TSTP Solution File: SET581+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET581+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 05:07:06 EDT 2022
% Result : Theorem 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET581+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 06:44:50 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 tff(member_type, type, (
% 0.20/0.43 member: ( $i * $i ) > $o)).
% 0.20/0.43 tff(empty_set_type, type, (
% 0.20/0.43 empty_set: $i)).
% 0.20/0.43 tff(tptp_fun_B_4_type, type, (
% 0.20/0.43 tptp_fun_B_4: $i)).
% 0.20/0.43 tff(intersection_type, type, (
% 0.20/0.43 intersection: ( $i * $i ) > $i)).
% 0.20/0.43 tff(tptp_fun_D_2_type, type, (
% 0.20/0.43 tptp_fun_D_2: $i)).
% 0.20/0.43 tff(tptp_fun_C_3_type, type, (
% 0.20/0.43 tptp_fun_C_3: $i)).
% 0.20/0.43 tff(tptp_fun_D_0_type, type, (
% 0.20/0.43 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.20/0.43 tff(not_equal_type, type, (
% 0.20/0.43 not_equal: ( $i * $i ) > $o)).
% 0.20/0.43 tff(1,plain,
% 0.20/0.43 (^[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))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(2,plain,
% 0.20/0.43 (![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)))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.43 tff(3,plain,
% 0.20/0.43 (^[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))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(4,plain,
% 0.20/0.43 (![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)))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.43 tff(5,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(6,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')).
% 0.20/0.43 tff(7,plain,
% 0.20/0.43 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.43 tff(8,plain,(
% 0.20/0.43 ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[7])).
% 0.20/0.43 tff(9,plain,
% 0.20/0.43 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.20/0.43 tff(10,plain,
% 0.20/0.43 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.43 tff(11,plain,
% 0.20/0.43 (((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(12,plain,
% 0.20/0.43 ((member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)) <=> (~((~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3))))) <=> (member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(13,plain,
% 0.20/0.43 (((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)) <=> (~((~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[12])).
% 0.20/0.43 tff(14,plain,
% 0.20/0.43 (((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)) <=> (~((~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[13, 11])).
% 0.20/0.43 tff(15,plain,
% 0.20/0.43 ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)) <=> (~((~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(16,plain,
% 0.20/0.43 ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.43 tff(17,plain,
% 0.20/0.43 (member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[16, 10])).
% 0.20/0.43 tff(18,assumption,((~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3))), introduced(assumption)).
% 0.20/0.43 tff(19,assumption,(~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3))), introduced(assumption)).
% 0.20/0.43 tff(20,plain,
% 0.20/0.43 ((~((~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))) | member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3) | member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(21,plain,
% 0.20/0.43 (member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[20, 19, 18])).
% 0.20/0.43 tff(22,plain,
% 0.20/0.43 ((~(member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3))) | member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)) | (~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(23,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[22, 21, 19, 17])).
% 0.20/0.43 tff(24,plain,(member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)) | (~((~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(25,plain,
% 0.20/0.43 (member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[24, 18])).
% 0.20/0.43 tff(26,plain,
% 0.20/0.43 ((~((~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))) | (~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)) | (~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(27,plain,
% 0.20/0.43 (~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[26, 25, 18])).
% 0.20/0.43 tff(28,plain,
% 0.20/0.43 ((~(member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3))) | (~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3))) | member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(29,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[28, 27, 25, 17])).
% 0.20/0.43 tff(30,plain,(~((~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(31,plain,
% 0.20/0.43 (^[B: $i, C: $i, D: $i] : refl((~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(32,plain,
% 0.20/0.43 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.43 tff(33,plain,
% 0.20/0.43 (![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 0.20/0.43 inference(pull_quant,[status(thm)],[])).
% 0.20/0.43 tff(34,plain,
% 0.20/0.43 (^[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_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))) <=> (?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))), pull_quant((?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> (~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))))), pull_quant((~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(35,plain,
% 0.20/0.43 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[34])).
% 0.20/0.44 tff(36,plain,
% 0.20/0.44 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[35, 33])).
% 0.20/0.44 tff(37,plain,
% 0.20/0.44 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[36, 32])).
% 0.20/0.44 tff(38,plain,
% 0.20/0.44 (^[B: $i, C: $i] : rewrite((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(39,plain,
% 0.20/0.44 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.44 tff(40,plain,
% 0.20/0.44 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[39, 37])).
% 0.20/0.44 tff(41,plain,
% 0.20/0.44 (^[B: $i, C: $i] : trans(monotonicity(rewrite(((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) <=> ((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))), rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(42,plain,
% 0.20/0.44 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.44 tff(43,plain,
% 0.20/0.44 (^[B: $i, C: $i] : rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(44,plain,
% 0.20/0.44 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))) <=> ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[43])).
% 0.20/0.44 tff(45,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(46,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')).
% 0.20/0.44 tff(47,plain,
% 0.20/0.44 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.44 tff(48,plain,(
% 0.20/0.44 ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[47])).
% 0.20/0.44 tff(49,plain,
% 0.20/0.44 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.20/0.44 tff(50,plain,
% 0.20/0.44 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.20/0.44 tff(51,plain,
% 0.20/0.44 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[50, 40])).
% 0.20/0.44 tff(52,plain,
% 0.20/0.44 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))) | (~((~((~(C!3 = intersection(C!3, C!3))) | (member(tptp_fun_D_0(D!2, C!3), C!3) <=> member(tptp_fun_D_0(D!2, C!3), intersection(C!3, C!3))))) | (~((C!3 = intersection(C!3, C!3)) | ((~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(53,plain,
% 0.20/0.44 (~((~((~(C!3 = intersection(C!3, C!3))) | (member(tptp_fun_D_0(D!2, C!3), C!3) <=> member(tptp_fun_D_0(D!2, C!3), intersection(C!3, C!3))))) | (~((C!3 = intersection(C!3, C!3)) | ((~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.20/0.44 tff(54,plain,
% 0.20/0.44 (((~((~(C!3 = intersection(C!3, C!3))) | (member(tptp_fun_D_0(D!2, C!3), C!3) <=> member(tptp_fun_D_0(D!2, C!3), intersection(C!3, C!3))))) | (~((C!3 = intersection(C!3, C!3)) | ((~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))))) | ((C!3 = intersection(C!3, C!3)) | ((~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(55,plain,
% 0.20/0.44 ((C!3 = intersection(C!3, C!3)) | ((~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.20/0.44 tff(56,plain,
% 0.20/0.44 ((~((C!3 = intersection(C!3, C!3)) | ((~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3))))) | (C!3 = intersection(C!3, C!3)) | ((~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(57,plain,
% 0.20/0.44 ((C!3 = intersection(C!3, C!3)) | ((~member(tptp_fun_D_0(intersection(C!3, C!3), C!3), C!3)) <=> member(tptp_fun_D_0(intersection(C!3, C!3), C!3), intersection(C!3, C!3)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.20/0.44 tff(58,plain,
% 0.20/0.44 (C!3 = intersection(C!3, C!3)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[57, 30])).
% 0.20/0.44 tff(59,plain,
% 0.20/0.44 (intersection(C!3, C!3) = C!3),
% 0.20/0.44 inference(symmetry,[status(thm)],[58])).
% 0.20/0.44 tff(60,plain,
% 0.20/0.44 (intersection(intersection(C!3, C!3), D!2) = intersection(C!3, D!2)),
% 0.20/0.44 inference(monotonicity,[status(thm)],[59])).
% 0.20/0.44 tff(61,plain,
% 0.20/0.44 (intersection(C!3, D!2) = intersection(intersection(C!3, C!3), D!2)),
% 0.20/0.44 inference(symmetry,[status(thm)],[60])).
% 0.20/0.44 tff(62,plain,
% 0.20/0.44 (^[B: $i, C: $i] : refl((not_equal(B, C) <=> (~(B = C))) <=> (not_equal(B, C) <=> (~(B = C))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(63,plain,
% 0.20/0.44 (![B: $i, C: $i] : (not_equal(B, C) <=> (~(B = C))) <=> ![B: $i, C: $i] : (not_equal(B, C) <=> (~(B = C)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[62])).
% 0.20/0.44 tff(64,plain,
% 0.20/0.44 (![B: $i, C: $i] : (not_equal(B, C) <=> (~(B = C))) <=> ![B: $i, C: $i] : (not_equal(B, C) <=> (~(B = C)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(65,axiom,(![B: $i, C: $i] : (not_equal(B, C) <=> (~(B = C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_equal_defn')).
% 0.20/0.44 tff(66,plain,
% 0.20/0.44 (![B: $i, C: $i] : (not_equal(B, C) <=> (~(B = C)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.20/0.44 tff(67,plain,(
% 0.20/0.44 ![B: $i, C: $i] : (not_equal(B, C) <=> (~(B = C)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[66])).
% 0.20/0.44 tff(68,plain,
% 0.20/0.44 (![B: $i, C: $i] : (not_equal(B, C) <=> (~(B = C)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.20/0.44 tff(69,plain,
% 0.20/0.44 ((~![B: $i, C: $i] : (not_equal(B, C) <=> (~(B = C)))) | (not_equal(intersection(C!3, D!2), empty_set) <=> (~(intersection(C!3, D!2) = empty_set)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(70,plain,
% 0.20/0.44 (not_equal(intersection(C!3, D!2), empty_set) <=> (~(intersection(C!3, D!2) = empty_set))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.20/0.44 tff(71,plain,
% 0.20/0.44 ((~![B: $i, C: $i, D: $i] : ((~(member(B, C) & member(B, D))) | not_equal(intersection(C, D), empty_set))) <=> (~![B: $i, C: $i, D: $i] : ((~(member(B, C) & member(B, D))) | not_equal(intersection(C, D), empty_set)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(72,plain,
% 0.20/0.44 ((~![B: $i, C: $i, D: $i] : ((member(B, C) & member(B, D)) => not_equal(intersection(C, D), empty_set))) <=> (~![B: $i, C: $i, D: $i] : ((~(member(B, C) & member(B, D))) | not_equal(intersection(C, D), empty_set)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(73,axiom,(~![B: $i, C: $i, D: $i] : ((member(B, C) & member(B, D)) => not_equal(intersection(C, D), empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_th24')).
% 0.20/0.44 tff(74,plain,
% 0.20/0.44 (~![B: $i, C: $i, D: $i] : ((~(member(B, C) & member(B, D))) | not_equal(intersection(C, D), empty_set))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.20/0.44 tff(75,plain,
% 0.20/0.44 (~![B: $i, C: $i, D: $i] : ((~(member(B, C) & member(B, D))) | not_equal(intersection(C, D), empty_set))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[74, 71])).
% 0.20/0.44 tff(76,plain,
% 0.20/0.44 (~![B: $i, C: $i, D: $i] : ((~(member(B, C) & member(B, D))) | not_equal(intersection(C, D), empty_set))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.20/0.44 tff(77,plain,
% 0.20/0.44 (~![B: $i, C: $i, D: $i] : ((~(member(B, C) & member(B, D))) | not_equal(intersection(C, D), empty_set))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[76, 71])).
% 0.20/0.44 tff(78,plain,
% 0.20/0.44 (~![B: $i, C: $i, D: $i] : ((~(member(B, C) & member(B, D))) | not_equal(intersection(C, D), empty_set))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[77, 71])).
% 0.20/0.44 tff(79,plain,
% 0.20/0.44 (~![B: $i, C: $i, D: $i] : ((~(member(B, C) & member(B, D))) | not_equal(intersection(C, D), empty_set))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[78, 71])).
% 0.20/0.44 tff(80,plain,
% 0.20/0.44 (~![B: $i, C: $i, D: $i] : ((~(member(B, C) & member(B, D))) | not_equal(intersection(C, D), empty_set))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[79, 71])).
% 0.20/0.44 tff(81,plain,(
% 0.20/0.44 ~((~(member(B!4, C!3) & member(B!4, D!2))) | not_equal(intersection(C!3, D!2), empty_set))),
% 0.20/0.44 inference(skolemize,[status(sab)],[80])).
% 0.20/0.44 tff(82,plain,
% 0.20/0.44 (~not_equal(intersection(C!3, D!2), empty_set)),
% 0.20/0.44 inference(or_elim,[status(thm)],[81])).
% 0.20/0.44 tff(83,plain,
% 0.20/0.44 ((~(not_equal(intersection(C!3, D!2), empty_set) <=> (~(intersection(C!3, D!2) = empty_set)))) | not_equal(intersection(C!3, D!2), empty_set) | (intersection(C!3, D!2) = empty_set)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(84,plain,
% 0.20/0.44 ((~(not_equal(intersection(C!3, D!2), empty_set) <=> (~(intersection(C!3, D!2) = empty_set)))) | (intersection(C!3, D!2) = empty_set)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.20/0.44 tff(85,plain,
% 0.20/0.44 (intersection(C!3, D!2) = empty_set),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[84, 70])).
% 0.20/0.44 tff(86,plain,
% 0.20/0.44 (empty_set = intersection(C!3, D!2)),
% 0.20/0.44 inference(symmetry,[status(thm)],[85])).
% 0.20/0.44 tff(87,plain,
% 0.20/0.44 (empty_set = intersection(intersection(C!3, C!3), D!2)),
% 0.20/0.44 inference(transitivity,[status(thm)],[86, 61])).
% 0.20/0.44 tff(88,plain,
% 0.20/0.44 (member(B!4, empty_set) <=> member(B!4, intersection(intersection(C!3, C!3), D!2))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[87])).
% 0.20/0.44 tff(89,plain,
% 0.20/0.44 (member(B!4, intersection(intersection(C!3, C!3), D!2)) <=> member(B!4, empty_set)),
% 0.20/0.44 inference(symmetry,[status(thm)],[88])).
% 0.20/0.44 tff(90,plain,
% 0.20/0.44 ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(B!4, intersection(intersection(C!3, C!3), D!2)) <=> (~((~member(B!4, D!2)) | (~member(B!4, intersection(C!3, C!3))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(91,plain,
% 0.20/0.44 (member(B!4, intersection(intersection(C!3, C!3), D!2)) <=> (~((~member(B!4, D!2)) | (~member(B!4, intersection(C!3, C!3)))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[90, 10])).
% 0.20/0.44 tff(92,plain,
% 0.20/0.44 (member(B!4, intersection(C!3, C!3)) <=> member(B!4, C!3)),
% 0.20/0.44 inference(monotonicity,[status(thm)],[59])).
% 0.20/0.44 tff(93,plain,
% 0.20/0.44 (member(B!4, C!3) <=> member(B!4, intersection(C!3, C!3))),
% 0.20/0.44 inference(symmetry,[status(thm)],[92])).
% 0.20/0.44 tff(94,plain,
% 0.20/0.44 (member(B!4, C!3) & member(B!4, D!2)),
% 0.20/0.44 inference(or_elim,[status(thm)],[81])).
% 0.20/0.44 tff(95,plain,
% 0.20/0.44 (member(B!4, C!3)),
% 0.20/0.44 inference(and_elim,[status(thm)],[94])).
% 0.20/0.44 tff(96,plain,
% 0.20/0.44 (member(B!4, intersection(C!3, C!3))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[95, 93])).
% 0.20/0.44 tff(97,plain,
% 0.20/0.44 (member(B!4, D!2)),
% 0.20/0.44 inference(and_elim,[status(thm)],[94])).
% 0.20/0.44 tff(98,plain,
% 0.20/0.44 ((~((~member(B!4, D!2)) | (~member(B!4, intersection(C!3, C!3))))) | (~member(B!4, D!2)) | (~member(B!4, intersection(C!3, C!3)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(99,plain,
% 0.20/0.44 ((~((~member(B!4, D!2)) | (~member(B!4, intersection(C!3, C!3))))) | (~member(B!4, intersection(C!3, C!3)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.20/0.44 tff(100,plain,
% 0.20/0.44 (~((~member(B!4, D!2)) | (~member(B!4, intersection(C!3, C!3))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[99, 96])).
% 0.20/0.44 tff(101,plain,
% 0.20/0.44 ((~(member(B!4, intersection(intersection(C!3, C!3), D!2)) <=> (~((~member(B!4, D!2)) | (~member(B!4, intersection(C!3, C!3))))))) | member(B!4, intersection(intersection(C!3, C!3), D!2)) | ((~member(B!4, D!2)) | (~member(B!4, intersection(C!3, C!3))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(102,plain,
% 0.20/0.44 (member(B!4, intersection(intersection(C!3, C!3), D!2))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[101, 100, 91])).
% 0.20/0.44 tff(103,plain,
% 0.20/0.44 (member(B!4, empty_set)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[102, 89])).
% 0.20/0.44 tff(104,plain,
% 0.20/0.44 (^[B: $i] : refl((~member(B, empty_set)) <=> (~member(B, empty_set)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(105,plain,
% 0.20/0.44 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[104])).
% 0.20/0.44 tff(106,plain,
% 0.20/0.44 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(107,axiom,(![B: $i] : (~member(B, empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','empty_set_defn')).
% 0.20/0.45 tff(108,plain,
% 0.20/0.45 (![B: $i] : (~member(B, empty_set))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.20/0.45 tff(109,plain,(
% 0.20/0.45 ![B: $i] : (~member(B, empty_set))),
% 0.20/0.45 inference(skolemize,[status(sab)],[108])).
% 0.20/0.45 tff(110,plain,
% 0.20/0.45 (![B: $i] : (~member(B, empty_set))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.20/0.45 tff(111,plain,
% 0.20/0.45 ((~![B: $i] : (~member(B, empty_set))) | (~member(B!4, empty_set))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(112,plain,
% 0.20/0.45 (~member(B!4, empty_set)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.20/0.45 tff(113,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[112, 103])).
% 0.20/0.45 % SZS output end Proof
%------------------------------------------------------------------------------