TSTP Solution File: SET587+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET587+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 05:07:09 EDT 2022
% Result : Theorem 9.11s 6.14s
% Output : Proof 9.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET587+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n005.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Sep 3 06:49:03 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 9.11/6.14 % SZS status Theorem
% 9.11/6.14 % SZS output start Proof
% 9.11/6.14 tff(member_type, type, (
% 9.11/6.14 member: ( $i * $i ) > $o)).
% 9.11/6.14 tff(empty_set_type, type, (
% 9.11/6.14 empty_set: $i)).
% 9.11/6.14 tff(tptp_fun_D_1_type, type, (
% 9.11/6.14 tptp_fun_D_1: ( $i * $i ) > $i)).
% 9.11/6.14 tff(tptp_fun_B_4_type, type, (
% 9.11/6.14 tptp_fun_B_4: $i)).
% 9.11/6.14 tff(tptp_fun_C_3_type, type, (
% 9.11/6.14 tptp_fun_C_3: $i)).
% 9.11/6.14 tff(difference_type, type, (
% 9.11/6.14 difference: ( $i * $i ) > $i)).
% 9.11/6.14 tff(subset_type, type, (
% 9.11/6.14 subset: ( $i * $i ) > $o)).
% 9.11/6.14 tff(tptp_fun_D_0_type, type, (
% 9.11/6.14 tptp_fun_D_0: ( $i * $i ) > $i)).
% 9.11/6.14 tff(1,assumption,(~(difference(B!4, C!3) = empty_set)), introduced(assumption)).
% 9.11/6.14 tff(2,plain,
% 9.11/6.14 ((~((difference(B!4, C!3) = empty_set) <=> subset(B!4, C!3))) <=> ((~(difference(B!4, C!3) = empty_set)) <=> subset(B!4, C!3))),
% 9.11/6.14 inference(rewrite,[status(thm)],[])).
% 9.11/6.14 tff(3,plain,
% 9.11/6.14 ((~![B: $i, C: $i] : ((difference(B, C) = empty_set) <=> subset(B, C))) <=> (~![B: $i, C: $i] : ((difference(B, C) = empty_set) <=> subset(B, C)))),
% 9.11/6.14 inference(rewrite,[status(thm)],[])).
% 9.11/6.14 tff(4,axiom,(~![B: $i, C: $i] : ((difference(B, C) = empty_set) <=> subset(B, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_difference_empty_set')).
% 9.11/6.14 tff(5,plain,
% 9.11/6.14 (~![B: $i, C: $i] : ((difference(B, C) = empty_set) <=> subset(B, C))),
% 9.11/6.14 inference(modus_ponens,[status(thm)],[4, 3])).
% 9.11/6.14 tff(6,plain,
% 9.11/6.14 (~![B: $i, C: $i] : ((difference(B, C) = empty_set) <=> subset(B, C))),
% 9.11/6.14 inference(modus_ponens,[status(thm)],[5, 3])).
% 9.11/6.14 tff(7,plain,
% 9.11/6.14 (~![B: $i, C: $i] : ((difference(B, C) = empty_set) <=> subset(B, C))),
% 9.11/6.14 inference(modus_ponens,[status(thm)],[6, 3])).
% 9.11/6.14 tff(8,plain,
% 9.11/6.14 (~![B: $i, C: $i] : ((difference(B, C) = empty_set) <=> subset(B, C))),
% 9.11/6.14 inference(modus_ponens,[status(thm)],[7, 3])).
% 9.11/6.14 tff(9,plain,
% 9.11/6.14 (~![B: $i, C: $i] : ((difference(B, C) = empty_set) <=> subset(B, C))),
% 9.11/6.14 inference(modus_ponens,[status(thm)],[8, 3])).
% 9.11/6.14 tff(10,plain,
% 9.11/6.14 (~![B: $i, C: $i] : ((difference(B, C) = empty_set) <=> subset(B, C))),
% 9.11/6.14 inference(modus_ponens,[status(thm)],[9, 3])).
% 9.11/6.14 tff(11,plain,
% 9.11/6.14 (~![B: $i, C: $i] : ((difference(B, C) = empty_set) <=> subset(B, C))),
% 9.11/6.14 inference(modus_ponens,[status(thm)],[10, 3])).
% 9.11/6.14 tff(12,plain,(
% 9.11/6.14 ~((difference(B!4, C!3) = empty_set) <=> subset(B!4, C!3))),
% 9.11/6.14 inference(skolemize,[status(sab)],[11])).
% 9.11/6.14 tff(13,plain,
% 9.11/6.14 ((~(difference(B!4, C!3) = empty_set)) <=> subset(B!4, C!3)),
% 9.11/6.14 inference(modus_ponens,[status(thm)],[12, 2])).
% 9.11/6.14 tff(14,plain,
% 9.11/6.14 ((difference(B!4, C!3) = empty_set) | subset(B!4, C!3) | (~((~(difference(B!4, C!3) = empty_set)) <=> subset(B!4, C!3)))),
% 9.11/6.14 inference(tautology,[status(thm)],[])).
% 9.11/6.14 tff(15,plain,
% 9.11/6.14 ((difference(B!4, C!3) = empty_set) | subset(B!4, C!3)),
% 9.11/6.14 inference(unit_resolution,[status(thm)],[14, 13])).
% 9.11/6.14 tff(16,plain,
% 9.11/6.14 (subset(B!4, C!3)),
% 9.11/6.14 inference(unit_resolution,[status(thm)],[15, 1])).
% 9.11/6.14 tff(17,plain,
% 9.11/6.14 (^[B: $i, C: $i] : refl((~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C))))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C))))))))),
% 9.11/6.14 inference(bind,[status(th)],[])).
% 9.11/6.14 tff(18,plain,
% 9.11/6.14 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(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_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))),
% 9.11/6.14 inference(quant_intro,[status(thm)],[17])).
% 9.11/6.14 tff(19,plain,
% 9.11/6.14 (^[B: $i, C: $i] : rewrite((~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C))))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C))))))))),
% 9.11/6.14 inference(bind,[status(th)],[])).
% 9.11/6.14 tff(20,plain,
% 9.11/6.14 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(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_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))),
% 9.11/6.14 inference(quant_intro,[status(thm)],[19])).
% 9.11/6.14 tff(21,plain,
% 9.11/6.14 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(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_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))),
% 9.11/6.14 inference(transitivity,[status(thm)],[20, 18])).
% 9.11/6.14 tff(22,plain,
% 9.11/6.14 (^[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_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))) <=> (subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C))))), ((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C))))) <=> (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C))))))), rewrite((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))), ((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))))),
% 9.11/6.14 inference(bind,[status(th)],[])).
% 9.11/6.14 tff(23,plain,
% 9.11/6.14 (![B: $i, C: $i] : (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(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_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))),
% 9.11/6.14 inference(quant_intro,[status(thm)],[22])).
% 9.11/6.14 tff(24,plain,
% 9.11/6.14 (![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)))),
% 9.11/6.14 inference(rewrite,[status(thm)],[])).
% 9.11/6.14 tff(25,plain,
% 9.11/6.14 (^[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))))),
% 9.11/6.14 inference(bind,[status(th)],[])).
% 9.11/6.14 tff(26,plain,
% 9.11/6.14 (![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)))),
% 9.11/6.14 inference(quant_intro,[status(thm)],[25])).
% 9.11/6.14 tff(27,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')).
% 9.11/6.14 tff(28,plain,
% 9.11/6.14 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 9.11/6.14 inference(modus_ponens,[status(thm)],[27, 26])).
% 9.11/6.14 tff(29,plain,
% 9.11/6.14 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 9.11/6.14 inference(modus_ponens,[status(thm)],[28, 24])).
% 9.11/6.14 tff(30,plain,(
% 9.11/6.14 ![B: $i, C: $i] : (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))),
% 9.11/6.14 inference(skolemize,[status(sab)],[29])).
% 9.11/6.14 tff(31,plain,
% 9.11/6.14 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))),
% 9.11/6.14 inference(modus_ponens,[status(thm)],[30, 23])).
% 9.11/6.14 tff(32,plain,
% 9.11/6.14 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))),
% 9.11/6.14 inference(modus_ponens,[status(thm)],[31, 21])).
% 9.11/6.14 tff(33,plain,
% 9.11/6.14 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~subset(B!4, C!3)) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3)))) | (~(subset(B!4, C!3) | (~((~member(tptp_fun_D_1(C!3, B!4), B!4)) | member(tptp_fun_D_1(C!3, B!4), C!3)))))))),
% 9.11/6.14 inference(quant_inst,[status(thm)],[])).
% 9.11/6.14 tff(34,plain,
% 9.11/6.14 (~((~((~subset(B!4, C!3)) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3)))) | (~(subset(B!4, C!3) | (~((~member(tptp_fun_D_1(C!3, B!4), B!4)) | member(tptp_fun_D_1(C!3, B!4), C!3))))))),
% 9.11/6.14 inference(unit_resolution,[status(thm)],[33, 32])).
% 9.11/6.14 tff(35,plain,
% 9.11/6.14 (((~((~subset(B!4, C!3)) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3)))) | (~(subset(B!4, C!3) | (~((~member(tptp_fun_D_1(C!3, B!4), B!4)) | member(tptp_fun_D_1(C!3, B!4), C!3)))))) | ((~subset(B!4, C!3)) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3)))),
% 9.11/6.14 inference(tautology,[status(thm)],[])).
% 9.11/6.14 tff(36,plain,
% 9.11/6.14 ((~subset(B!4, C!3)) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3))),
% 9.11/6.14 inference(unit_resolution,[status(thm)],[35, 34])).
% 9.11/6.14 tff(37,plain,
% 9.11/6.14 ((~((~subset(B!4, C!3)) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3)))) | (~subset(B!4, C!3)) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3))),
% 9.11/6.14 inference(tautology,[status(thm)],[])).
% 9.11/6.14 tff(38,plain,
% 9.11/6.14 ((~subset(B!4, C!3)) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3))),
% 9.11/6.14 inference(unit_resolution,[status(thm)],[37, 36])).
% 9.11/6.14 tff(39,plain,
% 9.11/6.14 (![D: $i] : ((~member(D, B!4)) | member(D, C!3))),
% 9.11/6.14 inference(unit_resolution,[status(thm)],[38, 16])).
% 9.11/6.14 tff(40,assumption,(member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), empty_set)), introduced(assumption)).
% 9.11/6.14 tff(41,plain,
% 9.11/6.14 (^[B: $i] : refl((~member(B, empty_set)) <=> (~member(B, empty_set)))),
% 9.11/6.14 inference(bind,[status(th)],[])).
% 9.11/6.14 tff(42,plain,
% 9.11/6.14 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 9.11/6.14 inference(quant_intro,[status(thm)],[41])).
% 9.11/6.14 tff(43,plain,
% 9.11/6.14 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 9.11/6.14 inference(rewrite,[status(thm)],[])).
% 9.11/6.14 tff(44,axiom,(![B: $i] : (~member(B, empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','empty_set_defn')).
% 9.11/6.14 tff(45,plain,
% 9.11/6.14 (![B: $i] : (~member(B, empty_set))),
% 9.11/6.14 inference(modus_ponens,[status(thm)],[44, 43])).
% 9.11/6.14 tff(46,plain,(
% 9.11/6.14 ![B: $i] : (~member(B, empty_set))),
% 9.11/6.14 inference(skolemize,[status(sab)],[45])).
% 9.11/6.14 tff(47,plain,
% 9.11/6.14 (![B: $i] : (~member(B, empty_set))),
% 9.11/6.14 inference(modus_ponens,[status(thm)],[46, 42])).
% 9.11/6.14 tff(48,plain,
% 9.11/6.14 ((~![B: $i] : (~member(B, empty_set))) | (~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), empty_set))),
% 9.11/6.14 inference(quant_inst,[status(thm)],[])).
% 9.11/6.14 tff(49,plain,
% 9.11/6.14 ($false),
% 9.11/6.14 inference(unit_resolution,[status(thm)],[48, 47, 40])).
% 9.11/6.14 tff(50,plain,(~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), empty_set)), inference(lemma,lemma(discharge,[]))).
% 9.11/6.14 tff(51,assumption,((~((~(difference(B!4, C!3) = empty_set)) | (member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), empty_set)))) | (~((difference(B!4, C!3) = empty_set) | ((~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), empty_set))))), introduced(assumption)).
% 9.11/6.14 tff(52,plain,
% 9.11/6.14 (^[B: $i, C: $i, D: $i] : refl((~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 9.11/6.14 inference(bind,[status(th)],[])).
% 9.11/6.14 tff(53,plain,
% 9.11/6.14 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 9.11/6.14 inference(quant_intro,[status(thm)],[52])).
% 9.11/6.14 tff(54,plain,
% 9.11/6.14 (![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 9.11/6.14 inference(pull_quant,[status(thm)],[])).
% 9.11/6.14 tff(55,plain,
% 9.11/6.14 (^[B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) <=> ![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))), ((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) <=> (~![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))))), pull_quant((~![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))) <=> ?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C))))), ((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) <=> ?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))) <=> (?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))), pull_quant((?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> (~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))))), pull_quant((~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))))),
% 9.11/6.14 inference(bind,[status(th)],[])).
% 9.11/6.14 tff(56,plain,
% 9.11/6.14 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 9.11/6.14 inference(quant_intro,[status(thm)],[55])).
% 9.11/6.14 tff(57,plain,
% 9.11/6.14 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 9.11/6.14 inference(transitivity,[status(thm)],[56, 54])).
% 9.11/6.14 tff(58,plain,
% 9.11/6.14 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 9.11/6.14 inference(transitivity,[status(thm)],[57, 53])).
% 9.11/6.14 tff(59,plain,
% 9.11/6.14 (^[B: $i, C: $i] : rewrite((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 9.11/6.14 inference(bind,[status(th)],[])).
% 9.11/6.14 tff(60,plain,
% 9.11/6.14 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 9.11/6.14 inference(quant_intro,[status(thm)],[59])).
% 9.11/6.14 tff(61,plain,
% 9.11/6.14 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 9.11/6.14 inference(transitivity,[status(thm)],[60, 58])).
% 9.11/6.14 tff(62,plain,
% 9.11/6.14 (^[B: $i, C: $i] : trans(monotonicity(rewrite(((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) <=> ((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))), rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))))),
% 9.11/6.14 inference(bind,[status(th)],[])).
% 9.11/6.14 tff(63,plain,
% 9.11/6.14 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 9.11/6.14 inference(quant_intro,[status(thm)],[62])).
% 9.11/6.14 tff(64,plain,
% 9.11/6.14 (^[B: $i, C: $i] : rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))),
% 9.11/6.14 inference(bind,[status(th)],[])).
% 9.11/6.14 tff(65,plain,
% 9.11/6.14 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))) <=> ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))),
% 9.11/6.14 inference(quant_intro,[status(thm)],[64])).
% 9.11/6.14 tff(66,plain,
% 9.11/6.14 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C))) <=> ![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 9.11/6.14 inference(rewrite,[status(thm)],[])).
% 9.11/6.14 tff(67,axiom,(![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','equal_member_defn')).
% 9.11/6.14 tff(68,plain,
% 9.11/6.14 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 9.11/6.14 inference(modus_ponens,[status(thm)],[67, 66])).
% 9.11/6.14 tff(69,plain,(
% 9.11/6.14 ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))),
% 9.11/6.14 inference(skolemize,[status(sab)],[68])).
% 9.11/6.14 tff(70,plain,
% 9.11/6.14 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))),
% 9.11/6.14 inference(modus_ponens,[status(thm)],[69, 65])).
% 9.11/6.14 tff(71,plain,
% 9.11/6.14 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 9.11/6.14 inference(modus_ponens,[status(thm)],[70, 63])).
% 9.11/6.14 tff(72,plain,
% 9.11/6.14 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 9.11/6.14 inference(modus_ponens,[status(thm)],[71, 61])).
% 9.11/6.14 tff(73,plain,
% 9.11/6.14 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))) | (~((~((~(difference(B!4, C!3) = empty_set)) | (member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), empty_set)))) | (~((difference(B!4, C!3) = empty_set) | ((~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), empty_set))))))),
% 9.11/6.14 inference(quant_inst,[status(thm)],[])).
% 9.11/6.14 tff(74,plain,
% 9.11/6.14 ($false),
% 9.11/6.14 inference(unit_resolution,[status(thm)],[73, 72, 51])).
% 9.11/6.14 tff(75,plain,(~((~((~(difference(B!4, C!3) = empty_set)) | (member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), empty_set)))) | (~((difference(B!4, C!3) = empty_set) | ((~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), empty_set)))))), inference(lemma,lemma(discharge,[]))).
% 9.11/6.14 tff(76,plain,
% 9.11/6.14 (((~((~(difference(B!4, C!3) = empty_set)) | (member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), empty_set)))) | (~((difference(B!4, C!3) = empty_set) | ((~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), empty_set))))) | ((difference(B!4, C!3) = empty_set) | ((~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), empty_set)))),
% 9.11/6.14 inference(tautology,[status(thm)],[])).
% 9.11/6.14 tff(77,plain,
% 9.11/6.14 ((difference(B!4, C!3) = empty_set) | ((~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), empty_set))),
% 9.11/6.14 inference(unit_resolution,[status(thm)],[76, 75])).
% 9.11/6.14 tff(78,plain,
% 9.11/6.14 ((~((difference(B!4, C!3) = empty_set) | ((~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), empty_set)))) | (difference(B!4, C!3) = empty_set) | ((~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), empty_set))),
% 9.11/6.14 inference(tautology,[status(thm)],[])).
% 9.11/6.14 tff(79,plain,
% 9.11/6.14 ((difference(B!4, C!3) = empty_set) | ((~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), empty_set))),
% 9.11/6.14 inference(unit_resolution,[status(thm)],[78, 77])).
% 9.11/6.14 tff(80,plain,
% 9.11/6.14 ((~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), empty_set)),
% 9.11/6.14 inference(unit_resolution,[status(thm)],[79, 1])).
% 9.11/6.14 tff(81,plain,
% 9.11/6.14 (^[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)))))),
% 9.11/6.14 inference(bind,[status(th)],[])).
% 9.11/6.14 tff(82,plain,
% 9.11/6.14 (![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))))),
% 9.11/6.14 inference(quant_intro,[status(thm)],[81])).
% 9.11/6.14 tff(83,plain,
% 9.11/6.14 (^[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)))))),
% 9.11/6.14 inference(bind,[status(th)],[])).
% 9.11/6.14 tff(84,plain,
% 9.11/6.14 (![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))))),
% 9.11/6.14 inference(quant_intro,[status(thm)],[83])).
% 9.11/6.14 tff(85,plain,
% 9.11/6.14 (![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))))),
% 9.11/6.14 inference(rewrite,[status(thm)],[])).
% 9.11/6.14 tff(86,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')).
% 9.11/6.14 tff(87,plain,
% 9.11/6.14 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 9.11/6.14 inference(modus_ponens,[status(thm)],[86, 85])).
% 9.11/6.14 tff(88,plain,(
% 9.11/6.14 ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 9.11/6.14 inference(skolemize,[status(sab)],[87])).
% 9.11/6.14 tff(89,plain,
% 9.11/6.14 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 9.11/6.14 inference(modus_ponens,[status(thm)],[88, 84])).
% 9.11/6.14 tff(90,plain,
% 9.11/6.14 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 9.11/6.14 inference(modus_ponens,[status(thm)],[89, 82])).
% 9.11/6.14 tff(91,plain,
% 9.11/6.14 ((~![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))) | (member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), difference(B!4, C!3)) <=> (~((~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), C!3))))),
% 9.11/6.14 inference(quant_inst,[status(thm)],[])).
% 9.11/6.14 tff(92,plain,
% 9.11/6.14 (member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), difference(B!4, C!3)) <=> (~((~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), C!3)))),
% 9.11/6.14 inference(unit_resolution,[status(thm)],[91, 90])).
% 9.11/6.14 tff(93,assumption,((~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), empty_set)), introduced(assumption)).
% 9.11/6.14 tff(94,assumption,(~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), empty_set)), introduced(assumption)).
% 9.11/6.14 tff(95,plain,
% 9.11/6.14 ((~((~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), empty_set))) | member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), difference(B!4, C!3)) | member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), empty_set)),
% 9.11/6.14 inference(tautology,[status(thm)],[])).
% 9.11/6.14 tff(96,plain,
% 9.11/6.14 (member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), difference(B!4, C!3))),
% 9.11/6.14 inference(unit_resolution,[status(thm)],[95, 94, 93])).
% 9.11/6.14 tff(97,assumption,((~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), C!3)), introduced(assumption)).
% 9.11/6.14 tff(98,plain,
% 9.11/6.14 ((~(member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), difference(B!4, C!3)) <=> (~((~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), C!3))))) | (~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), difference(B!4, C!3))) | (~((~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), C!3)))),
% 9.11/6.14 inference(tautology,[status(thm)],[])).
% 9.11/6.14 tff(99,plain,
% 9.11/6.14 ((~(member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), difference(B!4, C!3)) <=> (~((~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), C!3))))) | (~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), difference(B!4, C!3)))),
% 9.11/6.14 inference(unit_resolution,[status(thm)],[98, 97])).
% 9.11/6.14 tff(100,plain,
% 9.11/6.14 ($false),
% 9.11/6.14 inference(unit_resolution,[status(thm)],[99, 96, 92])).
% 9.11/6.14 tff(101,plain,(member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), empty_set) | (~((~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), C!3))) | (~((~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), empty_set)))), inference(lemma,lemma(discharge,[]))).
% 9.11/6.14 tff(102,plain,
% 9.11/6.14 (~((~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), C!3))),
% 9.11/6.14 inference(unit_resolution,[status(thm)],[101, 80, 50])).
% 9.11/6.14 tff(103,assumption,(~((~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), C!3))), introduced(assumption)).
% 9.11/6.14 tff(104,plain,
% 9.11/6.14 (((~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), C!3)) | (~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), C!3))),
% 9.11/6.14 inference(tautology,[status(thm)],[])).
% 9.11/6.14 tff(105,plain,
% 9.11/6.14 (~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), C!3)),
% 9.11/6.14 inference(unit_resolution,[status(thm)],[104, 103])).
% 9.11/6.14 tff(106,plain,
% 9.11/6.14 (((~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), C!3)) | member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), B!4)),
% 9.11/6.14 inference(tautology,[status(thm)],[])).
% 9.11/6.14 tff(107,plain,
% 9.11/6.14 (member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), B!4)),
% 9.11/6.14 inference(unit_resolution,[status(thm)],[106, 103])).
% 9.11/6.14 tff(108,assumption,(![D: $i] : ((~member(D, B!4)) | member(D, C!3))), introduced(assumption)).
% 9.11/6.14 tff(109,plain,
% 9.11/6.14 (((~![D: $i] : ((~member(D, B!4)) | member(D, C!3))) | ((~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), C!3))) <=> ((~![D: $i] : ((~member(D, B!4)) | member(D, C!3))) | (~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), C!3))),
% 9.11/6.14 inference(rewrite,[status(thm)],[])).
% 9.11/6.14 tff(110,plain,
% 9.11/6.14 ((~![D: $i] : ((~member(D, B!4)) | member(D, C!3))) | ((~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), C!3))),
% 9.11/6.14 inference(quant_inst,[status(thm)],[])).
% 9.11/6.14 tff(111,plain,
% 9.11/6.14 ((~![D: $i] : ((~member(D, B!4)) | member(D, C!3))) | (~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), C!3)),
% 9.11/6.14 inference(modus_ponens,[status(thm)],[110, 109])).
% 9.11/6.14 tff(112,plain,
% 9.11/6.14 ($false),
% 9.11/6.14 inference(unit_resolution,[status(thm)],[111, 108, 107, 105])).
% 9.11/6.14 tff(113,plain,(((~member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(empty_set, difference(B!4, C!3)), C!3)) | (~![D: $i] : ((~member(D, B!4)) | member(D, C!3)))), inference(lemma,lemma(discharge,[]))).
% 9.11/6.14 tff(114,plain,
% 9.11/6.14 ($false),
% 9.11/6.14 inference(unit_resolution,[status(thm)],[113, 102, 39])).
% 9.11/6.14 tff(115,plain,(difference(B!4, C!3) = empty_set), inference(lemma,lemma(discharge,[]))).
% 9.11/6.14 tff(116,plain,
% 9.11/6.14 (member(tptp_fun_D_1(C!3, B!4), difference(B!4, C!3)) <=> member(tptp_fun_D_1(C!3, B!4), empty_set)),
% 9.11/6.14 inference(monotonicity,[status(thm)],[115])).
% 9.11/6.14 tff(117,plain,
% 9.11/6.14 (member(tptp_fun_D_1(C!3, B!4), empty_set) <=> member(tptp_fun_D_1(C!3, B!4), difference(B!4, C!3))),
% 9.11/6.14 inference(symmetry,[status(thm)],[116])).
% 9.11/6.14 tff(118,plain,
% 9.11/6.14 ((~member(tptp_fun_D_1(C!3, B!4), empty_set)) <=> (~member(tptp_fun_D_1(C!3, B!4), difference(B!4, C!3)))),
% 9.11/6.14 inference(monotonicity,[status(thm)],[117])).
% 9.11/6.14 tff(119,assumption,(~member(tptp_fun_D_1(C!3, B!4), empty_set)), introduced(assumption)).
% 9.11/6.14 tff(120,plain,
% 9.11/6.14 (~member(tptp_fun_D_1(C!3, B!4), difference(B!4, C!3))),
% 9.11/6.14 inference(modus_ponens,[status(thm)],[119, 118])).
% 9.11/6.14 tff(121,plain,
% 9.11/6.14 ((~![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))) | (member(tptp_fun_D_1(C!3, B!4), difference(B!4, C!3)) <=> (~((~member(tptp_fun_D_1(C!3, B!4), B!4)) | member(tptp_fun_D_1(C!3, B!4), C!3))))),
% 9.11/6.14 inference(quant_inst,[status(thm)],[])).
% 9.11/6.14 tff(122,plain,
% 9.11/6.14 (member(tptp_fun_D_1(C!3, B!4), difference(B!4, C!3)) <=> (~((~member(tptp_fun_D_1(C!3, B!4), B!4)) | member(tptp_fun_D_1(C!3, B!4), C!3)))),
% 9.11/6.14 inference(unit_resolution,[status(thm)],[121, 90])).
% 9.11/6.14 tff(123,plain,
% 9.11/6.14 ((~(difference(B!4, C!3) = empty_set)) | (~subset(B!4, C!3)) | (~((~(difference(B!4, C!3) = empty_set)) <=> subset(B!4, C!3)))),
% 9.11/6.14 inference(tautology,[status(thm)],[])).
% 9.11/6.14 tff(124,plain,
% 9.11/6.14 ((~(difference(B!4, C!3) = empty_set)) | (~subset(B!4, C!3))),
% 9.11/6.14 inference(unit_resolution,[status(thm)],[123, 13])).
% 9.11/6.14 tff(125,plain,
% 9.11/6.14 (~subset(B!4, C!3)),
% 9.11/6.14 inference(unit_resolution,[status(thm)],[124, 115])).
% 9.11/6.14 tff(126,plain,
% 9.11/6.14 (((~((~subset(B!4, C!3)) | ![D: $i] : ((~member(D, B!4)) | member(D, C!3)))) | (~(subset(B!4, C!3) | (~((~member(tptp_fun_D_1(C!3, B!4), B!4)) | member(tptp_fun_D_1(C!3, B!4), C!3)))))) | (subset(B!4, C!3) | (~((~member(tptp_fun_D_1(C!3, B!4), B!4)) | member(tptp_fun_D_1(C!3, B!4), C!3))))),
% 9.11/6.14 inference(tautology,[status(thm)],[])).
% 9.11/6.14 tff(127,plain,
% 9.11/6.14 (subset(B!4, C!3) | (~((~member(tptp_fun_D_1(C!3, B!4), B!4)) | member(tptp_fun_D_1(C!3, B!4), C!3)))),
% 9.11/6.14 inference(unit_resolution,[status(thm)],[126, 34])).
% 9.11/6.14 tff(128,plain,
% 9.11/6.14 ((~(subset(B!4, C!3) | (~((~member(tptp_fun_D_1(C!3, B!4), B!4)) | member(tptp_fun_D_1(C!3, B!4), C!3))))) | subset(B!4, C!3) | (~((~member(tptp_fun_D_1(C!3, B!4), B!4)) | member(tptp_fun_D_1(C!3, B!4), C!3)))),
% 9.11/6.14 inference(tautology,[status(thm)],[])).
% 9.11/6.14 tff(129,plain,
% 9.11/6.14 (subset(B!4, C!3) | (~((~member(tptp_fun_D_1(C!3, B!4), B!4)) | member(tptp_fun_D_1(C!3, B!4), C!3)))),
% 9.11/6.14 inference(unit_resolution,[status(thm)],[128, 127])).
% 9.11/6.14 tff(130,plain,
% 9.11/6.14 (~((~member(tptp_fun_D_1(C!3, B!4), B!4)) | member(tptp_fun_D_1(C!3, B!4), C!3))),
% 9.11/6.14 inference(unit_resolution,[status(thm)],[129, 125])).
% 9.11/6.14 tff(131,plain,
% 9.11/6.14 ((~(member(tptp_fun_D_1(C!3, B!4), difference(B!4, C!3)) <=> (~((~member(tptp_fun_D_1(C!3, B!4), B!4)) | member(tptp_fun_D_1(C!3, B!4), C!3))))) | member(tptp_fun_D_1(C!3, B!4), difference(B!4, C!3)) | ((~member(tptp_fun_D_1(C!3, B!4), B!4)) | member(tptp_fun_D_1(C!3, B!4), C!3))),
% 9.11/6.14 inference(tautology,[status(thm)],[])).
% 9.11/6.14 tff(132,plain,
% 9.11/6.14 ((~(member(tptp_fun_D_1(C!3, B!4), difference(B!4, C!3)) <=> (~((~member(tptp_fun_D_1(C!3, B!4), B!4)) | member(tptp_fun_D_1(C!3, B!4), C!3))))) | member(tptp_fun_D_1(C!3, B!4), difference(B!4, C!3))),
% 9.11/6.14 inference(unit_resolution,[status(thm)],[131, 130])).
% 9.11/6.14 tff(133,plain,
% 9.11/6.14 (member(tptp_fun_D_1(C!3, B!4), difference(B!4, C!3))),
% 9.11/6.14 inference(unit_resolution,[status(thm)],[132, 122])).
% 9.11/6.14 tff(134,plain,
% 9.11/6.14 ($false),
% 9.11/6.14 inference(unit_resolution,[status(thm)],[133, 120])).
% 9.11/6.14 tff(135,plain,(member(tptp_fun_D_1(C!3, B!4), empty_set)), inference(lemma,lemma(discharge,[]))).
% 9.11/6.14 tff(136,plain,
% 9.11/6.14 ((~![B: $i] : (~member(B, empty_set))) | (~member(tptp_fun_D_1(C!3, B!4), empty_set))),
% 9.11/6.14 inference(quant_inst,[status(thm)],[])).
% 9.11/6.14 tff(137,plain,
% 9.11/6.15 ($false),
% 9.11/6.15 inference(unit_resolution,[status(thm)],[136, 47, 135])).
% 9.11/6.15 % SZS output end Proof
%------------------------------------------------------------------------------