TSTP Solution File: SET598+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET598+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 05:07:13 EDT 2022
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET598+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 06:55:25 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.34 Usage: tptp [options] [-file:]file
% 0.19/0.34 -h, -? prints this message.
% 0.19/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.34 -m, -model generate model.
% 0.19/0.34 -p, -proof generate proof.
% 0.19/0.34 -c, -core generate unsat core of named formulas.
% 0.19/0.34 -st, -statistics display statistics.
% 0.19/0.34 -t:timeout set timeout (in second).
% 0.19/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.34 -<param>:<value> configuration parameter and value.
% 0.19/0.34 -o:<output-file> file to place output in.
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(subset_type, type, (
% 0.19/0.39 subset: ( $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_D_2_type, type, (
% 0.19/0.39 tptp_fun_D_2: $i)).
% 0.19/0.39 tff(tptp_fun_E_5_type, type, (
% 0.19/0.39 tptp_fun_E_5: $i)).
% 0.19/0.39 tff(tptp_fun_C_3_type, type, (
% 0.19/0.39 tptp_fun_C_3: $i)).
% 0.19/0.39 tff(tptp_fun_B_4_type, type, (
% 0.19/0.39 tptp_fun_B_4: $i)).
% 0.19/0.39 tff(intersection_type, type, (
% 0.19/0.39 intersection: ( $i * $i ) > $i)).
% 0.19/0.39 tff(1,assumption,(subset(E!5, B!4) | (~subset(E!5, C!3)) | (~subset(E!5, D!2))), introduced(assumption)).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (^[B: $i, C: $i] : refl(((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))) <=> ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))) <=> ![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (^[B: $i, C: $i] : rewrite(((B = C) <=> (subset(B, C) & subset(C, B))) <=> ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B))) <=> ![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B))) <=> ![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(7,axiom,(![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','equal_defn')).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.19/0.39 tff(9,plain,(
% 0.19/0.39 ![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[8])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 (![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 ((~![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))) | ((B!4 = intersection(C!3, D!2)) <=> (~((~subset(B!4, intersection(C!3, D!2))) | (~subset(intersection(C!3, D!2), B!4)))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 ((B!4 = intersection(C!3, D!2)) <=> (~((~subset(B!4, intersection(C!3, D!2))) | (~subset(intersection(C!3, D!2), B!4))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.19/0.39 tff(14,assumption,(~((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))))), introduced(assumption)).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2))))) | subset(B!4, D!2)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (subset(B!4, D!2)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2))))) | subset(B!4, C!3)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (subset(B!4, C!3)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[17, 14])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (((~(B!4 = intersection(C!3, D!2))) | (~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~(subset(E!5, B!4) | (~subset(E!5, C!3)) | (~subset(E!5, D!2))))) <=> ((~(B!4 = intersection(C!3, D!2))) | (~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~(subset(E!5, B!4) | (~subset(E!5, C!3)) | (~subset(E!5, D!2)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 ((~((~(subset(E!5, C!3) & subset(E!5, D!2))) | subset(E!5, B!4))) <=> (~(subset(E!5, B!4) | (~subset(E!5, C!3)) | (~subset(E!5, D!2))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (((~(B!4 = intersection(C!3, D!2))) | (~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~((~(subset(E!5, C!3) & subset(E!5, D!2))) | subset(E!5, B!4)))) <=> ((~(B!4 = intersection(C!3, D!2))) | (~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~(subset(E!5, B!4) | (~subset(E!5, C!3)) | (~subset(E!5, D!2)))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[20])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (((~(B!4 = intersection(C!3, D!2))) | (~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~((~(subset(E!5, C!3) & subset(E!5, D!2))) | subset(E!5, B!4)))) <=> ((~(B!4 = intersection(C!3, D!2))) | (~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~(subset(E!5, B!4) | (~subset(E!5, C!3)) | (~subset(E!5, D!2)))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[21, 19])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 ((((B!4 = intersection(C!3, D!2)) | (subset(B!4, C!3) & subset(B!4, D!2) & ![E: $i] : ((~(subset(E, C!3) & subset(E, D!2))) | subset(E, B!4)))) & ((~(B!4 = intersection(C!3, D!2))) | ((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~((~(subset(E!5, C!3) & subset(E!5, D!2))) | subset(E!5, B!4)))))) <=> (((B!4 = intersection(C!3, D!2)) | (subset(B!4, C!3) & subset(B!4, D!2) & ![E: $i] : ((~(subset(E, C!3) & subset(E, D!2))) | subset(E, B!4)))) & ((~(B!4 = intersection(C!3, D!2))) | (~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~((~(subset(E!5, C!3) & subset(E!5, D!2))) | subset(E!5, B!4)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 ((~![B: $i, C: $i, D: $i] : ((B = intersection(C, D)) <=> (subset(B, C) & subset(B, D) & ![E: $i] : ((~(subset(E, C) & subset(E, D))) | subset(E, B))))) <=> (~![B: $i, C: $i, D: $i] : ((B = intersection(C, D)) <=> (subset(B, C) & subset(B, D) & ![E: $i] : ((~(subset(E, C) & subset(E, D))) | subset(E, B)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 ((~![B: $i, C: $i, D: $i] : ((B = intersection(C, D)) <=> ((subset(B, C) & subset(B, D)) & ![E: $i] : ((subset(E, C) & subset(E, D)) => subset(E, B))))) <=> (~![B: $i, C: $i, D: $i] : ((B = intersection(C, D)) <=> (subset(B, C) & subset(B, D) & ![E: $i] : ((~(subset(E, C) & subset(E, D))) | subset(E, B)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(26,axiom,(~![B: $i, C: $i, D: $i] : ((B = intersection(C, D)) <=> ((subset(B, C) & subset(B, D)) & ![E: $i] : ((subset(E, C) & subset(E, D)) => subset(E, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_th57')).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (~![B: $i, C: $i, D: $i] : ((B = intersection(C, D)) <=> (subset(B, C) & subset(B, D) & ![E: $i] : ((~(subset(E, C) & subset(E, D))) | subset(E, B))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (~![B: $i, C: $i, D: $i] : ((B = intersection(C, D)) <=> (subset(B, C) & subset(B, D) & ![E: $i] : ((~(subset(E, C) & subset(E, D))) | subset(E, B))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (~![B: $i, C: $i, D: $i] : ((B = intersection(C, D)) <=> (subset(B, C) & subset(B, D) & ![E: $i] : ((~(subset(E, C) & subset(E, D))) | subset(E, B))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (~![B: $i, C: $i, D: $i] : ((B = intersection(C, D)) <=> (subset(B, C) & subset(B, D) & ![E: $i] : ((~(subset(E, C) & subset(E, D))) | subset(E, B))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[29, 24])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (~![B: $i, C: $i, D: $i] : ((B = intersection(C, D)) <=> (subset(B, C) & subset(B, D) & ![E: $i] : ((~(subset(E, C) & subset(E, D))) | subset(E, B))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[30, 24])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (~![B: $i, C: $i, D: $i] : ((B = intersection(C, D)) <=> (subset(B, C) & subset(B, D) & ![E: $i] : ((~(subset(E, C) & subset(E, D))) | subset(E, B))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (~![B: $i, C: $i, D: $i] : ((B = intersection(C, D)) <=> (subset(B, C) & subset(B, D) & ![E: $i] : ((~(subset(E, C) & subset(E, D))) | subset(E, B))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[32, 24])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 (((B!4 = intersection(C!3, D!2)) | (subset(B!4, C!3) & subset(B!4, D!2) & ![E: $i] : ((~(subset(E, C!3) & subset(E, D!2))) | subset(E, B!4)))) & ((~(B!4 = intersection(C!3, D!2))) | (~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~((~(subset(E!5, C!3) & subset(E!5, D!2))) | subset(E!5, B!4))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[33, 23])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 ((~(B!4 = intersection(C!3, D!2))) | (~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~((~(subset(E!5, C!3) & subset(E!5, D!2))) | subset(E!5, B!4)))),
% 0.19/0.40 inference(and_elim,[status(thm)],[34])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 ((~(B!4 = intersection(C!3, D!2))) | (~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~(subset(E!5, B!4) | (~subset(E!5, C!3)) | (~subset(E!5, D!2))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[35, 22])).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 (~(B!4 = intersection(C!3, D!2))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[36, 18, 16, 1])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 ((~((B!4 = intersection(C!3, D!2)) <=> (~((~subset(B!4, intersection(C!3, D!2))) | (~subset(intersection(C!3, D!2), B!4)))))) | (B!4 = intersection(C!3, D!2)) | ((~subset(B!4, intersection(C!3, D!2))) | (~subset(intersection(C!3, D!2), B!4)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 ((~((B!4 = intersection(C!3, D!2)) <=> (~((~subset(B!4, intersection(C!3, D!2))) | (~subset(intersection(C!3, D!2), B!4)))))) | ((~subset(B!4, intersection(C!3, D!2))) | (~subset(intersection(C!3, D!2), B!4)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 ((~subset(B!4, intersection(C!3, D!2))) | (~subset(intersection(C!3, D!2), B!4))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[39, 13])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[41])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(44,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.40 tff(46,plain,(
% 0.19/0.40 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.40 inference(skolemize,[status(sab)],[45])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(D!2, C!3) = intersection(C!3, D!2))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 (intersection(D!2, C!3) = intersection(C!3, D!2)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (intersection(C!3, D!2) = intersection(D!2, C!3)),
% 0.19/0.40 inference(symmetry,[status(thm)],[49])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 (subset(intersection(C!3, D!2), D!2) <=> subset(intersection(D!2, C!3), D!2)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[50])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 (subset(intersection(D!2, C!3), D!2) <=> subset(intersection(C!3, D!2), D!2)),
% 0.19/0.40 inference(symmetry,[status(thm)],[51])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (^[B: $i, C: $i] : refl(subset(intersection(B, C), B) <=> subset(intersection(B, C), B))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 (![B: $i, C: $i] : subset(intersection(B, C), B) <=> ![B: $i, C: $i] : subset(intersection(B, C), B)),
% 0.19/0.40 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 (![B: $i, C: $i] : subset(intersection(B, C), B) <=> ![B: $i, C: $i] : subset(intersection(B, C), B)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(56,axiom,(![B: $i, C: $i] : subset(intersection(B, C), B)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','intersection_is_subset')).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 (![B: $i, C: $i] : subset(intersection(B, C), B)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.40 tff(58,plain,(
% 0.19/0.40 ![B: $i, C: $i] : subset(intersection(B, C), B)),
% 0.19/0.40 inference(skolemize,[status(sab)],[57])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 (![B: $i, C: $i] : subset(intersection(B, C), B)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 ((~![B: $i, C: $i] : subset(intersection(B, C), B)) | subset(intersection(D!2, C!3), D!2)),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 (subset(intersection(D!2, C!3), D!2)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 (subset(intersection(C!3, D!2), D!2)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[61, 52])).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 ((~![B: $i, C: $i] : subset(intersection(B, C), B)) | subset(intersection(C!3, D!2), C!3)),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (subset(intersection(C!3, D!2), C!3)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[63, 59])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2))))) | ![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 (![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[65, 14])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 (((~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))) | (subset(intersection(C!3, D!2), B!4) | (~subset(intersection(C!3, D!2), C!3)) | (~subset(intersection(C!3, D!2), D!2)))) <=> ((~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))) | subset(intersection(C!3, D!2), B!4) | (~subset(intersection(C!3, D!2), C!3)) | (~subset(intersection(C!3, D!2), D!2)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 ((~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))) | (subset(intersection(C!3, D!2), B!4) | (~subset(intersection(C!3, D!2), C!3)) | (~subset(intersection(C!3, D!2), D!2)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 ((~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))) | subset(intersection(C!3, D!2), B!4) | (~subset(intersection(C!3, D!2), C!3)) | (~subset(intersection(C!3, D!2), D!2))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (subset(intersection(C!3, D!2), B!4) | (~subset(intersection(C!3, D!2), D!2))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[69, 66, 64])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (subset(intersection(C!3, D!2), B!4)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[70, 62])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 ((~((~subset(B!4, intersection(C!3, D!2))) | (~subset(intersection(C!3, D!2), B!4)))) | (~subset(B!4, intersection(C!3, D!2))) | (~subset(intersection(C!3, D!2), B!4))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 ((~((~subset(B!4, intersection(C!3, D!2))) | (~subset(intersection(C!3, D!2), B!4)))) | (~subset(B!4, intersection(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 (~subset(B!4, intersection(C!3, D!2))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[73, 40])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 (^[B: $i, C: $i, D: $i] : refl((subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D))) <=> (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 (![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D))) <=> ![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[75])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 (^[B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(B, C) & subset(B, D)) <=> (~((~subset(B, C)) | (~subset(B, D))))), ((~(subset(B, C) & subset(B, D))) <=> (~(~((~subset(B, C)) | (~subset(B, D))))))), rewrite((~(~((~subset(B, C)) | (~subset(B, D))))) <=> ((~subset(B, C)) | (~subset(B, D)))), ((~(subset(B, C) & subset(B, D))) <=> ((~subset(B, C)) | (~subset(B, D))))), (((~(subset(B, C) & subset(B, D))) | subset(B, intersection(C, D))) <=> (((~subset(B, C)) | (~subset(B, D))) | subset(B, intersection(C, D))))), rewrite((((~subset(B, C)) | (~subset(B, D))) | subset(B, intersection(C, D))) <=> (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))), (((~(subset(B, C) & subset(B, D))) | subset(B, intersection(C, D))) <=> (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 (![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(B, D))) | subset(B, intersection(C, D))) <=> ![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[77])).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 (![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(B, D))) | subset(B, intersection(C, D))) <=> ![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(B, D))) | subset(B, intersection(C, D)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 (^[B: $i, C: $i, D: $i] : rewrite(((subset(B, C) & subset(B, D)) => subset(B, intersection(C, D))) <=> ((~(subset(B, C) & subset(B, D))) | subset(B, intersection(C, D))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 (![B: $i, C: $i, D: $i] : ((subset(B, C) & subset(B, D)) => subset(B, intersection(C, D))) <=> ![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(B, D))) | subset(B, intersection(C, D)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[80])).
% 0.19/0.40 tff(82,axiom,(![B: $i, C: $i, D: $i] : ((subset(B, C) & subset(B, D)) => subset(B, intersection(C, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','intersection_of_subsets')).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 (![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(B, D))) | subset(B, intersection(C, D)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 (![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(B, D))) | subset(B, intersection(C, D)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.19/0.40 tff(85,plain,(
% 0.19/0.40 ![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(B, D))) | subset(B, intersection(C, D)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[84])).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 (![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 (![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[86, 76])).
% 0.19/0.40 tff(88,plain,
% 0.19/0.40 (((~![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))) | ((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | subset(B!4, intersection(C!3, D!2)))) <=> ((~![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))) | (~subset(B!4, C!3)) | (~subset(B!4, D!2)) | subset(B!4, intersection(C!3, D!2)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 ((subset(B!4, intersection(C!3, D!2)) | (~subset(B!4, C!3)) | (~subset(B!4, D!2))) <=> ((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | subset(B!4, intersection(C!3, D!2)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(90,plain,
% 0.19/0.40 (((~![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))) | (subset(B!4, intersection(C!3, D!2)) | (~subset(B!4, C!3)) | (~subset(B!4, D!2)))) <=> ((~![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))) | ((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | subset(B!4, intersection(C!3, D!2))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[89])).
% 0.19/0.40 tff(91,plain,
% 0.19/0.40 (((~![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))) | (subset(B!4, intersection(C!3, D!2)) | (~subset(B!4, C!3)) | (~subset(B!4, D!2)))) <=> ((~![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))) | (~subset(B!4, C!3)) | (~subset(B!4, D!2)) | subset(B!4, intersection(C!3, D!2)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[90, 88])).
% 0.19/0.40 tff(92,plain,
% 0.19/0.40 ((~![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))) | (subset(B!4, intersection(C!3, D!2)) | (~subset(B!4, C!3)) | (~subset(B!4, D!2)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(93,plain,
% 0.19/0.40 ((~![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))) | (~subset(B!4, C!3)) | (~subset(B!4, D!2)) | subset(B!4, intersection(C!3, D!2))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[93, 87, 18, 16, 74])).
% 0.19/0.41 tff(95,plain,(((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2))))) | (~(subset(E!5, B!4) | (~subset(E!5, C!3)) | (~subset(E!5, D!2))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(96,plain,
% 0.19/0.41 ((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[95, 1])).
% 0.19/0.41 tff(97,plain,
% 0.19/0.41 (((B!4 = intersection(C!3, D!2)) | (~((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2))))))) <=> ((B!4 = intersection(C!3, D!2)) | (~((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(98,plain,
% 0.19/0.41 (((B!4 = intersection(C!3, D!2)) | (~((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2))))))) <=> ((B!4 = intersection(C!3, D!2)) | (~((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 ((subset(B!4, C!3) & subset(B!4, D!2) & ![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))) <=> (~((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 (^[E: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(E, C!3) & subset(E, D!2)) <=> (~((~subset(E, C!3)) | (~subset(E, D!2))))), ((~(subset(E, C!3) & subset(E, D!2))) <=> (~(~((~subset(E, C!3)) | (~subset(E, D!2))))))), rewrite((~(~((~subset(E, C!3)) | (~subset(E, D!2))))) <=> ((~subset(E, C!3)) | (~subset(E, D!2)))), ((~(subset(E, C!3) & subset(E, D!2))) <=> ((~subset(E, C!3)) | (~subset(E, D!2))))), (((~(subset(E, C!3) & subset(E, D!2))) | subset(E, B!4)) <=> (((~subset(E, C!3)) | (~subset(E, D!2))) | subset(E, B!4)))), rewrite((((~subset(E, C!3)) | (~subset(E, D!2))) | subset(E, B!4)) <=> (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))), (((~(subset(E, C!3) & subset(E, D!2))) | subset(E, B!4)) <=> (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(101,plain,
% 0.19/0.41 (![E: $i] : ((~(subset(E, C!3) & subset(E, D!2))) | subset(E, B!4)) <=> ![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[100])).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 ((subset(B!4, C!3) & subset(B!4, D!2) & ![E: $i] : ((~(subset(E, C!3) & subset(E, D!2))) | subset(E, B!4))) <=> (subset(B!4, C!3) & subset(B!4, D!2) & ![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[101])).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 ((subset(B!4, C!3) & subset(B!4, D!2) & ![E: $i] : ((~(subset(E, C!3) & subset(E, D!2))) | subset(E, B!4))) <=> (~((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[102, 99])).
% 0.19/0.41 tff(104,plain,
% 0.19/0.41 (((B!4 = intersection(C!3, D!2)) | (subset(B!4, C!3) & subset(B!4, D!2) & ![E: $i] : ((~(subset(E, C!3) & subset(E, D!2))) | subset(E, B!4)))) <=> ((B!4 = intersection(C!3, D!2)) | (~((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[103])).
% 0.19/0.41 tff(105,plain,
% 0.19/0.41 (((B!4 = intersection(C!3, D!2)) | (subset(B!4, C!3) & subset(B!4, D!2) & ![E: $i] : ((~(subset(E, C!3) & subset(E, D!2))) | subset(E, B!4)))) <=> ((B!4 = intersection(C!3, D!2)) | (~((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[104, 98])).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 ((B!4 = intersection(C!3, D!2)) | (subset(B!4, C!3) & subset(B!4, D!2) & ![E: $i] : ((~(subset(E, C!3) & subset(E, D!2))) | subset(E, B!4)))),
% 0.19/0.41 inference(and_elim,[status(thm)],[34])).
% 0.19/0.41 tff(107,plain,
% 0.19/0.41 ((B!4 = intersection(C!3, D!2)) | (~((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 ((B!4 = intersection(C!3, D!2)) | (~((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[107, 97])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 (B!4 = intersection(C!3, D!2)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[108, 96])).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 (intersection(C!3, D!2) = B!4),
% 0.19/0.41 inference(symmetry,[status(thm)],[109])).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 (intersection(D!2, C!3) = B!4),
% 0.19/0.41 inference(transitivity,[status(thm)],[49, 110])).
% 0.19/0.41 tff(112,plain,
% 0.19/0.41 (subset(intersection(D!2, C!3), D!2) <=> subset(B!4, D!2)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[111])).
% 0.19/0.41 tff(113,plain,
% 0.19/0.41 (subset(B!4, D!2) <=> subset(intersection(D!2, C!3), D!2)),
% 0.19/0.41 inference(symmetry,[status(thm)],[112])).
% 0.19/0.41 tff(114,plain,
% 0.19/0.41 ((~subset(B!4, D!2)) <=> (~subset(intersection(D!2, C!3), D!2))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[113])).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 (subset(intersection(C!3, D!2), C!3) <=> subset(B!4, C!3)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[110])).
% 0.19/0.41 tff(116,plain,
% 0.19/0.41 (subset(B!4, C!3)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[64, 115])).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 (~subset(B!4, D!2)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[36, 116, 109, 1])).
% 0.19/0.41 tff(118,plain,
% 0.19/0.41 (~subset(intersection(D!2, C!3), D!2)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[117, 114])).
% 0.19/0.41 tff(119,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[61, 118])).
% 0.19/0.41 tff(120,plain,(~(subset(E!5, B!4) | (~subset(E!5, C!3)) | (~subset(E!5, D!2)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(121,plain,
% 0.19/0.41 ((subset(E!5, B!4) | (~subset(E!5, C!3)) | (~subset(E!5, D!2))) | subset(E!5, D!2)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(122,plain,
% 0.19/0.41 (subset(E!5, D!2)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.19/0.41 tff(123,plain,
% 0.19/0.41 ((subset(E!5, B!4) | (~subset(E!5, C!3)) | (~subset(E!5, D!2))) | subset(E!5, C!3)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(124,plain,
% 0.19/0.41 (subset(E!5, C!3)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[123, 120])).
% 0.19/0.41 tff(125,plain,
% 0.19/0.41 ((subset(E!5, B!4) | (~subset(E!5, C!3)) | (~subset(E!5, D!2))) | (~subset(E!5, B!4))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(126,plain,
% 0.19/0.41 (~subset(E!5, B!4)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[125, 120])).
% 0.19/0.41 tff(127,assumption,(B!4 = intersection(C!3, D!2)), introduced(assumption)).
% 0.19/0.41 tff(128,plain,
% 0.19/0.41 (intersection(C!3, D!2) = B!4),
% 0.19/0.41 inference(symmetry,[status(thm)],[127])).
% 0.19/0.41 tff(129,plain,
% 0.19/0.41 (subset(E!5, intersection(C!3, D!2)) <=> subset(E!5, B!4)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[128])).
% 0.19/0.41 tff(130,plain,
% 0.19/0.41 (subset(E!5, B!4) <=> subset(E!5, intersection(C!3, D!2))),
% 0.19/0.41 inference(symmetry,[status(thm)],[129])).
% 0.19/0.41 tff(131,plain,
% 0.19/0.41 ((~subset(E!5, B!4)) <=> (~subset(E!5, intersection(C!3, D!2)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[130])).
% 0.19/0.41 tff(132,plain,
% 0.19/0.41 (~subset(E!5, intersection(C!3, D!2))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[126, 131])).
% 0.19/0.41 tff(133,plain,
% 0.19/0.41 (((~![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))) | ((~subset(E!5, C!3)) | (~subset(E!5, D!2)) | subset(E!5, intersection(C!3, D!2)))) <=> ((~![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))) | (~subset(E!5, C!3)) | (~subset(E!5, D!2)) | subset(E!5, intersection(C!3, D!2)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(134,plain,
% 0.19/0.41 ((subset(E!5, intersection(C!3, D!2)) | (~subset(E!5, C!3)) | (~subset(E!5, D!2))) <=> ((~subset(E!5, C!3)) | (~subset(E!5, D!2)) | subset(E!5, intersection(C!3, D!2)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(135,plain,
% 0.20/0.42 (((~![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))) | (subset(E!5, intersection(C!3, D!2)) | (~subset(E!5, C!3)) | (~subset(E!5, D!2)))) <=> ((~![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))) | ((~subset(E!5, C!3)) | (~subset(E!5, D!2)) | subset(E!5, intersection(C!3, D!2))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[134])).
% 0.20/0.42 tff(136,plain,
% 0.20/0.42 (((~![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))) | (subset(E!5, intersection(C!3, D!2)) | (~subset(E!5, C!3)) | (~subset(E!5, D!2)))) <=> ((~![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))) | (~subset(E!5, C!3)) | (~subset(E!5, D!2)) | subset(E!5, intersection(C!3, D!2)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[135, 133])).
% 0.20/0.42 tff(137,plain,
% 0.20/0.42 ((~![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))) | (subset(E!5, intersection(C!3, D!2)) | (~subset(E!5, C!3)) | (~subset(E!5, D!2)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(138,plain,
% 0.20/0.42 ((~![B: $i, C: $i, D: $i] : (subset(B, intersection(C, D)) | (~subset(B, C)) | (~subset(B, D)))) | (~subset(E!5, C!3)) | (~subset(E!5, D!2)) | subset(E!5, intersection(C!3, D!2))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.20/0.42 tff(139,plain,
% 0.20/0.42 (subset(E!5, intersection(C!3, D!2))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[138, 87, 124, 122])).
% 0.20/0.42 tff(140,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[139, 132])).
% 0.20/0.42 tff(141,plain,(~(B!4 = intersection(C!3, D!2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(142,plain,
% 0.20/0.42 (~((~subset(B!4, C!3)) | (~subset(B!4, D!2)) | (~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[108, 141])).
% 0.20/0.42 tff(143,plain,
% 0.20/0.42 (![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[65, 142])).
% 0.20/0.42 tff(144,plain,
% 0.20/0.42 (((~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))) | (subset(E!5, B!4) | (~subset(E!5, C!3)) | (~subset(E!5, D!2)))) <=> ((~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))) | subset(E!5, B!4) | (~subset(E!5, C!3)) | (~subset(E!5, D!2)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(145,plain,
% 0.20/0.42 ((~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))) | (subset(E!5, B!4) | (~subset(E!5, C!3)) | (~subset(E!5, D!2)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(146,plain,
% 0.20/0.42 ((~![E: $i] : (subset(E, B!4) | (~subset(E, C!3)) | (~subset(E, D!2)))) | subset(E!5, B!4) | (~subset(E!5, C!3)) | (~subset(E!5, D!2))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.20/0.42 tff(147,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[146, 143, 126, 124, 122])).
% 0.20/0.42 % SZS output end Proof
%------------------------------------------------------------------------------