TSTP Solution File: SET592+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET592+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 05:07:11 EDT 2022
% Result : Theorem 0.21s 0.45s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET592+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n020.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Sep 3 06:51:59 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.21/0.35 Usage: tptp [options] [-file:]file
% 0.21/0.35 -h, -? prints this message.
% 0.21/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.21/0.35 -m, -model generate model.
% 0.21/0.35 -p, -proof generate proof.
% 0.21/0.35 -c, -core generate unsat core of named formulas.
% 0.21/0.35 -st, -statistics display statistics.
% 0.21/0.35 -t:timeout set timeout (in second).
% 0.21/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.21/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.21/0.35 -<param>:<value> configuration parameter and value.
% 0.21/0.35 -o:<output-file> file to place output in.
% 0.21/0.45 % SZS status Theorem
% 0.21/0.45 % SZS output start Proof
% 0.21/0.45 tff(member_type, type, (
% 0.21/0.45 member: ( $i * $i ) > $o)).
% 0.21/0.45 tff(intersection_type, type, (
% 0.21/0.45 intersection: ( $i * $i ) > $i)).
% 0.21/0.45 tff(tptp_fun_D_3_type, type, (
% 0.21/0.45 tptp_fun_D_3: $i)).
% 0.21/0.45 tff(tptp_fun_D_2_type, type, (
% 0.21/0.45 tptp_fun_D_2: ( $i * $i ) > $i)).
% 0.21/0.45 tff(empty_set_type, type, (
% 0.21/0.45 empty_set: $i)).
% 0.21/0.45 tff(tptp_fun_B_5_type, type, (
% 0.21/0.45 tptp_fun_B_5: $i)).
% 0.21/0.45 tff(tptp_fun_C_4_type, type, (
% 0.21/0.45 tptp_fun_C_4: $i)).
% 0.21/0.45 tff(subset_type, type, (
% 0.21/0.45 subset: ( $i * $i ) > $o)).
% 0.21/0.45 tff(tptp_fun_D_0_type, type, (
% 0.21/0.45 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.21/0.45 tff(1,assumption,(~member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3))), introduced(assumption)).
% 0.21/0.45 tff(2,assumption,(~(member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3)) <=> member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3))), introduced(assumption)).
% 0.21/0.45 tff(3,plain,
% 0.21/0.45 (^[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))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(4,plain,
% 0.21/0.45 (![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)))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.45 tff(5,plain,
% 0.21/0.45 (^[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))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(6,plain,
% 0.21/0.45 (![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)))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[5])).
% 0.21/0.45 tff(7,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(8,axiom,(![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersection_defn')).
% 0.21/0.45 tff(9,plain,
% 0.21/0.45 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.21/0.45 tff(10,plain,(
% 0.21/0.45 ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[9])).
% 0.21/0.45 tff(11,plain,
% 0.21/0.45 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.21/0.45 tff(12,plain,
% 0.21/0.45 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.21/0.45 tff(13,plain,
% 0.21/0.45 (((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3)) <=> member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3)) <=> member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(14,plain,
% 0.21/0.45 ((member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3)) <=> (~((~member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3)) | (~member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3))))) <=> (member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3)) <=> member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(15,plain,
% 0.21/0.45 (((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3)) <=> (~((~member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3)) | (~member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3)))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3)) <=> member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3)))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[14])).
% 0.21/0.46 tff(16,plain,
% 0.21/0.46 (((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3)) <=> (~((~member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3)) | (~member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3)))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3)) <=> member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3)))),
% 0.21/0.46 inference(transitivity,[status(thm)],[15, 13])).
% 0.21/0.46 tff(17,plain,
% 0.21/0.46 ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3)) <=> (~((~member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3)) | (~member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3)))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(18,plain,
% 0.21/0.46 ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3)) <=> member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.21/0.46 tff(19,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[18, 12, 2])).
% 0.21/0.46 tff(20,plain,(member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3)) <=> member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(21,plain,
% 0.21/0.46 ((~(member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3)) <=> member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3))) | member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3)) | (~member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(22,plain,
% 0.21/0.46 (member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3)) | (~member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.21/0.46 tff(23,plain,
% 0.21/0.46 (~member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[22, 1])).
% 0.21/0.46 tff(24,assumption,((~((~(B!5 = empty_set)) | (member(tptp_fun_D_2(empty_set, B!5), B!5) <=> member(tptp_fun_D_2(empty_set, B!5), empty_set)))) | (~((B!5 = empty_set) | ((~member(tptp_fun_D_2(empty_set, B!5), B!5)) <=> member(tptp_fun_D_2(empty_set, B!5), empty_set))))), introduced(assumption)).
% 0.21/0.46 tff(25,plain,
% 0.21/0.46 (^[B: $i, C: $i, D: $i] : refl((~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))) <=> (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(26,plain,
% 0.21/0.46 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[25])).
% 0.21/0.46 tff(27,plain,
% 0.21/0.46 (![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))),
% 0.21/0.46 inference(pull_quant,[status(thm)],[])).
% 0.21/0.46 tff(28,plain,
% 0.21/0.46 (^[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_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))) <=> (?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))), pull_quant((?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))) <=> (~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))))), pull_quant((~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(29,plain,
% 0.21/0.46 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))) <=> ![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[28])).
% 0.21/0.46 tff(30,plain,
% 0.21/0.46 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[29, 27])).
% 0.21/0.46 tff(31,plain,
% 0.21/0.46 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[30, 26])).
% 0.21/0.46 tff(32,plain,
% 0.21/0.46 (^[B: $i, C: $i] : rewrite((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(33,plain,
% 0.21/0.46 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[32])).
% 0.21/0.46 tff(34,plain,
% 0.21/0.46 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[33, 31])).
% 0.21/0.46 tff(35,plain,
% 0.21/0.46 (^[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_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))), rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(36,plain,
% 0.21/0.46 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[35])).
% 0.21/0.46 tff(37,plain,
% 0.21/0.46 (^[B: $i, C: $i] : rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(38,plain,
% 0.21/0.46 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C))))) <=> ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[37])).
% 0.21/0.46 tff(39,plain,
% 0.21/0.46 (![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)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(40,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')).
% 0.21/0.46 tff(41,plain,
% 0.21/0.46 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.21/0.46 tff(42,plain,(
% 0.21/0.46 ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_2(C, B), B) <=> member(tptp_fun_D_2(C, B), C)))))),
% 0.21/0.46 inference(skolemize,[status(sab)],[41])).
% 0.21/0.46 tff(43,plain,
% 0.21/0.46 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.21/0.46 tff(44,plain,
% 0.21/0.46 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.21/0.46 tff(45,plain,
% 0.21/0.46 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[44, 34])).
% 0.21/0.46 tff(46,plain,
% 0.21/0.46 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))) | (~((~((~(B!5 = empty_set)) | (member(tptp_fun_D_2(empty_set, B!5), B!5) <=> member(tptp_fun_D_2(empty_set, B!5), empty_set)))) | (~((B!5 = empty_set) | ((~member(tptp_fun_D_2(empty_set, B!5), B!5)) <=> member(tptp_fun_D_2(empty_set, B!5), empty_set))))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(47,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[46, 45, 24])).
% 0.21/0.46 tff(48,plain,(~((~((~(B!5 = empty_set)) | (member(tptp_fun_D_2(empty_set, B!5), B!5) <=> member(tptp_fun_D_2(empty_set, B!5), empty_set)))) | (~((B!5 = empty_set) | ((~member(tptp_fun_D_2(empty_set, B!5), B!5)) <=> member(tptp_fun_D_2(empty_set, B!5), empty_set)))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(49,plain,
% 0.21/0.46 (((~((~(B!5 = empty_set)) | (member(tptp_fun_D_2(empty_set, B!5), B!5) <=> member(tptp_fun_D_2(empty_set, B!5), empty_set)))) | (~((B!5 = empty_set) | ((~member(tptp_fun_D_2(empty_set, B!5), B!5)) <=> member(tptp_fun_D_2(empty_set, B!5), empty_set))))) | ((B!5 = empty_set) | ((~member(tptp_fun_D_2(empty_set, B!5), B!5)) <=> member(tptp_fun_D_2(empty_set, B!5), empty_set)))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(50,plain,
% 0.21/0.46 ((B!5 = empty_set) | ((~member(tptp_fun_D_2(empty_set, B!5), B!5)) <=> member(tptp_fun_D_2(empty_set, B!5), empty_set))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.21/0.46 tff(51,plain,
% 0.21/0.46 ((~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(B, D) & (intersection(C, D) = empty_set))) | (B = empty_set))) <=> (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(B, D) & (intersection(C, D) = empty_set))) | (B = empty_set)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(52,plain,
% 0.21/0.46 ((~![B: $i, C: $i, D: $i] : (((subset(B, C) & subset(B, D)) & (intersection(C, D) = empty_set)) => (B = empty_set))) <=> (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(B, D) & (intersection(C, D) = empty_set))) | (B = empty_set)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(53,axiom,(~![B: $i, C: $i, D: $i] : (((subset(B, C) & subset(B, D)) & (intersection(C, D) = empty_set)) => (B = empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_th51')).
% 0.21/0.46 tff(54,plain,
% 0.21/0.46 (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(B, D) & (intersection(C, D) = empty_set))) | (B = empty_set))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.21/0.46 tff(55,plain,
% 0.21/0.46 (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(B, D) & (intersection(C, D) = empty_set))) | (B = empty_set))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[54, 51])).
% 0.21/0.46 tff(56,plain,
% 0.21/0.46 (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(B, D) & (intersection(C, D) = empty_set))) | (B = empty_set))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.21/0.46 tff(57,plain,
% 0.21/0.46 (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(B, D) & (intersection(C, D) = empty_set))) | (B = empty_set))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[56, 51])).
% 0.21/0.46 tff(58,plain,
% 0.21/0.46 (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(B, D) & (intersection(C, D) = empty_set))) | (B = empty_set))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[57, 51])).
% 0.21/0.46 tff(59,plain,
% 0.21/0.46 (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(B, D) & (intersection(C, D) = empty_set))) | (B = empty_set))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.21/0.46 tff(60,plain,
% 0.21/0.46 (~![B: $i, C: $i, D: $i] : ((~(subset(B, C) & subset(B, D) & (intersection(C, D) = empty_set))) | (B = empty_set))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[59, 51])).
% 0.21/0.46 tff(61,plain,(
% 0.21/0.46 ~((~(subset(B!5, C!4) & subset(B!5, D!3) & (intersection(C!4, D!3) = empty_set))) | (B!5 = empty_set))),
% 0.21/0.46 inference(skolemize,[status(sab)],[60])).
% 0.21/0.46 tff(62,plain,
% 0.21/0.46 (~(B!5 = empty_set)),
% 0.21/0.46 inference(or_elim,[status(thm)],[61])).
% 0.21/0.46 tff(63,plain,
% 0.21/0.46 ((~((B!5 = empty_set) | ((~member(tptp_fun_D_2(empty_set, B!5), B!5)) <=> member(tptp_fun_D_2(empty_set, B!5), empty_set)))) | (B!5 = empty_set) | ((~member(tptp_fun_D_2(empty_set, B!5), B!5)) <=> member(tptp_fun_D_2(empty_set, B!5), empty_set))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(64,plain,
% 0.21/0.46 ((~((B!5 = empty_set) | ((~member(tptp_fun_D_2(empty_set, B!5), B!5)) <=> member(tptp_fun_D_2(empty_set, B!5), empty_set)))) | ((~member(tptp_fun_D_2(empty_set, B!5), B!5)) <=> member(tptp_fun_D_2(empty_set, B!5), empty_set))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.21/0.46 tff(65,plain,
% 0.21/0.46 ((~member(tptp_fun_D_2(empty_set, B!5), B!5)) <=> member(tptp_fun_D_2(empty_set, B!5), empty_set)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[64, 50])).
% 0.21/0.46 tff(66,assumption,((~member(tptp_fun_D_2(empty_set, B!5), B!5)) <=> member(tptp_fun_D_2(empty_set, B!5), empty_set)), introduced(assumption)).
% 0.21/0.46 tff(67,plain,
% 0.21/0.46 (^[B: $i] : refl((~member(B, empty_set)) <=> (~member(B, empty_set)))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(68,plain,
% 0.21/0.46 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[67])).
% 0.21/0.46 tff(69,plain,
% 0.21/0.46 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(70,axiom,(![B: $i] : (~member(B, empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','empty_set_defn')).
% 0.21/0.46 tff(71,plain,
% 0.21/0.46 (![B: $i] : (~member(B, empty_set))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.21/0.46 tff(72,plain,(
% 0.21/0.46 ![B: $i] : (~member(B, empty_set))),
% 0.21/0.46 inference(skolemize,[status(sab)],[71])).
% 0.21/0.46 tff(73,plain,
% 0.21/0.46 (![B: $i] : (~member(B, empty_set))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.21/0.46 tff(74,plain,
% 0.21/0.46 ((~![B: $i] : (~member(B, empty_set))) | (~member(tptp_fun_D_2(empty_set, B!5), empty_set))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(75,plain,
% 0.21/0.46 (~member(tptp_fun_D_2(empty_set, B!5), empty_set)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.21/0.46 tff(76,plain,
% 0.21/0.46 ((~((~member(tptp_fun_D_2(empty_set, B!5), B!5)) <=> member(tptp_fun_D_2(empty_set, B!5), empty_set))) | member(tptp_fun_D_2(empty_set, B!5), B!5) | member(tptp_fun_D_2(empty_set, B!5), empty_set)),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(77,plain,
% 0.21/0.46 (member(tptp_fun_D_2(empty_set, B!5), B!5)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[76, 75, 66])).
% 0.21/0.46 tff(78,plain,
% 0.21/0.46 (^[B: $i, C: $i] : refl((~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(79,plain,
% 0.21/0.46 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[78])).
% 0.21/0.46 tff(80,plain,
% 0.21/0.46 (^[B: $i, C: $i] : rewrite((~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(81,plain,
% 0.21/0.46 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[80])).
% 0.21/0.46 tff(82,plain,
% 0.21/0.46 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[81, 79])).
% 0.21/0.46 tff(83,plain,
% 0.21/0.46 (^[B: $i, C: $i] : trans(monotonicity(rewrite(((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) <=> ((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))), rewrite((subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))) <=> (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))), ((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))), rewrite((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))), ((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(84,plain,
% 0.21/0.46 (![B: $i, C: $i] : (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[83])).
% 0.21/0.46 tff(85,plain,
% 0.21/0.46 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C))) <=> ![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(86,plain,
% 0.21/0.47 (^[B: $i, C: $i] : rewrite((subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C))) <=> (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(87,plain,
% 0.21/0.47 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C))) <=> ![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[86])).
% 0.21/0.47 tff(88,axiom,(![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','subset_defn')).
% 0.21/0.47 tff(89,plain,
% 0.21/0.47 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.21/0.47 tff(90,plain,
% 0.21/0.47 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.21/0.47 tff(91,plain,(
% 0.21/0.47 ![B: $i, C: $i] : (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))),
% 0.21/0.47 inference(skolemize,[status(sab)],[90])).
% 0.21/0.47 tff(92,plain,
% 0.21/0.47 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.21/0.47 tff(93,plain,
% 0.21/0.47 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[92, 82])).
% 0.21/0.47 tff(94,plain,
% 0.21/0.47 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(B!5, C!4)) | ![D: $i] : ((~member(D, B!5)) | member(D, C!4)))) | (~(subset(B!5, C!4) | (~((~member(tptp_fun_D_0(C!4, B!5), B!5)) | member(tptp_fun_D_0(C!4, B!5), C!4)))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(95,plain,
% 0.21/0.47 (~((~((~subset(B!5, C!4)) | ![D: $i] : ((~member(D, B!5)) | member(D, C!4)))) | (~(subset(B!5, C!4) | (~((~member(tptp_fun_D_0(C!4, B!5), B!5)) | member(tptp_fun_D_0(C!4, B!5), C!4))))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.21/0.47 tff(96,plain,
% 0.21/0.47 (((~((~subset(B!5, C!4)) | ![D: $i] : ((~member(D, B!5)) | member(D, C!4)))) | (~(subset(B!5, C!4) | (~((~member(tptp_fun_D_0(C!4, B!5), B!5)) | member(tptp_fun_D_0(C!4, B!5), C!4)))))) | ((~subset(B!5, C!4)) | ![D: $i] : ((~member(D, B!5)) | member(D, C!4)))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(97,plain,
% 0.21/0.47 ((~subset(B!5, C!4)) | ![D: $i] : ((~member(D, B!5)) | member(D, C!4))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.21/0.47 tff(98,plain,
% 0.21/0.47 (subset(B!5, C!4) & subset(B!5, D!3) & (intersection(C!4, D!3) = empty_set)),
% 0.21/0.47 inference(or_elim,[status(thm)],[61])).
% 0.21/0.47 tff(99,plain,
% 0.21/0.47 (subset(B!5, C!4)),
% 0.21/0.47 inference(and_elim,[status(thm)],[98])).
% 0.21/0.47 tff(100,plain,
% 0.21/0.47 ((~((~subset(B!5, C!4)) | ![D: $i] : ((~member(D, B!5)) | member(D, C!4)))) | (~subset(B!5, C!4)) | ![D: $i] : ((~member(D, B!5)) | member(D, C!4))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(101,plain,
% 0.21/0.47 ((~((~subset(B!5, C!4)) | ![D: $i] : ((~member(D, B!5)) | member(D, C!4)))) | ![D: $i] : ((~member(D, B!5)) | member(D, C!4))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.21/0.47 tff(102,plain,
% 0.21/0.47 (![D: $i] : ((~member(D, B!5)) | member(D, C!4))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[101, 97])).
% 0.21/0.47 tff(103,plain,
% 0.21/0.47 (((~![D: $i] : ((~member(D, B!5)) | member(D, C!4))) | ((~member(tptp_fun_D_2(empty_set, B!5), B!5)) | member(tptp_fun_D_2(empty_set, B!5), C!4))) <=> ((~![D: $i] : ((~member(D, B!5)) | member(D, C!4))) | (~member(tptp_fun_D_2(empty_set, B!5), B!5)) | member(tptp_fun_D_2(empty_set, B!5), C!4))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(104,plain,
% 0.21/0.47 ((~![D: $i] : ((~member(D, B!5)) | member(D, C!4))) | ((~member(tptp_fun_D_2(empty_set, B!5), B!5)) | member(tptp_fun_D_2(empty_set, B!5), C!4))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(105,plain,
% 0.21/0.47 ((~![D: $i] : ((~member(D, B!5)) | member(D, C!4))) | (~member(tptp_fun_D_2(empty_set, B!5), B!5)) | member(tptp_fun_D_2(empty_set, B!5), C!4)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.21/0.47 tff(106,plain,
% 0.21/0.47 ((~member(tptp_fun_D_2(empty_set, B!5), B!5)) | member(tptp_fun_D_2(empty_set, B!5), C!4)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[105, 102])).
% 0.21/0.47 tff(107,plain,
% 0.21/0.47 (member(tptp_fun_D_2(empty_set, B!5), C!4)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[106, 77])).
% 0.21/0.47 tff(108,assumption,(D!3 = intersection(D!3, D!3)), introduced(assumption)).
% 0.21/0.47 tff(109,plain,
% 0.21/0.47 (member(tptp_fun_D_2(empty_set, B!5), D!3) <=> member(tptp_fun_D_2(empty_set, B!5), intersection(D!3, D!3))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[108])).
% 0.21/0.47 tff(110,plain,
% 0.21/0.47 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(B!5, D!3)) | ![D: $i] : ((~member(D, B!5)) | member(D, D!3)))) | (~(subset(B!5, D!3) | (~((~member(tptp_fun_D_0(D!3, B!5), B!5)) | member(tptp_fun_D_0(D!3, B!5), D!3)))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(111,plain,
% 0.21/0.47 (~((~((~subset(B!5, D!3)) | ![D: $i] : ((~member(D, B!5)) | member(D, D!3)))) | (~(subset(B!5, D!3) | (~((~member(tptp_fun_D_0(D!3, B!5), B!5)) | member(tptp_fun_D_0(D!3, B!5), D!3))))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[110, 93])).
% 0.21/0.47 tff(112,plain,
% 0.21/0.47 (((~((~subset(B!5, D!3)) | ![D: $i] : ((~member(D, B!5)) | member(D, D!3)))) | (~(subset(B!5, D!3) | (~((~member(tptp_fun_D_0(D!3, B!5), B!5)) | member(tptp_fun_D_0(D!3, B!5), D!3)))))) | ((~subset(B!5, D!3)) | ![D: $i] : ((~member(D, B!5)) | member(D, D!3)))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(113,plain,
% 0.21/0.47 ((~subset(B!5, D!3)) | ![D: $i] : ((~member(D, B!5)) | member(D, D!3))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.21/0.47 tff(114,plain,
% 0.21/0.47 (subset(B!5, D!3)),
% 0.21/0.47 inference(and_elim,[status(thm)],[98])).
% 0.21/0.47 tff(115,plain,
% 0.21/0.47 ((~((~subset(B!5, D!3)) | ![D: $i] : ((~member(D, B!5)) | member(D, D!3)))) | (~subset(B!5, D!3)) | ![D: $i] : ((~member(D, B!5)) | member(D, D!3))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(116,plain,
% 0.21/0.47 ((~((~subset(B!5, D!3)) | ![D: $i] : ((~member(D, B!5)) | member(D, D!3)))) | ![D: $i] : ((~member(D, B!5)) | member(D, D!3))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.21/0.47 tff(117,plain,
% 0.21/0.47 (![D: $i] : ((~member(D, B!5)) | member(D, D!3))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[116, 113])).
% 0.21/0.47 tff(118,plain,
% 0.21/0.47 (((~![D: $i] : ((~member(D, B!5)) | member(D, D!3))) | ((~member(tptp_fun_D_2(empty_set, B!5), B!5)) | member(tptp_fun_D_2(empty_set, B!5), D!3))) <=> ((~![D: $i] : ((~member(D, B!5)) | member(D, D!3))) | (~member(tptp_fun_D_2(empty_set, B!5), B!5)) | member(tptp_fun_D_2(empty_set, B!5), D!3))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(119,plain,
% 0.21/0.47 ((~![D: $i] : ((~member(D, B!5)) | member(D, D!3))) | ((~member(tptp_fun_D_2(empty_set, B!5), B!5)) | member(tptp_fun_D_2(empty_set, B!5), D!3))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(120,plain,
% 0.21/0.47 ((~![D: $i] : ((~member(D, B!5)) | member(D, D!3))) | (~member(tptp_fun_D_2(empty_set, B!5), B!5)) | member(tptp_fun_D_2(empty_set, B!5), D!3)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.21/0.47 tff(121,plain,
% 0.21/0.47 ((~member(tptp_fun_D_2(empty_set, B!5), B!5)) | member(tptp_fun_D_2(empty_set, B!5), D!3)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[120, 117])).
% 0.21/0.47 tff(122,plain,
% 0.21/0.47 (member(tptp_fun_D_2(empty_set, B!5), D!3)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[121, 77])).
% 0.21/0.47 tff(123,plain,
% 0.21/0.47 (member(tptp_fun_D_2(empty_set, B!5), intersection(D!3, D!3))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[122, 109])).
% 0.21/0.47 tff(124,plain,
% 0.21/0.47 ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(tptp_fun_D_2(empty_set, B!5), intersection(intersection(D!3, D!3), C!4)) <=> (~((~member(tptp_fun_D_2(empty_set, B!5), C!4)) | (~member(tptp_fun_D_2(empty_set, B!5), intersection(D!3, D!3))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(125,plain,
% 0.21/0.47 (member(tptp_fun_D_2(empty_set, B!5), intersection(intersection(D!3, D!3), C!4)) <=> (~((~member(tptp_fun_D_2(empty_set, B!5), C!4)) | (~member(tptp_fun_D_2(empty_set, B!5), intersection(D!3, D!3)))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[124, 12])).
% 0.21/0.47 tff(126,plain,
% 0.21/0.47 (intersection(C!4, D!3) = empty_set),
% 0.21/0.47 inference(and_elim,[status(thm)],[98])).
% 0.21/0.47 tff(127,plain,
% 0.21/0.47 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(128,plain,
% 0.21/0.47 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[127])).
% 0.21/0.47 tff(129,plain,
% 0.21/0.47 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(130,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 0.21/0.47 tff(131,plain,
% 0.21/0.47 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.21/0.47 tff(132,plain,(
% 0.21/0.47 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.21/0.47 inference(skolemize,[status(sab)],[131])).
% 0.21/0.47 tff(133,plain,
% 0.21/0.47 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[132, 128])).
% 0.21/0.47 tff(134,plain,
% 0.21/0.47 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(C!4, D!3) = intersection(D!3, C!4))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(135,plain,
% 0.21/0.47 (intersection(C!4, D!3) = intersection(D!3, C!4)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.21/0.47 tff(136,plain,
% 0.21/0.47 (intersection(D!3, C!4) = intersection(C!4, D!3)),
% 0.21/0.47 inference(symmetry,[status(thm)],[135])).
% 0.21/0.47 tff(137,plain,
% 0.21/0.47 (intersection(D!3, D!3) = D!3),
% 0.21/0.47 inference(symmetry,[status(thm)],[108])).
% 0.21/0.47 tff(138,plain,
% 0.21/0.47 (intersection(intersection(D!3, D!3), C!4) = intersection(D!3, C!4)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[137])).
% 0.21/0.47 tff(139,plain,
% 0.21/0.47 (intersection(intersection(D!3, D!3), C!4) = empty_set),
% 0.21/0.47 inference(transitivity,[status(thm)],[138, 136, 126])).
% 0.21/0.47 tff(140,plain,
% 0.21/0.47 (member(tptp_fun_D_2(empty_set, B!5), intersection(intersection(D!3, D!3), C!4)) <=> member(tptp_fun_D_2(empty_set, B!5), empty_set)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[139])).
% 0.21/0.47 tff(141,plain,
% 0.21/0.47 (member(tptp_fun_D_2(empty_set, B!5), empty_set) <=> member(tptp_fun_D_2(empty_set, B!5), intersection(intersection(D!3, D!3), C!4))),
% 0.21/0.47 inference(symmetry,[status(thm)],[140])).
% 0.21/0.47 tff(142,plain,
% 0.21/0.47 ((~member(tptp_fun_D_2(empty_set, B!5), empty_set)) <=> (~member(tptp_fun_D_2(empty_set, B!5), intersection(intersection(D!3, D!3), C!4)))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[141])).
% 0.21/0.47 tff(143,plain,
% 0.21/0.47 (~member(tptp_fun_D_2(empty_set, B!5), intersection(intersection(D!3, D!3), C!4))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[75, 142])).
% 0.21/0.47 tff(144,plain,
% 0.21/0.47 ((~(member(tptp_fun_D_2(empty_set, B!5), intersection(intersection(D!3, D!3), C!4)) <=> (~((~member(tptp_fun_D_2(empty_set, B!5), C!4)) | (~member(tptp_fun_D_2(empty_set, B!5), intersection(D!3, D!3))))))) | member(tptp_fun_D_2(empty_set, B!5), intersection(intersection(D!3, D!3), C!4)) | ((~member(tptp_fun_D_2(empty_set, B!5), C!4)) | (~member(tptp_fun_D_2(empty_set, B!5), intersection(D!3, D!3))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(145,plain,
% 0.21/0.47 ((~member(tptp_fun_D_2(empty_set, B!5), C!4)) | (~member(tptp_fun_D_2(empty_set, B!5), intersection(D!3, D!3)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[144, 143, 125])).
% 0.21/0.47 tff(146,plain,
% 0.21/0.47 ((~((~member(tptp_fun_D_2(empty_set, B!5), C!4)) | (~member(tptp_fun_D_2(empty_set, B!5), intersection(D!3, D!3))))) | (~member(tptp_fun_D_2(empty_set, B!5), C!4)) | (~member(tptp_fun_D_2(empty_set, B!5), intersection(D!3, D!3)))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(147,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[146, 145, 123, 107])).
% 0.21/0.47 tff(148,plain,((~((~member(tptp_fun_D_2(empty_set, B!5), B!5)) <=> member(tptp_fun_D_2(empty_set, B!5), empty_set))) | (~(D!3 = intersection(D!3, D!3)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(149,plain,
% 0.21/0.47 (~(D!3 = intersection(D!3, D!3))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[148, 65])).
% 0.21/0.47 tff(150,plain,
% 0.21/0.47 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))) | (~((~((~(D!3 = intersection(D!3, D!3))) | (member(tptp_fun_D_0(B!5, D!3), D!3) <=> member(tptp_fun_D_0(B!5, D!3), intersection(D!3, D!3))))) | (~((D!3 = intersection(D!3, D!3)) | ((~member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3)) <=> member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3)))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(151,plain,
% 0.21/0.47 (~((~((~(D!3 = intersection(D!3, D!3))) | (member(tptp_fun_D_0(B!5, D!3), D!3) <=> member(tptp_fun_D_0(B!5, D!3), intersection(D!3, D!3))))) | (~((D!3 = intersection(D!3, D!3)) | ((~member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3)) <=> member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3))))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[150, 45])).
% 0.21/0.47 tff(152,plain,
% 0.21/0.47 (((~((~(D!3 = intersection(D!3, D!3))) | (member(tptp_fun_D_0(B!5, D!3), D!3) <=> member(tptp_fun_D_0(B!5, D!3), intersection(D!3, D!3))))) | (~((D!3 = intersection(D!3, D!3)) | ((~member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3)) <=> member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3)))))) | ((D!3 = intersection(D!3, D!3)) | ((~member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3)) <=> member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(153,plain,
% 0.21/0.47 ((D!3 = intersection(D!3, D!3)) | ((~member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3)) <=> member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.21/0.47 tff(154,plain,
% 0.21/0.47 ((~((D!3 = intersection(D!3, D!3)) | ((~member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3)) <=> member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3))))) | (D!3 = intersection(D!3, D!3)) | ((~member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3)) <=> member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3)))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(155,plain,
% 0.21/0.47 ((D!3 = intersection(D!3, D!3)) | ((~member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3)) <=> member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[154, 153])).
% 0.21/0.47 tff(156,plain,
% 0.21/0.47 ((~member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3)) <=> member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[155, 149])).
% 0.21/0.47 tff(157,plain,
% 0.21/0.47 ((~((~member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3)) <=> member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3)))) | member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3) | member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(158,plain,
% 0.21/0.47 (member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3) | member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[157, 156])).
% 0.21/0.47 tff(159,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[158, 23, 1])).
% 0.21/0.47 tff(160,plain,(member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(161,plain,
% 0.21/0.47 ((~((~member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3)) <=> member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3)))) | (~member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3)) | (~member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3)))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(162,plain,
% 0.21/0.47 ((~member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3)) | (~member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[161, 156])).
% 0.21/0.47 tff(163,plain,
% 0.21/0.47 (~member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[162, 160])).
% 0.21/0.47 tff(164,plain,
% 0.21/0.47 ((~(member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3)) <=> member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3))) | (~member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3))) | member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3)),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(165,plain,
% 0.21/0.47 ((~member(tptp_fun_D_2(intersection(D!3, D!3), D!3), intersection(D!3, D!3))) | member(tptp_fun_D_2(intersection(D!3, D!3), D!3), D!3)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[164, 20])).
% 0.21/0.48 tff(166,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[165, 163, 160])).
% 0.21/0.48 % SZS output end Proof
%------------------------------------------------------------------------------