TSTP Solution File: SET597+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET597+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 05:07:12 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET597+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n026.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 07:05:38 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.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(subset_type, type, (
% 0.20/0.40 subset: ( $i * $i ) > $o)).
% 0.20/0.40 tff(tptp_fun_E_5_type, type, (
% 0.20/0.40 tptp_fun_E_5: $i)).
% 0.20/0.40 tff(tptp_fun_D_2_type, type, (
% 0.20/0.40 tptp_fun_D_2: $i)).
% 0.20/0.40 tff(tptp_fun_C_3_type, type, (
% 0.20/0.40 tptp_fun_C_3: $i)).
% 0.20/0.40 tff(tptp_fun_B_4_type, type, (
% 0.20/0.40 tptp_fun_B_4: $i)).
% 0.20/0.40 tff(union_type, type, (
% 0.20/0.40 union: ( $i * $i ) > $i)).
% 0.20/0.40 tff(1,assumption,(subset(B!4, E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5))), introduced(assumption)).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (^[B: $i, C: $i] : refl(((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))) <=> ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))) <=> ![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 (^[B: $i, C: $i] : rewrite(((B = C) <=> (subset(B, C) & subset(C, B))) <=> ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B))) <=> ![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B))) <=> ![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(7,axiom,(![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','equal_defn')).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.20/0.40 tff(9,plain,(
% 0.20/0.40 ![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[8])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 ((~![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))) | ((B!4 = union(C!3, D!2)) <=> (~((~subset(B!4, union(C!3, D!2))) | (~subset(union(C!3, D!2), B!4)))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 ((B!4 = union(C!3, D!2)) <=> (~((~subset(B!4, union(C!3, D!2))) | (~subset(union(C!3, D!2), B!4))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.20/0.40 tff(14,assumption,(~((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))))), introduced(assumption)).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E))))) | subset(D!2, B!4)),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (subset(D!2, B!4)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E))))) | subset(C!3, B!4)),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (subset(C!3, B!4)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[17, 14])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (((~(B!4 = union(C!3, D!2))) | (~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~(subset(B!4, E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5))))) <=> ((~(B!4 = union(C!3, D!2))) | (~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~(subset(B!4, E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 ((~((~(subset(C!3, E!5) & subset(D!2, E!5))) | subset(B!4, E!5))) <=> (~(subset(B!4, E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 (((~(B!4 = union(C!3, D!2))) | (~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~((~(subset(C!3, E!5) & subset(D!2, E!5))) | subset(B!4, E!5)))) <=> ((~(B!4 = union(C!3, D!2))) | (~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~(subset(B!4, E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5)))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[20])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (((~(B!4 = union(C!3, D!2))) | (~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~((~(subset(C!3, E!5) & subset(D!2, E!5))) | subset(B!4, E!5)))) <=> ((~(B!4 = union(C!3, D!2))) | (~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~(subset(B!4, E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5)))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[21, 19])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 ((((B!4 = union(C!3, D!2)) | (subset(C!3, B!4) & subset(D!2, B!4) & ![E: $i] : ((~(subset(C!3, E) & subset(D!2, E))) | subset(B!4, E)))) & ((~(B!4 = union(C!3, D!2))) | ((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~((~(subset(C!3, E!5) & subset(D!2, E!5))) | subset(B!4, E!5)))))) <=> (((B!4 = union(C!3, D!2)) | (subset(C!3, B!4) & subset(D!2, B!4) & ![E: $i] : ((~(subset(C!3, E) & subset(D!2, E))) | subset(B!4, E)))) & ((~(B!4 = union(C!3, D!2))) | (~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~((~(subset(C!3, E!5) & subset(D!2, E!5))) | subset(B!4, E!5)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 ((~![B: $i, C: $i, D: $i] : ((B = union(C, D)) <=> (subset(C, B) & subset(D, B) & ![E: $i] : ((~(subset(C, E) & subset(D, E))) | subset(B, E))))) <=> (~![B: $i, C: $i, D: $i] : ((B = union(C, D)) <=> (subset(C, B) & subset(D, B) & ![E: $i] : ((~(subset(C, E) & subset(D, E))) | subset(B, E)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 ((~![B: $i, C: $i, D: $i] : ((B = union(C, D)) <=> ((subset(C, B) & subset(D, B)) & ![E: $i] : ((subset(C, E) & subset(D, E)) => subset(B, E))))) <=> (~![B: $i, C: $i, D: $i] : ((B = union(C, D)) <=> (subset(C, B) & subset(D, B) & ![E: $i] : ((~(subset(C, E) & subset(D, E))) | subset(B, E)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(26,axiom,(~![B: $i, C: $i, D: $i] : ((B = union(C, D)) <=> ((subset(C, B) & subset(D, B)) & ![E: $i] : ((subset(C, E) & subset(D, E)) => subset(B, E))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_th56')).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 (~![B: $i, C: $i, D: $i] : ((B = union(C, D)) <=> (subset(C, B) & subset(D, B) & ![E: $i] : ((~(subset(C, E) & subset(D, E))) | subset(B, E))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 (~![B: $i, C: $i, D: $i] : ((B = union(C, D)) <=> (subset(C, B) & subset(D, B) & ![E: $i] : ((~(subset(C, E) & subset(D, E))) | subset(B, E))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 (~![B: $i, C: $i, D: $i] : ((B = union(C, D)) <=> (subset(C, B) & subset(D, B) & ![E: $i] : ((~(subset(C, E) & subset(D, E))) | subset(B, E))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 (~![B: $i, C: $i, D: $i] : ((B = union(C, D)) <=> (subset(C, B) & subset(D, B) & ![E: $i] : ((~(subset(C, E) & subset(D, E))) | subset(B, E))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[29, 24])).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 (~![B: $i, C: $i, D: $i] : ((B = union(C, D)) <=> (subset(C, B) & subset(D, B) & ![E: $i] : ((~(subset(C, E) & subset(D, E))) | subset(B, E))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[30, 24])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 (~![B: $i, C: $i, D: $i] : ((B = union(C, D)) <=> (subset(C, B) & subset(D, B) & ![E: $i] : ((~(subset(C, E) & subset(D, E))) | subset(B, E))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (~![B: $i, C: $i, D: $i] : ((B = union(C, D)) <=> (subset(C, B) & subset(D, B) & ![E: $i] : ((~(subset(C, E) & subset(D, E))) | subset(B, E))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[32, 24])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 (((B!4 = union(C!3, D!2)) | (subset(C!3, B!4) & subset(D!2, B!4) & ![E: $i] : ((~(subset(C!3, E) & subset(D!2, E))) | subset(B!4, E)))) & ((~(B!4 = union(C!3, D!2))) | (~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~((~(subset(C!3, E!5) & subset(D!2, E!5))) | subset(B!4, E!5))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[33, 23])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 ((~(B!4 = union(C!3, D!2))) | (~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~((~(subset(C!3, E!5) & subset(D!2, E!5))) | subset(B!4, E!5)))),
% 0.20/0.41 inference(and_elim,[status(thm)],[34])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 ((~(B!4 = union(C!3, D!2))) | (~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~(subset(B!4, E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[35, 22])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 (~(B!4 = union(C!3, D!2))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[36, 18, 16, 1])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 ((~((B!4 = union(C!3, D!2)) <=> (~((~subset(B!4, union(C!3, D!2))) | (~subset(union(C!3, D!2), B!4)))))) | (B!4 = union(C!3, D!2)) | ((~subset(B!4, union(C!3, D!2))) | (~subset(union(C!3, D!2), B!4)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 ((~((B!4 = union(C!3, D!2)) <=> (~((~subset(B!4, union(C!3, D!2))) | (~subset(union(C!3, D!2), B!4)))))) | ((~subset(B!4, union(C!3, D!2))) | (~subset(union(C!3, D!2), B!4)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 ((~subset(B!4, union(C!3, D!2))) | (~subset(union(C!3, D!2), B!4))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[39, 13])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 (^[B: $i, C: $i] : refl((union(B, C) = union(C, B)) <=> (union(B, C) = union(C, B)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(44,axiom,(![B: $i, C: $i] : (union(B, C) = union(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_of_union')).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.41 tff(46,plain,(
% 0.20/0.41 ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.20/0.41 inference(skolemize,[status(sab)],[45])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(D!2, C!3) = union(C!3, D!2))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 (union(D!2, C!3) = union(C!3, D!2)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 (union(C!3, D!2) = union(D!2, C!3)),
% 0.20/0.41 inference(symmetry,[status(thm)],[49])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (subset(D!2, union(C!3, D!2)) <=> subset(D!2, union(D!2, C!3))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[50])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 (subset(D!2, union(D!2, C!3)) <=> subset(D!2, union(C!3, D!2))),
% 0.20/0.41 inference(symmetry,[status(thm)],[51])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 (^[B: $i, C: $i] : refl(subset(B, union(B, C)) <=> subset(B, union(B, C)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 (![B: $i, C: $i] : subset(B, union(B, C)) <=> ![B: $i, C: $i] : subset(B, union(B, C))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[53])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 (![B: $i, C: $i] : subset(B, union(B, C)) <=> ![B: $i, C: $i] : subset(B, union(B, C))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(56,axiom,(![B: $i, C: $i] : subset(B, union(B, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','subset_of_union')).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (![B: $i, C: $i] : subset(B, union(B, C))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.41 tff(58,plain,(
% 0.20/0.41 ![B: $i, C: $i] : subset(B, union(B, C))),
% 0.20/0.41 inference(skolemize,[status(sab)],[57])).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 (![B: $i, C: $i] : subset(B, union(B, C))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 ((~![B: $i, C: $i] : subset(B, union(B, C))) | subset(D!2, union(D!2, C!3))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 (subset(D!2, union(D!2, C!3))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 (subset(D!2, union(C!3, D!2))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[61, 52])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 ((~![B: $i, C: $i] : subset(B, union(B, C))) | subset(C!3, union(C!3, D!2))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(64,plain,
% 0.20/0.41 (subset(C!3, union(C!3, D!2))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[63, 59])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 (((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E))))) | ![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 (![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[65, 14])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 (((~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))) | (subset(B!4, union(C!3, D!2)) | (~subset(C!3, union(C!3, D!2))) | (~subset(D!2, union(C!3, D!2))))) <=> ((~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))) | subset(B!4, union(C!3, D!2)) | (~subset(C!3, union(C!3, D!2))) | (~subset(D!2, union(C!3, D!2))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 ((~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))) | (subset(B!4, union(C!3, D!2)) | (~subset(C!3, union(C!3, D!2))) | (~subset(D!2, union(C!3, D!2))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(69,plain,
% 0.20/0.41 ((~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))) | subset(B!4, union(C!3, D!2)) | (~subset(C!3, union(C!3, D!2))) | (~subset(D!2, union(C!3, D!2)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 (subset(B!4, union(C!3, D!2)) | (~subset(D!2, union(C!3, D!2)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[69, 66, 64])).
% 0.20/0.41 tff(71,plain,
% 0.20/0.41 (subset(B!4, union(C!3, D!2))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[70, 62])).
% 0.20/0.41 tff(72,plain,
% 0.20/0.41 ((~((~subset(B!4, union(C!3, D!2))) | (~subset(union(C!3, D!2), B!4)))) | (~subset(B!4, union(C!3, D!2))) | (~subset(union(C!3, D!2), B!4))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(73,plain,
% 0.20/0.41 ((~((~subset(B!4, union(C!3, D!2))) | (~subset(union(C!3, D!2), B!4)))) | (~subset(union(C!3, D!2), B!4))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.20/0.41 tff(74,plain,
% 0.20/0.41 (~subset(union(C!3, D!2), B!4)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[73, 40])).
% 0.20/0.41 tff(75,plain,
% 0.20/0.41 (^[B: $i, C: $i, D: $i] : refl((subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C))) <=> (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(76,plain,
% 0.20/0.41 (![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C))) <=> ![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[75])).
% 0.20/0.41 tff(77,plain,
% 0.20/0.41 (^[B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(B, C) & subset(D, C)) <=> (~((~subset(B, C)) | (~subset(D, C))))), ((~(subset(B, C) & subset(D, C))) <=> (~(~((~subset(B, C)) | (~subset(D, C))))))), rewrite((~(~((~subset(B, C)) | (~subset(D, C))))) <=> ((~subset(B, C)) | (~subset(D, C)))), ((~(subset(B, C) & subset(D, C))) <=> ((~subset(B, C)) | (~subset(D, C))))), (((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C)) <=> (((~subset(B, C)) | (~subset(D, C))) | subset(union(B, D), C)))), rewrite((((~subset(B, C)) | (~subset(D, C))) | subset(union(B, D), C)) <=> (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))), (((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C)) <=> (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(78,plain,
% 0.20/0.41 (![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C)) <=> ![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[77])).
% 0.20/0.41 tff(79,plain,
% 0.20/0.41 (![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C)) <=> ![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(80,plain,
% 0.20/0.41 (^[B: $i, C: $i, D: $i] : rewrite(((subset(B, C) & subset(D, C)) => subset(union(B, D), C)) <=> ((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(81,plain,
% 0.20/0.41 (![B: $i, C: $i, D: $i] : ((subset(B, C) & subset(D, C)) => subset(union(B, D), C)) <=> ![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[80])).
% 0.20/0.41 tff(82,axiom,(![B: $i, C: $i, D: $i] : ((subset(B, C) & subset(D, C)) => subset(union(B, D), C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','union_subset')).
% 0.20/0.41 tff(83,plain,
% 0.20/0.41 (![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.41 tff(84,plain,
% 0.20/0.41 (![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.20/0.41 tff(85,plain,(
% 0.20/0.41 ![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(D, C))) | subset(union(B, D), C))),
% 0.20/0.41 inference(skolemize,[status(sab)],[84])).
% 0.20/0.41 tff(86,plain,
% 0.20/0.41 (![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.20/0.41 tff(87,plain,
% 0.20/0.41 (![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[86, 76])).
% 0.20/0.41 tff(88,plain,
% 0.20/0.41 (((~![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))) | ((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | subset(union(C!3, D!2), B!4))) <=> ((~![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))) | (~subset(C!3, B!4)) | (~subset(D!2, B!4)) | subset(union(C!3, D!2), B!4))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(89,plain,
% 0.20/0.41 ((subset(union(C!3, D!2), B!4) | (~subset(C!3, B!4)) | (~subset(D!2, B!4))) <=> ((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | subset(union(C!3, D!2), B!4))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(90,plain,
% 0.20/0.41 (((~![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))) | (subset(union(C!3, D!2), B!4) | (~subset(C!3, B!4)) | (~subset(D!2, B!4)))) <=> ((~![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))) | ((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | subset(union(C!3, D!2), B!4)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[89])).
% 0.20/0.41 tff(91,plain,
% 0.20/0.41 (((~![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))) | (subset(union(C!3, D!2), B!4) | (~subset(C!3, B!4)) | (~subset(D!2, B!4)))) <=> ((~![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))) | (~subset(C!3, B!4)) | (~subset(D!2, B!4)) | subset(union(C!3, D!2), B!4))),
% 0.20/0.41 inference(transitivity,[status(thm)],[90, 88])).
% 0.20/0.41 tff(92,plain,
% 0.20/0.41 ((~![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))) | (subset(union(C!3, D!2), B!4) | (~subset(C!3, B!4)) | (~subset(D!2, B!4)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(93,plain,
% 0.20/0.41 ((~![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))) | (~subset(C!3, B!4)) | (~subset(D!2, B!4)) | subset(union(C!3, D!2), B!4)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.41 tff(94,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[93, 87, 18, 16, 74])).
% 0.20/0.41 tff(95,plain,(((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E))))) | (~(subset(B!4, E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(96,plain,
% 0.20/0.41 ((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[95, 1])).
% 0.20/0.41 tff(97,plain,
% 0.20/0.41 (((B!4 = union(C!3, D!2)) | (~((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E))))))) <=> ((B!4 = union(C!3, D!2)) | (~((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(98,plain,
% 0.20/0.41 (((B!4 = union(C!3, D!2)) | (~((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E))))))) <=> ((B!4 = union(C!3, D!2)) | (~((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(99,plain,
% 0.20/0.42 ((subset(C!3, B!4) & subset(D!2, B!4) & ![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))) <=> (~((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(100,plain,
% 0.20/0.42 (^[E: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(C!3, E) & subset(D!2, E)) <=> (~((~subset(C!3, E)) | (~subset(D!2, E))))), ((~(subset(C!3, E) & subset(D!2, E))) <=> (~(~((~subset(C!3, E)) | (~subset(D!2, E))))))), rewrite((~(~((~subset(C!3, E)) | (~subset(D!2, E))))) <=> ((~subset(C!3, E)) | (~subset(D!2, E)))), ((~(subset(C!3, E) & subset(D!2, E))) <=> ((~subset(C!3, E)) | (~subset(D!2, E))))), (((~(subset(C!3, E) & subset(D!2, E))) | subset(B!4, E)) <=> (((~subset(C!3, E)) | (~subset(D!2, E))) | subset(B!4, E)))), rewrite((((~subset(C!3, E)) | (~subset(D!2, E))) | subset(B!4, E)) <=> (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))), (((~(subset(C!3, E) & subset(D!2, E))) | subset(B!4, E)) <=> (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(101,plain,
% 0.20/0.42 (![E: $i] : ((~(subset(C!3, E) & subset(D!2, E))) | subset(B!4, E)) <=> ![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[100])).
% 0.20/0.42 tff(102,plain,
% 0.20/0.42 ((subset(C!3, B!4) & subset(D!2, B!4) & ![E: $i] : ((~(subset(C!3, E) & subset(D!2, E))) | subset(B!4, E))) <=> (subset(C!3, B!4) & subset(D!2, B!4) & ![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[101])).
% 0.20/0.42 tff(103,plain,
% 0.20/0.42 ((subset(C!3, B!4) & subset(D!2, B!4) & ![E: $i] : ((~(subset(C!3, E) & subset(D!2, E))) | subset(B!4, E))) <=> (~((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[102, 99])).
% 0.20/0.42 tff(104,plain,
% 0.20/0.42 (((B!4 = union(C!3, D!2)) | (subset(C!3, B!4) & subset(D!2, B!4) & ![E: $i] : ((~(subset(C!3, E) & subset(D!2, E))) | subset(B!4, E)))) <=> ((B!4 = union(C!3, D!2)) | (~((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[103])).
% 0.20/0.42 tff(105,plain,
% 0.20/0.42 (((B!4 = union(C!3, D!2)) | (subset(C!3, B!4) & subset(D!2, B!4) & ![E: $i] : ((~(subset(C!3, E) & subset(D!2, E))) | subset(B!4, E)))) <=> ((B!4 = union(C!3, D!2)) | (~((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[104, 98])).
% 0.20/0.42 tff(106,plain,
% 0.20/0.42 ((B!4 = union(C!3, D!2)) | (subset(C!3, B!4) & subset(D!2, B!4) & ![E: $i] : ((~(subset(C!3, E) & subset(D!2, E))) | subset(B!4, E)))),
% 0.20/0.42 inference(and_elim,[status(thm)],[34])).
% 0.20/0.42 tff(107,plain,
% 0.20/0.42 ((B!4 = union(C!3, D!2)) | (~((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.20/0.42 tff(108,plain,
% 0.20/0.42 ((B!4 = union(C!3, D!2)) | (~((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[107, 97])).
% 0.20/0.42 tff(109,plain,
% 0.20/0.42 (B!4 = union(C!3, D!2)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[108, 96])).
% 0.20/0.42 tff(110,plain,
% 0.20/0.42 (union(C!3, D!2) = B!4),
% 0.20/0.42 inference(symmetry,[status(thm)],[109])).
% 0.20/0.42 tff(111,plain,
% 0.20/0.42 (union(D!2, C!3) = B!4),
% 0.20/0.42 inference(transitivity,[status(thm)],[49, 110])).
% 0.20/0.42 tff(112,plain,
% 0.20/0.42 (subset(D!2, union(D!2, C!3)) <=> subset(D!2, B!4)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[111])).
% 0.20/0.42 tff(113,plain,
% 0.20/0.42 (subset(D!2, B!4) <=> subset(D!2, union(D!2, C!3))),
% 0.20/0.42 inference(symmetry,[status(thm)],[112])).
% 0.20/0.42 tff(114,plain,
% 0.20/0.42 ((~subset(D!2, B!4)) <=> (~subset(D!2, union(D!2, C!3)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[113])).
% 0.20/0.42 tff(115,plain,
% 0.20/0.42 (subset(C!3, union(C!3, D!2)) <=> subset(C!3, B!4)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[110])).
% 0.20/0.42 tff(116,plain,
% 0.20/0.42 (subset(C!3, B!4)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[64, 115])).
% 0.20/0.42 tff(117,plain,
% 0.20/0.42 (~subset(D!2, B!4)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[36, 116, 109, 1])).
% 0.20/0.42 tff(118,plain,
% 0.20/0.42 (~subset(D!2, union(D!2, C!3))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[117, 114])).
% 0.20/0.42 tff(119,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[61, 118])).
% 0.20/0.42 tff(120,plain,(~(subset(B!4, E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(121,plain,
% 0.20/0.42 ((subset(B!4, E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5))) | subset(D!2, E!5)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(122,plain,
% 0.20/0.42 (subset(D!2, E!5)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.20/0.42 tff(123,plain,
% 0.20/0.42 ((subset(B!4, E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5))) | subset(C!3, E!5)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(124,plain,
% 0.20/0.42 (subset(C!3, E!5)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[123, 120])).
% 0.20/0.42 tff(125,plain,
% 0.20/0.42 ((subset(B!4, E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5))) | (~subset(B!4, E!5))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(126,plain,
% 0.20/0.42 (~subset(B!4, E!5)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[125, 120])).
% 0.20/0.42 tff(127,assumption,(B!4 = union(C!3, D!2)), introduced(assumption)).
% 0.20/0.42 tff(128,plain,
% 0.20/0.42 (union(C!3, D!2) = B!4),
% 0.20/0.42 inference(symmetry,[status(thm)],[127])).
% 0.20/0.42 tff(129,plain,
% 0.20/0.42 (subset(union(C!3, D!2), E!5) <=> subset(B!4, E!5)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[128])).
% 0.20/0.42 tff(130,plain,
% 0.20/0.42 (subset(B!4, E!5) <=> subset(union(C!3, D!2), E!5)),
% 0.20/0.42 inference(symmetry,[status(thm)],[129])).
% 0.20/0.42 tff(131,plain,
% 0.20/0.42 ((~subset(B!4, E!5)) <=> (~subset(union(C!3, D!2), E!5))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[130])).
% 0.20/0.42 tff(132,plain,
% 0.20/0.42 (~subset(union(C!3, D!2), E!5)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[126, 131])).
% 0.20/0.42 tff(133,plain,
% 0.20/0.42 (((~![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))) | ((~subset(C!3, E!5)) | (~subset(D!2, E!5)) | subset(union(C!3, D!2), E!5))) <=> ((~![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))) | (~subset(C!3, E!5)) | (~subset(D!2, E!5)) | subset(union(C!3, D!2), E!5))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(134,plain,
% 0.20/0.42 ((subset(union(C!3, D!2), E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5))) <=> ((~subset(C!3, E!5)) | (~subset(D!2, E!5)) | subset(union(C!3, D!2), E!5))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(135,plain,
% 0.20/0.42 (((~![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))) | (subset(union(C!3, D!2), E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5)))) <=> ((~![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))) | ((~subset(C!3, E!5)) | (~subset(D!2, E!5)) | subset(union(C!3, D!2), E!5)))),
% 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(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))) | (subset(union(C!3, D!2), E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5)))) <=> ((~![B: $i, C: $i, D: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))) | (~subset(C!3, E!5)) | (~subset(D!2, E!5)) | subset(union(C!3, D!2), E!5))),
% 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(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))) | (subset(union(C!3, D!2), E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5)))),
% 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: $i] : (subset(union(B, D), C) | (~subset(B, C)) | (~subset(D, C)))) | (~subset(C!3, E!5)) | (~subset(D!2, E!5)) | subset(union(C!3, D!2), E!5)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.20/0.42 tff(139,plain,
% 0.20/0.42 (subset(union(C!3, D!2), E!5)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[138, 87, 124, 122])).
% 0.20/0.42 tff(140,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[139, 132])).
% 0.20/0.42 tff(141,plain,(~(B!4 = union(C!3, D!2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(142,plain,
% 0.20/0.42 (~((~subset(C!3, B!4)) | (~subset(D!2, B!4)) | (~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))))),
% 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(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))),
% 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(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))) | (subset(B!4, E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5)))) <=> ((~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))) | subset(B!4, E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(145,plain,
% 0.20/0.42 ((~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))) | (subset(B!4, E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(146,plain,
% 0.20/0.42 ((~![E: $i] : (subset(B!4, E) | (~subset(C!3, E)) | (~subset(D!2, E)))) | subset(B!4, E!5) | (~subset(C!3, E!5)) | (~subset(D!2, E!5))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.20/0.42 tff(147,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[146, 143, 126, 124, 122])).
% 0.20/0.42 % SZS output end Proof
%------------------------------------------------------------------------------