TSTP Solution File: SET637+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET637+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 05:07:27 EDT 2022
% Result : Theorem 210.57s 132.43s
% Output : Proof 210.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET637+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 06:27:39 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 210.57/132.43 % SZS status Theorem
% 210.57/132.43 % SZS output start Proof
% 210.57/132.43 tff(member_type, type, (
% 210.57/132.43 member: ( $i * $i ) > $o)).
% 210.57/132.43 tff(tptp_fun_B_4_type, type, (
% 210.57/132.43 tptp_fun_B_4: $i)).
% 210.57/132.43 tff(tptp_fun_D_1_type, type, (
% 210.57/132.43 tptp_fun_D_1: ( $i * $i ) > $i)).
% 210.57/132.43 tff(intersection_type, type, (
% 210.57/132.43 intersection: ( $i * $i ) > $i)).
% 210.57/132.43 tff(tptp_fun_C_3_type, type, (
% 210.57/132.43 tptp_fun_C_3: $i)).
% 210.57/132.43 tff(empty_set_type, type, (
% 210.57/132.43 empty_set: $i)).
% 210.57/132.43 tff(tptp_fun_D_0_type, type, (
% 210.57/132.43 tptp_fun_D_0: ( $i * $i ) > $i)).
% 210.57/132.43 tff(not_equal_type, type, (
% 210.57/132.43 not_equal: ( $i * $i ) > $o)).
% 210.57/132.43 tff(intersect_type, type, (
% 210.57/132.43 intersect: ( $i * $i ) > $o)).
% 210.57/132.43 tff(1,assumption,((~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4))), introduced(assumption)).
% 210.57/132.43 tff(2,assumption,(~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4))), introduced(assumption)).
% 210.57/132.43 tff(3,assumption,(~(member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4))), introduced(assumption)).
% 210.57/132.43 tff(4,plain,
% 210.57/132.43 (^[B: $i, C: $i, D: $i] : refl((member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B))))) <=> (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B))))))),
% 210.57/132.43 inference(bind,[status(th)],[])).
% 210.57/132.43 tff(5,plain,
% 210.57/132.43 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B))))) <=> ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))),
% 210.57/132.43 inference(quant_intro,[status(thm)],[4])).
% 210.57/132.43 tff(6,plain,
% 210.57/132.43 (^[B: $i, C: $i, D: $i] : rewrite((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B))))))),
% 210.57/132.43 inference(bind,[status(th)],[])).
% 210.57/132.43 tff(7,plain,
% 210.57/132.43 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))),
% 210.57/132.43 inference(quant_intro,[status(thm)],[6])).
% 210.57/132.43 tff(8,plain,
% 210.57/132.43 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 210.57/132.43 inference(rewrite,[status(thm)],[])).
% 210.57/132.43 tff(9,axiom,(![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','intersection_defn')).
% 210.57/132.43 tff(10,plain,
% 210.57/132.43 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 210.57/132.43 inference(modus_ponens,[status(thm)],[9, 8])).
% 210.57/132.43 tff(11,plain,(
% 210.57/132.43 ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 210.57/132.43 inference(skolemize,[status(sab)],[10])).
% 210.57/132.43 tff(12,plain,
% 210.57/132.43 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))),
% 210.57/132.43 inference(modus_ponens,[status(thm)],[11, 7])).
% 210.57/132.43 tff(13,plain,
% 210.57/132.43 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))),
% 210.57/132.43 inference(modus_ponens,[status(thm)],[12, 5])).
% 210.57/132.43 tff(14,plain,
% 210.57/132.43 (((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)))),
% 210.57/132.43 inference(rewrite,[status(thm)],[])).
% 210.57/132.43 tff(15,plain,
% 210.57/132.43 ((member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)) <=> (~((~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)) | (~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4))))) <=> (member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4))),
% 210.57/132.43 inference(rewrite,[status(thm)],[])).
% 210.57/132.43 tff(16,plain,
% 210.57/132.43 (((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)) <=> (~((~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)) | (~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)))),
% 210.57/132.43 inference(monotonicity,[status(thm)],[15])).
% 210.57/132.43 tff(17,plain,
% 210.57/132.43 (((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)) <=> (~((~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)) | (~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)))),
% 210.57/132.43 inference(transitivity,[status(thm)],[16, 14])).
% 210.57/132.43 tff(18,plain,
% 210.57/132.43 ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)) <=> (~((~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)) | (~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)))))),
% 210.57/132.43 inference(quant_inst,[status(thm)],[])).
% 210.57/132.43 tff(19,plain,
% 210.57/132.43 ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4))),
% 210.57/132.43 inference(modus_ponens,[status(thm)],[18, 17])).
% 210.57/132.43 tff(20,plain,
% 210.57/132.43 ($false),
% 210.57/132.43 inference(unit_resolution,[status(thm)],[19, 13, 3])).
% 210.57/132.43 tff(21,plain,(member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)), inference(lemma,lemma(discharge,[]))).
% 210.57/132.43 tff(22,plain,
% 210.57/132.43 ((~(member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4))) | member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)) | (~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4))),
% 210.57/132.43 inference(tautology,[status(thm)],[])).
% 210.57/132.43 tff(23,plain,
% 210.57/132.43 (member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)) | (~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4))),
% 210.57/132.43 inference(unit_resolution,[status(thm)],[22, 21])).
% 210.57/132.43 tff(24,plain,
% 210.57/132.43 (~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)),
% 210.57/132.43 inference(unit_resolution,[status(thm)],[23, 2])).
% 210.57/132.43 tff(25,plain,
% 210.57/132.43 ((~((~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))) | member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4) | member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4))),
% 210.57/132.43 inference(tautology,[status(thm)],[])).
% 210.57/132.43 tff(26,plain,
% 210.57/132.43 ($false),
% 210.57/132.43 inference(unit_resolution,[status(thm)],[25, 24, 2, 1])).
% 210.57/132.43 tff(27,plain,(member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)) | (~((~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))), inference(lemma,lemma(discharge,[]))).
% 210.57/132.43 tff(28,plain,
% 210.57/132.43 (member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4))),
% 210.57/132.43 inference(unit_resolution,[status(thm)],[27, 1])).
% 210.57/132.43 tff(29,plain,
% 210.57/132.43 ((~((~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)) | (~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))),
% 210.57/132.43 inference(tautology,[status(thm)],[])).
% 210.57/132.43 tff(30,plain,
% 210.57/132.43 (~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)),
% 210.57/132.43 inference(unit_resolution,[status(thm)],[29, 28, 1])).
% 210.57/132.43 tff(31,plain,
% 210.57/132.43 ((~(member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4))) | (~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4))) | member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)),
% 210.57/132.43 inference(tautology,[status(thm)],[])).
% 210.57/132.43 tff(32,plain,
% 210.57/132.43 ((~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4))) | member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)),
% 210.57/132.43 inference(unit_resolution,[status(thm)],[31, 21])).
% 210.57/132.43 tff(33,plain,
% 210.57/132.43 ($false),
% 210.57/132.43 inference(unit_resolution,[status(thm)],[32, 30, 28])).
% 210.57/132.43 tff(34,plain,(~((~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))), inference(lemma,lemma(discharge,[]))).
% 210.57/132.43 tff(35,plain,
% 210.57/132.43 (^[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)))))))),
% 210.57/132.43 inference(bind,[status(th)],[])).
% 210.57/132.43 tff(36,plain,
% 210.57/132.43 (![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))))))),
% 210.57/132.43 inference(quant_intro,[status(thm)],[35])).
% 210.57/132.43 tff(37,plain,
% 210.57/132.43 (![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))))))),
% 210.57/132.43 inference(pull_quant,[status(thm)],[])).
% 210.57/132.43 tff(38,plain,
% 210.57/132.43 (^[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))))))))),
% 210.57/132.43 inference(bind,[status(th)],[])).
% 210.57/132.43 tff(39,plain,
% 210.57/132.43 (![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))))))),
% 210.57/132.43 inference(quant_intro,[status(thm)],[38])).
% 210.57/132.43 tff(40,plain,
% 210.57/132.43 (![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))))))),
% 210.57/132.43 inference(transitivity,[status(thm)],[39, 37])).
% 210.57/132.43 tff(41,plain,
% 210.57/132.43 (![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))))))),
% 210.57/132.43 inference(transitivity,[status(thm)],[40, 36])).
% 210.57/132.43 tff(42,plain,
% 210.57/132.43 (^[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)))))))),
% 210.57/132.43 inference(bind,[status(th)],[])).
% 210.57/132.43 tff(43,plain,
% 210.57/132.43 (![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))))))),
% 210.57/132.43 inference(quant_intro,[status(thm)],[42])).
% 210.57/132.43 tff(44,plain,
% 210.57/132.43 (![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))))))),
% 210.57/132.43 inference(transitivity,[status(thm)],[43, 41])).
% 210.57/132.43 tff(45,plain,
% 210.57/132.43 (^[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))))))))),
% 210.57/132.43 inference(bind,[status(th)],[])).
% 210.57/132.43 tff(46,plain,
% 210.57/132.43 (![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))))))),
% 210.57/132.43 inference(quant_intro,[status(thm)],[45])).
% 210.57/132.43 tff(47,plain,
% 210.57/132.43 (^[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)))))),
% 210.57/132.43 inference(bind,[status(th)],[])).
% 210.57/132.43 tff(48,plain,
% 210.57/132.43 (![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))))),
% 210.57/132.43 inference(quant_intro,[status(thm)],[47])).
% 210.57/132.43 tff(49,plain,
% 210.57/132.43 (![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)))),
% 210.57/132.43 inference(rewrite,[status(thm)],[])).
% 210.57/132.43 tff(50,axiom,(![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','equal_member_defn')).
% 210.57/132.43 tff(51,plain,
% 210.57/132.43 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 210.57/132.43 inference(modus_ponens,[status(thm)],[50, 49])).
% 210.57/132.43 tff(52,plain,(
% 210.57/132.43 ![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)))))),
% 210.57/132.43 inference(skolemize,[status(sab)],[51])).
% 210.57/132.43 tff(53,plain,
% 210.57/132.43 (![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))))),
% 210.57/132.43 inference(modus_ponens,[status(thm)],[52, 48])).
% 210.57/132.43 tff(54,plain,
% 210.57/132.43 (![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))))))),
% 210.57/132.43 inference(modus_ponens,[status(thm)],[53, 46])).
% 210.57/132.43 tff(55,plain,
% 210.57/132.43 (![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))))))),
% 210.57/132.43 inference(modus_ponens,[status(thm)],[54, 44])).
% 210.57/132.43 tff(56,plain,
% 210.57/132.43 ((~![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!4 = intersection(B!4, B!4))) | (member(tptp_fun_D_0(B!4, B!4), B!4) <=> member(tptp_fun_D_0(B!4, B!4), intersection(B!4, B!4))))) | (~((B!4 = intersection(B!4, B!4)) | ((~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))))))),
% 210.57/132.43 inference(quant_inst,[status(thm)],[])).
% 210.57/132.43 tff(57,plain,
% 210.57/132.43 (~((~((~(B!4 = intersection(B!4, B!4))) | (member(tptp_fun_D_0(B!4, B!4), B!4) <=> member(tptp_fun_D_0(B!4, B!4), intersection(B!4, B!4))))) | (~((B!4 = intersection(B!4, B!4)) | ((~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))))),
% 210.57/132.43 inference(unit_resolution,[status(thm)],[56, 55])).
% 210.57/132.43 tff(58,plain,
% 210.57/132.43 (((~((~(B!4 = intersection(B!4, B!4))) | (member(tptp_fun_D_0(B!4, B!4), B!4) <=> member(tptp_fun_D_0(B!4, B!4), intersection(B!4, B!4))))) | (~((B!4 = intersection(B!4, B!4)) | ((~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))))) | ((B!4 = intersection(B!4, B!4)) | ((~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))),
% 210.57/132.43 inference(tautology,[status(thm)],[])).
% 210.57/132.43 tff(59,plain,
% 210.57/132.43 ((B!4 = intersection(B!4, B!4)) | ((~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))),
% 210.57/132.43 inference(unit_resolution,[status(thm)],[58, 57])).
% 210.57/132.43 tff(60,plain,
% 210.57/132.43 ((~((B!4 = intersection(B!4, B!4)) | ((~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4))))) | (B!4 = intersection(B!4, B!4)) | ((~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))),
% 210.57/132.43 inference(tautology,[status(thm)],[])).
% 210.57/132.43 tff(61,plain,
% 210.57/132.43 ((B!4 = intersection(B!4, B!4)) | ((~member(tptp_fun_D_1(intersection(B!4, B!4), B!4), B!4)) <=> member(tptp_fun_D_1(intersection(B!4, B!4), B!4), intersection(B!4, B!4)))),
% 210.57/132.43 inference(unit_resolution,[status(thm)],[60, 59])).
% 210.57/132.43 tff(62,plain,
% 210.57/132.43 (B!4 = intersection(B!4, B!4)),
% 210.57/132.43 inference(unit_resolution,[status(thm)],[61, 34])).
% 210.57/132.43 tff(63,plain,
% 210.57/132.43 (member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), B!4) <=> member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(B!4, B!4))),
% 210.57/132.43 inference(monotonicity,[status(thm)],[62])).
% 210.57/132.43 tff(64,plain,
% 210.57/132.43 (member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(B!4, B!4)) <=> member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), B!4)),
% 210.57/132.43 inference(symmetry,[status(thm)],[63])).
% 210.57/132.43 tff(65,plain,
% 210.57/132.43 ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(intersection(B!4, B!4), C!3)) <=> (~((~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), C!3)) | (~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(B!4, B!4))))))),
% 210.57/132.43 inference(quant_inst,[status(thm)],[])).
% 210.57/132.43 tff(66,plain,
% 210.57/132.43 (member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(intersection(B!4, B!4), C!3)) <=> (~((~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), C!3)) | (~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(B!4, B!4)))))),
% 210.57/132.43 inference(unit_resolution,[status(thm)],[65, 13])).
% 210.57/132.43 tff(67,plain,
% 210.57/132.43 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 210.57/132.43 inference(bind,[status(th)],[])).
% 210.57/132.43 tff(68,plain,
% 210.57/132.43 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 210.57/132.43 inference(quant_intro,[status(thm)],[67])).
% 210.57/132.43 tff(69,plain,
% 210.57/132.43 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 210.57/132.43 inference(rewrite,[status(thm)],[])).
% 210.57/132.43 tff(70,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 210.57/132.43 tff(71,plain,
% 210.57/132.43 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 210.57/132.43 inference(modus_ponens,[status(thm)],[70, 69])).
% 210.57/132.43 tff(72,plain,(
% 210.57/132.43 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 210.57/132.43 inference(skolemize,[status(sab)],[71])).
% 210.57/132.43 tff(73,plain,
% 210.57/132.43 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 210.57/132.43 inference(modus_ponens,[status(thm)],[72, 68])).
% 210.57/132.43 tff(74,plain,
% 210.57/132.43 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(B!4, C!3) = intersection(C!3, B!4))),
% 210.57/132.43 inference(quant_inst,[status(thm)],[])).
% 210.57/132.43 tff(75,plain,
% 210.57/132.43 (intersection(B!4, C!3) = intersection(C!3, B!4)),
% 210.57/132.43 inference(unit_resolution,[status(thm)],[74, 73])).
% 210.57/132.43 tff(76,plain,
% 210.57/132.43 (intersection(B!4, B!4) = B!4),
% 210.57/132.43 inference(symmetry,[status(thm)],[62])).
% 210.57/132.43 tff(77,plain,
% 210.57/132.43 (intersection(intersection(B!4, B!4), C!3) = intersection(B!4, C!3)),
% 210.57/132.43 inference(monotonicity,[status(thm)],[76])).
% 210.57/132.43 tff(78,plain,
% 210.57/132.43 (intersection(intersection(B!4, B!4), C!3) = intersection(C!3, B!4)),
% 210.57/132.43 inference(transitivity,[status(thm)],[77, 75])).
% 210.57/132.43 tff(79,plain,
% 210.57/132.43 (member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(intersection(B!4, B!4), C!3)) <=> member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(C!3, B!4))),
% 210.57/132.43 inference(monotonicity,[status(thm)],[78])).
% 210.57/132.43 tff(80,plain,
% 210.57/132.43 (member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(C!3, B!4)) <=> member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(intersection(B!4, B!4), C!3))),
% 210.57/132.43 inference(symmetry,[status(thm)],[79])).
% 210.57/132.43 tff(81,plain,
% 210.57/132.43 (((~![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))))))) | (~((~((intersection(C!3, B!4) = intersection(empty_set, B!4)) | ((~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(C!3, B!4))) <=> member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(empty_set, B!4))))) | (~((~(intersection(C!3, B!4) = intersection(empty_set, B!4))) | (member(tptp_fun_D_1(intersection(intersection(tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3)), tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3))), intersection(B!4, B!4)), C!3), intersection(C!3, B!4)) <=> member(tptp_fun_D_1(intersection(intersection(tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3)), tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3))), intersection(B!4, B!4)), C!3), intersection(empty_set, B!4)))))))) <=> ((~![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))))))) | (~((~((intersection(C!3, B!4) = intersection(empty_set, B!4)) | ((~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(C!3, B!4))) <=> member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(empty_set, B!4))))) | (~((~(intersection(C!3, B!4) = intersection(empty_set, B!4))) | (member(tptp_fun_D_1(intersection(intersection(tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3)), tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3))), intersection(B!4, B!4)), C!3), intersection(C!3, B!4)) <=> member(tptp_fun_D_1(intersection(intersection(tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3)), tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3))), intersection(B!4, B!4)), C!3), intersection(empty_set, B!4))))))))),
% 210.57/132.43 inference(rewrite,[status(thm)],[])).
% 210.57/132.43 tff(82,plain,
% 210.57/132.43 ((~((~((~(intersection(C!3, B!4) = intersection(empty_set, B!4))) | (member(tptp_fun_D_1(intersection(intersection(tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3)), tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3))), intersection(B!4, B!4)), C!3), intersection(C!3, B!4)) <=> member(tptp_fun_D_1(intersection(intersection(tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3)), tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3))), intersection(B!4, B!4)), C!3), intersection(empty_set, B!4))))) | (~((intersection(C!3, B!4) = intersection(empty_set, B!4)) | ((~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(C!3, B!4))) <=> member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(empty_set, B!4))))))) <=> (~((~((intersection(C!3, B!4) = intersection(empty_set, B!4)) | ((~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(C!3, B!4))) <=> member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(empty_set, B!4))))) | (~((~(intersection(C!3, B!4) = intersection(empty_set, B!4))) | (member(tptp_fun_D_1(intersection(intersection(tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3)), tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3))), intersection(B!4, B!4)), C!3), intersection(C!3, B!4)) <=> member(tptp_fun_D_1(intersection(intersection(tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3)), tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3))), intersection(B!4, B!4)), C!3), intersection(empty_set, B!4)))))))),
% 210.57/132.44 inference(rewrite,[status(thm)],[])).
% 210.57/132.44 tff(83,plain,
% 210.57/132.44 (((~![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))))))) | (~((~((~(intersection(C!3, B!4) = intersection(empty_set, B!4))) | (member(tptp_fun_D_1(intersection(intersection(tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3)), tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3))), intersection(B!4, B!4)), C!3), intersection(C!3, B!4)) <=> member(tptp_fun_D_1(intersection(intersection(tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3)), tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3))), intersection(B!4, B!4)), C!3), intersection(empty_set, B!4))))) | (~((intersection(C!3, B!4) = intersection(empty_set, B!4)) | ((~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(C!3, B!4))) <=> member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(empty_set, B!4)))))))) <=> ((~![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))))))) | (~((~((intersection(C!3, B!4) = intersection(empty_set, B!4)) | ((~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(C!3, B!4))) <=> member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(empty_set, B!4))))) | (~((~(intersection(C!3, B!4) = intersection(empty_set, B!4))) | (member(tptp_fun_D_1(intersection(intersection(tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3)), tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3))), intersection(B!4, B!4)), C!3), intersection(C!3, B!4)) <=> member(tptp_fun_D_1(intersection(intersection(tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3)), tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3))), intersection(B!4, B!4)), C!3), intersection(empty_set, B!4))))))))),
% 210.57/132.44 inference(monotonicity,[status(thm)],[82])).
% 210.57/132.44 tff(84,plain,
% 210.57/132.44 (((~![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))))))) | (~((~((~(intersection(C!3, B!4) = intersection(empty_set, B!4))) | (member(tptp_fun_D_1(intersection(intersection(tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3)), tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3))), intersection(B!4, B!4)), C!3), intersection(C!3, B!4)) <=> member(tptp_fun_D_1(intersection(intersection(tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3)), tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3))), intersection(B!4, B!4)), C!3), intersection(empty_set, B!4))))) | (~((intersection(C!3, B!4) = intersection(empty_set, B!4)) | ((~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(C!3, B!4))) <=> member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(empty_set, B!4)))))))) <=> ((~![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))))))) | (~((~((intersection(C!3, B!4) = intersection(empty_set, B!4)) | ((~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(C!3, B!4))) <=> member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(empty_set, B!4))))) | (~((~(intersection(C!3, B!4) = intersection(empty_set, B!4))) | (member(tptp_fun_D_1(intersection(intersection(tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3)), tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3))), intersection(B!4, B!4)), C!3), intersection(C!3, B!4)) <=> member(tptp_fun_D_1(intersection(intersection(tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3)), tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3))), intersection(B!4, B!4)), C!3), intersection(empty_set, B!4))))))))),
% 210.57/132.44 inference(transitivity,[status(thm)],[83, 81])).
% 210.57/132.44 tff(85,plain,
% 210.57/132.44 ((~![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))))))) | (~((~((~(intersection(C!3, B!4) = intersection(empty_set, B!4))) | (member(tptp_fun_D_1(intersection(intersection(tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3)), tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3))), intersection(B!4, B!4)), C!3), intersection(C!3, B!4)) <=> member(tptp_fun_D_1(intersection(intersection(tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3)), tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3))), intersection(B!4, B!4)), C!3), intersection(empty_set, B!4))))) | (~((intersection(C!3, B!4) = intersection(empty_set, B!4)) | ((~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(C!3, B!4))) <=> member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(empty_set, B!4)))))))),
% 210.57/132.44 inference(quant_inst,[status(thm)],[])).
% 210.57/132.44 tff(86,plain,
% 210.57/132.44 ((~![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))))))) | (~((~((intersection(C!3, B!4) = intersection(empty_set, B!4)) | ((~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(C!3, B!4))) <=> member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(empty_set, B!4))))) | (~((~(intersection(C!3, B!4) = intersection(empty_set, B!4))) | (member(tptp_fun_D_1(intersection(intersection(tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3)), tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3))), intersection(B!4, B!4)), C!3), intersection(C!3, B!4)) <=> member(tptp_fun_D_1(intersection(intersection(tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3)), tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3))), intersection(B!4, B!4)), C!3), intersection(empty_set, B!4)))))))),
% 210.57/132.44 inference(modus_ponens,[status(thm)],[85, 84])).
% 210.57/132.44 tff(87,plain,
% 210.57/132.44 (~((~((intersection(C!3, B!4) = intersection(empty_set, B!4)) | ((~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(C!3, B!4))) <=> member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(empty_set, B!4))))) | (~((~(intersection(C!3, B!4) = intersection(empty_set, B!4))) | (member(tptp_fun_D_1(intersection(intersection(tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3)), tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3))), intersection(B!4, B!4)), C!3), intersection(C!3, B!4)) <=> member(tptp_fun_D_1(intersection(intersection(tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3)), tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3))), intersection(B!4, B!4)), C!3), intersection(empty_set, B!4))))))),
% 210.57/132.44 inference(unit_resolution,[status(thm)],[86, 55])).
% 210.57/132.44 tff(88,plain,
% 210.57/132.44 (((~((intersection(C!3, B!4) = intersection(empty_set, B!4)) | ((~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(C!3, B!4))) <=> member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(empty_set, B!4))))) | (~((~(intersection(C!3, B!4) = intersection(empty_set, B!4))) | (member(tptp_fun_D_1(intersection(intersection(tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3)), tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3))), intersection(B!4, B!4)), C!3), intersection(C!3, B!4)) <=> member(tptp_fun_D_1(intersection(intersection(tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3)), tptp_fun_D_1(intersection(empty_set, B!4), tptp_fun_D_1(B!4, C!3))), intersection(B!4, B!4)), C!3), intersection(empty_set, B!4)))))) | ((intersection(C!3, B!4) = intersection(empty_set, B!4)) | ((~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(C!3, B!4))) <=> member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(empty_set, B!4))))),
% 210.57/132.44 inference(tautology,[status(thm)],[])).
% 210.57/132.44 tff(89,plain,
% 210.57/132.44 ((intersection(C!3, B!4) = intersection(empty_set, B!4)) | ((~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(C!3, B!4))) <=> member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(empty_set, B!4)))),
% 210.57/132.44 inference(unit_resolution,[status(thm)],[88, 87])).
% 210.57/132.44 tff(90,plain,
% 210.57/132.44 ((~![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))))))) | (~((~((~(intersection(empty_set, B!4) = empty_set)) | (member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), intersection(empty_set, B!4)) <=> member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), empty_set)))) | (~((intersection(empty_set, B!4) = empty_set) | ((~member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), intersection(empty_set, B!4))) <=> member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), empty_set))))))),
% 210.57/132.44 inference(quant_inst,[status(thm)],[])).
% 210.57/132.44 tff(91,plain,
% 210.57/132.44 (~((~((~(intersection(empty_set, B!4) = empty_set)) | (member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), intersection(empty_set, B!4)) <=> member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), empty_set)))) | (~((intersection(empty_set, B!4) = empty_set) | ((~member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), intersection(empty_set, B!4))) <=> member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), empty_set)))))),
% 210.57/132.44 inference(unit_resolution,[status(thm)],[90, 55])).
% 210.57/132.44 tff(92,plain,
% 210.57/132.44 (((~((~(intersection(empty_set, B!4) = empty_set)) | (member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), intersection(empty_set, B!4)) <=> member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), empty_set)))) | (~((intersection(empty_set, B!4) = empty_set) | ((~member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), intersection(empty_set, B!4))) <=> member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), empty_set))))) | ((intersection(empty_set, B!4) = empty_set) | ((~member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), intersection(empty_set, B!4))) <=> member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), empty_set)))),
% 210.57/132.44 inference(tautology,[status(thm)],[])).
% 210.57/132.44 tff(93,plain,
% 210.57/132.44 ((intersection(empty_set, B!4) = empty_set) | ((~member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), intersection(empty_set, B!4))) <=> member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), empty_set))),
% 210.57/132.44 inference(unit_resolution,[status(thm)],[92, 91])).
% 210.57/132.44 tff(94,plain,
% 210.57/132.44 ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), intersection(empty_set, B!4)) <=> (~((~member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), B!4)) | (~member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), empty_set)))))),
% 210.57/132.44 inference(quant_inst,[status(thm)],[])).
% 210.57/132.44 tff(95,plain,
% 210.57/132.44 (member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), intersection(empty_set, B!4)) <=> (~((~member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), B!4)) | (~member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), empty_set))))),
% 210.57/132.44 inference(unit_resolution,[status(thm)],[94, 13])).
% 210.57/132.44 tff(96,assumption,((~member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), intersection(empty_set, B!4))) <=> member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), empty_set)), introduced(assumption)).
% 210.57/132.44 tff(97,plain,
% 210.57/132.44 (^[B: $i] : refl((~member(B, empty_set)) <=> (~member(B, empty_set)))),
% 210.57/132.44 inference(bind,[status(th)],[])).
% 210.57/132.44 tff(98,plain,
% 210.57/132.44 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 210.57/132.44 inference(quant_intro,[status(thm)],[97])).
% 210.57/132.44 tff(99,plain,
% 210.57/132.44 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 210.57/132.44 inference(rewrite,[status(thm)],[])).
% 210.57/132.44 tff(100,axiom,(![B: $i] : (~member(B, empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','empty_set_defn')).
% 210.57/132.44 tff(101,plain,
% 210.57/132.44 (![B: $i] : (~member(B, empty_set))),
% 210.57/132.44 inference(modus_ponens,[status(thm)],[100, 99])).
% 210.57/132.44 tff(102,plain,(
% 210.57/132.44 ![B: $i] : (~member(B, empty_set))),
% 210.57/132.44 inference(skolemize,[status(sab)],[101])).
% 210.57/132.44 tff(103,plain,
% 210.57/132.44 (![B: $i] : (~member(B, empty_set))),
% 210.57/132.44 inference(modus_ponens,[status(thm)],[102, 98])).
% 210.57/132.44 tff(104,plain,
% 210.57/132.44 ((~![B: $i] : (~member(B, empty_set))) | (~member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), empty_set))),
% 210.57/132.44 inference(quant_inst,[status(thm)],[])).
% 210.57/132.44 tff(105,plain,
% 210.57/132.44 (~member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), empty_set)),
% 210.57/132.44 inference(unit_resolution,[status(thm)],[104, 103])).
% 210.57/132.44 tff(106,plain,
% 210.57/132.44 ((~((~member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), intersection(empty_set, B!4))) <=> member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), empty_set))) | member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), intersection(empty_set, B!4)) | member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), empty_set)),
% 210.57/132.44 inference(tautology,[status(thm)],[])).
% 210.57/132.44 tff(107,plain,
% 210.57/132.44 (member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), intersection(empty_set, B!4))),
% 210.57/132.44 inference(unit_resolution,[status(thm)],[106, 105, 96])).
% 210.57/132.44 tff(108,plain,
% 210.57/132.44 (((~member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), B!4)) | (~member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), empty_set))) | member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), empty_set)),
% 210.57/132.44 inference(tautology,[status(thm)],[])).
% 210.57/132.44 tff(109,plain,
% 210.57/132.44 ((~member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), B!4)) | (~member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), empty_set))),
% 210.57/132.44 inference(unit_resolution,[status(thm)],[108, 105])).
% 210.57/132.44 tff(110,plain,
% 210.57/132.44 ((~(member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), intersection(empty_set, B!4)) <=> (~((~member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), B!4)) | (~member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), empty_set)))))) | (~member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), intersection(empty_set, B!4))) | (~((~member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), B!4)) | (~member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), empty_set))))),
% 210.57/132.44 inference(tautology,[status(thm)],[])).
% 210.57/132.44 tff(111,plain,
% 210.57/132.44 ((~(member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), intersection(empty_set, B!4)) <=> (~((~member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), B!4)) | (~member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), empty_set)))))) | (~member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), intersection(empty_set, B!4)))),
% 210.57/132.44 inference(unit_resolution,[status(thm)],[110, 109])).
% 210.57/132.44 tff(112,plain,
% 210.57/132.44 ($false),
% 210.57/132.44 inference(unit_resolution,[status(thm)],[111, 107, 95])).
% 210.57/132.44 tff(113,plain,(~((~member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), intersection(empty_set, B!4))) <=> member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), empty_set))), inference(lemma,lemma(discharge,[]))).
% 210.57/132.44 tff(114,plain,
% 210.57/132.44 ((~((intersection(empty_set, B!4) = empty_set) | ((~member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), intersection(empty_set, B!4))) <=> member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), empty_set)))) | (intersection(empty_set, B!4) = empty_set) | ((~member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), intersection(empty_set, B!4))) <=> member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), empty_set))),
% 210.57/132.44 inference(tautology,[status(thm)],[])).
% 210.57/132.44 tff(115,plain,
% 210.57/132.44 ((~((intersection(empty_set, B!4) = empty_set) | ((~member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), intersection(empty_set, B!4))) <=> member(tptp_fun_D_1(empty_set, intersection(empty_set, B!4)), empty_set)))) | (intersection(empty_set, B!4) = empty_set)),
% 210.57/132.44 inference(unit_resolution,[status(thm)],[114, 113])).
% 210.57/132.44 tff(116,plain,
% 210.57/132.44 (intersection(empty_set, B!4) = empty_set),
% 210.57/132.44 inference(unit_resolution,[status(thm)],[115, 93])).
% 210.57/132.44 tff(117,plain,
% 210.57/132.44 (intersection(C!3, B!4) = intersection(B!4, C!3)),
% 210.57/132.44 inference(symmetry,[status(thm)],[75])).
% 210.57/132.44 tff(118,plain,
% 210.57/132.44 ((intersection(C!3, B!4) = intersection(empty_set, B!4)) <=> (intersection(B!4, C!3) = empty_set)),
% 210.57/132.44 inference(monotonicity,[status(thm)],[117, 116])).
% 210.57/132.44 tff(119,plain,
% 210.57/132.44 ((intersection(B!4, C!3) = empty_set) <=> (intersection(C!3, B!4) = intersection(empty_set, B!4))),
% 210.57/132.44 inference(symmetry,[status(thm)],[118])).
% 210.57/132.44 tff(120,plain,
% 210.57/132.44 ((~(intersection(B!4, C!3) = empty_set)) <=> (~(intersection(C!3, B!4) = intersection(empty_set, B!4)))),
% 210.57/132.44 inference(monotonicity,[status(thm)],[119])).
% 210.57/132.44 tff(121,assumption,(~not_equal(intersection(B!4, C!3), empty_set)), introduced(assumption)).
% 210.57/132.44 tff(122,plain,
% 210.57/132.44 (^[B: $i, C: $i] : refl((not_equal(B, C) <=> (~(B = C))) <=> (not_equal(B, C) <=> (~(B = C))))),
% 210.57/132.44 inference(bind,[status(th)],[])).
% 210.57/132.44 tff(123,plain,
% 210.57/132.44 (![B: $i, C: $i] : (not_equal(B, C) <=> (~(B = C))) <=> ![B: $i, C: $i] : (not_equal(B, C) <=> (~(B = C)))),
% 210.57/132.44 inference(quant_intro,[status(thm)],[122])).
% 210.57/132.44 tff(124,plain,
% 210.57/132.44 (![B: $i, C: $i] : (not_equal(B, C) <=> (~(B = C))) <=> ![B: $i, C: $i] : (not_equal(B, C) <=> (~(B = C)))),
% 210.57/132.44 inference(rewrite,[status(thm)],[])).
% 210.57/132.44 tff(125,axiom,(![B: $i, C: $i] : (not_equal(B, C) <=> (~(B = C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_equal_defn')).
% 210.57/132.44 tff(126,plain,
% 210.57/132.44 (![B: $i, C: $i] : (not_equal(B, C) <=> (~(B = C)))),
% 210.57/132.44 inference(modus_ponens,[status(thm)],[125, 124])).
% 210.57/132.44 tff(127,plain,(
% 210.57/132.44 ![B: $i, C: $i] : (not_equal(B, C) <=> (~(B = C)))),
% 210.57/132.44 inference(skolemize,[status(sab)],[126])).
% 210.57/132.44 tff(128,plain,
% 210.57/132.44 (![B: $i, C: $i] : (not_equal(B, C) <=> (~(B = C)))),
% 210.57/132.44 inference(modus_ponens,[status(thm)],[127, 123])).
% 210.57/132.44 tff(129,plain,
% 210.57/132.44 ((~![B: $i, C: $i] : (not_equal(B, C) <=> (~(B = C)))) | (not_equal(intersection(B!4, C!3), empty_set) <=> (~(intersection(B!4, C!3) = empty_set)))),
% 210.57/132.44 inference(quant_inst,[status(thm)],[])).
% 210.57/132.44 tff(130,plain,
% 210.57/132.44 (not_equal(intersection(B!4, C!3), empty_set) <=> (~(intersection(B!4, C!3) = empty_set))),
% 210.57/132.44 inference(unit_resolution,[status(thm)],[129, 128])).
% 210.57/132.44 tff(131,plain,
% 210.57/132.44 ((~(not_equal(intersection(B!4, C!3), empty_set) <=> (~(intersection(B!4, C!3) = empty_set)))) | not_equal(intersection(B!4, C!3), empty_set) | (intersection(B!4, C!3) = empty_set)),
% 210.57/132.44 inference(tautology,[status(thm)],[])).
% 210.57/132.44 tff(132,plain,
% 210.57/132.44 (not_equal(intersection(B!4, C!3), empty_set) | (intersection(B!4, C!3) = empty_set)),
% 210.57/132.44 inference(unit_resolution,[status(thm)],[131, 130])).
% 210.57/132.44 tff(133,plain,
% 210.57/132.44 (intersection(B!4, C!3) = empty_set),
% 210.57/132.44 inference(unit_resolution,[status(thm)],[132, 121])).
% 210.57/132.44 tff(134,plain,
% 210.57/132.44 (intersection(C!3, B!4) = empty_set),
% 210.57/132.44 inference(transitivity,[status(thm)],[117, 133])).
% 210.57/132.44 tff(135,plain,
% 210.57/132.44 (member(tptp_fun_D_0(C!3, B!4), intersection(C!3, B!4)) <=> member(tptp_fun_D_0(C!3, B!4), empty_set)),
% 210.57/132.44 inference(monotonicity,[status(thm)],[134])).
% 210.57/132.44 tff(136,plain,
% 210.57/132.44 (member(tptp_fun_D_0(C!3, B!4), empty_set) <=> member(tptp_fun_D_0(C!3, B!4), intersection(C!3, B!4))),
% 210.57/132.44 inference(symmetry,[status(thm)],[135])).
% 210.57/132.44 tff(137,plain,
% 210.57/132.44 ((~member(tptp_fun_D_0(C!3, B!4), empty_set)) <=> (~member(tptp_fun_D_0(C!3, B!4), intersection(C!3, B!4)))),
% 210.57/132.44 inference(monotonicity,[status(thm)],[136])).
% 210.57/132.44 tff(138,plain,
% 210.57/132.44 ((~![B: $i] : (~member(B, empty_set))) | (~member(tptp_fun_D_0(C!3, B!4), empty_set))),
% 210.57/132.44 inference(quant_inst,[status(thm)],[])).
% 210.57/132.44 tff(139,plain,
% 210.57/132.44 (~member(tptp_fun_D_0(C!3, B!4), empty_set)),
% 210.57/132.44 inference(unit_resolution,[status(thm)],[138, 103])).
% 210.57/132.44 tff(140,plain,
% 210.57/132.44 (~member(tptp_fun_D_0(C!3, B!4), intersection(C!3, B!4))),
% 210.57/132.44 inference(modus_ponens,[status(thm)],[139, 137])).
% 210.57/132.44 tff(141,plain,
% 210.57/132.44 ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(tptp_fun_D_0(C!3, B!4), intersection(C!3, B!4)) <=> (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))),
% 210.57/132.44 inference(quant_inst,[status(thm)],[])).
% 210.57/132.44 tff(142,plain,
% 210.57/132.44 (member(tptp_fun_D_0(C!3, B!4), intersection(C!3, B!4)) <=> (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3))))),
% 210.57/132.44 inference(unit_resolution,[status(thm)],[141, 13])).
% 210.57/132.44 tff(143,plain,
% 210.57/132.44 ((~(intersect(B!4, C!3) <=> not_equal(intersection(B!4, C!3), empty_set))) <=> ((~intersect(B!4, C!3)) <=> not_equal(intersection(B!4, C!3), empty_set))),
% 210.57/132.44 inference(rewrite,[status(thm)],[])).
% 210.57/132.44 tff(144,plain,
% 210.57/132.44 ((~![B: $i, C: $i] : (intersect(B, C) <=> not_equal(intersection(B, C), empty_set))) <=> (~![B: $i, C: $i] : (intersect(B, C) <=> not_equal(intersection(B, C), empty_set)))),
% 210.57/132.44 inference(rewrite,[status(thm)],[])).
% 210.57/132.44 tff(145,axiom,(~![B: $i, C: $i] : (intersect(B, C) <=> not_equal(intersection(B, C), empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_th119')).
% 210.57/132.44 tff(146,plain,
% 210.57/132.44 (~![B: $i, C: $i] : (intersect(B, C) <=> not_equal(intersection(B, C), empty_set))),
% 210.57/132.44 inference(modus_ponens,[status(thm)],[145, 144])).
% 210.57/132.44 tff(147,plain,
% 210.57/132.44 (~![B: $i, C: $i] : (intersect(B, C) <=> not_equal(intersection(B, C), empty_set))),
% 210.57/132.44 inference(modus_ponens,[status(thm)],[146, 144])).
% 210.57/132.44 tff(148,plain,
% 210.57/132.44 (~![B: $i, C: $i] : (intersect(B, C) <=> not_equal(intersection(B, C), empty_set))),
% 210.57/132.44 inference(modus_ponens,[status(thm)],[147, 144])).
% 210.57/132.44 tff(149,plain,
% 210.57/132.44 (~![B: $i, C: $i] : (intersect(B, C) <=> not_equal(intersection(B, C), empty_set))),
% 210.57/132.44 inference(modus_ponens,[status(thm)],[148, 144])).
% 210.57/132.44 tff(150,plain,
% 210.57/132.44 (~![B: $i, C: $i] : (intersect(B, C) <=> not_equal(intersection(B, C), empty_set))),
% 210.57/132.44 inference(modus_ponens,[status(thm)],[149, 144])).
% 210.57/132.44 tff(151,plain,
% 210.57/132.44 (~![B: $i, C: $i] : (intersect(B, C) <=> not_equal(intersection(B, C), empty_set))),
% 210.57/132.44 inference(modus_ponens,[status(thm)],[150, 144])).
% 210.57/132.44 tff(152,plain,
% 210.57/132.44 (~![B: $i, C: $i] : (intersect(B, C) <=> not_equal(intersection(B, C), empty_set))),
% 210.57/132.44 inference(modus_ponens,[status(thm)],[151, 144])).
% 210.57/132.44 tff(153,plain,(
% 210.57/132.44 ~(intersect(B!4, C!3) <=> not_equal(intersection(B!4, C!3), empty_set))),
% 210.57/132.44 inference(skolemize,[status(sab)],[152])).
% 210.57/132.44 tff(154,plain,
% 210.57/132.44 ((~intersect(B!4, C!3)) <=> not_equal(intersection(B!4, C!3), empty_set)),
% 210.57/132.44 inference(modus_ponens,[status(thm)],[153, 143])).
% 210.57/132.44 tff(155,plain,
% 210.57/132.44 (intersect(B!4, C!3) | not_equal(intersection(B!4, C!3), empty_set) | (~((~intersect(B!4, C!3)) <=> not_equal(intersection(B!4, C!3), empty_set)))),
% 210.57/132.44 inference(tautology,[status(thm)],[])).
% 210.57/132.44 tff(156,plain,
% 210.57/132.44 (intersect(B!4, C!3) | not_equal(intersection(B!4, C!3), empty_set)),
% 210.57/132.44 inference(unit_resolution,[status(thm)],[155, 154])).
% 210.57/132.44 tff(157,plain,
% 210.57/132.44 (intersect(B!4, C!3)),
% 210.57/132.44 inference(unit_resolution,[status(thm)],[156, 121])).
% 210.57/132.44 tff(158,plain,
% 210.57/132.44 (^[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))))))))),
% 210.57/132.44 inference(bind,[status(th)],[])).
% 210.57/132.44 tff(159,plain,
% 210.57/132.44 (![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)))))))),
% 210.57/132.44 inference(quant_intro,[status(thm)],[158])).
% 210.57/132.44 tff(160,plain,
% 210.57/132.44 (^[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))))))))),
% 210.57/132.44 inference(bind,[status(th)],[])).
% 210.57/132.44 tff(161,plain,
% 210.57/132.44 (![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)))))))),
% 210.57/132.44 inference(quant_intro,[status(thm)],[160])).
% 210.57/132.44 tff(162,plain,
% 210.57/132.44 (![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)))))))),
% 210.57/132.44 inference(transitivity,[status(thm)],[161, 159])).
% 210.57/132.44 tff(163,plain,
% 210.57/132.44 (^[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)))))))))),
% 210.57/132.44 inference(bind,[status(th)],[])).
% 210.57/132.44 tff(164,plain,
% 210.57/132.44 (![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)))))))),
% 210.57/132.44 inference(quant_intro,[status(thm)],[163])).
% 210.57/132.44 tff(165,plain,
% 210.57/132.44 (![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)))),
% 210.57/132.44 inference(rewrite,[status(thm)],[])).
% 210.57/132.44 tff(166,axiom,(![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','intersect_defn')).
% 210.57/132.44 tff(167,plain,
% 210.57/132.44 (![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C)))),
% 210.57/132.44 inference(modus_ponens,[status(thm)],[166, 165])).
% 210.57/132.45 tff(168,plain,(
% 210.57/132.45 ![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)))))),
% 210.57/132.45 inference(skolemize,[status(sab)],[167])).
% 210.57/132.45 tff(169,plain,
% 210.57/132.45 (![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)))))))),
% 210.57/132.45 inference(modus_ponens,[status(thm)],[168, 164])).
% 210.57/132.45 tff(170,plain,
% 210.57/132.45 (![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)))))))),
% 210.57/132.45 inference(modus_ponens,[status(thm)],[169, 162])).
% 210.57/132.45 tff(171,plain,
% 210.57/132.45 ((~![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!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))) | (~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, C!3)) | (~member(D, B!4)))))))),
% 210.57/132.45 inference(quant_inst,[status(thm)],[])).
% 210.57/132.45 tff(172,plain,
% 210.57/132.45 (~((~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))) | (~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, C!3)) | (~member(D, B!4))))))),
% 210.57/132.45 inference(unit_resolution,[status(thm)],[171, 170])).
% 210.57/132.45 tff(173,plain,
% 210.57/132.45 (((~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))) | (~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, C!3)) | (~member(D, B!4)))))) | ((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))),
% 210.57/132.45 inference(tautology,[status(thm)],[])).
% 210.57/132.45 tff(174,plain,
% 210.57/132.45 ((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3))))),
% 210.57/132.45 inference(unit_resolution,[status(thm)],[173, 172])).
% 210.57/132.45 tff(175,plain,
% 210.57/132.45 ((~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))) | (~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3))))),
% 210.57/132.45 inference(tautology,[status(thm)],[])).
% 210.57/132.45 tff(176,plain,
% 210.57/132.45 ((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3))))),
% 210.57/132.45 inference(unit_resolution,[status(thm)],[175, 174])).
% 210.57/132.45 tff(177,plain,
% 210.57/132.45 (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))),
% 210.57/132.45 inference(unit_resolution,[status(thm)],[176, 157])).
% 210.57/132.45 tff(178,plain,
% 210.57/132.45 ((~(member(tptp_fun_D_0(C!3, B!4), intersection(C!3, B!4)) <=> (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))) | member(tptp_fun_D_0(C!3, B!4), intersection(C!3, B!4)) | ((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))),
% 210.57/132.45 inference(tautology,[status(thm)],[])).
% 210.57/132.45 tff(179,plain,
% 210.57/132.45 ((~(member(tptp_fun_D_0(C!3, B!4), intersection(C!3, B!4)) <=> (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))) | member(tptp_fun_D_0(C!3, B!4), intersection(C!3, B!4))),
% 210.57/132.45 inference(unit_resolution,[status(thm)],[178, 177])).
% 210.57/132.45 tff(180,plain,
% 210.57/132.45 (member(tptp_fun_D_0(C!3, B!4), intersection(C!3, B!4))),
% 210.57/132.45 inference(unit_resolution,[status(thm)],[179, 142])).
% 210.57/132.45 tff(181,plain,
% 210.57/132.45 ($false),
% 210.57/132.45 inference(unit_resolution,[status(thm)],[180, 140])).
% 210.57/132.45 tff(182,plain,(not_equal(intersection(B!4, C!3), empty_set)), inference(lemma,lemma(discharge,[]))).
% 210.57/132.45 tff(183,plain,
% 210.57/132.45 ((~(not_equal(intersection(B!4, C!3), empty_set) <=> (~(intersection(B!4, C!3) = empty_set)))) | (~not_equal(intersection(B!4, C!3), empty_set)) | (~(intersection(B!4, C!3) = empty_set))),
% 210.57/132.45 inference(tautology,[status(thm)],[])).
% 210.57/132.45 tff(184,plain,
% 210.57/132.45 ((~not_equal(intersection(B!4, C!3), empty_set)) | (~(intersection(B!4, C!3) = empty_set))),
% 210.57/132.45 inference(unit_resolution,[status(thm)],[183, 130])).
% 210.57/132.45 tff(185,plain,
% 210.57/132.45 (~(intersection(B!4, C!3) = empty_set)),
% 210.57/132.45 inference(unit_resolution,[status(thm)],[184, 182])).
% 210.57/132.45 tff(186,plain,
% 210.57/132.45 (~(intersection(C!3, B!4) = intersection(empty_set, B!4))),
% 210.57/132.45 inference(modus_ponens,[status(thm)],[185, 120])).
% 210.57/132.45 tff(187,plain,
% 210.57/132.45 ((~((intersection(C!3, B!4) = intersection(empty_set, B!4)) | ((~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(C!3, B!4))) <=> member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(empty_set, B!4))))) | (intersection(C!3, B!4) = intersection(empty_set, B!4)) | ((~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(C!3, B!4))) <=> member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(empty_set, B!4)))),
% 210.57/132.45 inference(tautology,[status(thm)],[])).
% 210.57/132.45 tff(188,plain,
% 210.57/132.45 ((~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(C!3, B!4))) <=> member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(empty_set, B!4))),
% 210.57/132.45 inference(unit_resolution,[status(thm)],[187, 186, 89])).
% 210.57/132.45 tff(189,plain,
% 210.57/132.45 (empty_set = intersection(empty_set, B!4)),
% 210.57/132.45 inference(symmetry,[status(thm)],[116])).
% 210.57/132.45 tff(190,plain,
% 210.57/132.45 (member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), empty_set) <=> member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(empty_set, B!4))),
% 210.57/132.45 inference(monotonicity,[status(thm)],[189])).
% 210.57/132.45 tff(191,plain,
% 210.57/132.45 ((~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), empty_set)) <=> (~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(empty_set, B!4)))),
% 210.57/132.45 inference(monotonicity,[status(thm)],[190])).
% 210.57/132.45 tff(192,plain,
% 210.57/132.45 ((~![B: $i] : (~member(B, empty_set))) | (~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), empty_set))),
% 210.57/132.45 inference(quant_inst,[status(thm)],[])).
% 210.57/132.45 tff(193,plain,
% 210.57/132.45 (~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), empty_set)),
% 210.57/132.45 inference(unit_resolution,[status(thm)],[192, 103])).
% 210.57/132.45 tff(194,plain,
% 210.57/132.45 (~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(empty_set, B!4))),
% 210.57/132.45 inference(modus_ponens,[status(thm)],[193, 191])).
% 210.57/132.45 tff(195,plain,
% 210.57/132.45 ((~((~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(C!3, B!4))) <=> member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(empty_set, B!4)))) | member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(C!3, B!4)) | member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(empty_set, B!4))),
% 210.57/132.45 inference(tautology,[status(thm)],[])).
% 210.57/132.45 tff(196,plain,
% 210.57/132.45 (member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(C!3, B!4))),
% 210.57/132.45 inference(unit_resolution,[status(thm)],[195, 194, 188])).
% 210.57/132.45 tff(197,plain,
% 210.57/132.45 (member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(intersection(B!4, B!4), C!3))),
% 210.57/132.45 inference(modus_ponens,[status(thm)],[196, 80])).
% 210.57/132.45 tff(198,plain,
% 210.57/132.45 ((~(member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(intersection(B!4, B!4), C!3)) <=> (~((~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), C!3)) | (~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(B!4, B!4))))))) | (~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(intersection(B!4, B!4), C!3))) | (~((~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), C!3)) | (~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(B!4, B!4)))))),
% 210.57/132.45 inference(tautology,[status(thm)],[])).
% 210.57/132.45 tff(199,plain,
% 210.57/132.45 (~((~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), C!3)) | (~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(B!4, B!4))))),
% 210.57/132.45 inference(unit_resolution,[status(thm)],[198, 197, 66])).
% 210.57/132.45 tff(200,plain,
% 210.57/132.45 (((~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), C!3)) | (~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(B!4, B!4)))) | member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(B!4, B!4))),
% 210.57/132.45 inference(tautology,[status(thm)],[])).
% 210.57/132.45 tff(201,plain,
% 210.57/132.45 (member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(B!4, B!4))),
% 210.57/132.45 inference(unit_resolution,[status(thm)],[200, 199])).
% 210.57/132.45 tff(202,plain,
% 210.57/132.45 (member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), B!4)),
% 210.57/132.45 inference(modus_ponens,[status(thm)],[201, 64])).
% 210.57/132.45 tff(203,plain,
% 210.57/132.45 (((~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), C!3)) | (~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), intersection(B!4, B!4)))) | member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), C!3)),
% 210.57/132.45 inference(tautology,[status(thm)],[])).
% 210.57/132.45 tff(204,plain,
% 210.57/132.45 (member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), C!3)),
% 210.57/132.45 inference(unit_resolution,[status(thm)],[203, 199])).
% 210.57/132.45 tff(205,plain,
% 210.57/132.45 ((~intersect(B!4, C!3)) | (~not_equal(intersection(B!4, C!3), empty_set)) | (~((~intersect(B!4, C!3)) <=> not_equal(intersection(B!4, C!3), empty_set)))),
% 210.57/132.45 inference(tautology,[status(thm)],[])).
% 210.57/132.45 tff(206,plain,
% 210.57/132.45 ((~intersect(B!4, C!3)) | (~not_equal(intersection(B!4, C!3), empty_set))),
% 210.57/132.45 inference(unit_resolution,[status(thm)],[205, 154])).
% 210.57/132.45 tff(207,plain,
% 210.57/132.45 (~intersect(B!4, C!3)),
% 210.57/132.45 inference(unit_resolution,[status(thm)],[206, 182])).
% 210.57/132.45 tff(208,plain,
% 210.57/132.45 (((~((~intersect(B!4, C!3)) | (~((~member(tptp_fun_D_0(C!3, B!4), B!4)) | (~member(tptp_fun_D_0(C!3, B!4), C!3)))))) | (~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, C!3)) | (~member(D, B!4)))))) | (intersect(B!4, C!3) | ![D: $i] : ((~member(D, C!3)) | (~member(D, B!4))))),
% 210.57/132.45 inference(tautology,[status(thm)],[])).
% 210.57/132.45 tff(209,plain,
% 210.57/132.45 (intersect(B!4, C!3) | ![D: $i] : ((~member(D, C!3)) | (~member(D, B!4)))),
% 210.57/132.45 inference(unit_resolution,[status(thm)],[208, 172])).
% 210.57/132.45 tff(210,plain,
% 210.57/132.45 ((~(intersect(B!4, C!3) | ![D: $i] : ((~member(D, C!3)) | (~member(D, B!4))))) | intersect(B!4, C!3) | ![D: $i] : ((~member(D, C!3)) | (~member(D, B!4)))),
% 210.57/132.45 inference(tautology,[status(thm)],[])).
% 210.57/132.45 tff(211,plain,
% 210.57/132.45 (intersect(B!4, C!3) | ![D: $i] : ((~member(D, C!3)) | (~member(D, B!4)))),
% 210.57/132.45 inference(unit_resolution,[status(thm)],[210, 209])).
% 210.57/132.45 tff(212,plain,
% 210.57/132.45 (![D: $i] : ((~member(D, C!3)) | (~member(D, B!4)))),
% 210.57/132.45 inference(unit_resolution,[status(thm)],[211, 207])).
% 210.57/132.45 tff(213,plain,
% 210.57/132.45 (((~![D: $i] : ((~member(D, C!3)) | (~member(D, B!4)))) | ((~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), C!3)) | (~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), B!4)))) <=> ((~![D: $i] : ((~member(D, C!3)) | (~member(D, B!4)))) | (~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), C!3)) | (~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), B!4)))),
% 210.57/132.45 inference(rewrite,[status(thm)],[])).
% 210.57/132.45 tff(214,plain,
% 210.57/132.45 ((~![D: $i] : ((~member(D, C!3)) | (~member(D, B!4)))) | ((~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), C!3)) | (~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), B!4)))),
% 210.57/132.45 inference(quant_inst,[status(thm)],[])).
% 210.57/132.45 tff(215,plain,
% 210.57/132.45 ((~![D: $i] : ((~member(D, C!3)) | (~member(D, B!4)))) | (~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), C!3)) | (~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), B!4))),
% 210.57/132.45 inference(modus_ponens,[status(thm)],[214, 213])).
% 210.57/132.45 tff(216,plain,
% 210.57/132.45 (~member(tptp_fun_D_1(intersection(empty_set, B!4), intersection(C!3, B!4)), B!4)),
% 210.57/132.45 inference(unit_resolution,[status(thm)],[215, 212, 204])).
% 210.57/132.46 tff(217,plain,
% 210.57/132.46 ($false),
% 210.57/132.46 inference(unit_resolution,[status(thm)],[216, 202])).
% 210.57/132.46 % SZS output end Proof
%------------------------------------------------------------------------------