TSTP Solution File: SET591+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET591+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 05:07:10 EDT 2022
% Result : Theorem 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET591+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n001.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Sep 3 07:11:10 EDT 2022
% 0.18/0.33 % CPUTime :
% 0.18/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.18/0.34 Usage: tptp [options] [-file:]file
% 0.18/0.34 -h, -? prints this message.
% 0.18/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.18/0.34 -m, -model generate model.
% 0.18/0.34 -p, -proof generate proof.
% 0.18/0.34 -c, -core generate unsat core of named formulas.
% 0.18/0.34 -st, -statistics display statistics.
% 0.18/0.34 -t:timeout set timeout (in second).
% 0.18/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.18/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.18/0.34 -<param>:<value> configuration parameter and value.
% 0.18/0.34 -o:<output-file> file to place output in.
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 % SZS output start Proof
% 0.19/0.43 tff(member_type, type, (
% 0.19/0.43 member: ( $i * $i ) > $o)).
% 0.19/0.43 tff(empty_set_type, type, (
% 0.19/0.43 empty_set: $i)).
% 0.19/0.43 tff(tptp_fun_D_0_type, type, (
% 0.19/0.43 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.19/0.43 tff(tptp_fun_B_3_type, type, (
% 0.19/0.43 tptp_fun_B_3: $i)).
% 0.19/0.43 tff(subset_type, type, (
% 0.19/0.43 subset: ( $i * $i ) > $o)).
% 0.19/0.43 tff(difference_type, type, (
% 0.19/0.43 difference: ( $i * $i ) > $i)).
% 0.19/0.43 tff(tptp_fun_C_2_type, type, (
% 0.19/0.43 tptp_fun_C_2: $i)).
% 0.19/0.43 tff(1,assumption,(~((B!3 = empty_set) <=> (~((~subset(B!3, empty_set)) | (~subset(empty_set, B!3)))))), introduced(assumption)).
% 0.19/0.43 tff(2,plain,
% 0.19/0.43 (^[B: $i, C: $i] : refl(((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))) <=> ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(3,plain,
% 0.19/0.43 (![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))) <=> ![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.43 tff(4,plain,
% 0.19/0.43 (^[B: $i, C: $i] : rewrite(((B = C) <=> (subset(B, C) & subset(C, B))) <=> ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(5,plain,
% 0.19/0.43 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B))) <=> ![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.43 tff(6,plain,
% 0.19/0.43 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B))) <=> ![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(7,axiom,(![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','equal_defn')).
% 0.19/0.43 tff(8,plain,
% 0.19/0.43 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.19/0.43 tff(9,plain,(
% 0.19/0.43 ![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[8])).
% 0.19/0.43 tff(10,plain,
% 0.19/0.43 (![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.19/0.43 tff(11,plain,
% 0.19/0.43 (![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.19/0.43 tff(12,plain,
% 0.19/0.43 ((~![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))) | ((B!3 = empty_set) <=> (~((~subset(B!3, empty_set)) | (~subset(empty_set, B!3)))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(13,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[12, 11, 1])).
% 0.19/0.43 tff(14,plain,((B!3 = empty_set) <=> (~((~subset(B!3, empty_set)) | (~subset(empty_set, B!3))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(15,plain,
% 0.19/0.43 ((~![B: $i, C: $i] : ((~subset(B, difference(C, B))) | (B = empty_set))) <=> (~![B: $i, C: $i] : ((~subset(B, difference(C, B))) | (B = empty_set)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(16,plain,
% 0.19/0.43 ((~![B: $i, C: $i] : (subset(B, difference(C, B)) => (B = empty_set))) <=> (~![B: $i, C: $i] : ((~subset(B, difference(C, B))) | (B = empty_set)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(17,axiom,(~![B: $i, C: $i] : (subset(B, difference(C, B)) => (B = empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_th50')).
% 0.19/0.43 tff(18,plain,
% 0.19/0.43 (~![B: $i, C: $i] : ((~subset(B, difference(C, B))) | (B = empty_set))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.19/0.43 tff(19,plain,
% 0.19/0.43 (~![B: $i, C: $i] : ((~subset(B, difference(C, B))) | (B = empty_set))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.19/0.43 tff(20,plain,
% 0.19/0.43 (~![B: $i, C: $i] : ((~subset(B, difference(C, B))) | (B = empty_set))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.19/0.43 tff(21,plain,
% 0.19/0.43 (~![B: $i, C: $i] : ((~subset(B, difference(C, B))) | (B = empty_set))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[20, 15])).
% 0.19/0.43 tff(22,plain,
% 0.19/0.43 (~![B: $i, C: $i] : ((~subset(B, difference(C, B))) | (B = empty_set))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[21, 15])).
% 0.19/0.43 tff(23,plain,
% 0.19/0.43 (~![B: $i, C: $i] : ((~subset(B, difference(C, B))) | (B = empty_set))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.19/0.44 tff(24,plain,
% 0.19/0.44 (~![B: $i, C: $i] : ((~subset(B, difference(C, B))) | (B = empty_set))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[23, 15])).
% 0.19/0.44 tff(25,plain,(
% 0.19/0.44 ~((~subset(B!3, difference(C!2, B!3))) | (B!3 = empty_set))),
% 0.19/0.44 inference(skolemize,[status(sab)],[24])).
% 0.19/0.44 tff(26,plain,
% 0.19/0.44 (~(B!3 = empty_set)),
% 0.19/0.44 inference(or_elim,[status(thm)],[25])).
% 0.19/0.44 tff(27,plain,
% 0.19/0.44 ((~((B!3 = empty_set) <=> (~((~subset(B!3, empty_set)) | (~subset(empty_set, B!3)))))) | (B!3 = empty_set) | ((~subset(B!3, empty_set)) | (~subset(empty_set, B!3)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(28,plain,
% 0.19/0.44 ((~((B!3 = empty_set) <=> (~((~subset(B!3, empty_set)) | (~subset(empty_set, B!3)))))) | ((~subset(B!3, empty_set)) | (~subset(empty_set, B!3)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.19/0.44 tff(29,plain,
% 0.19/0.44 ((~subset(B!3, empty_set)) | (~subset(empty_set, B!3))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[28, 14])).
% 0.19/0.44 tff(30,assumption,((~((~subset(B!3, empty_set)) | ![D: $i] : ((~member(D, B!3)) | member(D, empty_set)))) | (~(subset(B!3, empty_set) | (~((~member(tptp_fun_D_0(empty_set, B!3), B!3)) | member(tptp_fun_D_0(empty_set, B!3), empty_set)))))), introduced(assumption)).
% 0.19/0.44 tff(31,plain,
% 0.19/0.44 (^[B: $i, C: $i] : refl((~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(32,plain,
% 0.19/0.44 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[31])).
% 0.19/0.44 tff(33,plain,
% 0.19/0.44 (^[B: $i, C: $i] : rewrite((~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(34,plain,
% 0.19/0.44 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[33])).
% 0.19/0.44 tff(35,plain,
% 0.19/0.44 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[34, 32])).
% 0.19/0.44 tff(36,plain,
% 0.19/0.44 (^[B: $i, C: $i] : trans(monotonicity(rewrite(((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) <=> ((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))), rewrite((subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))) <=> (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))), ((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))), rewrite((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))), ((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(37,plain,
% 0.19/0.44 (![B: $i, C: $i] : (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[36])).
% 0.19/0.44 tff(38,plain,
% 0.19/0.44 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C))) <=> ![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(39,plain,
% 0.19/0.44 (^[B: $i, C: $i] : rewrite((subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C))) <=> (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(40,plain,
% 0.19/0.44 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C))) <=> ![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[39])).
% 0.19/0.44 tff(41,axiom,(![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','subset_defn')).
% 0.19/0.44 tff(42,plain,
% 0.19/0.44 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.19/0.44 tff(43,plain,
% 0.19/0.44 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.19/0.44 tff(44,plain,(
% 0.19/0.44 ![B: $i, C: $i] : (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))),
% 0.19/0.44 inference(skolemize,[status(sab)],[43])).
% 0.19/0.44 tff(45,plain,
% 0.19/0.44 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.19/0.44 tff(46,plain,
% 0.19/0.44 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[45, 35])).
% 0.19/0.44 tff(47,plain,
% 0.19/0.44 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(B!3, empty_set)) | ![D: $i] : ((~member(D, B!3)) | member(D, empty_set)))) | (~(subset(B!3, empty_set) | (~((~member(tptp_fun_D_0(empty_set, B!3), B!3)) | member(tptp_fun_D_0(empty_set, B!3), empty_set)))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(48,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[47, 46, 30])).
% 0.19/0.44 tff(49,plain,(~((~((~subset(B!3, empty_set)) | ![D: $i] : ((~member(D, B!3)) | member(D, empty_set)))) | (~(subset(B!3, empty_set) | (~((~member(tptp_fun_D_0(empty_set, B!3), B!3)) | member(tptp_fun_D_0(empty_set, B!3), empty_set))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(50,plain,
% 0.19/0.44 (((~((~subset(B!3, empty_set)) | ![D: $i] : ((~member(D, B!3)) | member(D, empty_set)))) | (~(subset(B!3, empty_set) | (~((~member(tptp_fun_D_0(empty_set, B!3), B!3)) | member(tptp_fun_D_0(empty_set, B!3), empty_set)))))) | (subset(B!3, empty_set) | (~((~member(tptp_fun_D_0(empty_set, B!3), B!3)) | member(tptp_fun_D_0(empty_set, B!3), empty_set))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(51,plain,
% 0.19/0.44 (subset(B!3, empty_set) | (~((~member(tptp_fun_D_0(empty_set, B!3), B!3)) | member(tptp_fun_D_0(empty_set, B!3), empty_set)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.19/0.44 tff(52,assumption,(member(tptp_fun_D_0(empty_set, B!3), B!3)), introduced(assumption)).
% 0.19/0.44 tff(53,assumption,(~(member(tptp_fun_D_0(empty_set, B!3), difference(C!2, B!3)) <=> (~((~member(tptp_fun_D_0(empty_set, B!3), C!2)) | member(tptp_fun_D_0(empty_set, B!3), B!3))))), introduced(assumption)).
% 0.19/0.44 tff(54,plain,
% 0.19/0.44 (^[B: $i, C: $i, D: $i] : refl((member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))) <=> (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(55,plain,
% 0.19/0.44 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))) <=> ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.44 tff(56,plain,
% 0.19/0.44 (^[B: $i, C: $i, D: $i] : rewrite((member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(57,plain,
% 0.19/0.44 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[56])).
% 0.19/0.44 tff(58,plain,
% 0.19/0.44 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(59,axiom,(![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','difference_defn')).
% 0.19/0.44 tff(60,plain,
% 0.19/0.44 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.19/0.44 tff(61,plain,(
% 0.19/0.44 ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.19/0.44 inference(skolemize,[status(sab)],[60])).
% 0.19/0.44 tff(62,plain,
% 0.19/0.44 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.19/0.44 tff(63,plain,
% 0.19/0.44 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.19/0.44 tff(64,plain,
% 0.19/0.44 ((~![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))) | (member(tptp_fun_D_0(empty_set, B!3), difference(C!2, B!3)) <=> (~((~member(tptp_fun_D_0(empty_set, B!3), C!2)) | member(tptp_fun_D_0(empty_set, B!3), B!3))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(65,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[64, 63, 53])).
% 0.19/0.44 tff(66,plain,(member(tptp_fun_D_0(empty_set, B!3), difference(C!2, B!3)) <=> (~((~member(tptp_fun_D_0(empty_set, B!3), C!2)) | member(tptp_fun_D_0(empty_set, B!3), B!3)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(67,plain,
% 0.19/0.44 (((~member(tptp_fun_D_0(empty_set, B!3), C!2)) | member(tptp_fun_D_0(empty_set, B!3), B!3)) | (~member(tptp_fun_D_0(empty_set, B!3), B!3))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(68,plain,
% 0.19/0.44 ((~member(tptp_fun_D_0(empty_set, B!3), C!2)) | member(tptp_fun_D_0(empty_set, B!3), B!3)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[67, 52])).
% 0.19/0.44 tff(69,plain,
% 0.19/0.44 ((~(member(tptp_fun_D_0(empty_set, B!3), difference(C!2, B!3)) <=> (~((~member(tptp_fun_D_0(empty_set, B!3), C!2)) | member(tptp_fun_D_0(empty_set, B!3), B!3))))) | (~member(tptp_fun_D_0(empty_set, B!3), difference(C!2, B!3))) | (~((~member(tptp_fun_D_0(empty_set, B!3), C!2)) | member(tptp_fun_D_0(empty_set, B!3), B!3)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(70,plain,
% 0.19/0.45 (~member(tptp_fun_D_0(empty_set, B!3), difference(C!2, B!3))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[69, 68, 66])).
% 0.19/0.45 tff(71,plain,
% 0.19/0.45 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(B!3, difference(C!2, B!3))) | ![D: $i] : ((~member(D, B!3)) | member(D, difference(C!2, B!3))))) | (~(subset(B!3, difference(C!2, B!3)) | (~((~member(tptp_fun_D_0(difference(C!2, B!3), B!3), B!3)) | member(tptp_fun_D_0(difference(C!2, B!3), B!3), difference(C!2, B!3))))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(72,plain,
% 0.19/0.45 (~((~((~subset(B!3, difference(C!2, B!3))) | ![D: $i] : ((~member(D, B!3)) | member(D, difference(C!2, B!3))))) | (~(subset(B!3, difference(C!2, B!3)) | (~((~member(tptp_fun_D_0(difference(C!2, B!3), B!3), B!3)) | member(tptp_fun_D_0(difference(C!2, B!3), B!3), difference(C!2, B!3)))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[71, 46])).
% 0.19/0.45 tff(73,plain,
% 0.19/0.45 (((~((~subset(B!3, difference(C!2, B!3))) | ![D: $i] : ((~member(D, B!3)) | member(D, difference(C!2, B!3))))) | (~(subset(B!3, difference(C!2, B!3)) | (~((~member(tptp_fun_D_0(difference(C!2, B!3), B!3), B!3)) | member(tptp_fun_D_0(difference(C!2, B!3), B!3), difference(C!2, B!3))))))) | ((~subset(B!3, difference(C!2, B!3))) | ![D: $i] : ((~member(D, B!3)) | member(D, difference(C!2, B!3))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(74,plain,
% 0.19/0.45 ((~subset(B!3, difference(C!2, B!3))) | ![D: $i] : ((~member(D, B!3)) | member(D, difference(C!2, B!3)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.19/0.45 tff(75,plain,
% 0.19/0.45 (subset(B!3, difference(C!2, B!3))),
% 0.19/0.45 inference(or_elim,[status(thm)],[25])).
% 0.19/0.45 tff(76,plain,
% 0.19/0.45 ((~((~subset(B!3, difference(C!2, B!3))) | ![D: $i] : ((~member(D, B!3)) | member(D, difference(C!2, B!3))))) | (~subset(B!3, difference(C!2, B!3))) | ![D: $i] : ((~member(D, B!3)) | member(D, difference(C!2, B!3)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(77,plain,
% 0.19/0.45 ((~((~subset(B!3, difference(C!2, B!3))) | ![D: $i] : ((~member(D, B!3)) | member(D, difference(C!2, B!3))))) | ![D: $i] : ((~member(D, B!3)) | member(D, difference(C!2, B!3)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.19/0.45 tff(78,plain,
% 0.19/0.45 (![D: $i] : ((~member(D, B!3)) | member(D, difference(C!2, B!3)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[77, 74])).
% 0.19/0.45 tff(79,plain,
% 0.19/0.45 (((~![D: $i] : ((~member(D, B!3)) | member(D, difference(C!2, B!3)))) | ((~member(tptp_fun_D_0(empty_set, B!3), B!3)) | member(tptp_fun_D_0(empty_set, B!3), difference(C!2, B!3)))) <=> ((~![D: $i] : ((~member(D, B!3)) | member(D, difference(C!2, B!3)))) | (~member(tptp_fun_D_0(empty_set, B!3), B!3)) | member(tptp_fun_D_0(empty_set, B!3), difference(C!2, B!3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(80,plain,
% 0.19/0.45 ((~![D: $i] : ((~member(D, B!3)) | member(D, difference(C!2, B!3)))) | ((~member(tptp_fun_D_0(empty_set, B!3), B!3)) | member(tptp_fun_D_0(empty_set, B!3), difference(C!2, B!3)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(81,plain,
% 0.19/0.45 ((~![D: $i] : ((~member(D, B!3)) | member(D, difference(C!2, B!3)))) | (~member(tptp_fun_D_0(empty_set, B!3), B!3)) | member(tptp_fun_D_0(empty_set, B!3), difference(C!2, B!3))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.19/0.45 tff(82,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[81, 78, 70, 52])).
% 0.19/0.45 tff(83,plain,(~member(tptp_fun_D_0(empty_set, B!3), B!3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(84,plain,
% 0.19/0.45 (((~member(tptp_fun_D_0(empty_set, B!3), B!3)) | member(tptp_fun_D_0(empty_set, B!3), empty_set)) | member(tptp_fun_D_0(empty_set, B!3), B!3)),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(85,plain,
% 0.19/0.45 ((~member(tptp_fun_D_0(empty_set, B!3), B!3)) | member(tptp_fun_D_0(empty_set, B!3), empty_set)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.19/0.45 tff(86,plain,
% 0.19/0.45 ((~(subset(B!3, empty_set) | (~((~member(tptp_fun_D_0(empty_set, B!3), B!3)) | member(tptp_fun_D_0(empty_set, B!3), empty_set))))) | subset(B!3, empty_set) | (~((~member(tptp_fun_D_0(empty_set, B!3), B!3)) | member(tptp_fun_D_0(empty_set, B!3), empty_set)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(87,plain,
% 0.19/0.45 ((~(subset(B!3, empty_set) | (~((~member(tptp_fun_D_0(empty_set, B!3), B!3)) | member(tptp_fun_D_0(empty_set, B!3), empty_set))))) | subset(B!3, empty_set)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.19/0.45 tff(88,plain,
% 0.19/0.45 (subset(B!3, empty_set)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[87, 51])).
% 0.19/0.45 tff(89,plain,
% 0.19/0.45 ((~((~subset(B!3, empty_set)) | (~subset(empty_set, B!3)))) | (~subset(B!3, empty_set)) | (~subset(empty_set, B!3))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(90,plain,
% 0.19/0.45 ((~((~subset(B!3, empty_set)) | (~subset(empty_set, B!3)))) | (~subset(empty_set, B!3))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.19/0.45 tff(91,plain,
% 0.19/0.45 (~subset(empty_set, B!3)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[90, 29])).
% 0.19/0.45 tff(92,plain,
% 0.19/0.45 (((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(empty_set, B!3)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!3)))) | (~((~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))) | subset(empty_set, B!3)))))) <=> ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(empty_set, B!3)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!3)))) | (~((~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))) | subset(empty_set, B!3))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(93,plain,
% 0.19/0.45 ((~((~((~subset(empty_set, B!3)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!3)))) | (~(subset(empty_set, B!3) | (~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))))))) <=> (~((~((~subset(empty_set, B!3)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!3)))) | (~((~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))) | subset(empty_set, B!3)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(94,plain,
% 0.19/0.45 (((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(empty_set, B!3)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!3)))) | (~(subset(empty_set, B!3) | (~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3)))))))) <=> ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(empty_set, B!3)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!3)))) | (~((~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))) | subset(empty_set, B!3))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[93])).
% 0.19/0.45 tff(95,plain,
% 0.19/0.45 (((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(empty_set, B!3)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!3)))) | (~(subset(empty_set, B!3) | (~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3)))))))) <=> ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(empty_set, B!3)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!3)))) | (~((~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))) | subset(empty_set, B!3))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[94, 92])).
% 0.19/0.45 tff(96,plain,
% 0.19/0.45 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(empty_set, B!3)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!3)))) | (~(subset(empty_set, B!3) | (~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3)))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(97,plain,
% 0.19/0.45 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(empty_set, B!3)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!3)))) | (~((~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))) | subset(empty_set, B!3)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.19/0.45 tff(98,plain,
% 0.19/0.45 (~((~((~subset(empty_set, B!3)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!3)))) | (~((~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))) | subset(empty_set, B!3))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[97, 46])).
% 0.19/0.45 tff(99,plain,
% 0.19/0.45 (((~((~subset(empty_set, B!3)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!3)))) | (~((~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))) | subset(empty_set, B!3)))) | ((~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))) | subset(empty_set, B!3))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(100,plain,
% 0.19/0.45 ((~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))) | subset(empty_set, B!3)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.19/0.45 tff(101,plain,
% 0.19/0.45 ((~((~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))) | subset(empty_set, B!3))) | (~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))) | subset(empty_set, B!3)),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(102,plain,
% 0.19/0.45 ((~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))) | subset(empty_set, B!3)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.19/0.45 tff(103,plain,
% 0.19/0.45 (~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[102, 91])).
% 0.19/0.45 tff(104,plain,
% 0.19/0.45 (((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3)) | member(tptp_fun_D_0(B!3, empty_set), empty_set)),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(105,plain,
% 0.19/0.45 (member(tptp_fun_D_0(B!3, empty_set), empty_set)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.19/0.45 tff(106,plain,
% 0.19/0.45 (^[B: $i] : refl((~member(B, empty_set)) <=> (~member(B, empty_set)))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(107,plain,
% 0.19/0.45 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[106])).
% 0.19/0.45 tff(108,plain,
% 0.19/0.45 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(109,axiom,(![B: $i] : (~member(B, empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','empty_set_defn')).
% 0.19/0.45 tff(110,plain,
% 0.19/0.45 (![B: $i] : (~member(B, empty_set))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.19/0.45 tff(111,plain,(
% 0.19/0.45 ![B: $i] : (~member(B, empty_set))),
% 0.19/0.45 inference(skolemize,[status(sab)],[110])).
% 0.19/0.45 tff(112,plain,
% 0.19/0.45 (![B: $i] : (~member(B, empty_set))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.19/0.45 tff(113,plain,
% 0.19/0.45 ((~![B: $i] : (~member(B, empty_set))) | (~member(tptp_fun_D_0(B!3, empty_set), empty_set))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(114,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[113, 112, 105])).
% 0.19/0.46 % SZS output end Proof
%------------------------------------------------------------------------------