(quant_intro,[status(thm)],[30])).
% 2.42/1.78 tff(32,plain,
% 2.42/1.78 (![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)))),
% 2.42/1.78 inference(rewrite,[status(thm)],[])).
% 2.42/1.78 tff(33,axiom,(![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','equal_member_defn')).
% 2.42/1.78 tff(34,plain,
% 2.42/1.78 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[33, 32])).
% 2.42/1.78 tff(35,plain,(
% 2.42/1.78 ![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)))))),
% 2.42/1.78 inference(skolemize,[status(sab)],[34])).
% 2.42/1.78 tff(36,plain,
% 2.42/1.78 (![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))))),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[35, 31])).
% 2.42/1.78 tff(37,plain,
% 2.42/1.78 (![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))))))),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[36, 29])).
% 2.42/1.78 tff(38,plain,
% 2.42/1.78 (![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))))))),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[37, 27])).
% 2.42/1.78 tff(39,plain,
% 2.42/1.78 ((~![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!4 = union(B!4, intersection(B!4, D!2)))) | (member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4) <=> member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2)))))) | (~((B!4 = union(B!4, intersection(B!4, D!2))) | ((~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4)) <=> member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2))))))))),
% 2.42/1.78 inference(quant_inst,[status(thm)],[])).
% 2.42/1.78 tff(40,plain,
% 2.42/1.78 (~((~((~(B!4 = union(B!4, intersection(B!4, D!2)))) | (member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4) <=> member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2)))))) | (~((B!4 = union(B!4, intersection(B!4, D!2))) | ((~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4)) <=> member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2)))))))),
% 2.42/1.78 inference(unit_resolution,[status(thm)],[39, 38])).
% 2.42/1.78 tff(41,plain,
% 2.42/1.78 (((~((~(B!4 = union(B!4, intersection(B!4, D!2)))) | (member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4) <=> member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2)))))) | (~((B!4 = union(B!4, intersection(B!4, D!2))) | ((~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4)) <=> member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2))))))) | ((B!4 = union(B!4, intersection(B!4, D!2))) | ((~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4)) <=> member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2)))))),
% 2.42/1.78 inference(tautology,[status(thm)],[])).
% 2.42/1.78 tff(42,plain,
% 2.42/1.78 ((B!4 = union(B!4, intersection(B!4, D!2))) | ((~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4)) <=> member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2))))),
% 2.42/1.78 inference(unit_resolution,[status(thm)],[41, 40])).
% 2.42/1.78 tff(43,assumption,((~member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2)) <=> member(tptp_fun_D_1(union(D!2, D!2), D!2), union(D!2, D!2))), introduced(assumption)).
% 2.42/1.78 tff(44,assumption,(~member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2)), introduced(assumption)).
% 2.42/1.78 tff(45,assumption,(~(member(tptp_fun_D_1(union(D!2, D!2), D!2), union(D!2, D!2)) <=> member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2))), introduced(assumption)).
% 2.42/1.78 tff(46,plain,
% 2.42/1.78 (((~![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, D!2), D!2), union(D!2, D!2)) <=> member(tptp_fun_D_1(union(D!2, D!2), D!2), 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, D!2), D!2), union(D!2, D!2)) <=> member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2)))),
% 2.42/1.78 inference(rewrite,[status(thm)],[])).
% 2.42/1.78 tff(47,plain,
% 2.42/1.78 ((member(tptp_fun_D_1(union(D!2, D!2), D!2), union(D!2, D!2)) <=> (member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2) | member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2))) <=> (member(tptp_fun_D_1(union(D!2, D!2), D!2), union(D!2, D!2)) <=> member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2))),
% 2.42/1.78 inference(rewrite,[status(thm)],[])).
% 2.42/1.78 tff(48,plain,
% 2.42/1.78 (((~![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, D!2), D!2), union(D!2, D!2)) <=> (member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2) | member(tptp_fun_D_1(union(D!2, D!2), D!2), 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, D!2), D!2), union(D!2, D!2)) <=> member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2)))),
% 2.42/1.78 inference(monotonicity,[status(thm)],[47])).
% 2.42/1.78 tff(49,plain,
% 2.42/1.78 (((~![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, D!2), D!2), union(D!2, D!2)) <=> (member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2) | member(tptp_fun_D_1(union(D!2, D!2), D!2), 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, D!2), D!2), union(D!2, D!2)) <=> member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2)))),
% 2.42/1.78 inference(transitivity,[status(thm)],[48, 46])).
% 2.42/1.78 tff(50,plain,
% 2.42/1.78 ((~![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, D!2), D!2), union(D!2, D!2)) <=> (member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2) | member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2)))),
% 2.42/1.78 inference(quant_inst,[status(thm)],[])).
% 2.42/1.78 tff(51,plain,
% 2.42/1.78 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(D!2, D!2), D!2), union(D!2, D!2)) <=> member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2))),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[50, 49])).
% 2.42/1.78 tff(52,plain,
% 2.42/1.78 ($false),
% 2.42/1.78 inference(unit_resolution,[status(thm)],[51, 10, 45])).
% 2.42/1.78 tff(53,plain,(member(tptp_fun_D_1(union(D!2, D!2), D!2), union(D!2, D!2)) <=> member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2)), inference(lemma,lemma(discharge,[]))).
% 2.42/1.78 tff(54,plain,
% 2.42/1.78 ((~(member(tptp_fun_D_1(union(D!2, D!2), D!2), union(D!2, D!2)) <=> member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2))) | (~member(tptp_fun_D_1(union(D!2, D!2), D!2), union(D!2, D!2))) | member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2)),
% 2.42/1.78 inference(tautology,[status(thm)],[])).
% 2.42/1.78 tff(55,plain,
% 2.42/1.78 ((~member(tptp_fun_D_1(union(D!2, D!2), D!2), union(D!2, D!2))) | member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2)),
% 2.42/1.78 inference(unit_resolution,[status(thm)],[54, 53])).
% 2.42/1.78 tff(56,plain,
% 2.42/1.78 (~member(tptp_fun_D_1(union(D!2, D!2), D!2), union(D!2, D!2))),
% 2.42/1.78 inference(unit_resolution,[status(thm)],[55, 44])).
% 2.42/1.78 tff(57,plain,
% 2.42/1.78 ((~((~member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2)) <=> member(tptp_fun_D_1(union(D!2, D!2), D!2), union(D!2, D!2)))) | member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2) | member(tptp_fun_D_1(union(D!2, D!2), D!2), union(D!2, D!2))),
% 2.42/1.78 inference(tautology,[status(thm)],[])).
% 2.42/1.79 tff(58,plain,
% 2.42/1.79 ($false),
% 2.42/1.79 inference(unit_resolution,[status(thm)],[57, 56, 44, 43])).
% 2.42/1.79 tff(59,plain,(member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2) | (~((~member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2)) <=> member(tptp_fun_D_1(union(D!2, D!2), D!2), union(D!2, D!2))))), inference(lemma,lemma(discharge,[]))).
% 2.42/1.79 tff(60,plain,
% 2.42/1.79 (member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2)),
% 2.42/1.79 inference(unit_resolution,[status(thm)],[59, 43])).
% 2.42/1.79 tff(61,plain,
% 2.42/1.79 ((~((~member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2)) <=> member(tptp_fun_D_1(union(D!2, D!2), D!2), union(D!2, D!2)))) | (~member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2)) | (~member(tptp_fun_D_1(union(D!2, D!2), D!2), union(D!2, D!2)))),
% 2.42/1.79 inference(tautology,[status(thm)],[])).
% 2.42/1.79 tff(62,plain,
% 2.42/1.79 (~member(tptp_fun_D_1(union(D!2, D!2), D!2), union(D!2, D!2))),
% 2.42/1.79 inference(unit_resolution,[status(thm)],[61, 60, 43])).
% 2.42/1.79 tff(63,plain,
% 2.42/1.79 ((~(member(tptp_fun_D_1(union(D!2, D!2), D!2), union(D!2, D!2)) <=> member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2))) | member(tptp_fun_D_1(union(D!2, D!2), D!2), union(D!2, D!2)) | (~member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2))),
% 2.42/1.79 inference(tautology,[status(thm)],[])).
% 2.42/1.79 tff(64,plain,
% 2.42/1.79 (member(tptp_fun_D_1(union(D!2, D!2), D!2), union(D!2, D!2)) | (~member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2))),
% 2.42/1.79 inference(unit_resolution,[status(thm)],[63, 53])).
% 2.42/1.79 tff(65,plain,
% 2.42/1.79 ($false),
% 2.42/1.79 inference(unit_resolution,[status(thm)],[64, 62, 60])).
% 2.42/1.79 tff(66,plain,(~((~member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2)) <=> member(tptp_fun_D_1(union(D!2, D!2), D!2), union(D!2, D!2)))), inference(lemma,lemma(discharge,[]))).
% 2.42/1.79 tff(67,plain,
% 2.42/1.79 ((~![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))))))) | (~((~((~(D!2 = union(D!2, D!2))) | (member(tptp_fun_D_1(intersection(D!2, C!3), B!4), D!2) <=> member(tptp_fun_D_1(intersection(D!2, C!3), B!4), union(D!2, D!2))))) | (~((D!2 = union(D!2, D!2)) | ((~member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2)) <=> member(tptp_fun_D_1(union(D!2, D!2), D!2), union(D!2, D!2)))))))),
% 2.42/1.79 inference(quant_inst,[status(thm)],[])).
% 2.42/1.79 tff(68,plain,
% 2.42/1.79 (~((~((~(D!2 = union(D!2, D!2))) | (member(tptp_fun_D_1(intersection(D!2, C!3), B!4), D!2) <=> member(tptp_fun_D_1(intersection(D!2, C!3), B!4), union(D!2, D!2))))) | (~((D!2 = union(D!2, D!2)) | ((~member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2)) <=> member(tptp_fun_D_1(union(D!2, D!2), D!2), union(D!2, D!2))))))),
% 2.42/1.79 inference(unit_resolution,[status(thm)],[67, 38])).
% 2.42/1.79 tff(69,plain,
% 2.42/1.79 (((~((~(D!2 = union(D!2, D!2))) | (member(tptp_fun_D_1(intersection(D!2, C!3), B!4), D!2) <=> member(tptp_fun_D_1(intersection(D!2, C!3), B!4), union(D!2, D!2))))) | (~((D!2 = union(D!2, D!2)) | ((~member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2)) <=> member(tptp_fun_D_1(union(D!2, D!2), D!2), union(D!2, D!2)))))) | ((D!2 = union(D!2, D!2)) | ((~member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2)) <=> member(tptp_fun_D_1(union(D!2, D!2), D!2), union(D!2, D!2))))),
% 2.42/1.79 inference(tautology,[status(thm)],[])).
% 2.42/1.79 tff(70,plain,
% 2.42/1.79 ((D!2 = union(D!2, D!2)) | ((~member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2)) <=> member(tptp_fun_D_1(union(D!2, D!2), D!2), union(D!2, D!2)))),
% 2.42/1.79 inference(unit_resolution,[status(thm)],[69, 68])).
% 2.42/1.79 tff(71,plain,
% 2.42/1.79 ((~((D!2 = union(D!2, D!2)) | ((~member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2)) <=> member(tptp_fun_D_1(union(D!2, D!2), D!2), union(D!2, D!2))))) | (D!2 = union(D!2, D!2)) | ((~member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2)) <=> member(tptp_fun_D_1(union(D!2, D!2), D!2), union(D!2, D!2)))),
% 2.42/1.79 inference(tautology,[status(thm)],[])).
% 2.42/1.79 tff(72,plain,
% 2.42/1.79 ((D!2 = union(D!2, D!2)) | ((~member(tptp_fun_D_1(union(D!2, D!2), D!2), D!2)) <=> member(tptp_fun_D_1(union(D!2, D!2), D!2), union(D!2, D!2)))),
% 2.42/1.79 inference(unit_resolution,[status(thm)],[71, 70])).
% 2.42/1.79 tff(73,plain,
% 2.42/1.79 (D!2 = union(D!2, D!2)),
% 2.42/1.79 inference(unit_resolution,[status(thm)],[72, 66])).
% 2.42/1.79 tff(74,plain,
% 2.42/1.79 (union(D!2, D!2) = D!2),
% 2.42/1.79 inference(symmetry,[status(thm)],[73])).
% 2.42/1.79 tff(75,plain,
% 2.42/1.79 (intersection(B!4, union(D!2, D!2)) = intersection(B!4, D!2)),
% 2.42/1.79 inference(monotonicity,[status(thm)],[74])).
% 2.42/1.79 tff(76,plain,
% 2.42/1.79 (member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), intersection(B!4, union(D!2, D!2))) <=> member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), intersection(B!4, D!2))),
% 2.42/1.79 inference(monotonicity,[status(thm)],[75])).
% 2.42/1.79 tff(77,plain,
% 2.42/1.79 (member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), intersection(B!4, D!2)) <=> member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), intersection(B!4, union(D!2, D!2)))),
% 2.42/1.79 inference(symmetry,[status(thm)],[76])).
% 2.42/1.79 tff(78,plain,
% 2.42/1.79 (((~![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, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2))) <=> (member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4) | member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), intersection(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, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2))) <=> (member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4) | member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), intersection(B!4, D!2)))))),
% 2.42/1.79 inference(rewrite,[status(thm)],[])).
% 2.42/1.79 tff(79,plain,
% 2.42/1.79 ((member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2))) <=> (member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), intersection(B!4, D!2)) | member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4))) <=> (member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2))) <=> (member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4) | member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), intersection(B!4, D!2))))),
% 2.42/1.79 inference(rewrite,[status(thm)],[])).
% 2.42/1.79 tff(80,plain,
% 2.42/1.79 (((~![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, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2))) <=> (member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), intersection(B!4, D!2)) | member(tptp_fun_D_1(union(B!4, intersection(B!4, 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, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2))) <=> (member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4) | member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), intersection(B!4, D!2)))))),
% 2.42/1.79 inference(monotonicity,[status(thm)],[79])).
% 2.42/1.79 tff(81,plain,
% 2.42/1.79 (((~![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, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2))) <=> (member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), intersection(B!4, D!2)) | member(tptp_fun_D_1(union(B!4, intersection(B!4, 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, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2))) <=> (member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4) | member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), intersection(B!4, D!2)))))),
% 2.42/1.79 inference(transitivity,[status(thm)],[80, 78])).
% 2.42/1.79 tff(82,plain,
% 2.42/1.79 ((~![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, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2))) <=> (member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), intersection(B!4, D!2)) | member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4)))),
% 2.42/1.79 inference(quant_inst,[status(thm)],[])).
% 2.42/1.79 tff(83,plain,
% 2.42/1.79 ((~![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, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2))) <=> (member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4) | member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), intersection(B!4, D!2))))),
% 2.42/1.79 inference(modus_ponens,[status(thm)],[82, 81])).
% 2.42/1.79 tff(84,plain,
% 2.42/1.79 (member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2))) <=> (member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4) | member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), intersection(B!4, D!2)))),
% 2.42/1.79 inference(unit_resolution,[status(thm)],[83, 10])).
% 2.42/1.79 tff(85,assumption,((~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4)) <=> member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2)))), introduced(assumption)).
% 2.42/1.79 tff(86,assumption,(~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2)))), introduced(assumption)).
% 2.42/1.79 tff(87,plain,
% 2.42/1.79 ((~((~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4)) <=> member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2))))) | member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4) | member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2)))),
% 2.42/1.79 inference(tautology,[status(thm)],[])).
% 2.42/1.79 tff(88,plain,
% 2.42/1.79 (member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4)),
% 2.42/1.79 inference(unit_resolution,[status(thm)],[87, 86, 85])).
% 2.42/1.79 tff(89,plain,
% 2.42/1.79 ((~(member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2))) <=> (member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4) | member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), intersection(B!4, D!2))))) | member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2))) | (~(member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4) | member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), intersection(B!4, D!2))))),
% 2.42/1.79 inference(tautology,[status(thm)],[])).
% 2.42/1.79 tff(90,plain,
% 2.42/1.79 (~(member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4) | member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), intersection(B!4, D!2)))),
% 2.42/1.79 inference(unit_resolution,[status(thm)],[89, 86, 84])).
% 2.42/1.79 tff(91,plain,
% 2.42/1.79 ((member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4) | member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), intersection(B!4, D!2))) | (~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4))),
% 2.42/1.79 inference(tautology,[status(thm)],[])).
% 2.42/1.79 tff(92,plain,
% 2.42/1.79 ($false),
% 2.42/1.79 inference(unit_resolution,[status(thm)],[91, 90, 88])).
% 2.42/1.79 tff(93,plain,(member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2))) | (~((~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4)) <=> member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2)))))), inference(lemma,lemma(discharge,[]))).
% 2.42/1.79 tff(94,plain,
% 2.42/1.79 (member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2)))),
% 2.42/1.79 inference(unit_resolution,[status(thm)],[93, 85])).
% 2.42/1.79 tff(95,plain,
% 2.42/1.79 ((~(member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2))) <=> (member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4) | member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), intersection(B!4, D!2))))) | (~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2)))) | (member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4) | member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), intersection(B!4, D!2)))),
% 2.42/1.79 inference(tautology,[status(thm)],[])).
% 2.42/1.79 tff(96,plain,
% 2.42/1.79 (member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4) | member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), intersection(B!4, D!2))),
% 2.42/1.79 inference(unit_resolution,[status(thm)],[95, 94, 84])).
% 2.42/1.79 tff(97,plain,
% 2.42/1.79 ((~((~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4)) <=> member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2))))) | (~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4)) | (~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2))))),
% 2.42/1.79 inference(tautology,[status(thm)],[])).
% 2.42/1.79 tff(98,plain,
% 2.42/1.79 (~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4)),
% 2.42/1.79 inference(unit_resolution,[status(thm)],[97, 94, 85])).
% 2.42/1.79 tff(99,plain,
% 2.42/1.79 ((~(member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4) | member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), intersection(B!4, D!2)))) | member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4) | member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), intersection(B!4, D!2))),
% 2.42/1.79 inference(tautology,[status(thm)],[])).
% 2.42/1.79 tff(100,plain,
% 2.42/1.79 (member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), intersection(B!4, D!2))),
% 2.42/1.79 inference(unit_resolution,[status(thm)],[99, 98, 96])).
% 2.42/1.79 tff(101,plain,
% 2.42/1.79 (member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), intersection(B!4, union(D!2, D!2)))),
% 2.42/1.79 inference(modus_ponens,[status(thm)],[100, 77])).
% 2.42/1.79 tff(102,plain,
% 2.42/1.79 (^[B: $i, C: $i, D: $i] : refl((member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C))))) <=> (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C))))))),
% 2.42/1.79 inference(bind,[status(th)],[])).
% 2.42/1.79 tff(103,plain,
% 2.42/1.79 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C))))) <=> ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))),
% 2.42/1.79 inference(quant_intro,[status(thm)],[102])).
% 2.42/1.79 tff(104,plain,
% 2.42/1.79 (^[B: $i, C: $i, D: $i] : rewrite((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C))))))),
% 2.42/1.79 inference(bind,[status(th)],[])).
% 2.42/1.79 tff(105,plain,
% 2.42/1.79 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))),
% 2.42/1.79 inference(quant_intro,[status(thm)],[104])).
% 2.42/1.79 tff(106,plain,
% 2.42/1.79 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 2.42/1.79 inference(rewrite,[status(thm)],[])).
% 2.42/1.79 tff(107,axiom,(![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','intersection_defn')).
% 2.42/1.79 tff(108,plain,
% 2.42/1.79 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 2.42/1.79 inference(modus_ponens,[status(thm)],[107, 106])).
% 2.42/1.79 tff(109,plain,(
% 2.42/1.79 ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 2.42/1.79 inference(skolemize,[status(sab)],[108])).
% 2.42/1.79 tff(110,plain,
% 2.42/1.79 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))),
% 2.42/1.79 inference(modus_ponens,[status(thm)],[109, 105])).
% 2.42/1.79 tff(111,plain,
% 2.42/1.79 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))),
% 2.42/1.79 inference(modus_ponens,[status(thm)],[110, 103])).
% 2.42/1.79 tff(112,plain,
% 2.42/1.79 ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), intersection(B!4, union(D!2, D!2))) <=> (~((~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4)) | (~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(D!2, D!2))))))),
% 2.42/1.79 inference(quant_inst,[status(thm)],[])).
% 2.42/1.79 tff(113,plain,
% 2.42/1.79 (member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), intersection(B!4, union(D!2, D!2))) <=> (~((~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4)) | (~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(D!2, D!2)))))),
% 2.42/1.79 inference(unit_resolution,[status(thm)],[112, 111])).
% 2.42/1.79 tff(114,plain,
% 2.42/1.79 (((~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4)) | (~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(D!2, D!2)))) | member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4)),
% 2.42/1.79 inference(tautology,[status(thm)],[])).
% 2.42/1.79 tff(115,plain,
% 2.42/1.79 ((~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4)) | (~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(D!2, D!2)))),
% 2.42/1.79 inference(unit_resolution,[status(thm)],[114, 98])).
% 2.42/1.79 tff(116,plain,
% 2.42/1.79 ((~(member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), intersection(B!4, union(D!2, D!2))) <=> (~((~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4)) | (~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(D!2, D!2))))))) | (~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), intersection(B!4, union(D!2, D!2)))) | (~((~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4)) | (~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(D!2, D!2)))))),
% 2.42/1.79 inference(tautology,[status(thm)],[])).
% 2.42/1.79 tff(117,plain,
% 2.42/1.79 ((~(member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), intersection(B!4, union(D!2, D!2))) <=> (~((~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4)) | (~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(D!2, D!2))))))) | (~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), intersection(B!4, union(D!2, D!2))))),
% 2.42/1.79 inference(unit_resolution,[status(thm)],[116, 115])).
% 2.42/1.79 tff(118,plain,
% 2.42/1.79 (~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), intersection(B!4, union(D!2, D!2)))),
% 2.42/1.79 inference(unit_resolution,[status(thm)],[117, 113])).
% 2.42/1.79 tff(119,plain,
% 2.42/1.79 ($false),
% 2.42/1.79 inference(unit_resolution,[status(thm)],[118, 101])).
% 2.42/1.79 tff(120,plain,(~((~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4)) <=> member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2))))), inference(lemma,lemma(discharge,[]))).
% 2.42/1.79 tff(121,plain,
% 2.42/1.79 ((~((B!4 = union(B!4, intersection(B!4, D!2))) | ((~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4)) <=> member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2)))))) | (B!4 = union(B!4, intersection(B!4, D!2))) | ((~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4)) <=> member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2))))),
% 2.42/1.79 inference(tautology,[status(thm)],[])).
% 2.42/1.79 tff(122,plain,
% 2.42/1.79 ((~((B!4 = union(B!4, intersection(B!4, D!2))) | ((~member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), B!4)) <=> member(tptp_fun_D_1(union(B!4, intersection(B!4, D!2)), B!4), union(B!4, intersection(B!4, D!2)))))) | (B!4 = union(B!4, intersection(B!4, D!2)))),
% 2.42/1.79 inference(unit_resolution,[status(thm)],[121, 120])).
% 2.42/1.79 tff(123,plain,
% 2.42/1.79 (B!4 = union(B!4, intersection(B!4, D!2))),
% 2.42/1.79 inference(unit_resolution,[status(thm)],[122, 42])).
% 2.42/1.79 tff(124,plain,
% 2.42/1.79 (union(B!4, intersection(B!4, D!2)) = B!4),
% 2.42/1.79 inference(symmetry,[status(thm)],[123])).
% 2.42/1.79 tff(125,plain,
% 2.42/1.79 (union(C!3, union(B!4, intersection(B!4, D!2))) = union(C!3, B!4)),
% 2.42/1.79 inference(monotonicity,[status(thm)],[124])).
% 2.42/1.79 tff(126,plain,
% 2.42/1.79 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, union(B!4, intersection(B!4, D!2)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))),
% 2.42/1.79 inference(monotonicity,[status(thm)],[125])).
% 2.42/1.79 tff(127,plain,
% 2.42/1.79 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4)) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, union(B!4, intersection(B!4, D!2))))),
% 2.42/1.79 inference(symmetry,[status(thm)],[126])).
% 2.42/1.79 tff(128,plain,
% 2.42/1.79 (((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4))) <=> (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4))) <=> (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))))))),
% 2.42/1.80 inference(rewrite,[status(thm)],[])).
% 2.42/1.80 tff(129,plain,
% 2.42/1.80 ((member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4))) <=> (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4)))))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4))) <=> (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))))))),
% 2.42/1.80 inference(rewrite,[status(thm)],[])).
% 2.42/1.80 tff(130,plain,
% 2.42/1.80 (((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4))) <=> (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4))) <=> (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))))))),
% 2.42/1.80 inference(monotonicity,[status(thm)],[129])).
% 2.42/1.80 tff(131,plain,
% 2.42/1.80 (((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4))) <=> (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4))) <=> (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))))))),
% 2.44/1.80 inference(transitivity,[status(thm)],[130, 128])).
% 2.44/1.80 tff(132,plain,
% 2.44/1.80 ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4))) <=> (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))))))),
% 2.44/1.80 inference(quant_inst,[status(thm)],[])).
% 2.44/1.80 tff(133,plain,
% 2.44/1.80 ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4))) <=> (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))))))),
% 2.44/1.80 inference(modus_ponens,[status(thm)],[132, 131])).
% 2.44/1.80 tff(134,plain,
% 2.44/1.80 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4))) <=> (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))))),
% 2.44/1.80 inference(unit_resolution,[status(thm)],[133, 111])).
% 2.44/1.80 tff(135,plain,
% 2.44/1.80 (^[B: $i, C: $i] : refl((union(B, C) = union(C, B)) <=> (union(B, C) = union(C, B)))),
% 2.44/1.80 inference(bind,[status(th)],[])).
% 2.44/1.80 tff(136,plain,
% 2.44/1.80 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 2.44/1.80 inference(quant_intro,[status(thm)],[135])).
% 2.44/1.80 tff(137,plain,
% 2.44/1.80 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 2.44/1.80 inference(rewrite,[status(thm)],[])).
% 2.44/1.80 tff(138,axiom,(![B: $i, C: $i] : (union(B, C) = union(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_of_union')).
% 2.44/1.80 tff(139,plain,
% 2.44/1.80 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 2.44/1.80 inference(modus_ponens,[status(thm)],[138, 137])).
% 2.44/1.80 tff(140,plain,(
% 2.44/1.80 ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 2.44/1.80 inference(skolemize,[status(sab)],[139])).
% 2.44/1.80 tff(141,plain,
% 2.44/1.80 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 2.44/1.80 inference(modus_ponens,[status(thm)],[140, 136])).
% 2.44/1.80 tff(142,plain,
% 2.44/1.80 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(B!4, C!3) = union(C!3, B!4))),
% 2.44/1.80 inference(quant_inst,[status(thm)],[])).
% 2.44/1.80 tff(143,plain,
% 2.44/1.80 (union(B!4, C!3) = union(C!3, B!4)),
% 2.44/1.80 inference(unit_resolution,[status(thm)],[142, 141])).
% 2.44/1.80 tff(144,plain,
% 2.44/1.80 (union(C!3, B!4) = union(B!4, C!3)),
% 2.44/1.80 inference(symmetry,[status(thm)],[143])).
% 2.44/1.80 tff(145,plain,
% 2.44/1.80 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(B!4, D!2) = union(D!2, B!4))),
% 2.44/1.80 inference(quant_inst,[status(thm)],[])).
% 2.44/1.80 tff(146,plain,
% 2.44/1.80 (union(B!4, D!2) = union(D!2, B!4)),
% 2.44/1.80 inference(unit_resolution,[status(thm)],[145, 141])).
% 2.44/1.80 tff(147,plain,
% 2.44/1.80 (union(D!2, B!4) = union(B!4, D!2)),
% 2.44/1.80 inference(symmetry,[status(thm)],[146])).
% 2.44/1.80 tff(148,plain,
% 2.44/1.80 (intersection(union(D!2, B!4), union(C!3, B!4)) = intersection(union(B!4, D!2), union(B!4, C!3))),
% 2.44/1.80 inference(monotonicity,[status(thm)],[147, 144])).
% 2.44/1.80 tff(149,plain,
% 2.44/1.80 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3)))),
% 2.44/1.80 inference(monotonicity,[status(thm)],[148])).
% 2.44/1.80 tff(150,plain,
% 2.44/1.80 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4)))),
% 2.44/1.80 inference(symmetry,[status(thm)],[149])).
% 2.44/1.80 tff(151,assumption,(~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3)))), introduced(assumption)).
% 2.44/1.80 tff(152,assumption,((~((~(intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))))) | (~((intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4)) | ((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))))), introduced(assumption)).
% 2.44/1.80 tff(153,plain,
% 2.44/1.80 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))) | (~((~((~(intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))))) | (~((intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4)) | ((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))))))),
% 2.44/1.80 inference(quant_inst,[status(thm)],[])).
% 2.44/1.80 tff(154,plain,
% 2.44/1.80 ($false),
% 2.44/1.80 inference(unit_resolution,[status(thm)],[153, 38, 152])).
% 2.44/1.80 tff(155,plain,(~((~((~(intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))))) | (~((intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4)) | ((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))))))), inference(lemma,lemma(discharge,[]))).
% 2.44/1.80 tff(156,plain,
% 2.44/1.80 (((~((~(intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))))) | (~((intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4)) | ((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))))) | ((intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4)) | ((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))))),
% 2.44/1.80 inference(tautology,[status(thm)],[])).
% 2.44/1.80 tff(157,plain,
% 2.44/1.80 ((intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4)) | ((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))),
% 2.44/1.80 inference(unit_resolution,[status(thm)],[156, 155])).
% 2.44/1.80 tff(158,plain,
% 2.44/1.80 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 2.44/1.80 inference(bind,[status(th)],[])).
% 2.44/1.80 tff(159,plain,
% 2.44/1.80 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 2.44/1.80 inference(quant_intro,[status(thm)],[158])).
% 2.44/1.80 tff(160,plain,
% 2.44/1.80 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 2.44/1.80 inference(rewrite,[status(thm)],[])).
% 2.44/1.80 tff(161,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 2.44/1.80 tff(162,plain,
% 2.44/1.80 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 2.44/1.80 inference(modus_ponens,[status(thm)],[161, 160])).
% 2.44/1.80 tff(163,plain,(
% 2.44/1.80 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 2.44/1.80 inference(skolemize,[status(sab)],[162])).
% 2.44/1.80 tff(164,plain,
% 2.44/1.80 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 2.44/1.80 inference(modus_ponens,[status(thm)],[163, 159])).
% 2.44/1.80 tff(165,plain,
% 2.44/1.80 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(union(B!4, C!3), union(B!4, D!2)) = intersection(union(B!4, D!2), union(B!4, C!3)))),
% 2.44/1.80 inference(quant_inst,[status(thm)],[])).
% 2.44/1.80 tff(166,plain,
% 2.44/1.80 (intersection(union(B!4, C!3), union(B!4, D!2)) = intersection(union(B!4, D!2), union(B!4, C!3))),
% 2.44/1.80 inference(unit_resolution,[status(thm)],[165, 164])).
% 2.44/1.80 tff(167,plain,
% 2.44/1.80 (intersection(union(B!4, D!2), union(B!4, C!3)) = intersection(union(B!4, C!3), union(B!4, D!2))),
% 2.44/1.80 inference(symmetry,[status(thm)],[166])).
% 2.44/1.80 tff(168,assumption,(intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4)), introduced(assumption)).
% 2.44/1.80 tff(169,plain,
% 2.44/1.80 (union(intersection(C!3, D!2), B!4) = intersection(union(B!4, D!2), union(B!4, C!3))),
% 2.44/1.80 inference(symmetry,[status(thm)],[168])).
% 2.44/1.80 tff(170,plain,
% 2.44/1.80 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(B!4, intersection(C!3, D!2)) = union(intersection(C!3, D!2), B!4))),
% 2.44/1.80 inference(quant_inst,[status(thm)],[])).
% 2.44/1.80 tff(171,plain,
% 2.44/1.80 (union(B!4, intersection(C!3, D!2)) = union(intersection(C!3, D!2), B!4)),
% 2.44/1.80 inference(unit_resolution,[status(thm)],[170, 141])).
% 2.44/1.80 tff(172,plain,
% 2.44/1.80 (union(B!4, intersection(C!3, D!2)) = intersection(union(B!4, C!3), union(B!4, D!2))),
% 2.44/1.80 inference(transitivity,[status(thm)],[171, 169, 167])).
% 2.44/1.80 tff(173,plain,
% 2.44/1.80 ((~![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))) <=> (~![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D))))),
% 2.44/1.80 inference(rewrite,[status(thm)],[])).
% 2.44/1.80 tff(174,axiom,(~![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_union_distributes_over_intersection')).
% 2.44/1.80 tff(175,plain,
% 2.44/1.80 (~![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))),
% 2.44/1.80 inference(modus_ponens,[status(thm)],[174, 173])).
% 2.44/1.80 tff(176,plain,
% 2.44/1.80 (~![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))),
% 2.44/1.80 inference(modus_ponens,[status(thm)],[175, 173])).
% 2.44/1.80 tff(177,plain,
% 2.44/1.80 (~![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))),
% 2.44/1.80 inference(modus_ponens,[status(thm)],[176, 173])).
% 2.44/1.80 tff(178,plain,
% 2.44/1.80 (~![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))),
% 2.44/1.80 inference(modus_ponens,[status(thm)],[177, 173])).
% 2.44/1.80 tff(179,plain,
% 2.44/1.80 (~![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))),
% 2.44/1.80 inference(modus_ponens,[status(thm)],[178, 173])).
% 2.44/1.80 tff(180,plain,
% 2.44/1.80 (~![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))),
% 2.44/1.80 inference(modus_ponens,[status(thm)],[179, 173])).
% 2.44/1.80 tff(181,plain,
% 2.44/1.80 (~![B: $i, C: $i, D: $i] : (union(B, intersection(C, D)) = intersection(union(B, C), union(B, D)))),
% 2.44/1.80 inference(modus_ponens,[status(thm)],[180, 173])).
% 2.44/1.80 tff(182,plain,(
% 2.44/1.80 ~(union(B!4, intersection(C!3, D!2)) = intersection(union(B!4, C!3), union(B!4, D!2)))),
% 2.44/1.80 inference(skolemize,[status(sab)],[181])).
% 2.44/1.80 tff(183,plain,
% 2.44/1.80 ($false),
% 2.44/1.80 inference(unit_resolution,[status(thm)],[182, 172])).
% 2.44/1.80 tff(184,plain,(~(intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4))), inference(lemma,lemma(discharge,[]))).
% 2.44/1.80 tff(185,plain,
% 2.44/1.80 ((~((intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4)) | ((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))))) | (intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4)) | ((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))),
% 2.44/1.80 inference(tautology,[status(thm)],[])).
% 2.44/1.80 tff(186,plain,
% 2.44/1.80 ((~((intersection(union(B!4, D!2), union(B!4, C!3)) = union(intersection(C!3, D!2), B!4)) | ((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))))) | ((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))),
% 2.44/1.80 inference(unit_resolution,[status(thm)],[185, 184])).
% 2.44/1.80 tff(187,plain,
% 2.44/1.80 ((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))),
% 2.44/1.80 inference(unit_resolution,[status(thm)],[186, 157])).
% 2.44/1.80 tff(188,plain,
% 2.44/1.80 ((~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))),
% 2.44/1.80 inference(tautology,[status(thm)],[])).
% 2.44/1.80 tff(189,plain,
% 2.44/1.80 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))),
% 2.44/1.80 inference(unit_resolution,[status(thm)],[188, 187])).
% 2.44/1.80 tff(190,plain,
% 2.44/1.80 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))),
% 2.44/1.80 inference(unit_resolution,[status(thm)],[189, 151])).
% 2.44/1.80 tff(191,plain,
% 2.44/1.80 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3)) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(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_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3)) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(B!4, D!2))))))),
% 2.44/1.80 inference(rewrite,[status(thm)],[])).
% 2.44/1.80 tff(192,plain,
% 2.44/1.80 ((member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3)))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3)) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(B!4, D!2)))))),
% 2.44/1.80 inference(rewrite,[status(thm)],[])).
% 2.44/1.80 tff(193,plain,
% 2.44/1.80 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(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_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3)) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(B!4, D!2))))))),
% 2.44/1.80 inference(monotonicity,[status(thm)],[192])).
% 2.44/1.80 tff(194,plain,
% 2.44/1.80 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(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_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3)) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(B!4, D!2))))))),
% 2.44/1.81 inference(transitivity,[status(thm)],[193, 191])).
% 2.44/1.81 tff(195,plain,
% 2.44/1.81 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))))),
% 2.44/1.81 inference(quant_inst,[status(thm)],[])).
% 2.44/1.81 tff(196,plain,
% 2.44/1.81 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3)) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(B!4, D!2)))))),
% 2.44/1.81 inference(modus_ponens,[status(thm)],[195, 194])).
% 2.44/1.81 tff(197,plain,
% 2.44/1.81 (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3)) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(B!4, D!2))))),
% 2.44/1.81 inference(unit_resolution,[status(thm)],[196, 10])).
% 2.44/1.81 tff(198,plain,
% 2.44/1.81 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(C!3, D!2) = intersection(D!2, C!3))),
% 2.44/1.81 inference(quant_inst,[status(thm)],[])).
% 2.44/1.81 tff(199,plain,
% 2.44/1.81 (intersection(C!3, D!2) = intersection(D!2, C!3)),
% 2.44/1.81 inference(unit_resolution,[status(thm)],[198, 164])).
% 2.44/1.81 tff(200,plain,
% 2.44/1.81 (intersection(D!2, C!3) = intersection(C!3, D!2)),
% 2.44/1.81 inference(symmetry,[status(thm)],[199])).
% 2.44/1.81 tff(201,plain,
% 2.44/1.81 (union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2))) = union(intersection(C!3, D!2), B!4)),
% 2.44/1.81 inference(monotonicity,[status(thm)],[200, 124])).
% 2.44/1.81 tff(202,plain,
% 2.44/1.81 (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2)))) <=> member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))),
% 2.44/1.81 inference(monotonicity,[status(thm)],[201])).
% 2.44/1.81 tff(203,plain,
% 2.44/1.81 (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4)) <=> member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2))))),
% 2.44/1.81 inference(symmetry,[status(thm)],[202])).
% 2.44/1.81 tff(204,assumption,(~((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)))), introduced(assumption)).
% 2.44/1.81 tff(205,plain,
% 2.44/1.81 (((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))),
% 2.44/1.81 inference(tautology,[status(thm)],[])).
% 2.44/1.81 tff(206,plain,
% 2.44/1.81 (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))),
% 2.44/1.81 inference(unit_resolution,[status(thm)],[205, 204])).
% 2.44/1.81 tff(207,plain,
% 2.44/1.81 (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2))))),
% 2.44/1.81 inference(modus_ponens,[status(thm)],[206, 203])).
% 2.44/1.81 tff(208,plain,
% 2.44/1.81 ((~(member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3)) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(B!4, D!2)))))) | (~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2))))) | (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3)) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(B!4, D!2))))),
% 2.44/1.81 inference(tautology,[status(thm)],[])).
% 2.44/1.81 tff(209,plain,
% 2.44/1.81 (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3)) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(B!4, D!2)))),
% 2.44/1.81 inference(unit_resolution,[status(thm)],[208, 207, 197])).
% 2.44/1.81 tff(210,plain,
% 2.44/1.81 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), C!3) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(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_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), C!3) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(B!4, D!2))))))),
% 2.44/1.81 inference(rewrite,[status(thm)],[])).
% 2.44/1.81 tff(211,plain,
% 2.44/1.81 ((member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), C!3))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), C!3) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(B!4, D!2)))))),
% 2.44/1.81 inference(rewrite,[status(thm)],[])).
% 2.44/1.81 tff(212,plain,
% 2.44/1.81 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), C!3)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), C!3) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(B!4, D!2))))))),
% 2.44/1.81 inference(monotonicity,[status(thm)],[211])).
% 2.44/1.81 tff(213,plain,
% 2.44/1.81 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), C!3)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), C!3) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(B!4, D!2))))))),
% 2.44/1.81 inference(transitivity,[status(thm)],[212, 210])).
% 2.44/1.81 tff(214,plain,
% 2.44/1.81 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), C!3)))),
% 2.44/1.81 inference(quant_inst,[status(thm)],[])).
% 2.44/1.81 tff(215,plain,
% 2.44/1.81 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), C!3) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(B!4, D!2)))))),
% 2.44/1.81 inference(modus_ponens,[status(thm)],[214, 213])).
% 2.44/1.81 tff(216,plain,
% 2.44/1.81 (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), C!3) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(B!4, D!2))))),
% 2.44/1.81 inference(unit_resolution,[status(thm)],[215, 10])).
% 2.44/1.81 tff(217,plain,
% 2.44/1.81 (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, union(B!4, intersection(B!4, D!2)))) <=> member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4))),
% 2.44/1.81 inference(monotonicity,[status(thm)],[125])).
% 2.44/1.81 tff(218,plain,
% 2.44/1.81 (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)) <=> member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, union(B!4, intersection(B!4, D!2))))),
% 2.44/1.81 inference(symmetry,[status(thm)],[217])).
% 2.44/1.81 tff(219,plain,
% 2.44/1.81 ((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4))) <=> (~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, union(B!4, intersection(B!4, D!2)))))),
% 2.44/1.81 inference(monotonicity,[status(thm)],[218])).
% 2.44/1.81 tff(220,plain,
% 2.44/1.81 (((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4))) | (~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)))),
% 2.44/1.81 inference(tautology,[status(thm)],[])).
% 2.44/1.81 tff(221,plain,
% 2.44/1.81 (~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4))),
% 2.44/1.81 inference(unit_resolution,[status(thm)],[220, 204])).
% 2.44/1.81 tff(222,plain,
% 2.44/1.81 (~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, union(B!4, intersection(B!4, D!2))))),
% 2.44/1.81 inference(modus_ponens,[status(thm)],[221, 219])).
% 2.44/1.81 tff(223,plain,
% 2.44/1.81 ((~(member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), C!3) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(B!4, D!2)))))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, union(B!4, intersection(B!4, D!2)))) | (~(member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), C!3) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(B!4, D!2)))))),
% 2.44/1.81 inference(tautology,[status(thm)],[])).
% 2.44/1.81 tff(224,plain,
% 2.44/1.81 (~(member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), C!3) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(B!4, D!2))))),
% 2.44/1.81 inference(unit_resolution,[status(thm)],[223, 222, 216])).
% 2.44/1.81 tff(225,plain,
% 2.44/1.81 ((member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), C!3) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(B!4, D!2)))) | (~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(B!4, D!2))))),
% 2.44/1.81 inference(tautology,[status(thm)],[])).
% 2.44/1.81 tff(226,plain,
% 2.44/1.81 (~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(B!4, D!2)))),
% 2.44/1.81 inference(unit_resolution,[status(thm)],[225, 224])).
% 2.44/1.81 tff(227,plain,
% 2.44/1.81 (intersection(union(D!2, D!2), C!3) = intersection(D!2, C!3)),
% 2.44/1.81 inference(monotonicity,[status(thm)],[74])).
% 2.44/1.81 tff(228,plain,
% 2.44/1.81 (member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(union(D!2, D!2), C!3)) <=> member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(D!2, C!3))),
% 2.44/1.81 inference(monotonicity,[status(thm)],[227])).
% 2.44/1.81 tff(229,plain,
% 2.44/1.81 (member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(D!2, C!3)) <=> member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(union(D!2, D!2), C!3))),
% 2.44/1.81 inference(symmetry,[status(thm)],[228])).
% 2.44/1.81 tff(230,assumption,(~((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(C!3, B!4)))), introduced(assumption)).
% 2.44/1.81 tff(231,plain,
% 2.44/1.81 (((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(C!3, B!4))) | member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(D!2, C!3))),
% 2.44/1.81 inference(tautology,[status(thm)],[])).
% 2.44/1.81 tff(232,plain,
% 2.44/1.81 (member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(D!2, C!3))),
% 2.44/1.81 inference(unit_resolution,[status(thm)],[231, 230])).
% 2.44/1.81 tff(233,plain,
% 2.44/1.81 (member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(union(D!2, D!2), C!3))),
% 2.44/1.81 inference(modus_ponens,[status(thm)],[232, 229])).
% 2.44/1.81 tff(234,plain,
% 2.44/1.81 (((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(union(D!2, D!2), C!3)) <=> (~((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(D!2, D!2))))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(union(D!2, D!2), C!3)) <=> (~((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(D!2, D!2)))))))),
% 2.44/1.81 inference(rewrite,[status(thm)],[])).
% 2.44/1.81 tff(235,plain,
% 2.44/1.81 ((member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(union(D!2, D!2), C!3)) <=> (~((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(D!2, D!2))) | (~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), C!3))))) <=> (member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(union(D!2, D!2), C!3)) <=> (~((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(D!2, D!2))))))),
% 2.44/1.81 inference(rewrite,[status(thm)],[])).
% 2.44/1.81 tff(236,plain,
% 2.44/1.81 (((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(union(D!2, D!2), C!3)) <=> (~((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(D!2, D!2))) | (~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), C!3)))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(union(D!2, D!2), C!3)) <=> (~((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(D!2, D!2)))))))),
% 2.44/1.81 inference(monotonicity,[status(thm)],[235])).
% 2.44/1.81 tff(237,plain,
% 2.44/1.81 (((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(union(D!2, D!2), C!3)) <=> (~((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(D!2, D!2))) | (~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), C!3)))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(union(D!2, D!2), C!3)) <=> (~((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(D!2, D!2)))))))),
% 2.44/1.81 inference(transitivity,[status(thm)],[236, 234])).
% 2.44/1.81 tff(238,plain,
% 2.44/1.81 ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(union(D!2, D!2), C!3)) <=> (~((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(D!2, D!2))) | (~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), C!3)))))),
% 2.44/1.81 inference(quant_inst,[status(thm)],[])).
% 2.44/1.81 tff(239,plain,
% 2.44/1.81 ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(union(D!2, D!2), C!3)) <=> (~((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(D!2, D!2))))))),
% 2.44/1.81 inference(modus_ponens,[status(thm)],[238, 237])).
% 2.44/1.81 tff(240,plain,
% 2.44/1.81 (member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(union(D!2, D!2), C!3)) <=> (~((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(D!2, D!2)))))),
% 2.44/1.81 inference(unit_resolution,[status(thm)],[239, 111])).
% 2.44/1.81 tff(241,plain,
% 2.44/1.81 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(C!3, B!4)) <=> (member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), B!4) | member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), C!3)))),
% 2.44/1.81 inference(quant_inst,[status(thm)],[])).
% 2.44/1.81 tff(242,plain,
% 2.44/1.81 (member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(C!3, B!4)) <=> (member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), B!4) | member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), C!3))),
% 2.44/1.81 inference(unit_resolution,[status(thm)],[241, 10])).
% 2.44/1.81 tff(243,plain,
% 2.44/1.81 (((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(C!3, B!4))) | (~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(C!3, B!4)))),
% 2.44/1.81 inference(tautology,[status(thm)],[])).
% 2.44/1.81 tff(244,plain,
% 2.44/1.81 (~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(C!3, B!4))),
% 2.44/1.81 inference(unit_resolution,[status(thm)],[243, 230])).
% 2.44/1.81 tff(245,plain,
% 2.44/1.81 ((~(member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(C!3, B!4)) <=> (member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), B!4) | member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), C!3)))) | member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(C!3, B!4)) | (~(member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), B!4) | member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), C!3)))),
% 2.46/1.81 inference(tautology,[status(thm)],[])).
% 2.46/1.81 tff(246,plain,
% 2.46/1.81 ((~(member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(C!3, B!4)) <=> (member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), B!4) | member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), C!3)))) | (~(member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), B!4) | member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), C!3)))),
% 2.46/1.81 inference(unit_resolution,[status(thm)],[245, 244])).
% 2.46/1.81 tff(247,plain,
% 2.46/1.81 (~(member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), B!4) | member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), C!3))),
% 2.46/1.81 inference(unit_resolution,[status(thm)],[246, 242])).
% 2.46/1.81 tff(248,plain,
% 2.46/1.81 ((member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), B!4) | member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), C!3))),
% 2.46/1.81 inference(tautology,[status(thm)],[])).
% 2.46/1.81 tff(249,plain,
% 2.46/1.81 (~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), C!3)),
% 2.46/1.81 inference(unit_resolution,[status(thm)],[248, 247])).
% 2.46/1.81 tff(250,plain,
% 2.46/1.81 (((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(D!2, D!2)))) | member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), C!3)),
% 2.46/1.81 inference(tautology,[status(thm)],[])).
% 2.46/1.81 tff(251,plain,
% 2.46/1.81 ((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(D!2, D!2)))),
% 2.46/1.81 inference(unit_resolution,[status(thm)],[250, 249])).
% 2.46/1.81 tff(252,plain,
% 2.46/1.81 ((~(member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(union(D!2, D!2), C!3)) <=> (~((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(D!2, D!2))))))) | (~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(union(D!2, D!2), C!3))) | (~((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), C!3)) | (~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(D!2, D!2)))))),
% 2.46/1.81 inference(tautology,[status(thm)],[])).
% 2.46/1.81 tff(253,plain,
% 2.46/1.81 (~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(union(D!2, D!2), C!3))),
% 2.46/1.81 inference(unit_resolution,[status(thm)],[252, 251, 240])).
% 2.46/1.81 tff(254,plain,
% 2.46/1.81 ($false),
% 2.46/1.81 inference(unit_resolution,[status(thm)],[253, 233])).
% 2.46/1.81 tff(255,plain,((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(C!3, B!4))), inference(lemma,lemma(discharge,[]))).
% 2.46/1.81 tff(256,plain,
% 2.46/1.81 (^[B: $i, C: $i] : refl((~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))))),
% 2.46/1.81 inference(bind,[status(th)],[])).
% 2.46/1.81 tff(257,plain,
% 2.46/1.81 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 2.46/1.81 inference(quant_intro,[status(thm)],[256])).
% 2.46/1.81 tff(258,plain,
% 2.46/1.81 (^[B: $i, C: $i] : rewrite((~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))))),
% 2.46/1.81 inference(bind,[status(th)],[])).
% 2.46/1.81 tff(259,plain,
% 2.46/1.81 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 2.46/1.81 inference(quant_intro,[status(thm)],[258])).
% 2.46/1.81 tff(260,plain,
% 2.46/1.81 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 2.46/1.81 inference(transitivity,[status(thm)],[259, 257])).
% 2.46/1.81 tff(261,plain,
% 2.46/1.81 (^[B: $i, C: $i] : trans(monotonicity(rewrite(((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) <=> ((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))), rewrite((subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))) <=> (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))), ((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))), rewrite((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))), ((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))))),
% 2.46/1.82 inference(bind,[status(th)],[])).
% 2.46/1.82 tff(262,plain,
% 2.46/1.82 (![B: $i, C: $i] : (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 2.46/1.82 inference(quant_intro,[status(thm)],[261])).
% 2.46/1.82 tff(263,plain,
% 2.46/1.82 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C))) <=> ![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 2.46/1.82 inference(rewrite,[status(thm)],[])).
% 2.46/1.82 tff(264,plain,
% 2.46/1.82 (^[B: $i, C: $i] : rewrite((subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C))) <=> (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C))))),
% 2.46/1.82 inference(bind,[status(th)],[])).
% 2.46/1.82 tff(265,plain,
% 2.46/1.82 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C))) <=> ![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 2.46/1.82 inference(quant_intro,[status(thm)],[264])).
% 2.46/1.82 tff(266,axiom,(![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','subset_defn')).
% 2.46/1.82 tff(267,plain,
% 2.46/1.82 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 2.46/1.82 inference(modus_ponens,[status(thm)],[266, 265])).
% 2.46/1.82 tff(268,plain,
% 2.46/1.82 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 2.46/1.82 inference(modus_ponens,[status(thm)],[267, 263])).
% 2.46/1.82 tff(269,plain,(
% 2.46/1.82 ![B: $i, C: $i] : (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))),
% 2.46/1.82 inference(skolemize,[status(sab)],[268])).
% 2.46/1.82 tff(270,plain,
% 2.46/1.82 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 2.46/1.82 inference(modus_ponens,[status(thm)],[269, 262])).
% 2.46/1.82 tff(271,plain,
% 2.46/1.82 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 2.46/1.82 inference(modus_ponens,[status(thm)],[270, 260])).
% 2.46/1.82 tff(272,plain,
% 2.46/1.82 (((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(intersection(D!2, C!3), union(C!3, B!4))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, union(C!3, B!4))))) | (~((~((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(C!3, B!4)))) | subset(intersection(D!2, C!3), union(C!3, B!4))))))) <=> ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(intersection(D!2, C!3), union(C!3, B!4))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, union(C!3, B!4))))) | (~((~((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(C!3, B!4)))) | subset(intersection(D!2, C!3), union(C!3, B!4)))))))),
% 2.46/1.82 inference(rewrite,[status(thm)],[])).
% 2.46/1.82 tff(273,plain,
% 2.46/1.82 ((~((~((~subset(intersection(D!2, C!3), union(C!3, B!4))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, union(C!3, B!4))))) | (~(subset(intersection(D!2, C!3), union(C!3, B!4)) | (~((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(C!3, B!4)))))))) <=> (~((~((~subset(intersection(D!2, C!3), union(C!3, B!4))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, union(C!3, B!4))))) | (~((~((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(C!3, B!4)))) | subset(intersection(D!2, C!3), union(C!3, B!4))))))),
% 2.46/1.82 inference(rewrite,[status(thm)],[])).
% 2.46/1.82 tff(274,plain,
% 2.46/1.82 (((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(intersection(D!2, C!3), union(C!3, B!4))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, union(C!3, B!4))))) | (~(subset(intersection(D!2, C!3), union(C!3, B!4)) | (~((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(C!3, B!4))))))))) <=> ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(intersection(D!2, C!3), union(C!3, B!4))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, union(C!3, B!4))))) | (~((~((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(C!3, B!4)))) | subset(intersection(D!2, C!3), union(C!3, B!4)))))))),
% 2.46/1.82 inference(monotonicity,[status(thm)],[273])).
% 2.46/1.82 tff(275,plain,
% 2.46/1.82 (((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(intersection(D!2, C!3), union(C!3, B!4))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, union(C!3, B!4))))) | (~(subset(intersection(D!2, C!3), union(C!3, B!4)) | (~((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(C!3, B!4))))))))) <=> ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(intersection(D!2, C!3), union(C!3, B!4))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, union(C!3, B!4))))) | (~((~((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(C!3, B!4)))) | subset(intersection(D!2, C!3), union(C!3, B!4)))))))),
% 2.46/1.82 inference(transitivity,[status(thm)],[274, 272])).
% 2.46/1.82 tff(276,plain,
% 2.46/1.82 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(intersection(D!2, C!3), union(C!3, B!4))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, union(C!3, B!4))))) | (~(subset(intersection(D!2, C!3), union(C!3, B!4)) | (~((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(C!3, B!4))))))))),
% 2.46/1.82 inference(quant_inst,[status(thm)],[])).
% 2.46/1.82 tff(277,plain,
% 2.46/1.82 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(intersection(D!2, C!3), union(C!3, B!4))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, union(C!3, B!4))))) | (~((~((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(C!3, B!4)))) | subset(intersection(D!2, C!3), union(C!3, B!4))))))),
% 2.46/1.82 inference(modus_ponens,[status(thm)],[276, 275])).
% 2.46/1.82 tff(278,plain,
% 2.46/1.82 (~((~((~subset(intersection(D!2, C!3), union(C!3, B!4))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, union(C!3, B!4))))) | (~((~((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(C!3, B!4)))) | subset(intersection(D!2, C!3), union(C!3, B!4)))))),
% 2.46/1.82 inference(unit_resolution,[status(thm)],[277, 271])).
% 2.46/1.82 tff(279,plain,
% 2.46/1.82 (((~((~subset(intersection(D!2, C!3), union(C!3, B!4))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, union(C!3, B!4))))) | (~((~((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(C!3, B!4)))) | subset(intersection(D!2, C!3), union(C!3, B!4))))) | ((~((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(C!3, B!4)))) | subset(intersection(D!2, C!3), union(C!3, B!4)))),
% 2.46/1.82 inference(tautology,[status(thm)],[])).
% 2.46/1.82 tff(280,plain,
% 2.46/1.82 ((~((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(C!3, B!4)))) | subset(intersection(D!2, C!3), union(C!3, B!4))),
% 2.46/1.82 inference(unit_resolution,[status(thm)],[279, 278])).
% 2.46/1.82 tff(281,plain,
% 2.46/1.82 ((~((~((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(C!3, B!4)))) | subset(intersection(D!2, C!3), union(C!3, B!4)))) | (~((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(C!3, B!4)))) | subset(intersection(D!2, C!3), union(C!3, B!4))),
% 2.46/1.82 inference(tautology,[status(thm)],[])).
% 2.46/1.82 tff(282,plain,
% 2.46/1.82 ((~((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(C!3, B!4)))) | subset(intersection(D!2, C!3), union(C!3, B!4))),
% 2.46/1.82 inference(unit_resolution,[status(thm)],[281, 280])).
% 2.46/1.82 tff(283,plain,
% 2.46/1.82 (subset(intersection(D!2, C!3), union(C!3, B!4))),
% 2.46/1.82 inference(unit_resolution,[status(thm)],[282, 255])).
% 2.46/1.82 tff(284,plain,
% 2.46/1.82 (((~((~subset(intersection(D!2, C!3), union(C!3, B!4))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, union(C!3, B!4))))) | (~((~((~member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), intersection(D!2, C!3))) | member(tptp_fun_D_0(union(C!3, B!4), intersection(D!2, C!3)), union(C!3, B!4)))) | subset(intersection(D!2, C!3), union(C!3, B!4))))) | ((~subset(intersection(D!2, C!3), union(C!3, B!4))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, union(C!3, B!4))))),
% 2.46/1.82 inference(tautology,[status(thm)],[])).
% 2.46/1.82 tff(285,plain,
% 2.46/1.82 ((~subset(intersection(D!2, C!3), union(C!3, B!4))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, union(C!3, B!4)))),
% 2.46/1.82 inference(unit_resolution,[status(thm)],[284, 278])).
% 2.46/1.82 tff(286,plain,
% 2.46/1.82 ((~((~subset(intersection(D!2, C!3), union(C!3, B!4))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, union(C!3, B!4))))) | (~subset(intersection(D!2, C!3), union(C!3, B!4))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, union(C!3, B!4)))),
% 2.46/1.82 inference(tautology,[status(thm)],[])).
% 2.46/1.82 tff(287,plain,
% 2.46/1.82 ((~subset(intersection(D!2, C!3), union(C!3, B!4))) | ![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, union(C!3, B!4)))),
% 2.46/1.82 inference(unit_resolution,[status(thm)],[286, 285])).
% 2.46/1.82 tff(288,plain,
% 2.46/1.82 (![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, union(C!3, B!4)))),
% 2.46/1.82 inference(unit_resolution,[status(thm)],[287, 283])).
% 2.46/1.82 tff(289,plain,
% 2.46/1.82 (((~![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, union(C!3, B!4)))) | ((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)))) <=> ((~![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, union(C!3, B!4)))) | (~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)))),
% 2.46/1.82 inference(rewrite,[status(thm)],[])).
% 2.46/1.82 tff(290,plain,
% 2.46/1.82 ((~![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, union(C!3, B!4)))) | ((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)))),
% 2.46/1.82 inference(quant_inst,[status(thm)],[])).
% 2.46/1.82 tff(291,plain,
% 2.46/1.82 ((~![D: $i] : ((~member(D, intersection(D!2, C!3))) | member(D, union(C!3, B!4)))) | (~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4))),
% 2.46/1.82 inference(modus_ponens,[status(thm)],[290, 289])).
% 2.46/1.82 tff(292,plain,
% 2.46/1.82 (~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3))),
% 2.46/1.82 inference(unit_resolution,[status(thm)],[291, 288, 221])).
% 2.46/1.82 tff(293,plain,
% 2.46/1.82 ((~(member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3)) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(B!4, D!2))))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3)) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(B!4, D!2)))),
% 2.46/1.82 inference(tautology,[status(thm)],[])).
% 2.46/1.82 tff(294,plain,
% 2.46/1.82 ((~(member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), intersection(D!2, C!3)) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(B!4, D!2))))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(B!4, intersection(B!4, D!2)))),
% 2.46/1.82 inference(unit_resolution,[status(thm)],[293, 292])).
% 2.46/1.82 tff(295,plain,
% 2.46/1.82 ($false),
% 2.46/1.82 inference(unit_resolution,[status(thm)],[294, 226, 209])).
% 2.46/1.82 tff(296,plain,((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4))), inference(lemma,lemma(discharge,[]))).
% 2.46/1.82 tff(297,plain,
% 2.46/1.82 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))) | ![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4))))) | (~(subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4)) | (~((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4))))))))),
% 2.46/1.82 inference(quant_inst,[status(thm)],[])).
% 2.46/1.82 tff(298,plain,
% 2.46/1.82 (~((~((~subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))) | ![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4))))) | (~(subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4)) | (~((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)))))))),
% 2.46/1.82 inference(unit_resolution,[status(thm)],[297, 271])).
% 2.46/1.82 tff(299,plain,
% 2.46/1.82 (((~((~subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))) | ![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4))))) | (~(subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4)) | (~((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4))))))) | (subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4)) | (~((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)))))),
% 2.46/1.82 inference(tautology,[status(thm)],[])).
% 2.46/1.82 tff(300,plain,
% 2.46/1.82 (subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4)) | (~((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4))))),
% 2.46/1.82 inference(unit_resolution,[status(thm)],[299, 298])).
% 2.46/1.82 tff(301,plain,
% 2.46/1.82 ((~(subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4)) | (~((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4)))))) | subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4)) | (~((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4))))),
% 2.46/1.82 inference(tautology,[status(thm)],[])).
% 2.46/1.82 tff(302,plain,
% 2.46/1.82 (subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4)) | (~((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4))))),
% 2.46/1.82 inference(unit_resolution,[status(thm)],[301, 300])).
% 2.46/1.82 tff(303,plain,
% 2.46/1.82 (subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))),
% 2.46/1.82 inference(unit_resolution,[status(thm)],[302, 296])).
% 2.46/1.82 tff(304,plain,
% 2.46/1.82 (((~((~subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))) | ![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4))))) | (~(subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4)) | (~((~member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_0(union(C!3, B!4), union(intersection(C!3, D!2), B!4)), union(C!3, B!4))))))) | ((~subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))) | ![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4))))),
% 2.46/1.82 inference(tautology,[status(thm)],[])).
% 2.46/1.82 tff(305,plain,
% 2.46/1.82 ((~subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))) | ![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4)))),
% 2.46/1.82 inference(unit_resolution,[status(thm)],[304, 298])).
% 2.46/1.82 tff(306,plain,
% 2.46/1.82 ((~((~subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))) | ![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4))))) | (~subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))) | ![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4)))),
% 2.46/1.82 inference(tautology,[status(thm)],[])).
% 2.46/1.82 tff(307,plain,
% 2.46/1.82 ((~subset(union(intersection(C!3, D!2), B!4), union(C!3, B!4))) | ![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4)))),
% 2.46/1.82 inference(unit_resolution,[status(thm)],[306, 305])).
% 2.46/1.82 tff(308,plain,
% 2.46/1.82 (![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4)))),
% 2.46/1.82 inference(unit_resolution,[status(thm)],[307, 303])).
% 2.46/1.82 tff(309,plain,
% 2.46/1.82 (((~![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4)))) | ((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4)))) <=> ((~![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4)))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4)))),
% 2.46/1.82 inference(rewrite,[status(thm)],[])).
% 2.46/1.82 tff(310,plain,
% 2.46/1.82 ((~![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4)))) | ((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4)))),
% 2.46/1.82 inference(quant_inst,[status(thm)],[])).
% 2.46/1.82 tff(311,plain,
% 2.46/1.82 ((~![D: $i] : ((~member(D, union(intersection(C!3, D!2), B!4))) | member(D, union(C!3, B!4)))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))),
% 2.46/1.82 inference(modus_ponens,[status(thm)],[310, 309])).
% 2.46/1.82 tff(312,plain,
% 2.46/1.82 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))),
% 2.46/1.82 inference(unit_resolution,[status(thm)],[311, 308, 190])).
% 2.46/1.82 tff(313,plain,
% 2.46/1.82 ((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3)))) <=> (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4))))),
% 2.46/1.82 inference(monotonicity,[status(thm)],[150])).
% 2.46/1.82 tff(314,plain,
% 2.46/1.82 (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4)))),
% 2.46/1.83 inference(modus_ponens,[status(thm)],[151, 313])).
% 2.46/1.83 tff(315,assumption,(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))), introduced(assumption)).
% 2.46/1.83 tff(316,assumption,(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))), introduced(assumption)).
% 2.46/1.83 tff(317,plain,
% 2.46/1.83 ((~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))),
% 2.46/1.83 inference(tautology,[status(thm)],[])).
% 2.46/1.83 tff(318,plain,
% 2.46/1.83 (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))))),
% 2.46/1.83 inference(unit_resolution,[status(thm)],[317, 316, 315])).
% 2.46/1.83 tff(319,plain,
% 2.46/1.83 ((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4))) <=> (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))))))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4))) | ((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))))),
% 2.46/1.83 inference(tautology,[status(thm)],[])).
% 2.46/1.83 tff(320,plain,
% 2.46/1.83 ((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4))) <=> (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))))))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4)))),
% 2.46/1.83 inference(unit_resolution,[status(thm)],[319, 318])).
% 2.46/1.83 tff(321,plain,
% 2.46/1.83 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4)))),
% 2.46/1.83 inference(unit_resolution,[status(thm)],[320, 134])).
% 2.46/1.83 tff(322,plain,
% 2.46/1.83 ($false),
% 2.46/1.83 inference(unit_resolution,[status(thm)],[321, 314])).
% 2.46/1.83 tff(323,plain,(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4)))), inference(lemma,lemma(discharge,[]))).
% 2.46/1.83 tff(324,plain,
% 2.46/1.83 (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))),
% 2.46/1.83 inference(unit_resolution,[status(thm)],[323, 312, 151])).
% 2.46/1.83 tff(325,plain,
% 2.46/1.83 (union(union(D!2, D!2), union(B!4, intersection(B!4, D!2))) = union(D!2, B!4)),
% 2.46/1.83 inference(monotonicity,[status(thm)],[74, 124])).
% 2.46/1.83 tff(326,plain,
% 2.46/1.83 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(union(D!2, D!2), union(B!4, intersection(B!4, D!2)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))),
% 2.46/1.83 inference(monotonicity,[status(thm)],[325])).
% 2.46/1.83 tff(327,plain,
% 2.46/1.83 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(union(D!2, D!2), union(B!4, intersection(B!4, D!2))))),
% 2.46/1.83 inference(symmetry,[status(thm)],[326])).
% 2.46/1.83 tff(328,plain,
% 2.46/1.83 ((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))) <=> (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(union(D!2, D!2), union(B!4, intersection(B!4, D!2)))))),
% 2.46/1.83 inference(monotonicity,[status(thm)],[327])).
% 2.46/1.83 tff(329,assumption,(~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))), introduced(assumption)).
% 2.46/1.83 tff(330,plain,
% 2.46/1.83 (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(union(D!2, D!2), union(B!4, intersection(B!4, D!2))))),
% 2.46/1.83 inference(modus_ponens,[status(thm)],[329, 328])).
% 2.46/1.83 tff(331,plain,
% 2.46/1.83 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(union(D!2, D!2), union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2))))),
% 2.46/1.83 inference(quant_inst,[status(thm)],[])).
% 2.46/1.83 tff(332,plain,
% 2.46/1.83 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(union(D!2, D!2), union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2)))),
% 2.46/1.83 inference(unit_resolution,[status(thm)],[331, 10])).
% 2.46/1.83 tff(333,assumption,(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2))), introduced(assumption)).
% 2.46/1.83 tff(334,plain,
% 2.46/1.83 ((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(union(D!2, D!2), union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2))))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(union(D!2, D!2), union(B!4, intersection(B!4, D!2)))) | (~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2))))),
% 2.46/1.83 inference(tautology,[status(thm)],[])).
% 2.46/1.83 tff(335,plain,
% 2.46/1.83 ((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(union(D!2, D!2), union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2))))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(union(D!2, D!2), union(B!4, intersection(B!4, D!2))))),
% 2.46/1.83 inference(unit_resolution,[status(thm)],[334, 333])).
% 2.46/1.83 tff(336,plain,
% 2.46/1.83 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(union(D!2, D!2), union(B!4, intersection(B!4, D!2))))),
% 2.46/1.83 inference(unit_resolution,[status(thm)],[335, 332])).
% 2.46/1.83 tff(337,plain,
% 2.46/1.83 ($false),
% 2.46/1.83 inference(unit_resolution,[status(thm)],[336, 330])).
% 2.46/1.83 tff(338,plain,(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)) | (~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2))))), inference(lemma,lemma(discharge,[]))).
% 2.46/1.83 tff(339,plain,
% 2.46/1.83 (~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2)))),
% 2.46/1.83 inference(unit_resolution,[status(thm)],[338, 324])).
% 2.46/1.83 tff(340,plain,
% 2.46/1.83 ((member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2)))),
% 2.46/1.83 inference(tautology,[status(thm)],[])).
% 2.46/1.83 tff(341,plain,
% 2.46/1.83 (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2))),
% 2.46/1.83 inference(unit_resolution,[status(thm)],[340, 339])).
% 2.46/1.83 tff(342,plain,
% 2.46/1.83 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))))),
% 2.46/1.83 inference(quant_inst,[status(thm)],[])).
% 2.46/1.83 tff(343,plain,
% 2.46/1.83 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3)))),
% 2.46/1.83 inference(unit_resolution,[status(thm)],[342, 10])).
% 2.46/1.83 tff(344,plain,
% 2.46/1.83 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))),
% 2.46/1.83 inference(monotonicity,[status(thm)],[201])).
% 2.46/1.83 tff(345,plain,
% 2.46/1.83 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2))))),
% 2.46/1.83 inference(symmetry,[status(thm)],[344])).
% 2.46/1.83 tff(346,assumption,(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))), introduced(assumption)).
% 2.46/1.83 tff(347,plain,
% 2.46/1.83 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2))))),
% 2.46/1.83 inference(modus_ponens,[status(thm)],[346, 345])).
% 2.46/1.83 tff(348,assumption,(~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2))))), introduced(assumption)).
% 2.46/1.83 tff(349,plain,
% 2.46/1.83 ($false),
% 2.46/1.83 inference(unit_resolution,[status(thm)],[348, 347])).
% 2.46/1.83 tff(350,plain,(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2)))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))), inference(lemma,lemma(discharge,[]))).
% 2.46/1.83 tff(351,plain,
% 2.46/1.83 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2))))),
% 2.46/1.83 inference(unit_resolution,[status(thm)],[350, 190])).
% 2.46/1.83 tff(352,plain,
% 2.46/1.83 ((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2))))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3)))),
% 2.46/1.83 inference(tautology,[status(thm)],[])).
% 2.46/1.83 tff(353,plain,
% 2.46/1.83 ((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3)))),
% 2.46/1.83 inference(unit_resolution,[status(thm)],[352, 351])).
% 2.46/1.83 tff(354,plain,
% 2.46/1.83 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))),
% 2.46/1.83 inference(unit_resolution,[status(thm)],[353, 343])).
% 2.46/1.83 tff(355,plain,
% 2.46/1.83 ((member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))))),
% 2.46/1.83 inference(tautology,[status(thm)],[])).
% 2.46/1.83 tff(356,plain,
% 2.46/1.83 (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2)))),
% 2.46/1.83 inference(unit_resolution,[status(thm)],[355, 339])).
% 2.46/1.83 tff(357,plain,
% 2.46/1.83 ((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3)))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))),
% 2.46/1.83 inference(tautology,[status(thm)],[])).
% 2.46/1.83 tff(358,plain,
% 2.46/1.83 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))),
% 2.46/1.83 inference(unit_resolution,[status(thm)],[357, 356, 354])).
% 2.46/1.83 tff(359,plain,
% 2.46/1.83 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, D!2), C!3)) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))),
% 2.46/1.83 inference(monotonicity,[status(thm)],[227])).
% 2.46/1.83 tff(360,plain,
% 2.46/1.83 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3)) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, D!2), C!3))),
% 2.46/1.83 inference(symmetry,[status(thm)],[359])).
% 2.46/1.83 tff(361,assumption,(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))), introduced(assumption)).
% 2.46/1.83 tff(362,plain,
% 2.46/1.83 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, D!2), C!3))),
% 2.46/1.83 inference(modus_ponens,[status(thm)],[361, 360])).
% 2.46/1.83 tff(363,plain,
% 2.46/1.83 (((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, D!2), C!3)) <=> (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3)) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2))))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, D!2), C!3)) <=> (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3)) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2)))))))),
% 2.46/1.83 inference(rewrite,[status(thm)],[])).
% 2.46/1.83 tff(364,plain,
% 2.46/1.83 ((member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, D!2), C!3)) <=> (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3))))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, D!2), C!3)) <=> (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3)) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2))))))),
% 2.46/1.83 inference(rewrite,[status(thm)],[])).
% 2.46/1.83 tff(365,plain,
% 2.46/1.83 (((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, D!2), C!3)) <=> (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3)))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, D!2), C!3)) <=> (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3)) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2)))))))),
% 2.46/1.84 inference(monotonicity,[status(thm)],[364])).
% 2.46/1.84 tff(366,plain,
% 2.46/1.84 (((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, D!2), C!3)) <=> (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3)))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, D!2), C!3)) <=> (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3)) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2)))))))),
% 2.46/1.84 inference(transitivity,[status(thm)],[365, 363])).
% 2.46/1.84 tff(367,plain,
% 2.46/1.84 ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, D!2), C!3)) <=> (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3)))))),
% 2.46/1.84 inference(quant_inst,[status(thm)],[])).
% 2.46/1.84 tff(368,plain,
% 2.46/1.84 ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, D!2), C!3)) <=> (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3)) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2))))))),
% 2.46/1.84 inference(modus_ponens,[status(thm)],[367, 366])).
% 2.46/1.84 tff(369,plain,
% 2.46/1.84 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, D!2), C!3)) <=> (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3)) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2)))))),
% 2.46/1.84 inference(unit_resolution,[status(thm)],[368, 111])).
% 2.46/1.84 tff(370,assumption,(~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2))), introduced(assumption)).
% 2.46/1.84 tff(371,plain,
% 2.46/1.84 (((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3)) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2)))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2))),
% 2.46/1.84 inference(tautology,[status(thm)],[])).
% 2.46/1.84 tff(372,plain,
% 2.46/1.84 ((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3)) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2)))),
% 2.46/1.84 inference(unit_resolution,[status(thm)],[371, 370])).
% 2.46/1.84 tff(373,plain,
% 2.46/1.84 ((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, D!2), C!3)) <=> (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3)) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2))))))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, D!2), C!3))) | (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3)) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2)))))),
% 2.46/1.84 inference(tautology,[status(thm)],[])).
% 2.46/1.84 tff(374,plain,
% 2.46/1.84 ((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, D!2), C!3)) <=> (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3)) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2))))))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, D!2), C!3)))),
% 2.46/1.84 inference(unit_resolution,[status(thm)],[373, 372])).
% 2.46/1.84 tff(375,plain,
% 2.46/1.84 (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, D!2), C!3))),
% 2.46/1.84 inference(unit_resolution,[status(thm)],[374, 369])).
% 2.46/1.84 tff(376,plain,
% 2.46/1.84 ($false),
% 2.46/1.84 inference(unit_resolution,[status(thm)],[375, 362])).
% 2.46/1.84 tff(377,plain,((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2))), inference(lemma,lemma(discharge,[]))).
% 2.46/1.84 tff(378,plain,
% 2.46/1.84 ($false),
% 2.46/1.84 inference(unit_resolution,[status(thm)],[377, 358, 341])).
% 2.46/1.84 tff(379,plain,(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3)))), inference(lemma,lemma(discharge,[]))).
% 2.46/1.84 tff(380,plain,
% 2.46/1.84 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4)))),
% 2.46/1.84 inference(modus_ponens,[status(thm)],[379, 150])).
% 2.46/1.84 tff(381,assumption,(~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4)))), introduced(assumption)).
% 2.46/1.84 tff(382,plain,
% 2.46/1.84 ($false),
% 2.46/1.84 inference(unit_resolution,[status(thm)],[381, 380])).
% 2.46/1.84 tff(383,plain,(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4)))), inference(lemma,lemma(discharge,[]))).
% 2.46/1.84 tff(384,plain,
% 2.46/1.84 ((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4))) <=> (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))))))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4)))) | (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))))),
% 2.46/1.84 inference(tautology,[status(thm)],[])).
% 2.46/1.84 tff(385,plain,
% 2.46/1.84 ((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, B!4), union(C!3, B!4))) <=> (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))))))) | (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))))),
% 2.46/1.84 inference(unit_resolution,[status(thm)],[384, 383])).
% 2.46/1.84 tff(386,plain,
% 2.46/1.84 (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))))),
% 2.46/1.84 inference(unit_resolution,[status(thm)],[385, 134])).
% 2.46/1.84 tff(387,plain,
% 2.46/1.84 (((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))),
% 2.46/1.84 inference(tautology,[status(thm)],[])).
% 2.46/1.84 tff(388,plain,
% 2.46/1.84 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))),
% 2.46/1.84 inference(unit_resolution,[status(thm)],[387, 386])).
% 2.46/1.84 tff(389,plain,
% 2.46/1.84 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, union(B!4, intersection(B!4, D!2))))),
% 2.46/1.84 inference(modus_ponens,[status(thm)],[388, 127])).
% 2.46/1.84 tff(390,plain,
% 2.46/1.84 ((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2)))))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, union(B!4, intersection(B!4, D!2))))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))))),
% 2.46/1.84 inference(tautology,[status(thm)],[])).
% 2.46/1.84 tff(391,plain,
% 2.46/1.84 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2)))),
% 2.46/1.84 inference(unit_resolution,[status(thm)],[390, 389, 17])).
% 2.46/1.84 tff(392,assumption,(~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))))), introduced(assumption)).
% 2.46/1.84 tff(393,plain,
% 2.46/1.84 ($false),
% 2.46/1.84 inference(unit_resolution,[status(thm)],[342, 10, 392])).
% 2.46/1.84 tff(394,plain,(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3)))), inference(lemma,lemma(discharge,[]))).
% 2.46/1.84 tff(395,plain,
% 2.46/1.84 ((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))) <=> (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2)))))),
% 2.46/1.84 inference(monotonicity,[status(thm)],[345])).
% 2.46/1.84 tff(396,plain,
% 2.46/1.84 ((~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3)))) <=> member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3)))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))),
% 2.46/1.84 inference(tautology,[status(thm)],[])).
% 2.46/1.84 tff(397,plain,
% 2.46/1.84 ((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(B!4, D!2), union(B!4, C!3)))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4)))),
% 2.46/1.84 inference(unit_resolution,[status(thm)],[396, 187])).
% 2.46/1.84 tff(398,plain,
% 2.46/1.84 (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(C!3, D!2), B!4))),
% 2.46/1.84 inference(unit_resolution,[status(thm)],[397, 379])).
% 2.46/1.84 tff(399,plain,
% 2.46/1.84 (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2))))),
% 2.46/1.84 inference(modus_ponens,[status(thm)],[398, 395])).
% 2.46/1.84 tff(400,plain,
% 2.46/1.84 ((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2)))) | (~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))))),
% 2.46/1.84 inference(tautology,[status(thm)],[])).
% 2.46/1.84 tff(401,plain,
% 2.46/1.84 ((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(intersection(D!2, C!3), union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))))) | (~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))))),
% 2.46/1.84 inference(unit_resolution,[status(thm)],[400, 399])).
% 2.46/1.84 tff(402,plain,
% 2.46/1.84 (~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3)))),
% 2.46/1.84 inference(unit_resolution,[status(thm)],[401, 394])).
% 2.46/1.84 tff(403,plain,
% 2.46/1.84 ((member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))))),
% 2.46/1.84 inference(tautology,[status(thm)],[])).
% 2.46/1.84 tff(404,plain,
% 2.46/1.84 (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2)))),
% 2.46/1.84 inference(unit_resolution,[status(thm)],[403, 402])).
% 2.46/1.84 tff(405,plain,
% 2.46/1.84 ((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2)))),
% 2.46/1.84 inference(tautology,[status(thm)],[])).
% 2.46/1.84 tff(406,plain,
% 2.46/1.84 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3)),
% 2.46/1.84 inference(unit_resolution,[status(thm)],[405, 404, 391])).
% 2.46/1.84 tff(407,plain,
% 2.46/1.84 (((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(C!3, B!4))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4)))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))),
% 2.46/1.84 inference(tautology,[status(thm)],[])).
% 2.46/1.84 tff(408,plain,
% 2.46/1.84 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, B!4))),
% 2.46/1.84 inference(unit_resolution,[status(thm)],[407, 386])).
% 2.46/1.84 tff(409,plain,
% 2.46/1.84 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(union(D!2, D!2), union(B!4, intersection(B!4, D!2))))),
% 2.46/1.84 inference(modus_ponens,[status(thm)],[408, 327])).
% 2.46/1.84 tff(410,plain,
% 2.46/1.84 ((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(union(D!2, D!2), union(B!4, intersection(B!4, D!2)))) <=> (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2))))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(union(D!2, D!2), union(B!4, intersection(B!4, D!2))))) | (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2)))),
% 2.46/1.84 inference(tautology,[status(thm)],[])).
% 2.46/1.84 tff(411,plain,
% 2.46/1.84 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2))),
% 2.46/1.84 inference(unit_resolution,[status(thm)],[410, 409, 332])).
% 2.46/1.84 tff(412,plain,
% 2.46/1.84 ((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2)))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2))),
% 2.46/1.84 inference(tautology,[status(thm)],[])).
% 2.46/1.84 tff(413,plain,
% 2.46/1.84 (member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2))),
% 2.46/1.84 inference(unit_resolution,[status(thm)],[412, 404, 411])).
% 2.46/1.84 tff(414,plain,
% 2.46/1.84 ((~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3)) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2))))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3)) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2)))),
% 2.46/1.84 inference(tautology,[status(thm)],[])).
% 2.46/1.84 tff(415,plain,
% 2.46/1.84 (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3)) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2))))),
% 2.46/1.84 inference(unit_resolution,[status(thm)],[414, 413, 406])).
% 2.46/1.84 tff(416,plain,
% 2.46/1.84 ((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))) <=> (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, D!2), C!3)))),
% 2.46/1.85 inference(monotonicity,[status(thm)],[360])).
% 2.46/1.85 tff(417,plain,
% 2.46/1.85 ((member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(B!4, intersection(B!4, D!2))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3)))),
% 2.46/1.85 inference(tautology,[status(thm)],[])).
% 2.46/1.85 tff(418,plain,
% 2.46/1.85 (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(D!2, C!3))),
% 2.46/1.85 inference(unit_resolution,[status(thm)],[417, 402])).
% 2.46/1.85 tff(419,plain,
% 2.46/1.85 (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, D!2), C!3))),
% 2.46/1.85 inference(modus_ponens,[status(thm)],[418, 416])).
% 2.46/1.85 tff(420,assumption,(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, D!2), C!3))), introduced(assumption)).
% 2.46/1.85 tff(421,plain,
% 2.46/1.85 ($false),
% 2.46/1.85 inference(unit_resolution,[status(thm)],[420, 419])).
% 2.46/1.85 tff(422,plain,(~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, D!2), C!3))), inference(lemma,lemma(discharge,[]))).
% 2.46/1.85 tff(423,plain,
% 2.46/1.85 ((~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, D!2), C!3)) <=> (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3)) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2))))))) | member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, D!2), C!3)) | ((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3)) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2))))),
% 2.46/1.85 inference(tautology,[status(thm)],[])).
% 2.46/1.85 tff(424,plain,
% 2.46/1.85 (~(member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), intersection(union(D!2, D!2), C!3)) <=> (~((~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), C!3)) | (~member(tptp_fun_D_1(union(intersection(C!3, D!2), B!4), intersection(union(B!4, D!2), union(B!4, C!3))), union(D!2, D!2))))))),
% 2.46/1.85 inference(unit_resolution,[status(thm)],[423, 422, 415])).
% 2.46/1.85 tff(425,plain,
% 2.46/1.85 ($false),
% 2.46/1.85 inference(unit_resolution,[status(thm)],[368, 111, 424])).
% 2.46/1.85 % SZS output end Proof
%------------------------------------------------------------------------------