TSTP Solution File: SET175+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET175+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 05:06:01 EDT 2022
% Result : Theorem 0.18s 0.47s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET175+3 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 03:05:44 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.18/0.47 % SZS status Theorem
% 0.18/0.47 % SZS output start Proof
% 0.18/0.47 tff(member_type, type, (
% 0.18/0.47 member: ( $i * $i ) > $o)).
% 0.18/0.47 tff(union_type, type, (
% 0.18/0.47 union: ( $i * $i ) > $i)).
% 0.18/0.47 tff(tptp_fun_B_3_type, type, (
% 0.18/0.47 tptp_fun_B_3: $i)).
% 0.18/0.47 tff(intersection_type, type, (
% 0.18/0.47 intersection: ( $i * $i ) > $i)).
% 0.18/0.47 tff(tptp_fun_C_2_type, type, (
% 0.18/0.47 tptp_fun_C_2: $i)).
% 0.18/0.47 tff(tptp_fun_D_1_type, type, (
% 0.18/0.47 tptp_fun_D_1: ( $i * $i ) > $i)).
% 0.18/0.47 tff(1,plain,
% 0.18/0.47 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(2,plain,
% 0.18/0.47 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.47 tff(3,plain,
% 0.18/0.47 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(4,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 0.18/0.47 tff(5,plain,
% 0.18/0.47 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.18/0.47 tff(6,plain,(
% 0.18/0.47 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.18/0.47 inference(skolemize,[status(sab)],[5])).
% 0.18/0.47 tff(7,plain,
% 0.18/0.47 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.18/0.47 tff(8,plain,
% 0.18/0.47 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(B!3, C!2) = intersection(C!2, B!3))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(9,plain,
% 0.18/0.47 (intersection(B!3, C!2) = intersection(C!2, B!3)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.18/0.47 tff(10,plain,
% 0.18/0.47 (intersection(C!2, B!3) = intersection(B!3, C!2)),
% 0.18/0.47 inference(symmetry,[status(thm)],[9])).
% 0.18/0.47 tff(11,plain,
% 0.18/0.47 (union(intersection(C!2, B!3), B!3) = union(intersection(B!3, C!2), B!3)),
% 0.18/0.47 inference(monotonicity,[status(thm)],[10])).
% 0.18/0.47 tff(12,plain,
% 0.18/0.47 (union(intersection(B!3, C!2), B!3) = union(intersection(C!2, B!3), B!3)),
% 0.18/0.47 inference(symmetry,[status(thm)],[11])).
% 0.18/0.47 tff(13,plain,
% 0.18/0.47 (member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(C!2, B!3), B!3))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[12])).
% 0.18/0.47 tff(14,plain,
% 0.18/0.47 (member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(C!2, B!3), B!3)) <=> member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3))),
% 0.18/0.47 inference(symmetry,[status(thm)],[13])).
% 0.18/0.47 tff(15,plain,
% 0.18/0.47 (member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(C!2, B!3), B!3)) <=> member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[11])).
% 0.18/0.47 tff(16,plain,
% 0.18/0.47 ((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(C!2, B!3), B!3))) <=> (~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3)))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[15])).
% 0.18/0.47 tff(17,assumption,(~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(C!2, B!3), B!3))), introduced(assumption)).
% 0.18/0.47 tff(18,plain,
% 0.18/0.47 (~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.18/0.47 tff(19,plain,
% 0.18/0.47 (^[B: $i, C: $i, D: $i] : refl((~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(20,plain,
% 0.18/0.47 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[19])).
% 0.18/0.47 tff(21,plain,
% 0.18/0.47 (![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.18/0.47 inference(pull_quant,[status(thm)],[])).
% 0.18/0.47 tff(22,plain,
% 0.18/0.47 (^[B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) <=> ![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))), ((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) <=> (~![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))))), pull_quant((~![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))) <=> ?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C))))), ((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) <=> ?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))) <=> (?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))), pull_quant((?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> (~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))))), pull_quant((~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(23,plain,
% 0.18/0.47 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[22])).
% 0.18/0.47 tff(24,plain,
% 0.18/0.47 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[23, 21])).
% 0.18/0.47 tff(25,plain,
% 0.18/0.47 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[24, 20])).
% 0.18/0.47 tff(26,plain,
% 0.18/0.47 (^[B: $i, C: $i] : rewrite((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(27,plain,
% 0.18/0.47 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[26])).
% 0.18/0.47 tff(28,plain,
% 0.18/0.47 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[27, 25])).
% 0.18/0.47 tff(29,plain,
% 0.18/0.47 (^[B: $i, C: $i] : trans(monotonicity(rewrite(((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) <=> ((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))), rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(30,plain,
% 0.18/0.47 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[29])).
% 0.18/0.47 tff(31,plain,
% 0.18/0.47 (^[B: $i, C: $i] : rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(32,plain,
% 0.18/0.47 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))) <=> ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[31])).
% 0.18/0.47 tff(33,plain,
% 0.18/0.47 (![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)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(34,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')).
% 0.18/0.48 tff(35,plain,
% 0.18/0.48 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.18/0.48 tff(36,plain,(
% 0.18/0.48 ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))),
% 0.18/0.48 inference(skolemize,[status(sab)],[35])).
% 0.18/0.48 tff(37,plain,
% 0.18/0.48 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.18/0.48 tff(38,plain,
% 0.18/0.48 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.18/0.48 tff(39,plain,
% 0.18/0.48 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[38, 28])).
% 0.18/0.48 tff(40,plain,
% 0.18/0.48 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))) | (~((~((~(union(intersection(B!3, C!2), B!3) = B!3)) | (member(tptp_fun_D_1(C!2, B!3), union(intersection(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(C!2, B!3), B!3)))) | (~((union(intersection(B!3, C!2), B!3) = B!3) | ((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3))) <=> member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3))))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(41,plain,
% 0.18/0.48 (~((~((~(union(intersection(B!3, C!2), B!3) = B!3)) | (member(tptp_fun_D_1(C!2, B!3), union(intersection(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(C!2, B!3), B!3)))) | (~((union(intersection(B!3, C!2), B!3) = B!3) | ((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3))) <=> member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3)))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.18/0.48 tff(42,plain,
% 0.18/0.48 (((~((~(union(intersection(B!3, C!2), B!3) = B!3)) | (member(tptp_fun_D_1(C!2, B!3), union(intersection(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(C!2, B!3), B!3)))) | (~((union(intersection(B!3, C!2), B!3) = B!3) | ((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3))) <=> member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3))))) | ((union(intersection(B!3, C!2), B!3) = B!3) | ((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3))) <=> member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3)))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(43,plain,
% 0.18/0.48 ((union(intersection(B!3, C!2), B!3) = B!3) | ((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3))) <=> member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.18/0.48 tff(44,plain,
% 0.18/0.48 (^[B: $i, C: $i] : refl((union(B, C) = union(C, B)) <=> (union(B, C) = union(C, B)))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(45,plain,
% 0.18/0.48 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[44])).
% 0.18/0.48 tff(46,plain,
% 0.18/0.48 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(47,axiom,(![B: $i, C: $i] : (union(B, C) = union(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_union')).
% 0.18/0.48 tff(48,plain,
% 0.18/0.48 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.18/0.48 tff(49,plain,(
% 0.18/0.48 ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.18/0.48 inference(skolemize,[status(sab)],[48])).
% 0.18/0.48 tff(50,plain,
% 0.18/0.48 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.18/0.48 tff(51,plain,
% 0.18/0.48 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(B!3, intersection(B!3, C!2)) = union(intersection(B!3, C!2), B!3))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(52,plain,
% 0.18/0.48 (union(B!3, intersection(B!3, C!2)) = union(intersection(B!3, C!2), B!3)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.18/0.48 tff(53,plain,
% 0.18/0.48 (union(intersection(B!3, C!2), B!3) = union(B!3, intersection(B!3, C!2))),
% 0.18/0.48 inference(symmetry,[status(thm)],[52])).
% 0.18/0.48 tff(54,plain,
% 0.18/0.48 ((union(intersection(B!3, C!2), B!3) = B!3) <=> (union(B!3, intersection(B!3, C!2)) = B!3)),
% 0.18/0.48 inference(monotonicity,[status(thm)],[53])).
% 0.18/0.48 tff(55,plain,
% 0.18/0.48 ((union(B!3, intersection(B!3, C!2)) = B!3) <=> (union(intersection(B!3, C!2), B!3) = B!3)),
% 0.18/0.48 inference(symmetry,[status(thm)],[54])).
% 0.18/0.48 tff(56,plain,
% 0.18/0.48 ((~(union(B!3, intersection(B!3, C!2)) = B!3)) <=> (~(union(intersection(B!3, C!2), B!3) = B!3))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[55])).
% 0.18/0.48 tff(57,plain,
% 0.18/0.48 ((~![B: $i, C: $i] : (union(B, intersection(B, C)) = B)) <=> (~![B: $i, C: $i] : (union(B, intersection(B, C)) = B))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(58,axiom,(~![B: $i, C: $i] : (union(B, intersection(B, C)) = B)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_absorbtion_for_union')).
% 0.18/0.48 tff(59,plain,
% 0.18/0.48 (~![B: $i, C: $i] : (union(B, intersection(B, C)) = B)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.18/0.48 tff(60,plain,
% 0.18/0.48 (~![B: $i, C: $i] : (union(B, intersection(B, C)) = B)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[59, 57])).
% 0.18/0.48 tff(61,plain,
% 0.18/0.48 (~![B: $i, C: $i] : (union(B, intersection(B, C)) = B)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[60, 57])).
% 0.18/0.48 tff(62,plain,
% 0.18/0.48 (~![B: $i, C: $i] : (union(B, intersection(B, C)) = B)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.18/0.48 tff(63,plain,
% 0.18/0.48 (~![B: $i, C: $i] : (union(B, intersection(B, C)) = B)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[62, 57])).
% 0.18/0.48 tff(64,plain,
% 0.18/0.48 (~![B: $i, C: $i] : (union(B, intersection(B, C)) = B)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[63, 57])).
% 0.18/0.48 tff(65,plain,
% 0.18/0.48 (~![B: $i, C: $i] : (union(B, intersection(B, C)) = B)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.18/0.48 tff(66,plain,(
% 0.18/0.48 ~(union(B!3, intersection(B!3, C!2)) = B!3)),
% 0.18/0.48 inference(skolemize,[status(sab)],[65])).
% 0.18/0.48 tff(67,plain,
% 0.18/0.48 (~(union(intersection(B!3, C!2), B!3) = B!3)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[66, 56])).
% 0.18/0.48 tff(68,plain,
% 0.18/0.48 ((~((union(intersection(B!3, C!2), B!3) = B!3) | ((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3))) <=> member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3)))) | (union(intersection(B!3, C!2), B!3) = B!3) | ((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3))) <=> member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(69,plain,
% 0.18/0.48 ((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3))) <=> member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[68, 67, 43])).
% 0.18/0.48 tff(70,plain,
% 0.18/0.48 (^[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))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(71,plain,
% 0.18/0.48 (![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)))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[70])).
% 0.18/0.48 tff(72,plain,
% 0.18/0.48 (![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)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(73,plain,
% 0.18/0.48 (^[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))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(74,plain,
% 0.18/0.48 (![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)))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[73])).
% 0.18/0.48 tff(75,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')).
% 0.18/0.48 tff(76,plain,
% 0.18/0.48 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.18/0.48 tff(77,plain,
% 0.18/0.48 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.18/0.48 tff(78,plain,(
% 0.18/0.48 ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.18/0.48 inference(skolemize,[status(sab)],[77])).
% 0.18/0.48 tff(79,plain,
% 0.18/0.48 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[78, 71])).
% 0.18/0.48 tff(80,plain,
% 0.18/0.48 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(C!2, B!3), B!3)) <=> (member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3) | member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(81,plain,
% 0.18/0.48 (member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(C!2, B!3), B!3)) <=> (member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3) | member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.18/0.48 tff(82,plain,
% 0.18/0.48 ((~(member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(C!2, B!3), B!3)) <=> (member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3) | member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3))))) | member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(C!2, B!3), B!3)) | (~(member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3) | member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3))))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(83,plain,
% 0.18/0.48 (~(member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3) | member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[82, 17, 81])).
% 0.18/0.48 tff(84,plain,
% 0.18/0.48 ((member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3) | member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3))) | (~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(85,plain,
% 0.18/0.48 (~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.18/0.48 tff(86,plain,
% 0.18/0.48 ((~((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3))) <=> member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3))) | member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3)) | member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3)),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(87,plain,
% 0.18/0.48 (member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[86, 85, 69])).
% 0.18/0.48 tff(88,plain,
% 0.18/0.48 ($false),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[87, 18])).
% 0.18/0.48 tff(89,plain,(member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(C!2, B!3), B!3))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.48 tff(90,plain,
% 0.18/0.48 (member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[89, 14])).
% 0.18/0.48 tff(91,plain,
% 0.18/0.48 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))) | (~((~((~(union(intersection(B!3, C!2), B!3) = B!3)) | (member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3)))) | (~((union(intersection(B!3, C!2), B!3) = B!3) | ((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3))) <=> member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3))))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(92,plain,
% 0.18/0.48 (~((~((~(union(intersection(B!3, C!2), B!3) = B!3)) | (member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3)))) | (~((union(intersection(B!3, C!2), B!3) = B!3) | ((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3))) <=> member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3)))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[91, 39])).
% 0.18/0.48 tff(93,plain,
% 0.18/0.48 (((~((~(union(intersection(B!3, C!2), B!3) = B!3)) | (member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3)))) | (~((union(intersection(B!3, C!2), B!3) = B!3) | ((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3))) <=> member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3))))) | ((union(intersection(B!3, C!2), B!3) = B!3) | ((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3))) <=> member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3)))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(94,plain,
% 0.18/0.48 ((union(intersection(B!3, C!2), B!3) = B!3) | ((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3))) <=> member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.18/0.48 tff(95,plain,
% 0.18/0.48 ((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3))) <=> member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[68, 67, 94])).
% 0.18/0.48 tff(96,assumption,(~(member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3)) <=> (~((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3)) | (~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), C!2)))))), introduced(assumption)).
% 0.18/0.48 tff(97,plain,
% 0.18/0.48 (^[B: $i, C: $i, D: $i] : refl((member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C))))) <=> (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C))))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(98,plain,
% 0.18/0.48 (![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)))))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[97])).
% 0.18/0.48 tff(99,plain,
% 0.18/0.48 (^[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, B)) | (~member(D, C))))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(100,plain,
% 0.18/0.48 (![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)))))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[99])).
% 0.18/0.48 tff(101,plain,
% 0.18/0.48 (![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)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(102,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')).
% 0.18/0.48 tff(103,plain,
% 0.18/0.48 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.18/0.48 tff(104,plain,(
% 0.18/0.48 ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.18/0.48 inference(skolemize,[status(sab)],[103])).
% 0.18/0.48 tff(105,plain,
% 0.18/0.48 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.18/0.48 tff(106,plain,
% 0.18/0.48 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.18/0.48 tff(107,plain,
% 0.18/0.48 (((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3)) <=> (~((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3)) | (~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), C!2)))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3)) <=> (~((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3)) | (~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), C!2))))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(108,plain,
% 0.18/0.48 ((member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3)) <=> (~((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), C!2)) | (~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3))))) <=> (member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3)) <=> (~((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3)) | (~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), C!2)))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(109,plain,
% 0.18/0.48 (((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3)) <=> (~((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), C!2)) | (~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3)))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3)) <=> (~((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3)) | (~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), C!2))))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[108])).
% 0.18/0.48 tff(110,plain,
% 0.18/0.48 (((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3)) <=> (~((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), C!2)) | (~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3)))))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3)) <=> (~((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3)) | (~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), C!2))))))),
% 0.18/0.48 inference(transitivity,[status(thm)],[109, 107])).
% 0.18/0.48 tff(111,plain,
% 0.18/0.48 ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3)) <=> (~((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), C!2)) | (~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3)))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(112,plain,
% 0.18/0.49 ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C)))))) | (member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3)) <=> (~((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3)) | (~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), C!2)))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.18/0.49 tff(113,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[112, 106, 96])).
% 0.18/0.49 tff(114,plain,(member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3)) <=> (~((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3)) | (~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), C!2))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.49 tff(115,assumption,(~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3)), introduced(assumption)).
% 0.18/0.49 tff(116,plain,
% 0.18/0.49 ((~(member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(C!2, B!3), B!3)) <=> (member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3) | member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3))))) | (~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(C!2, B!3), B!3))) | (member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3) | member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3)))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(117,plain,
% 0.18/0.49 ((~(member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(C!2, B!3), B!3)) <=> (member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3) | member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3))))) | (member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3) | member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[116, 89])).
% 0.18/0.49 tff(118,plain,
% 0.18/0.49 (member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3) | member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[117, 81])).
% 0.18/0.49 tff(119,plain,
% 0.18/0.49 ((~(member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3) | member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3)))) | member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3) | member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(120,plain,
% 0.18/0.49 (member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3) | member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.18/0.49 tff(121,plain,
% 0.18/0.49 (member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[120, 115])).
% 0.18/0.49 tff(122,plain,
% 0.18/0.49 (((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3)) | (~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), C!2))) | member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3)),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(123,plain,
% 0.18/0.49 ((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3)) | (~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), C!2))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[122, 115])).
% 0.18/0.49 tff(124,plain,
% 0.18/0.49 ((~(member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3)) <=> (~((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3)) | (~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), C!2)))))) | (~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), intersection(C!2, B!3))) | (~((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3)) | (~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), C!2))))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(125,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[124, 123, 121, 114])).
% 0.18/0.49 tff(126,plain,(member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.49 tff(127,plain,
% 0.18/0.49 ((~((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3))) <=> member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3))) | (~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3))) | (~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(128,plain,
% 0.18/0.49 ((~((~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3))) <=> member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), B!3))) | (~member(tptp_fun_D_1(B!3, union(intersection(B!3, C!2), B!3)), union(intersection(B!3, C!2), B!3)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.18/0.49 tff(129,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[128, 95, 90])).
% 0.18/0.49 % SZS output end Proof
%------------------------------------------------------------------------------