TSTP Solution File: SET624+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET624+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 05:07:23 EDT 2022
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET624+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 07:03:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(member_type, type, (
% 0.19/0.38 member: ( $i * $i ) > $o)).
% 0.19/0.38 tff(tptp_fun_C_3_type, type, (
% 0.19/0.38 tptp_fun_C_3: $i)).
% 0.19/0.38 tff(tptp_fun_B_4_type, type, (
% 0.19/0.38 tptp_fun_B_4: $i)).
% 0.19/0.38 tff(intersect_type, type, (
% 0.19/0.38 intersect: ( $i * $i ) > $o)).
% 0.19/0.38 tff(tptp_fun_D_0_type, type, (
% 0.19/0.38 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.19/0.38 tff(union_type, type, (
% 0.19/0.38 union: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_D_2_type, type, (
% 0.19/0.38 tptp_fun_D_2: $i)).
% 0.19/0.38 tff(1,assumption,(~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))), introduced(assumption)).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 (((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3))) | member(tptp_fun_D_0(C!3, B!4), B!4)),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 (member(tptp_fun_D_0(C!3, B!4), B!4)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.19/0.38 tff(4,plain,
% 0.19/0.38 (((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3))) | member(tptp_fun_D_0(C!3, B!4), C!3)),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (member(tptp_fun_D_0(C!3, B!4), C!3)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.19/0.38 tff(6,plain,
% 0.19/0.38 ((member(tptp_fun_D_0(C!3, B!4), C!3) | member(tptp_fun_D_0(C!3, B!4), D!2)) | (~member(tptp_fun_D_0(C!3, B!4), C!3))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 (member(tptp_fun_D_0(C!3, B!4), C!3) | member(tptp_fun_D_0(C!3, B!4), D!2)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[6, 5])).
% 0.19/0.38 tff(8,assumption,(~(member(tptp_fun_D_0(C!3, B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(C!3, B!4), C!3) | member(tptp_fun_D_0(C!3, B!4), D!2)))), introduced(assumption)).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 (^[B: $i, C: $i, D: $i] : refl((member(D, union(B, C)) <=> (member(D, C) | member(D, B))) <=> (member(D, union(B, C)) <=> (member(D, C) | member(D, B))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B))) <=> ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[9])).
% 0.19/0.38 tff(11,plain,
% 0.19/0.38 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B))) <=> ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (^[B: $i, C: $i, D: $i] : rewrite((member(D, union(B, C)) <=> (member(D, B) | member(D, C))) <=> (member(D, union(B, C)) <=> (member(D, C) | member(D, B))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, B) | member(D, C))) <=> ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.38 tff(14,axiom,(![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, B) | member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','union_defn')).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.19/0.38 tff(17,plain,(
% 0.19/0.38 ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[16])).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(C!3, B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(C!3, B!4), C!3) | member(tptp_fun_D_0(C!3, 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(C!3, B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(C!3, B!4), C!3) | member(tptp_fun_D_0(C!3, B!4), D!2))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 ((member(tptp_fun_D_0(C!3, B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(C!3, B!4), D!2) | member(tptp_fun_D_0(C!3, B!4), C!3))) <=> (member(tptp_fun_D_0(C!3, B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(C!3, B!4), C!3) | member(tptp_fun_D_0(C!3, B!4), D!2)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(C!3, B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(C!3, B!4), D!2) | member(tptp_fun_D_0(C!3, 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(C!3, B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(C!3, B!4), C!3) | member(tptp_fun_D_0(C!3, B!4), D!2))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[20])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(C!3, B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(C!3, B!4), D!2) | member(tptp_fun_D_0(C!3, 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(C!3, B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(C!3, B!4), C!3) | member(tptp_fun_D_0(C!3, B!4), D!2))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[21, 19])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(C!3, B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(C!3, B!4), D!2) | member(tptp_fun_D_0(C!3, B!4), C!3)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(C!3, B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(C!3, B!4), C!3) | member(tptp_fun_D_0(C!3, B!4), D!2)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[24, 18, 8])).
% 0.19/0.39 tff(26,plain,(member(tptp_fun_D_0(C!3, B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(C!3, B!4), C!3) | member(tptp_fun_D_0(C!3, B!4), D!2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 ((~(member(tptp_fun_D_0(C!3, B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(C!3, B!4), C!3) | member(tptp_fun_D_0(C!3, B!4), D!2)))) | member(tptp_fun_D_0(C!3, B!4), union(C!3, D!2)) | (~(member(tptp_fun_D_0(C!3, B!4), C!3) | member(tptp_fun_D_0(C!3, B!4), D!2)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (member(tptp_fun_D_0(C!3, B!4), union(C!3, D!2)) | (~(member(tptp_fun_D_0(C!3, B!4), C!3) | member(tptp_fun_D_0(C!3, B!4), D!2)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (member(tptp_fun_D_0(C!3, B!4), union(C!3, D!2))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[28, 7])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 ((~![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, D!2), B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2) | member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2) | member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[30, 18])).
% 0.19/0.39 tff(32,assumption,(~(intersect(B!4, D!2) | intersect(B!4, C!3))), introduced(assumption)).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 ((~(intersect(B!4, union(C!3, D!2)) <=> (intersect(B!4, D!2) | intersect(B!4, C!3)))) <=> ((~intersect(B!4, union(C!3, D!2))) <=> (intersect(B!4, D!2) | intersect(B!4, C!3)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 ((intersect(B!4, union(C!3, D!2)) <=> (intersect(B!4, D!2) | intersect(B!4, C!3))) <=> (intersect(B!4, union(C!3, D!2)) <=> (intersect(B!4, D!2) | intersect(B!4, C!3)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 ((~(intersect(B!4, union(C!3, D!2)) <=> (intersect(B!4, D!2) | intersect(B!4, C!3)))) <=> (~(intersect(B!4, union(C!3, D!2)) <=> (intersect(B!4, D!2) | intersect(B!4, C!3))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[34])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 ((~(intersect(B!4, union(C!3, D!2)) <=> (intersect(B!4, D!2) | intersect(B!4, C!3)))) <=> ((~intersect(B!4, union(C!3, D!2))) <=> (intersect(B!4, D!2) | intersect(B!4, C!3)))),
% 0.19/0.39 inference(transitivity,[status(thm)],[35, 33])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 ((~![B: $i, C: $i, D: $i] : (intersect(B, union(C, D)) <=> (intersect(B, D) | intersect(B, C)))) <=> (~![B: $i, C: $i, D: $i] : (intersect(B, union(C, D)) <=> (intersect(B, D) | intersect(B, C))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 ((~![B: $i, C: $i, D: $i] : (intersect(B, union(C, D)) <=> (intersect(B, C) | intersect(B, D)))) <=> (~![B: $i, C: $i, D: $i] : (intersect(B, union(C, D)) <=> (intersect(B, D) | intersect(B, C))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(39,axiom,(~![B: $i, C: $i, D: $i] : (intersect(B, union(C, D)) <=> (intersect(B, C) | intersect(B, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_intersect_with_union')).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (~![B: $i, C: $i, D: $i] : (intersect(B, union(C, D)) <=> (intersect(B, D) | intersect(B, C)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (~![B: $i, C: $i, D: $i] : (intersect(B, union(C, D)) <=> (intersect(B, D) | intersect(B, C)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[40, 37])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (~![B: $i, C: $i, D: $i] : (intersect(B, union(C, D)) <=> (intersect(B, D) | intersect(B, C)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 (~![B: $i, C: $i, D: $i] : (intersect(B, union(C, D)) <=> (intersect(B, D) | intersect(B, C)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[42, 37])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 (~![B: $i, C: $i, D: $i] : (intersect(B, union(C, D)) <=> (intersect(B, D) | intersect(B, C)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[43, 37])).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 (~![B: $i, C: $i, D: $i] : (intersect(B, union(C, D)) <=> (intersect(B, D) | intersect(B, C)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 (~![B: $i, C: $i, D: $i] : (intersect(B, union(C, D)) <=> (intersect(B, D) | intersect(B, C)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[45, 37])).
% 0.19/0.39 tff(47,plain,(
% 0.19/0.39 ~(intersect(B!4, union(C!3, D!2)) <=> (intersect(B!4, D!2) | intersect(B!4, C!3)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[46])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 ((~intersect(B!4, union(C!3, D!2))) <=> (intersect(B!4, D!2) | intersect(B!4, C!3))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[47, 36])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 (intersect(B!4, union(C!3, D!2)) | (intersect(B!4, D!2) | intersect(B!4, C!3)) | (~((~intersect(B!4, union(C!3, D!2))) <=> (intersect(B!4, D!2) | intersect(B!4, C!3))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 (intersect(B!4, union(C!3, D!2)) | (intersect(B!4, D!2) | intersect(B!4, C!3))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 (intersect(B!4, union(C!3, D!2))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[50, 32])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 (^[B: $i, C: $i] : refl((~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C))))))) <=> (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C))))))) <=> ![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[52])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 (^[B: $i, C: $i] : rewrite((~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C))))))) <=> (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C))))))) <=> ![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C))))))) <=> ![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[55, 53])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 (^[B: $i, C: $i] : trans(monotonicity(rewrite(((~intersect(B, C)) | (member(tptp_fun_D_0(C, B), B) & member(tptp_fun_D_0(C, B), C))) <=> ((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))), rewrite((intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C)))) <=> (intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C))))), ((((~intersect(B, C)) | (member(tptp_fun_D_0(C, B), B) & member(tptp_fun_D_0(C, B), C))) & (intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C))))) <=> (((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C))))) & (intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C))))))), rewrite((((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C))))) & (intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C))))) <=> (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))), ((((~intersect(B, C)) | (member(tptp_fun_D_0(C, B), B) & member(tptp_fun_D_0(C, B), C))) & (intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C))))) <=> (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 (![B: $i, C: $i] : (((~intersect(B, C)) | (member(tptp_fun_D_0(C, B), B) & member(tptp_fun_D_0(C, B), C))) & (intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C))))) <=> ![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[57])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 (![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C))) <=> ![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(60,axiom,(![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersect_defn')).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 (![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.39 tff(62,plain,(
% 0.19/0.39 ![B: $i, C: $i] : (((~intersect(B, C)) | (member(tptp_fun_D_0(C, B), B) & member(tptp_fun_D_0(C, B), C))) & (intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C)))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[61])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))) | (~((~((~intersect(B!4, union(C!3, D!2))) | (~((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2))))))) | (~(intersect(B!4, union(C!3, D!2)) | ![D: $i] : ((~member(D, B!4)) | (~member(D, union(C!3, D!2))))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 (~((~((~intersect(B!4, union(C!3, D!2))) | (~((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2))))))) | (~(intersect(B!4, union(C!3, D!2)) | ![D: $i] : ((~member(D, B!4)) | (~member(D, union(C!3, D!2)))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 (((~((~intersect(B!4, union(C!3, D!2))) | (~((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2))))))) | (~(intersect(B!4, union(C!3, D!2)) | ![D: $i] : ((~member(D, B!4)) | (~member(D, union(C!3, D!2))))))) | ((~intersect(B!4, union(C!3, D!2))) | (~((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2))))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 ((~intersect(B!4, union(C!3, D!2))) | (~((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 ((~((~intersect(B!4, union(C!3, D!2))) | (~((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2))))))) | (~intersect(B!4, union(C!3, D!2))) | (~((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2)))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 ((~intersect(B!4, union(C!3, D!2))) | (~((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (~((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[70, 51])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 (((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2)))) | member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 (member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 ((~(member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2) | member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3)))) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2))) | (member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2) | member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 ((~(member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2) | member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3)))) | (member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2) | member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 (member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2) | member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[75, 31])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))) | (~((~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))) | (~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, B!4)) | (~member(D, C!3)))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 (~((~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))) | (~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, B!4)) | (~member(D, C!3))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[77, 64])).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 (((~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))) | (~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, B!4)) | (~member(D, C!3)))))) | (intersect(B!4, C!3) | ![D: $i] : ((~member(D, B!4)) | (~member(D, C!3))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 (intersect(B!4, C!3) | ![D: $i] : ((~member(D, B!4)) | (~member(D, C!3)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 ((intersect(B!4, D!2) | intersect(B!4, C!3)) | (~intersect(B!4, C!3))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(82,plain,
% 0.19/0.40 (~intersect(B!4, C!3)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[81, 32])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 ((~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, B!4)) | (~member(D, C!3))))) | intersect(B!4, C!3) | ![D: $i] : ((~member(D, B!4)) | (~member(D, C!3)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 ((~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, B!4)) | (~member(D, C!3))))) | ![D: $i] : ((~member(D, B!4)) | (~member(D, C!3)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.19/0.40 tff(85,plain,
% 0.19/0.40 (![D: $i] : ((~member(D, B!4)) | (~member(D, C!3)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[84, 80])).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 (((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2)))) | member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 (member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[86, 71])).
% 0.19/0.40 tff(88,plain,
% 0.19/0.40 (((~![D: $i] : ((~member(D, B!4)) | (~member(D, C!3)))) | ((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3)))) <=> ((~![D: $i] : ((~member(D, B!4)) | (~member(D, C!3)))) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 ((~![D: $i] : ((~member(D, B!4)) | (~member(D, C!3)))) | ((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(90,plain,
% 0.19/0.40 ((~![D: $i] : ((~member(D, B!4)) | (~member(D, C!3)))) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.19/0.40 tff(91,plain,
% 0.19/0.40 (~member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[90, 87, 85])).
% 0.19/0.40 tff(92,plain,
% 0.19/0.40 ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, B)) | (~member(D, C)))))))) | (~((~((~intersect(B!4, D!2)) | (~((~member(tptp_fun_D_0(D!2, B!4), B!4)) | (~member(tptp_fun_D_0(D!2, B!4), D!2)))))) | (~(intersect(B!4, D!2) | ![D: $i] : ((~member(D, B!4)) | (~member(D, D!2)))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(93,plain,
% 0.19/0.40 (~((~((~intersect(B!4, D!2)) | (~((~member(tptp_fun_D_0(D!2, B!4), B!4)) | (~member(tptp_fun_D_0(D!2, B!4), D!2)))))) | (~(intersect(B!4, D!2) | ![D: $i] : ((~member(D, B!4)) | (~member(D, D!2))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[92, 64])).
% 0.19/0.40 tff(94,plain,
% 0.19/0.40 (((~((~intersect(B!4, D!2)) | (~((~member(tptp_fun_D_0(D!2, B!4), B!4)) | (~member(tptp_fun_D_0(D!2, B!4), D!2)))))) | (~(intersect(B!4, D!2) | ![D: $i] : ((~member(D, B!4)) | (~member(D, D!2)))))) | (intersect(B!4, D!2) | ![D: $i] : ((~member(D, B!4)) | (~member(D, D!2))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(95,plain,
% 0.19/0.40 (intersect(B!4, D!2) | ![D: $i] : ((~member(D, B!4)) | (~member(D, D!2)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.19/0.40 tff(96,plain,
% 0.19/0.40 ((intersect(B!4, D!2) | intersect(B!4, C!3)) | (~intersect(B!4, D!2))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(97,plain,
% 0.19/0.40 (~intersect(B!4, D!2)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[96, 32])).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 ((~(intersect(B!4, D!2) | ![D: $i] : ((~member(D, B!4)) | (~member(D, D!2))))) | intersect(B!4, D!2) | ![D: $i] : ((~member(D, B!4)) | (~member(D, D!2)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(99,plain,
% 0.19/0.40 ((~(intersect(B!4, D!2) | ![D: $i] : ((~member(D, B!4)) | (~member(D, D!2))))) | ![D: $i] : ((~member(D, B!4)) | (~member(D, D!2)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.19/0.40 tff(100,plain,
% 0.19/0.40 (![D: $i] : ((~member(D, B!4)) | (~member(D, D!2)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[99, 95])).
% 0.19/0.40 tff(101,plain,
% 0.19/0.40 (((~![D: $i] : ((~member(D, B!4)) | (~member(D, D!2)))) | ((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2)))) <=> ((~![D: $i] : ((~member(D, B!4)) | (~member(D, D!2)))) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(102,plain,
% 0.19/0.40 ((~![D: $i] : ((~member(D, B!4)) | (~member(D, D!2)))) | ((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(103,plain,
% 0.19/0.40 ((~![D: $i] : ((~member(D, B!4)) | (~member(D, D!2)))) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.19/0.40 tff(104,plain,
% 0.19/0.40 (~member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[103, 87, 100])).
% 0.19/0.40 tff(105,plain,
% 0.19/0.40 ((~(member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2) | member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3))) | member(tptp_fun_D_0(union(C!3, D!2), B!4), D!2) | member(tptp_fun_D_0(union(C!3, D!2), B!4), C!3)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(106,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[105, 104, 91, 76])).
% 0.19/0.40 tff(107,plain,(intersect(B!4, D!2) | intersect(B!4, C!3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(108,plain,
% 0.19/0.40 ((~intersect(B!4, union(C!3, D!2))) | (~(intersect(B!4, D!2) | intersect(B!4, C!3))) | (~((~intersect(B!4, union(C!3, D!2))) <=> (intersect(B!4, D!2) | intersect(B!4, C!3))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(109,plain,
% 0.19/0.40 ((~intersect(B!4, union(C!3, D!2))) | (~(intersect(B!4, D!2) | intersect(B!4, C!3)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[108, 48])).
% 0.19/0.40 tff(110,plain,
% 0.19/0.40 (~intersect(B!4, union(C!3, D!2))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[109, 107])).
% 0.19/0.40 tff(111,plain,
% 0.19/0.40 (((~((~intersect(B!4, union(C!3, D!2))) | (~((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | (~member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2))))))) | (~(intersect(B!4, union(C!3, D!2)) | ![D: $i] : ((~member(D, B!4)) | (~member(D, union(C!3, D!2))))))) | (intersect(B!4, union(C!3, D!2)) | ![D: $i] : ((~member(D, B!4)) | (~member(D, union(C!3, D!2)))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(112,plain,
% 0.19/0.40 (intersect(B!4, union(C!3, D!2)) | ![D: $i] : ((~member(D, B!4)) | (~member(D, union(C!3, D!2))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[111, 66])).
% 0.19/0.40 tff(113,plain,
% 0.19/0.40 ((~(intersect(B!4, union(C!3, D!2)) | ![D: $i] : ((~member(D, B!4)) | (~member(D, union(C!3, D!2)))))) | intersect(B!4, union(C!3, D!2)) | ![D: $i] : ((~member(D, B!4)) | (~member(D, union(C!3, D!2))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(114,plain,
% 0.19/0.41 (intersect(B!4, union(C!3, D!2)) | ![D: $i] : ((~member(D, B!4)) | (~member(D, union(C!3, D!2))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 (![D: $i] : ((~member(D, B!4)) | (~member(D, union(C!3, D!2))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[114, 110])).
% 0.19/0.41 tff(116,plain,
% 0.19/0.41 (((~![D: $i] : ((~member(D, B!4)) | (~member(D, union(C!3, D!2))))) | ((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), union(C!3, D!2))))) <=> ((~![D: $i] : ((~member(D, B!4)) | (~member(D, union(C!3, D!2))))) | (~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), union(C!3, D!2))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 ((~![D: $i] : ((~member(D, B!4)) | (~member(D, union(C!3, D!2))))) | ((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), union(C!3, D!2))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(118,plain,
% 0.19/0.41 ((~![D: $i] : ((~member(D, B!4)) | (~member(D, union(C!3, D!2))))) | (~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), union(C!3, D!2)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.19/0.41 tff(119,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[118, 115, 29, 3])).
% 0.19/0.41 tff(120,plain,((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(121,assumption,((~((~intersect(B!4, D!2)) | (~((~member(tptp_fun_D_0(D!2, B!4), B!4)) | (~member(tptp_fun_D_0(D!2, B!4), D!2)))))) | (~(intersect(B!4, D!2) | ![D: $i] : ((~member(D, B!4)) | (~member(D, D!2)))))), introduced(assumption)).
% 0.19/0.41 tff(122,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[92, 64, 121])).
% 0.19/0.41 tff(123,plain,(~((~((~intersect(B!4, D!2)) | (~((~member(tptp_fun_D_0(D!2, B!4), B!4)) | (~member(tptp_fun_D_0(D!2, B!4), D!2)))))) | (~(intersect(B!4, D!2) | ![D: $i] : ((~member(D, B!4)) | (~member(D, D!2))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(124,plain,
% 0.19/0.41 (((~((~intersect(B!4, D!2)) | (~((~member(tptp_fun_D_0(D!2, B!4), B!4)) | (~member(tptp_fun_D_0(D!2, B!4), D!2)))))) | (~(intersect(B!4, D!2) | ![D: $i] : ((~member(D, B!4)) | (~member(D, D!2)))))) | ((~intersect(B!4, D!2)) | (~((~member(tptp_fun_D_0(D!2, B!4), B!4)) | (~member(tptp_fun_D_0(D!2, B!4), D!2)))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(125,plain,
% 0.19/0.41 ((~intersect(B!4, D!2)) | (~((~member(tptp_fun_D_0(D!2, B!4), B!4)) | (~member(tptp_fun_D_0(D!2, B!4), D!2))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.19/0.41 tff(126,assumption,(~((~member(tptp_fun_D_0(D!2, B!4), B!4)) | (~member(tptp_fun_D_0(D!2, B!4), D!2)))), introduced(assumption)).
% 0.19/0.41 tff(127,plain,
% 0.19/0.41 (((~member(tptp_fun_D_0(D!2, B!4), B!4)) | (~member(tptp_fun_D_0(D!2, B!4), D!2))) | member(tptp_fun_D_0(D!2, B!4), B!4)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(128,plain,
% 0.19/0.41 (member(tptp_fun_D_0(D!2, B!4), B!4)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.19/0.41 tff(129,plain,
% 0.19/0.41 (((~member(tptp_fun_D_0(D!2, B!4), B!4)) | (~member(tptp_fun_D_0(D!2, B!4), D!2))) | member(tptp_fun_D_0(D!2, B!4), D!2)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(130,plain,
% 0.19/0.41 (member(tptp_fun_D_0(D!2, B!4), D!2)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[129, 126])).
% 0.19/0.41 tff(131,plain,
% 0.19/0.41 ((member(tptp_fun_D_0(D!2, B!4), D!2) | member(tptp_fun_D_0(D!2, B!4), C!3)) | (~member(tptp_fun_D_0(D!2, B!4), D!2))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(132,plain,
% 0.19/0.41 (member(tptp_fun_D_0(D!2, B!4), D!2) | member(tptp_fun_D_0(D!2, B!4), C!3)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.19/0.41 tff(133,assumption,(~(member(tptp_fun_D_0(D!2, B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(D!2, B!4), D!2) | member(tptp_fun_D_0(D!2, B!4), C!3)))), introduced(assumption)).
% 0.19/0.41 tff(134,plain,
% 0.19/0.41 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(D!2, B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(D!2, B!4), D!2) | member(tptp_fun_D_0(D!2, B!4), C!3)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(135,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[134, 18, 133])).
% 0.19/0.41 tff(136,plain,(member(tptp_fun_D_0(D!2, B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(D!2, B!4), D!2) | member(tptp_fun_D_0(D!2, B!4), C!3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(137,plain,
% 0.19/0.41 ((~(member(tptp_fun_D_0(D!2, B!4), union(C!3, D!2)) <=> (member(tptp_fun_D_0(D!2, B!4), D!2) | member(tptp_fun_D_0(D!2, B!4), C!3)))) | member(tptp_fun_D_0(D!2, B!4), union(C!3, D!2)) | (~(member(tptp_fun_D_0(D!2, B!4), D!2) | member(tptp_fun_D_0(D!2, B!4), C!3)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(138,plain,
% 0.19/0.41 (member(tptp_fun_D_0(D!2, B!4), union(C!3, D!2)) | (~(member(tptp_fun_D_0(D!2, B!4), D!2) | member(tptp_fun_D_0(D!2, B!4), C!3)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.19/0.41 tff(139,plain,
% 0.19/0.41 (member(tptp_fun_D_0(D!2, B!4), union(C!3, D!2))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[138, 132])).
% 0.19/0.41 tff(140,plain,
% 0.19/0.41 (((~![D: $i] : ((~member(D, B!4)) | (~member(D, union(C!3, D!2))))) | ((~member(tptp_fun_D_0(D!2, B!4), B!4)) | (~member(tptp_fun_D_0(D!2, B!4), union(C!3, D!2))))) <=> ((~![D: $i] : ((~member(D, B!4)) | (~member(D, union(C!3, D!2))))) | (~member(tptp_fun_D_0(D!2, B!4), B!4)) | (~member(tptp_fun_D_0(D!2, B!4), union(C!3, D!2))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(141,plain,
% 0.19/0.41 ((~![D: $i] : ((~member(D, B!4)) | (~member(D, union(C!3, D!2))))) | ((~member(tptp_fun_D_0(D!2, B!4), B!4)) | (~member(tptp_fun_D_0(D!2, B!4), union(C!3, D!2))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(142,plain,
% 0.19/0.41 ((~![D: $i] : ((~member(D, B!4)) | (~member(D, union(C!3, D!2))))) | (~member(tptp_fun_D_0(D!2, B!4), B!4)) | (~member(tptp_fun_D_0(D!2, B!4), union(C!3, D!2)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.19/0.41 tff(143,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[142, 115, 139, 128])).
% 0.19/0.41 tff(144,plain,((~member(tptp_fun_D_0(D!2, B!4), B!4)) | (~member(tptp_fun_D_0(D!2, B!4), D!2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(145,plain,
% 0.19/0.41 ((~((~intersect(B!4, D!2)) | (~((~member(tptp_fun_D_0(D!2, B!4), B!4)) | (~member(tptp_fun_D_0(D!2, B!4), D!2)))))) | (~intersect(B!4, D!2)) | (~((~member(tptp_fun_D_0(D!2, B!4), B!4)) | (~member(tptp_fun_D_0(D!2, B!4), D!2))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(146,plain,
% 0.19/0.41 ((~((~intersect(B!4, D!2)) | (~((~member(tptp_fun_D_0(D!2, B!4), B!4)) | (~member(tptp_fun_D_0(D!2, B!4), D!2)))))) | (~intersect(B!4, D!2))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.19/0.41 tff(147,plain,
% 0.19/0.41 (~intersect(B!4, D!2)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[146, 125])).
% 0.19/0.41 tff(148,plain,
% 0.19/0.41 ((~(intersect(B!4, D!2) | intersect(B!4, C!3))) | intersect(B!4, D!2) | intersect(B!4, C!3)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(149,plain,
% 0.19/0.41 (intersect(B!4, D!2) | intersect(B!4, C!3)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[148, 107])).
% 0.19/0.41 tff(150,plain,
% 0.19/0.41 (intersect(B!4, C!3)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[149, 147])).
% 0.19/0.41 tff(151,plain,
% 0.19/0.41 ((~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))) | (~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(152,plain,
% 0.19/0.41 (~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[151, 150, 120])).
% 0.19/0.41 tff(153,plain,
% 0.19/0.41 (((~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))) | (~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, B!4)) | (~member(D, C!3)))))) | ((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(154,plain,
% 0.19/0.41 ((~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))) | (~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, B!4)) | (~member(D, C!3)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[153, 152])).
% 0.19/0.41 tff(155,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[77, 64, 154])).
% 0.19/0.41 % SZS output end Proof
%------------------------------------------------------------------------------