TSTP Solution File: SET628+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET628+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 05:07:24 EDT 2022
% Result : Theorem 0.16s 0.37s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SET628+3 : TPTP v8.1.0. Released v2.2.0.
% 0.09/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31 % Computer : n029.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sat Sep 3 07:11:15 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.16/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.16/0.32 Usage: tptp [options] [-file:]file
% 0.16/0.32 -h, -? prints this message.
% 0.16/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.16/0.32 -m, -model generate model.
% 0.16/0.32 -p, -proof generate proof.
% 0.16/0.32 -c, -core generate unsat core of named formulas.
% 0.16/0.32 -st, -statistics display statistics.
% 0.16/0.32 -t:timeout set timeout (in second).
% 0.16/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.16/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.16/0.32 -<param>:<value> configuration parameter and value.
% 0.16/0.32 -o:<output-file> file to place output in.
% 0.16/0.37 % SZS status Theorem
% 0.16/0.37 % SZS output start Proof
% 0.16/0.37 tff(member_type, type, (
% 0.16/0.37 member: ( $i * $i ) > $o)).
% 0.16/0.37 tff(empty_set_type, type, (
% 0.16/0.37 empty_set: $i)).
% 0.16/0.37 tff(tptp_fun_D_1_type, type, (
% 0.16/0.37 tptp_fun_D_1: ( $i * $i ) > $i)).
% 0.16/0.37 tff(tptp_fun_B_3_type, type, (
% 0.16/0.37 tptp_fun_B_3: $i)).
% 0.16/0.37 tff(not_equal_type, type, (
% 0.16/0.37 not_equal: ( $i * $i ) > $o)).
% 0.16/0.37 tff(tptp_fun_D_0_type, type, (
% 0.16/0.37 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.16/0.37 tff(intersect_type, type, (
% 0.16/0.37 intersect: ( $i * $i ) > $o)).
% 0.16/0.37 tff(1,plain,
% 0.16/0.37 (^[B: $i, C: $i, D: $i] : refl((~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(2,plain,
% 0.16/0.37 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.16/0.37 tff(3,plain,
% 0.16/0.37 (![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.16/0.37 inference(pull_quant,[status(thm)],[])).
% 0.16/0.37 tff(4,plain,
% 0.16/0.37 (^[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_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))) <=> (?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))), pull_quant((?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> (~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))))), pull_quant((~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(5,plain,
% 0.16/0.37 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[4])).
% 0.16/0.37 tff(6,plain,
% 0.16/0.37 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.16/0.37 inference(transitivity,[status(thm)],[5, 3])).
% 0.16/0.37 tff(7,plain,
% 0.16/0.37 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.16/0.37 inference(transitivity,[status(thm)],[6, 2])).
% 0.16/0.37 tff(8,plain,
% 0.16/0.37 (^[B: $i, C: $i] : rewrite((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(9,plain,
% 0.16/0.37 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[8])).
% 0.16/0.37 tff(10,plain,
% 0.16/0.37 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.16/0.37 inference(transitivity,[status(thm)],[9, 7])).
% 0.16/0.37 tff(11,plain,
% 0.16/0.37 (^[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_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))), rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(12,plain,
% 0.16/0.37 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[11])).
% 0.16/0.37 tff(13,plain,
% 0.16/0.37 (^[B: $i, C: $i] : rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(14,plain,
% 0.16/0.37 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))) <=> ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.16/0.37 tff(15,plain,
% 0.16/0.37 (![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)))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(16,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')).
% 0.16/0.37 tff(17,plain,
% 0.16/0.37 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.16/0.37 tff(18,plain,(
% 0.16/0.37 ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))),
% 0.16/0.37 inference(skolemize,[status(sab)],[17])).
% 0.16/0.37 tff(19,plain,
% 0.16/0.37 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.16/0.37 tff(20,plain,
% 0.16/0.37 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.16/0.37 tff(21,plain,
% 0.16/0.37 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[20, 10])).
% 0.16/0.37 tff(22,plain,
% 0.16/0.37 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))) | (~((~((~(B!3 = empty_set)) | (member(B!3, B!3) <=> member(B!3, empty_set)))) | (~((B!3 = empty_set) | ((~member(tptp_fun_D_1(empty_set, B!3), B!3)) <=> member(tptp_fun_D_1(empty_set, B!3), empty_set))))))),
% 0.16/0.37 inference(quant_inst,[status(thm)],[])).
% 0.16/0.37 tff(23,plain,
% 0.16/0.37 (~((~((~(B!3 = empty_set)) | (member(B!3, B!3) <=> member(B!3, empty_set)))) | (~((B!3 = empty_set) | ((~member(tptp_fun_D_1(empty_set, B!3), B!3)) <=> member(tptp_fun_D_1(empty_set, B!3), empty_set)))))),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.16/0.37 tff(24,plain,
% 0.16/0.37 (((~((~(B!3 = empty_set)) | (member(B!3, B!3) <=> member(B!3, empty_set)))) | (~((B!3 = empty_set) | ((~member(tptp_fun_D_1(empty_set, B!3), B!3)) <=> member(tptp_fun_D_1(empty_set, B!3), empty_set))))) | ((B!3 = empty_set) | ((~member(tptp_fun_D_1(empty_set, B!3), B!3)) <=> member(tptp_fun_D_1(empty_set, B!3), empty_set)))),
% 0.16/0.37 inference(tautology,[status(thm)],[])).
% 0.16/0.37 tff(25,plain,
% 0.16/0.37 ((B!3 = empty_set) | ((~member(tptp_fun_D_1(empty_set, B!3), B!3)) <=> member(tptp_fun_D_1(empty_set, B!3), empty_set))),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.16/0.37 tff(26,assumption,(~not_equal(B!3, empty_set)), introduced(assumption)).
% 0.16/0.37 tff(27,plain,
% 0.16/0.37 (^[B: $i, C: $i] : refl((not_equal(B, C) <=> (~(B = C))) <=> (not_equal(B, C) <=> (~(B = C))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(28,plain,
% 0.16/0.37 (![B: $i, C: $i] : (not_equal(B, C) <=> (~(B = C))) <=> ![B: $i, C: $i] : (not_equal(B, C) <=> (~(B = C)))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[27])).
% 0.16/0.37 tff(29,plain,
% 0.16/0.37 (![B: $i, C: $i] : (not_equal(B, C) <=> (~(B = C))) <=> ![B: $i, C: $i] : (not_equal(B, C) <=> (~(B = C)))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(30,axiom,(![B: $i, C: $i] : (not_equal(B, C) <=> (~(B = C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_equal_defn')).
% 0.16/0.37 tff(31,plain,
% 0.16/0.37 (![B: $i, C: $i] : (not_equal(B, C) <=> (~(B = C)))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.16/0.37 tff(32,plain,(
% 0.16/0.37 ![B: $i, C: $i] : (not_equal(B, C) <=> (~(B = C)))),
% 0.16/0.37 inference(skolemize,[status(sab)],[31])).
% 0.16/0.37 tff(33,plain,
% 0.16/0.37 (![B: $i, C: $i] : (not_equal(B, C) <=> (~(B = C)))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.16/0.37 tff(34,plain,
% 0.16/0.37 ((~![B: $i, C: $i] : (not_equal(B, C) <=> (~(B = C)))) | (not_equal(B!3, empty_set) <=> (~(B!3 = empty_set)))),
% 0.16/0.37 inference(quant_inst,[status(thm)],[])).
% 0.16/0.37 tff(35,plain,
% 0.16/0.37 (not_equal(B!3, empty_set) <=> (~(B!3 = empty_set))),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.16/0.37 tff(36,plain,
% 0.16/0.37 ((~(not_equal(B!3, empty_set) <=> (~(B!3 = empty_set)))) | not_equal(B!3, empty_set) | (B!3 = empty_set)),
% 0.16/0.37 inference(tautology,[status(thm)],[])).
% 0.16/0.37 tff(37,plain,
% 0.16/0.37 (not_equal(B!3, empty_set) | (B!3 = empty_set)),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.16/0.37 tff(38,plain,
% 0.16/0.37 (B!3 = empty_set),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[37, 26])).
% 0.16/0.37 tff(39,plain,
% 0.16/0.37 (empty_set = B!3),
% 0.16/0.37 inference(symmetry,[status(thm)],[38])).
% 0.16/0.37 tff(40,plain,
% 0.16/0.37 (member(tptp_fun_D_0(B!3, B!3), empty_set) <=> member(tptp_fun_D_0(B!3, B!3), B!3)),
% 0.16/0.37 inference(monotonicity,[status(thm)],[39])).
% 0.16/0.37 tff(41,plain,
% 0.16/0.37 (member(tptp_fun_D_0(B!3, B!3), B!3) <=> member(tptp_fun_D_0(B!3, B!3), empty_set)),
% 0.16/0.37 inference(symmetry,[status(thm)],[40])).
% 0.16/0.37 tff(42,plain,
% 0.16/0.37 ((~(intersect(B!3, B!3) <=> not_equal(B!3, empty_set))) <=> ((~intersect(B!3, B!3)) <=> not_equal(B!3, empty_set))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(43,plain,
% 0.16/0.37 ((~![B: $i] : (intersect(B, B) <=> not_equal(B, empty_set))) <=> (~![B: $i] : (intersect(B, B) <=> not_equal(B, empty_set)))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(44,axiom,(~![B: $i] : (intersect(B, B) <=> not_equal(B, empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_th110')).
% 0.16/0.37 tff(45,plain,
% 0.16/0.37 (~![B: $i] : (intersect(B, B) <=> not_equal(B, empty_set))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.16/0.37 tff(46,plain,
% 0.16/0.37 (~![B: $i] : (intersect(B, B) <=> not_equal(B, empty_set))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[45, 43])).
% 0.16/0.37 tff(47,plain,
% 0.16/0.37 (~![B: $i] : (intersect(B, B) <=> not_equal(B, empty_set))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[46, 43])).
% 0.16/0.37 tff(48,plain,
% 0.16/0.37 (~![B: $i] : (intersect(B, B) <=> not_equal(B, empty_set))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.16/0.37 tff(49,plain,
% 0.16/0.37 (~![B: $i] : (intersect(B, B) <=> not_equal(B, empty_set))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[48, 43])).
% 0.16/0.37 tff(50,plain,
% 0.16/0.37 (~![B: $i] : (intersect(B, B) <=> not_equal(B, empty_set))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[49, 43])).
% 0.16/0.37 tff(51,plain,
% 0.16/0.37 (~![B: $i] : (intersect(B, B) <=> not_equal(B, empty_set))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.16/0.37 tff(52,plain,(
% 0.16/0.37 ~(intersect(B!3, B!3) <=> not_equal(B!3, empty_set))),
% 0.16/0.37 inference(skolemize,[status(sab)],[51])).
% 0.16/0.37 tff(53,plain,
% 0.16/0.37 ((~intersect(B!3, B!3)) <=> not_equal(B!3, empty_set)),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[52, 42])).
% 0.16/0.37 tff(54,plain,
% 0.16/0.37 (intersect(B!3, B!3) | not_equal(B!3, empty_set) | (~((~intersect(B!3, B!3)) <=> not_equal(B!3, empty_set)))),
% 0.16/0.37 inference(tautology,[status(thm)],[])).
% 0.16/0.37 tff(55,plain,
% 0.16/0.37 (intersect(B!3, B!3) | not_equal(B!3, empty_set)),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.16/0.37 tff(56,plain,
% 0.16/0.37 (intersect(B!3, B!3)),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[55, 26])).
% 0.16/0.37 tff(57,plain,
% 0.16/0.37 (^[B: $i, C: $i] : refl((~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))) <=> (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(58,plain,
% 0.16/0.37 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))) <=> ![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[57])).
% 0.16/0.37 tff(59,plain,
% 0.16/0.37 (^[B: $i, C: $i] : rewrite((~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))) <=> (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(60,plain,
% 0.16/0.37 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))) <=> ![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[59])).
% 0.16/0.37 tff(61,plain,
% 0.16/0.37 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))) <=> ![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))),
% 0.16/0.37 inference(transitivity,[status(thm)],[60, 58])).
% 0.16/0.37 tff(62,plain,
% 0.16/0.37 (^[B: $i, C: $i] : trans(monotonicity(rewrite(((~intersect(B, C)) | (member(tptp_fun_D_0(C, B), B) & member(tptp_fun_D_0(C, B), C))) <=> ((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))), rewrite((intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C)))) <=> (intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))), ((((~intersect(B, C)) | (member(tptp_fun_D_0(C, B), B) & member(tptp_fun_D_0(C, B), C))) & (intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C))))) <=> (((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C))))) & (intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))), rewrite((((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C))))) & (intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))) <=> (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))), ((((~intersect(B, C)) | (member(tptp_fun_D_0(C, B), B) & member(tptp_fun_D_0(C, B), C))) & (intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C))))) <=> (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(63,plain,
% 0.16/0.37 (![B: $i, C: $i] : (((~intersect(B, C)) | (member(tptp_fun_D_0(C, B), B) & member(tptp_fun_D_0(C, B), C))) & (intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C))))) <=> ![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[62])).
% 0.16/0.37 tff(64,plain,
% 0.16/0.37 (![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C))) <=> ![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C)))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(65,axiom,(![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersect_defn')).
% 0.16/0.38 tff(66,plain,
% 0.16/0.38 (![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C)))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.16/0.38 tff(67,plain,(
% 0.16/0.38 ![B: $i, C: $i] : (((~intersect(B, C)) | (member(tptp_fun_D_0(C, B), B) & member(tptp_fun_D_0(C, B), C))) & (intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C)))))),
% 0.16/0.38 inference(skolemize,[status(sab)],[66])).
% 0.16/0.38 tff(68,plain,
% 0.16/0.38 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.16/0.38 tff(69,plain,
% 0.16/0.38 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.16/0.38 tff(70,plain,
% 0.16/0.38 (((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~((~intersect(B!3, B!3)) | member(tptp_fun_D_0(B!3, B!3), B!3))) | (~(intersect(B!3, B!3) | ![D: $i] : (~member(D, B!3))))))) <=> ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~((~intersect(B!3, B!3)) | member(tptp_fun_D_0(B!3, B!3), B!3))) | (~(intersect(B!3, B!3) | ![D: $i] : (~member(D, B!3)))))))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(71,plain,
% 0.16/0.38 ((~((~((~intersect(B!3, B!3)) | (~((~member(tptp_fun_D_0(B!3, B!3), B!3)) | (~member(tptp_fun_D_0(B!3, B!3), B!3)))))) | (~(intersect(B!3, B!3) | ![D: $i] : ((~member(D, B!3)) | (~member(D, B!3))))))) <=> (~((~((~intersect(B!3, B!3)) | member(tptp_fun_D_0(B!3, B!3), B!3))) | (~(intersect(B!3, B!3) | ![D: $i] : (~member(D, B!3))))))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(72,plain,
% 0.16/0.38 (((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~((~intersect(B!3, B!3)) | (~((~member(tptp_fun_D_0(B!3, B!3), B!3)) | (~member(tptp_fun_D_0(B!3, B!3), B!3)))))) | (~(intersect(B!3, B!3) | ![D: $i] : ((~member(D, B!3)) | (~member(D, B!3)))))))) <=> ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~((~intersect(B!3, B!3)) | member(tptp_fun_D_0(B!3, B!3), B!3))) | (~(intersect(B!3, B!3) | ![D: $i] : (~member(D, B!3)))))))),
% 0.16/0.38 inference(monotonicity,[status(thm)],[71])).
% 0.16/0.38 tff(73,plain,
% 0.16/0.38 (((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~((~intersect(B!3, B!3)) | (~((~member(tptp_fun_D_0(B!3, B!3), B!3)) | (~member(tptp_fun_D_0(B!3, B!3), B!3)))))) | (~(intersect(B!3, B!3) | ![D: $i] : ((~member(D, B!3)) | (~member(D, B!3)))))))) <=> ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~((~intersect(B!3, B!3)) | member(tptp_fun_D_0(B!3, B!3), B!3))) | (~(intersect(B!3, B!3) | ![D: $i] : (~member(D, B!3)))))))),
% 0.16/0.38 inference(transitivity,[status(thm)],[72, 70])).
% 0.16/0.38 tff(74,plain,
% 0.16/0.38 ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~((~intersect(B!3, B!3)) | (~((~member(tptp_fun_D_0(B!3, B!3), B!3)) | (~member(tptp_fun_D_0(B!3, B!3), B!3)))))) | (~(intersect(B!3, B!3) | ![D: $i] : ((~member(D, B!3)) | (~member(D, B!3)))))))),
% 0.16/0.38 inference(quant_inst,[status(thm)],[])).
% 0.16/0.38 tff(75,plain,
% 0.16/0.38 ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~((~intersect(B!3, B!3)) | member(tptp_fun_D_0(B!3, B!3), B!3))) | (~(intersect(B!3, B!3) | ![D: $i] : (~member(D, B!3))))))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.16/0.38 tff(76,plain,
% 0.16/0.38 (~((~((~intersect(B!3, B!3)) | member(tptp_fun_D_0(B!3, B!3), B!3))) | (~(intersect(B!3, B!3) | ![D: $i] : (~member(D, B!3)))))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[75, 69])).
% 0.16/0.38 tff(77,plain,
% 0.16/0.38 (((~((~intersect(B!3, B!3)) | member(tptp_fun_D_0(B!3, B!3), B!3))) | (~(intersect(B!3, B!3) | ![D: $i] : (~member(D, B!3))))) | ((~intersect(B!3, B!3)) | member(tptp_fun_D_0(B!3, B!3), B!3))),
% 0.16/0.38 inference(tautology,[status(thm)],[])).
% 0.16/0.38 tff(78,plain,
% 0.16/0.38 ((~intersect(B!3, B!3)) | member(tptp_fun_D_0(B!3, B!3), B!3)),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.16/0.38 tff(79,plain,
% 0.16/0.38 ((~((~intersect(B!3, B!3)) | member(tptp_fun_D_0(B!3, B!3), B!3))) | (~intersect(B!3, B!3)) | member(tptp_fun_D_0(B!3, B!3), B!3)),
% 0.16/0.38 inference(tautology,[status(thm)],[])).
% 0.16/0.38 tff(80,plain,
% 0.16/0.38 ((~intersect(B!3, B!3)) | member(tptp_fun_D_0(B!3, B!3), B!3)),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.16/0.38 tff(81,plain,
% 0.16/0.38 (member(tptp_fun_D_0(B!3, B!3), B!3)),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[80, 56])).
% 0.16/0.38 tff(82,plain,
% 0.16/0.38 (member(tptp_fun_D_0(B!3, B!3), empty_set)),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[81, 41])).
% 0.16/0.38 tff(83,plain,
% 0.16/0.38 (^[B: $i] : refl((~member(B, empty_set)) <=> (~member(B, empty_set)))),
% 0.16/0.38 inference(bind,[status(th)],[])).
% 0.16/0.38 tff(84,plain,
% 0.16/0.38 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.16/0.38 inference(quant_intro,[status(thm)],[83])).
% 0.16/0.38 tff(85,plain,
% 0.16/0.38 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(86,axiom,(![B: $i] : (~member(B, empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','empty_set_defn')).
% 0.16/0.38 tff(87,plain,
% 0.16/0.38 (![B: $i] : (~member(B, empty_set))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.16/0.38 tff(88,plain,(
% 0.16/0.38 ![B: $i] : (~member(B, empty_set))),
% 0.16/0.38 inference(skolemize,[status(sab)],[87])).
% 0.16/0.38 tff(89,plain,
% 0.16/0.38 (![B: $i] : (~member(B, empty_set))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.16/0.38 tff(90,plain,
% 0.16/0.38 ((~![B: $i] : (~member(B, empty_set))) | (~member(tptp_fun_D_0(B!3, B!3), empty_set))),
% 0.16/0.38 inference(quant_inst,[status(thm)],[])).
% 0.16/0.38 tff(91,plain,
% 0.16/0.38 (~member(tptp_fun_D_0(B!3, B!3), empty_set)),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.16/0.38 tff(92,plain,
% 0.16/0.38 ($false),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[91, 82])).
% 0.16/0.38 tff(93,plain,(not_equal(B!3, empty_set)), inference(lemma,lemma(discharge,[]))).
% 0.16/0.38 tff(94,plain,
% 0.16/0.38 ((~(not_equal(B!3, empty_set) <=> (~(B!3 = empty_set)))) | (~not_equal(B!3, empty_set)) | (~(B!3 = empty_set))),
% 0.16/0.38 inference(tautology,[status(thm)],[])).
% 0.16/0.38 tff(95,plain,
% 0.16/0.38 ((~not_equal(B!3, empty_set)) | (~(B!3 = empty_set))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[94, 35])).
% 0.16/0.38 tff(96,plain,
% 0.16/0.38 (~(B!3 = empty_set)),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[95, 93])).
% 0.16/0.38 tff(97,plain,
% 0.16/0.38 ((~((B!3 = empty_set) | ((~member(tptp_fun_D_1(empty_set, B!3), B!3)) <=> member(tptp_fun_D_1(empty_set, B!3), empty_set)))) | (B!3 = empty_set) | ((~member(tptp_fun_D_1(empty_set, B!3), B!3)) <=> member(tptp_fun_D_1(empty_set, B!3), empty_set))),
% 0.16/0.38 inference(tautology,[status(thm)],[])).
% 0.16/0.38 tff(98,plain,
% 0.16/0.38 ((~((B!3 = empty_set) | ((~member(tptp_fun_D_1(empty_set, B!3), B!3)) <=> member(tptp_fun_D_1(empty_set, B!3), empty_set)))) | ((~member(tptp_fun_D_1(empty_set, B!3), B!3)) <=> member(tptp_fun_D_1(empty_set, B!3), empty_set))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.16/0.38 tff(99,plain,
% 0.16/0.38 ((~member(tptp_fun_D_1(empty_set, B!3), B!3)) <=> member(tptp_fun_D_1(empty_set, B!3), empty_set)),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[98, 25])).
% 0.16/0.38 tff(100,plain,
% 0.16/0.38 ((~![B: $i] : (~member(B, empty_set))) | (~member(tptp_fun_D_1(empty_set, B!3), empty_set))),
% 0.16/0.38 inference(quant_inst,[status(thm)],[])).
% 0.16/0.38 tff(101,plain,
% 0.16/0.38 (~member(tptp_fun_D_1(empty_set, B!3), empty_set)),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[100, 89])).
% 0.16/0.38 tff(102,plain,
% 0.16/0.38 ((~intersect(B!3, B!3)) | (~not_equal(B!3, empty_set)) | (~((~intersect(B!3, B!3)) <=> not_equal(B!3, empty_set)))),
% 0.16/0.38 inference(tautology,[status(thm)],[])).
% 0.16/0.38 tff(103,plain,
% 0.16/0.38 ((~intersect(B!3, B!3)) | (~not_equal(B!3, empty_set))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[102, 53])).
% 0.16/0.38 tff(104,plain,
% 0.16/0.38 (~intersect(B!3, B!3)),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[103, 93])).
% 0.16/0.38 tff(105,plain,
% 0.16/0.38 (((~((~intersect(B!3, B!3)) | member(tptp_fun_D_0(B!3, B!3), B!3))) | (~(intersect(B!3, B!3) | ![D: $i] : (~member(D, B!3))))) | (intersect(B!3, B!3) | ![D: $i] : (~member(D, B!3)))),
% 0.16/0.38 inference(tautology,[status(thm)],[])).
% 0.16/0.38 tff(106,plain,
% 0.16/0.38 (intersect(B!3, B!3) | ![D: $i] : (~member(D, B!3))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[105, 76])).
% 0.16/0.38 tff(107,plain,
% 0.16/0.38 ((~(intersect(B!3, B!3) | ![D: $i] : (~member(D, B!3)))) | intersect(B!3, B!3) | ![D: $i] : (~member(D, B!3))),
% 0.16/0.38 inference(tautology,[status(thm)],[])).
% 0.16/0.38 tff(108,plain,
% 0.16/0.38 (intersect(B!3, B!3) | ![D: $i] : (~member(D, B!3))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.16/0.38 tff(109,plain,
% 0.16/0.38 (![D: $i] : (~member(D, B!3))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[108, 104])).
% 0.16/0.38 tff(110,plain,
% 0.16/0.38 ((~![D: $i] : (~member(D, B!3))) | (~member(tptp_fun_D_1(empty_set, B!3), B!3))),
% 0.16/0.38 inference(quant_inst,[status(thm)],[])).
% 0.16/0.38 tff(111,plain,
% 0.16/0.38 (~member(tptp_fun_D_1(empty_set, B!3), B!3)),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.16/0.38 tff(112,plain,
% 0.16/0.38 ((~((~member(tptp_fun_D_1(empty_set, B!3), B!3)) <=> member(tptp_fun_D_1(empty_set, B!3), empty_set))) | member(tptp_fun_D_1(empty_set, B!3), B!3) | member(tptp_fun_D_1(empty_set, B!3), empty_set)),
% 0.16/0.38 inference(tautology,[status(thm)],[])).
% 0.16/0.38 tff(113,plain,
% 0.16/0.38 ($false),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[112, 111, 101, 99])).
% 0.16/0.38 % SZS output end Proof
%------------------------------------------------------------------------------