TSTP Solution File: SET162+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET162+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 05:05:57 EDT 2022
% Result : Theorem 0.20s 0.50s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET162+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 : n001.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 03:23:09 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.
% 0.20/0.50 % SZS status Theorem
% 0.20/0.50 % SZS output start Proof
% 0.20/0.50 tff(member_type, type, (
% 0.20/0.50 member: ( $i * $i ) > $o)).
% 0.20/0.50 tff(tptp_fun_B_3_type, type, (
% 0.20/0.50 tptp_fun_B_3: $i)).
% 0.20/0.50 tff(tptp_fun_D_2_type, type, (
% 0.20/0.50 tptp_fun_D_2: ( $i * $i ) > $i)).
% 0.20/0.50 tff(union_type, type, (
% 0.20/0.50 union: ( $i * $i ) > $i)).
% 0.20/0.50 tff(empty_set_type, type, (
% 0.20/0.50 empty_set: $i)).
% 0.20/0.50 tff(tptp_fun_C_1_type, type, (
% 0.20/0.50 tptp_fun_C_1: $i > $i)).
% 0.20/0.50 tff(subset_type, type, (
% 0.20/0.50 subset: ( $i * $i ) > $o)).
% 0.20/0.50 tff(tptp_fun_D_0_type, type, (
% 0.20/0.50 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.20/0.50 tff(1,assumption,((~((~(union(empty_set, B!3) = B!3)) | (member(tptp_fun_D_2(tptp_fun_D_2(tptp_fun_D_2(B!3, empty_set), B!3), tptp_fun_C_1(B!3)), union(empty_set, B!3)) <=> member(tptp_fun_D_2(tptp_fun_D_2(tptp_fun_D_2(B!3, empty_set), B!3), tptp_fun_C_1(B!3)), B!3)))) | (~((union(empty_set, B!3) = B!3) | ((~member(tptp_fun_D_2(B!3, union(empty_set, B!3)), union(empty_set, B!3))) <=> member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3))))), introduced(assumption)).
% 0.20/0.50 tff(2,plain,
% 0.20/0.50 (^[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)))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(3,plain,
% 0.20/0.50 (![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))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.50 tff(4,plain,
% 0.20/0.50 (![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))))))),
% 0.20/0.50 inference(pull_quant,[status(thm)],[])).
% 0.20/0.50 tff(5,plain,
% 0.20/0.50 (^[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))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(6,plain,
% 0.20/0.50 (![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))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[5])).
% 0.20/0.50 tff(7,plain,
% 0.20/0.50 (![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))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[6, 4])).
% 0.20/0.50 tff(8,plain,
% 0.20/0.50 (![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))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[7, 3])).
% 0.20/0.50 tff(9,plain,
% 0.20/0.50 (^[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)))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(10,plain,
% 0.20/0.50 (![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))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[9])).
% 0.20/0.50 tff(11,plain,
% 0.20/0.50 (![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))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[10, 8])).
% 0.20/0.50 tff(12,plain,
% 0.20/0.50 (^[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))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(13,plain,
% 0.20/0.50 (![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))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.50 tff(14,plain,
% 0.20/0.50 (^[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)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(15,plain,
% 0.20/0.50 (![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))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.50 tff(16,plain,
% 0.20/0.50 (![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)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(17,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')).
% 0.20/0.50 tff(18,plain,
% 0.20/0.50 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.50 tff(19,plain,(
% 0.20/0.50 ![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)))))),
% 0.20/0.50 inference(skolemize,[status(sab)],[18])).
% 0.20/0.50 tff(20,plain,
% 0.20/0.50 (![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))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.20/0.50 tff(21,plain,
% 0.20/0.50 (![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))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.20/0.50 tff(22,plain,
% 0.20/0.50 (![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))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[21, 11])).
% 0.20/0.50 tff(23,plain,
% 0.20/0.50 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_2(C, B), B)) <=> member(tptp_fun_D_2(C, B), C))))))) | (~((~((~(union(empty_set, B!3) = B!3)) | (member(tptp_fun_D_2(tptp_fun_D_2(tptp_fun_D_2(B!3, empty_set), B!3), tptp_fun_C_1(B!3)), union(empty_set, B!3)) <=> member(tptp_fun_D_2(tptp_fun_D_2(tptp_fun_D_2(B!3, empty_set), B!3), tptp_fun_C_1(B!3)), B!3)))) | (~((union(empty_set, B!3) = B!3) | ((~member(tptp_fun_D_2(B!3, union(empty_set, B!3)), union(empty_set, B!3))) <=> member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(24,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[23, 22, 1])).
% 0.20/0.50 tff(25,plain,(~((~((~(union(empty_set, B!3) = B!3)) | (member(tptp_fun_D_2(tptp_fun_D_2(tptp_fun_D_2(B!3, empty_set), B!3), tptp_fun_C_1(B!3)), union(empty_set, B!3)) <=> member(tptp_fun_D_2(tptp_fun_D_2(tptp_fun_D_2(B!3, empty_set), B!3), tptp_fun_C_1(B!3)), B!3)))) | (~((union(empty_set, B!3) = B!3) | ((~member(tptp_fun_D_2(B!3, union(empty_set, B!3)), union(empty_set, B!3))) <=> member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(26,assumption,(~(member(tptp_fun_D_2(B!3, union(empty_set, B!3)), union(empty_set, B!3)) <=> (member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3) | member(tptp_fun_D_2(B!3, union(empty_set, B!3)), empty_set)))), introduced(assumption)).
% 0.20/0.51 tff(27,plain,
% 0.20/0.51 (^[B: $i, C: $i, D: $i] : refl((member(D, union(B, C)) <=> (member(D, C) | member(D, B))) <=> (member(D, union(B, C)) <=> (member(D, C) | member(D, B))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(28,plain,
% 0.20/0.51 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B))) <=> ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.51 tff(29,plain,
% 0.20/0.51 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B))) <=> ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(30,plain,
% 0.20/0.51 (^[B: $i, C: $i, D: $i] : rewrite((member(D, union(B, C)) <=> (member(D, B) | member(D, C))) <=> (member(D, union(B, C)) <=> (member(D, C) | member(D, B))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(31,plain,
% 0.20/0.51 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, B) | member(D, C))) <=> ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[30])).
% 0.20/0.51 tff(32,axiom,(![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, B) | member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','union_defn')).
% 0.20/0.51 tff(33,plain,
% 0.20/0.51 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.51 tff(34,plain,
% 0.20/0.51 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.20/0.51 tff(35,plain,(
% 0.20/0.51 ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[34])).
% 0.20/0.51 tff(36,plain,
% 0.20/0.51 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.20/0.51 tff(37,plain,
% 0.20/0.51 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_2(B!3, union(empty_set, B!3)), union(empty_set, B!3)) <=> (member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3) | member(tptp_fun_D_2(B!3, union(empty_set, B!3)), empty_set)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(38,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[37, 36, 26])).
% 0.20/0.51 tff(39,plain,(member(tptp_fun_D_2(B!3, union(empty_set, B!3)), union(empty_set, B!3)) <=> (member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3) | member(tptp_fun_D_2(B!3, union(empty_set, B!3)), empty_set))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(40,plain,
% 0.20/0.51 (~((~((~(union(empty_set, B!3) = B!3)) | (member(tptp_fun_D_2(tptp_fun_D_2(tptp_fun_D_2(B!3, empty_set), B!3), tptp_fun_C_1(B!3)), union(empty_set, B!3)) <=> member(tptp_fun_D_2(tptp_fun_D_2(tptp_fun_D_2(B!3, empty_set), B!3), tptp_fun_C_1(B!3)), B!3)))) | (~((union(empty_set, B!3) = B!3) | ((~member(tptp_fun_D_2(B!3, union(empty_set, B!3)), union(empty_set, B!3))) <=> member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.20/0.51 tff(41,plain,
% 0.20/0.51 (((~((~(union(empty_set, B!3) = B!3)) | (member(tptp_fun_D_2(tptp_fun_D_2(tptp_fun_D_2(B!3, empty_set), B!3), tptp_fun_C_1(B!3)), union(empty_set, B!3)) <=> member(tptp_fun_D_2(tptp_fun_D_2(tptp_fun_D_2(B!3, empty_set), B!3), tptp_fun_C_1(B!3)), B!3)))) | (~((union(empty_set, B!3) = B!3) | ((~member(tptp_fun_D_2(B!3, union(empty_set, B!3)), union(empty_set, B!3))) <=> member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3))))) | ((union(empty_set, B!3) = B!3) | ((~member(tptp_fun_D_2(B!3, union(empty_set, B!3)), union(empty_set, B!3))) <=> member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(42,plain,
% 0.20/0.51 ((union(empty_set, B!3) = B!3) | ((~member(tptp_fun_D_2(B!3, union(empty_set, B!3)), union(empty_set, B!3))) <=> member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.20/0.51 tff(43,plain,
% 0.20/0.51 (^[B: $i, C: $i] : refl((union(B, C) = union(C, B)) <=> (union(B, C) = union(C, B)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(44,plain,
% 0.20/0.51 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[43])).
% 0.20/0.51 tff(45,plain,
% 0.20/0.51 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(46,axiom,(![B: $i, C: $i] : (union(B, C) = union(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_union')).
% 0.20/0.51 tff(47,plain,
% 0.20/0.51 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.51 tff(48,plain,(
% 0.20/0.51 ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.20/0.51 inference(skolemize,[status(sab)],[47])).
% 0.20/0.51 tff(49,plain,
% 0.20/0.51 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.20/0.51 tff(50,plain,
% 0.20/0.51 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(B!3, empty_set) = union(empty_set, B!3))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(51,plain,
% 0.20/0.51 (union(B!3, empty_set) = union(empty_set, B!3)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.20/0.51 tff(52,plain,
% 0.20/0.51 (union(empty_set, B!3) = union(B!3, empty_set)),
% 0.20/0.51 inference(symmetry,[status(thm)],[51])).
% 0.20/0.51 tff(53,plain,
% 0.20/0.51 ((union(empty_set, B!3) = B!3) <=> (union(B!3, empty_set) = B!3)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[52])).
% 0.20/0.51 tff(54,plain,
% 0.20/0.51 ((union(B!3, empty_set) = B!3) <=> (union(empty_set, B!3) = B!3)),
% 0.20/0.51 inference(symmetry,[status(thm)],[53])).
% 0.20/0.51 tff(55,plain,
% 0.20/0.51 ((~(union(B!3, empty_set) = B!3)) <=> (~(union(empty_set, B!3) = B!3))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[54])).
% 0.20/0.51 tff(56,plain,
% 0.20/0.51 ((~![B: $i] : (union(B, empty_set) = B)) <=> (~![B: $i] : (union(B, empty_set) = B))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(57,axiom,(~![B: $i] : (union(B, empty_set) = B)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_union_empty_set')).
% 0.20/0.51 tff(58,plain,
% 0.20/0.51 (~![B: $i] : (union(B, empty_set) = B)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.20/0.51 tff(59,plain,
% 0.20/0.51 (~![B: $i] : (union(B, empty_set) = B)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[58, 56])).
% 0.20/0.51 tff(60,plain,
% 0.20/0.51 (~![B: $i] : (union(B, empty_set) = B)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[59, 56])).
% 0.20/0.51 tff(61,plain,
% 0.20/0.51 (~![B: $i] : (union(B, empty_set) = B)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.20/0.51 tff(62,plain,
% 0.20/0.51 (~![B: $i] : (union(B, empty_set) = B)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[61, 56])).
% 0.20/0.51 tff(63,plain,
% 0.20/0.51 (~![B: $i] : (union(B, empty_set) = B)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[62, 56])).
% 0.20/0.51 tff(64,plain,
% 0.20/0.51 (~![B: $i] : (union(B, empty_set) = B)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.20/0.51 tff(65,plain,(
% 0.20/0.51 ~(union(B!3, empty_set) = B!3)),
% 0.20/0.51 inference(skolemize,[status(sab)],[64])).
% 0.20/0.51 tff(66,plain,
% 0.20/0.51 (~(union(empty_set, B!3) = B!3)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[65, 55])).
% 0.20/0.51 tff(67,plain,
% 0.20/0.51 ((~((union(empty_set, B!3) = B!3) | ((~member(tptp_fun_D_2(B!3, union(empty_set, B!3)), union(empty_set, B!3))) <=> member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3)))) | (union(empty_set, B!3) = B!3) | ((~member(tptp_fun_D_2(B!3, union(empty_set, B!3)), union(empty_set, B!3))) <=> member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(68,plain,
% 0.20/0.51 ((~member(tptp_fun_D_2(B!3, union(empty_set, B!3)), union(empty_set, B!3))) <=> member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[67, 66, 42])).
% 0.20/0.51 tff(69,assumption,(~(member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3) | member(tptp_fun_D_2(B!3, union(empty_set, B!3)), empty_set))), introduced(assumption)).
% 0.20/0.51 tff(70,plain,
% 0.20/0.51 ((member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3) | member(tptp_fun_D_2(B!3, union(empty_set, B!3)), empty_set)) | (~member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(71,plain,
% 0.20/0.51 (~member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.20/0.51 tff(72,plain,
% 0.20/0.51 (member(tptp_fun_D_2(B!3, union(empty_set, B!3)), union(empty_set, B!3)) <=> (member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3) | member(tptp_fun_D_2(B!3, union(empty_set, B!3)), empty_set))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.20/0.51 tff(73,plain,
% 0.20/0.51 ((~(member(tptp_fun_D_2(B!3, union(empty_set, B!3)), union(empty_set, B!3)) <=> (member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3) | member(tptp_fun_D_2(B!3, union(empty_set, B!3)), empty_set)))) | (~member(tptp_fun_D_2(B!3, union(empty_set, B!3)), union(empty_set, B!3))) | (member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3) | member(tptp_fun_D_2(B!3, union(empty_set, B!3)), empty_set))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(74,plain,
% 0.20/0.51 (~member(tptp_fun_D_2(B!3, union(empty_set, B!3)), union(empty_set, B!3))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[73, 69, 72])).
% 0.20/0.51 tff(75,plain,
% 0.20/0.51 ((~((~member(tptp_fun_D_2(B!3, union(empty_set, B!3)), union(empty_set, B!3))) <=> member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3))) | member(tptp_fun_D_2(B!3, union(empty_set, B!3)), union(empty_set, B!3)) | member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(76,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[75, 74, 71, 68])).
% 0.20/0.51 tff(77,plain,(member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3) | member(tptp_fun_D_2(B!3, union(empty_set, B!3)), empty_set)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(78,plain,
% 0.20/0.51 ((~(member(tptp_fun_D_2(B!3, union(empty_set, B!3)), union(empty_set, B!3)) <=> (member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3) | member(tptp_fun_D_2(B!3, union(empty_set, B!3)), empty_set)))) | member(tptp_fun_D_2(B!3, union(empty_set, B!3)), union(empty_set, B!3)) | (~(member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3) | member(tptp_fun_D_2(B!3, union(empty_set, B!3)), empty_set)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(79,plain,
% 0.20/0.51 ((~(member(tptp_fun_D_2(B!3, union(empty_set, B!3)), union(empty_set, B!3)) <=> (member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3) | member(tptp_fun_D_2(B!3, union(empty_set, B!3)), empty_set)))) | member(tptp_fun_D_2(B!3, union(empty_set, B!3)), union(empty_set, B!3))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.20/0.51 tff(80,plain,
% 0.20/0.51 (member(tptp_fun_D_2(B!3, union(empty_set, B!3)), union(empty_set, B!3))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[79, 39])).
% 0.20/0.51 tff(81,assumption,(~member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3)), introduced(assumption)).
% 0.20/0.51 tff(82,plain,
% 0.20/0.51 ((~(member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3) | member(tptp_fun_D_2(B!3, union(empty_set, B!3)), empty_set))) | member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3) | member(tptp_fun_D_2(B!3, union(empty_set, B!3)), empty_set)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(83,plain,
% 0.20/0.51 (member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3) | member(tptp_fun_D_2(B!3, union(empty_set, B!3)), empty_set)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[82, 77])).
% 0.20/0.51 tff(84,plain,
% 0.20/0.51 (member(tptp_fun_D_2(B!3, union(empty_set, B!3)), empty_set)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[83, 81])).
% 0.20/0.51 tff(85,assumption,(member(tptp_fun_D_0(B!3, empty_set), empty_set)), introduced(assumption)).
% 0.20/0.51 tff(86,plain,
% 0.20/0.51 (^[B: $i] : refl((~member(B, empty_set)) <=> (~member(B, empty_set)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(87,plain,
% 0.20/0.51 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[86])).
% 0.20/0.51 tff(88,plain,
% 0.20/0.51 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(89,axiom,(![B: $i] : (~member(B, empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','empty_set_defn')).
% 0.20/0.51 tff(90,plain,
% 0.20/0.51 (![B: $i] : (~member(B, empty_set))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.20/0.51 tff(91,plain,(
% 0.20/0.51 ![B: $i] : (~member(B, empty_set))),
% 0.20/0.51 inference(skolemize,[status(sab)],[90])).
% 0.20/0.51 tff(92,plain,
% 0.20/0.51 (![B: $i] : (~member(B, empty_set))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.20/0.51 tff(93,plain,
% 0.20/0.51 ((~![B: $i] : (~member(B, empty_set))) | (~member(tptp_fun_D_0(B!3, empty_set), empty_set))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(94,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[93, 92, 85])).
% 0.20/0.51 tff(95,plain,(~member(tptp_fun_D_0(B!3, empty_set), empty_set)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(96,plain,
% 0.20/0.51 (((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3)) | member(tptp_fun_D_0(B!3, empty_set), empty_set)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(97,plain,
% 0.20/0.51 ((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.20/0.51 tff(98,plain,
% 0.20/0.51 (^[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))))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(99,plain,
% 0.20/0.51 (![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)))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[98])).
% 0.20/0.51 tff(100,plain,
% 0.20/0.51 (^[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))))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(101,plain,
% 0.20/0.51 (![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)))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[100])).
% 0.20/0.51 tff(102,plain,
% 0.20/0.51 (![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)))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[101, 99])).
% 0.20/0.51 tff(103,plain,
% 0.20/0.51 (^[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)))))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(104,plain,
% 0.20/0.51 (![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)))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[103])).
% 0.20/0.51 tff(105,plain,
% 0.20/0.51 (![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)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(106,plain,
% 0.20/0.51 (^[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))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(107,plain,
% 0.20/0.51 (![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)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[106])).
% 0.20/0.51 tff(108,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')).
% 0.20/0.51 tff(109,plain,
% 0.20/0.51 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.20/0.51 tff(110,plain,
% 0.20/0.51 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.20/0.51 tff(111,plain,(
% 0.20/0.51 ![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)))))),
% 0.20/0.51 inference(skolemize,[status(sab)],[110])).
% 0.20/0.51 tff(112,plain,
% 0.20/0.51 (![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)))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.20/0.51 tff(113,plain,
% 0.20/0.51 (![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)))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[112, 102])).
% 0.20/0.51 tff(114,plain,
% 0.20/0.51 (((~![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(empty_set, B!3)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!3)))) | (~((~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))) | subset(empty_set, B!3)))))) <=> ((~![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(empty_set, B!3)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!3)))) | (~((~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))) | subset(empty_set, B!3))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(115,plain,
% 0.20/0.51 ((~((~((~subset(empty_set, B!3)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!3)))) | (~(subset(empty_set, B!3) | (~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))))))) <=> (~((~((~subset(empty_set, B!3)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!3)))) | (~((~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))) | subset(empty_set, B!3)))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(116,plain,
% 0.20/0.51 (((~![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(empty_set, B!3)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!3)))) | (~(subset(empty_set, B!3) | (~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3)))))))) <=> ((~![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(empty_set, B!3)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!3)))) | (~((~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))) | subset(empty_set, B!3))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[115])).
% 0.20/0.51 tff(117,plain,
% 0.20/0.51 (((~![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(empty_set, B!3)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!3)))) | (~(subset(empty_set, B!3) | (~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3)))))))) <=> ((~![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(empty_set, B!3)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!3)))) | (~((~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))) | subset(empty_set, B!3))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[116, 114])).
% 0.20/0.51 tff(118,plain,
% 0.20/0.51 ((~![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(empty_set, B!3)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!3)))) | (~(subset(empty_set, B!3) | (~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3)))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(119,plain,
% 0.20/0.51 ((~![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(empty_set, B!3)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!3)))) | (~((~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))) | subset(empty_set, B!3)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.20/0.51 tff(120,plain,
% 0.20/0.51 (~((~((~subset(empty_set, B!3)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!3)))) | (~((~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))) | subset(empty_set, B!3))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[119, 113])).
% 0.20/0.51 tff(121,plain,
% 0.20/0.51 (((~((~subset(empty_set, B!3)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!3)))) | (~((~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))) | subset(empty_set, B!3)))) | ((~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))) | subset(empty_set, B!3))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(122,plain,
% 0.20/0.51 ((~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))) | subset(empty_set, B!3)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.20/0.51 tff(123,plain,
% 0.20/0.51 ((~((~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))) | subset(empty_set, B!3))) | (~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))) | subset(empty_set, B!3)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(124,plain,
% 0.20/0.52 ((~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))) | subset(empty_set, B!3)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.20/0.52 tff(125,plain,
% 0.20/0.52 (subset(empty_set, B!3)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[124, 97])).
% 0.20/0.52 tff(126,plain,
% 0.20/0.52 (((~((~subset(empty_set, B!3)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!3)))) | (~((~((~member(tptp_fun_D_0(B!3, empty_set), empty_set)) | member(tptp_fun_D_0(B!3, empty_set), B!3))) | subset(empty_set, B!3)))) | ((~subset(empty_set, B!3)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!3)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(127,plain,
% 0.20/0.52 ((~subset(empty_set, B!3)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!3))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[126, 120])).
% 0.20/0.52 tff(128,plain,
% 0.20/0.52 ((~((~subset(empty_set, B!3)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!3)))) | (~subset(empty_set, B!3)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!3))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(129,plain,
% 0.20/0.52 ((~subset(empty_set, B!3)) | ![D: $i] : ((~member(D, empty_set)) | member(D, B!3))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.20/0.52 tff(130,plain,
% 0.20/0.52 (![D: $i] : ((~member(D, empty_set)) | member(D, B!3))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[129, 125])).
% 0.20/0.52 tff(131,plain,
% 0.20/0.52 (((~![D: $i] : ((~member(D, empty_set)) | member(D, B!3))) | ((~member(tptp_fun_D_2(B!3, union(empty_set, B!3)), empty_set)) | member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3))) <=> ((~![D: $i] : ((~member(D, empty_set)) | member(D, B!3))) | (~member(tptp_fun_D_2(B!3, union(empty_set, B!3)), empty_set)) | member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(132,plain,
% 0.20/0.52 ((~![D: $i] : ((~member(D, empty_set)) | member(D, B!3))) | ((~member(tptp_fun_D_2(B!3, union(empty_set, B!3)), empty_set)) | member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(133,plain,
% 0.20/0.52 ((~![D: $i] : ((~member(D, empty_set)) | member(D, B!3))) | (~member(tptp_fun_D_2(B!3, union(empty_set, B!3)), empty_set)) | member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.20/0.52 tff(134,plain,
% 0.20/0.52 ((~member(tptp_fun_D_2(B!3, union(empty_set, B!3)), empty_set)) | member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[133, 130])).
% 0.20/0.52 tff(135,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[134, 84, 81])).
% 0.20/0.52 tff(136,plain,(member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(137,plain,
% 0.20/0.52 ((~((~member(tptp_fun_D_2(B!3, union(empty_set, B!3)), union(empty_set, B!3))) <=> member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3))) | (~member(tptp_fun_D_2(B!3, union(empty_set, B!3)), union(empty_set, B!3))) | (~member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(138,plain,
% 0.20/0.52 (~((~member(tptp_fun_D_2(B!3, union(empty_set, B!3)), union(empty_set, B!3))) <=> member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[137, 136, 80])).
% 0.20/0.52 tff(139,assumption,(union(empty_set, B!3) = B!3), introduced(assumption)).
% 0.20/0.52 tff(140,plain,
% 0.20/0.52 (union(B!3, empty_set) = B!3),
% 0.20/0.52 inference(transitivity,[status(thm)],[51, 139])).
% 0.20/0.52 tff(141,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[65, 140])).
% 0.20/0.52 tff(142,plain,(~(union(empty_set, B!3) = B!3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(143,plain,
% 0.20/0.52 (~((union(empty_set, B!3) = B!3) | ((~member(tptp_fun_D_2(B!3, union(empty_set, B!3)), union(empty_set, B!3))) <=> member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[67, 142, 138])).
% 0.20/0.52 tff(144,plain,
% 0.20/0.52 ((~((~(union(empty_set, B!3) = B!3)) | (member(tptp_fun_D_2(tptp_fun_D_2(tptp_fun_D_2(B!3, empty_set), B!3), tptp_fun_C_1(B!3)), union(empty_set, B!3)) <=> member(tptp_fun_D_2(tptp_fun_D_2(tptp_fun_D_2(B!3, empty_set), B!3), tptp_fun_C_1(B!3)), B!3)))) | (~((union(empty_set, B!3) = B!3) | ((~member(tptp_fun_D_2(B!3, union(empty_set, B!3)), union(empty_set, B!3))) <=> member(tptp_fun_D_2(B!3, union(empty_set, B!3)), B!3))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[41, 143])).
% 0.20/0.52 tff(145,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[144, 25])).
% 0.20/0.52 % SZS output end Proof
%------------------------------------------------------------------------------