TSTP Solution File: SET608+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET608+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 05:07:17 EDT 2022
% Result : Theorem 0.27s 0.71s
% Output : Proof 0.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.33 % Problem : SET608+3 : TPTP v8.1.0. Released v2.2.0.
% 0.05/0.33 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.53 % Computer : n012.cluster.edu
% 0.09/0.53 % Model : x86_64 x86_64
% 0.09/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.53 % Memory : 8042.1875MB
% 0.09/0.53 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.53 % CPULimit : 300
% 0.09/0.53 % WCLimit : 300
% 0.09/0.53 % DateTime : Sat Sep 3 06:53:34 EDT 2022
% 0.09/0.53 % CPUTime :
% 0.09/0.54 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.54 Usage: tptp [options] [-file:]file
% 0.09/0.54 -h, -? prints this message.
% 0.09/0.54 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.54 -m, -model generate model.
% 0.09/0.54 -p, -proof generate proof.
% 0.09/0.54 -c, -core generate unsat core of named formulas.
% 0.09/0.54 -st, -statistics display statistics.
% 0.09/0.54 -t:timeout set timeout (in second).
% 0.09/0.54 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.54 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.54 -<param>:<value> configuration parameter and value.
% 0.09/0.54 -o:<output-file> file to place output in.
% 0.27/0.71 % SZS status Theorem
% 0.27/0.71 % SZS output start Proof
% 0.27/0.71 tff(tptp_fun_B_3_type, type, (
% 0.27/0.71 tptp_fun_B_3: $i)).
% 0.27/0.71 tff(union_type, type, (
% 0.27/0.71 union: ( $i * $i ) > $i)).
% 0.27/0.71 tff(difference_type, type, (
% 0.27/0.71 difference: ( $i * $i ) > $i)).
% 0.27/0.71 tff(tptp_fun_C_2_type, type, (
% 0.27/0.71 tptp_fun_C_2: $i)).
% 0.27/0.71 tff(intersection_type, type, (
% 0.27/0.71 intersection: ( $i * $i ) > $i)).
% 0.27/0.71 tff(member_type, type, (
% 0.27/0.71 member: ( $i * $i ) > $o)).
% 0.27/0.71 tff(tptp_fun_D_1_type, type, (
% 0.27/0.71 tptp_fun_D_1: ( $i * $i ) > $i)).
% 0.27/0.71 tff(subset_type, type, (
% 0.27/0.71 subset: ( $i * $i ) > $o)).
% 0.27/0.71 tff(tptp_fun_D_0_type, type, (
% 0.27/0.71 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.27/0.71 tff(1,plain,
% 0.27/0.71 (^[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)))))))),
% 0.27/0.71 inference(bind,[status(th)],[])).
% 0.27/0.71 tff(2,plain,
% 0.27/0.71 (![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))))))),
% 0.27/0.71 inference(quant_intro,[status(thm)],[1])).
% 0.27/0.71 tff(3,plain,
% 0.27/0.71 (![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))))))),
% 0.27/0.71 inference(pull_quant,[status(thm)],[])).
% 0.27/0.71 tff(4,plain,
% 0.27/0.71 (^[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))))))))),
% 0.41/0.71 inference(bind,[status(th)],[])).
% 0.41/0.71 tff(5,plain,
% 0.41/0.71 (![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))))))),
% 0.41/0.71 inference(quant_intro,[status(thm)],[4])).
% 0.41/0.71 tff(6,plain,
% 0.41/0.71 (![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))))))),
% 0.41/0.71 inference(transitivity,[status(thm)],[5, 3])).
% 0.41/0.71 tff(7,plain,
% 0.41/0.71 (![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))))))),
% 0.41/0.71 inference(transitivity,[status(thm)],[6, 2])).
% 0.41/0.71 tff(8,plain,
% 0.41/0.71 (^[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)))))))),
% 0.41/0.71 inference(bind,[status(th)],[])).
% 0.41/0.71 tff(9,plain,
% 0.41/0.71 (![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))))))),
% 0.41/0.71 inference(quant_intro,[status(thm)],[8])).
% 0.41/0.71 tff(10,plain,
% 0.41/0.71 (![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))))))),
% 0.41/0.71 inference(transitivity,[status(thm)],[9, 7])).
% 0.41/0.71 tff(11,plain,
% 0.41/0.71 (^[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))))))))),
% 0.41/0.71 inference(bind,[status(th)],[])).
% 0.41/0.71 tff(12,plain,
% 0.41/0.71 (![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))))))),
% 0.41/0.71 inference(quant_intro,[status(thm)],[11])).
% 0.41/0.71 tff(13,plain,
% 0.41/0.71 (^[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)))))),
% 0.41/0.71 inference(bind,[status(th)],[])).
% 0.41/0.71 tff(14,plain,
% 0.41/0.71 (![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))))),
% 0.41/0.71 inference(quant_intro,[status(thm)],[13])).
% 0.41/0.71 tff(15,plain,
% 0.41/0.71 (![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)))),
% 0.41/0.71 inference(rewrite,[status(thm)],[])).
% 0.41/0.71 tff(16,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')).
% 0.41/0.71 tff(17,plain,
% 0.41/0.71 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.41/0.71 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.41/0.71 tff(18,plain,(
% 0.41/0.71 ![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)))))),
% 0.41/0.71 inference(skolemize,[status(sab)],[17])).
% 0.41/0.71 tff(19,plain,
% 0.41/0.71 (![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))))),
% 0.41/0.71 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.41/0.71 tff(20,plain,
% 0.41/0.71 (![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))))))),
% 0.41/0.71 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.41/0.71 tff(21,plain,
% 0.41/0.71 (![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))))))),
% 0.41/0.71 inference(modus_ponens,[status(thm)],[20, 10])).
% 0.41/0.71 tff(22,plain,
% 0.41/0.71 ((~![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(difference(B!3, C!2), intersection(B!3, C!2)) = B!3)) | (member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(B!3, C!2))) <=> member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)))) | (~((union(difference(B!3, C!2), intersection(B!3, C!2)) = B!3) | ((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(B!3, C!2)))) <=> member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3))))))),
% 0.41/0.71 inference(quant_inst,[status(thm)],[])).
% 0.41/0.71 tff(23,plain,
% 0.41/0.71 (~((~((~(union(difference(B!3, C!2), intersection(B!3, C!2)) = B!3)) | (member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(B!3, C!2))) <=> member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)))) | (~((union(difference(B!3, C!2), intersection(B!3, C!2)) = B!3) | ((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(B!3, C!2)))) <=> member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)))))),
% 0.41/0.71 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.41/0.71 tff(24,plain,
% 0.41/0.71 (((~((~(union(difference(B!3, C!2), intersection(B!3, C!2)) = B!3)) | (member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(B!3, C!2))) <=> member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)))) | (~((union(difference(B!3, C!2), intersection(B!3, C!2)) = B!3) | ((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(B!3, C!2)))) <=> member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3))))) | ((union(difference(B!3, C!2), intersection(B!3, C!2)) = B!3) | ((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(B!3, C!2)))) <=> member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)))),
% 0.41/0.72 inference(tautology,[status(thm)],[])).
% 0.41/0.72 tff(25,plain,
% 0.41/0.72 ((union(difference(B!3, C!2), intersection(B!3, C!2)) = B!3) | ((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(B!3, C!2)))) <=> member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3))),
% 0.41/0.72 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.41/0.72 tff(26,plain,
% 0.41/0.72 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 0.41/0.72 inference(bind,[status(th)],[])).
% 0.41/0.72 tff(27,plain,
% 0.41/0.72 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.41/0.72 inference(quant_intro,[status(thm)],[26])).
% 0.41/0.72 tff(28,plain,
% 0.41/0.72 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.41/0.72 inference(rewrite,[status(thm)],[])).
% 0.41/0.72 tff(29,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 0.41/0.72 tff(30,plain,
% 0.41/0.72 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.41/0.72 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.41/0.72 tff(31,plain,(
% 0.41/0.72 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.41/0.72 inference(skolemize,[status(sab)],[30])).
% 0.41/0.72 tff(32,plain,
% 0.41/0.72 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.41/0.72 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.41/0.72 tff(33,plain,
% 0.41/0.72 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(B!3, C!2) = intersection(C!2, B!3))),
% 0.41/0.72 inference(quant_inst,[status(thm)],[])).
% 0.41/0.72 tff(34,plain,
% 0.41/0.72 (intersection(B!3, C!2) = intersection(C!2, B!3)),
% 0.41/0.72 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.41/0.72 tff(35,plain,
% 0.41/0.72 (intersection(C!2, B!3) = intersection(B!3, C!2)),
% 0.41/0.72 inference(symmetry,[status(thm)],[34])).
% 0.41/0.72 tff(36,plain,
% 0.41/0.72 (union(difference(B!3, C!2), intersection(C!2, B!3)) = union(difference(B!3, C!2), intersection(B!3, C!2))),
% 0.41/0.72 inference(monotonicity,[status(thm)],[35])).
% 0.41/0.72 tff(37,plain,
% 0.41/0.72 (member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(C!2, B!3))) <=> member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(B!3, C!2)))),
% 0.41/0.72 inference(monotonicity,[status(thm)],[36])).
% 0.41/0.72 tff(38,plain,
% 0.41/0.72 (member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(B!3, C!2))) <=> member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(C!2, B!3)))),
% 0.41/0.72 inference(symmetry,[status(thm)],[37])).
% 0.41/0.72 tff(39,plain,
% 0.41/0.72 ((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(B!3, C!2)))) <=> (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(C!2, B!3))))),
% 0.41/0.72 inference(monotonicity,[status(thm)],[38])).
% 0.41/0.72 tff(40,assumption,(~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(B!3, C!2)))), introduced(assumption)).
% 0.41/0.72 tff(41,plain,
% 0.41/0.72 (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(C!2, B!3)))),
% 0.41/0.72 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.41/0.72 tff(42,plain,
% 0.41/0.72 (^[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))))),
% 0.41/0.72 inference(bind,[status(th)],[])).
% 0.41/0.72 tff(43,plain,
% 0.41/0.72 (![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)))),
% 0.41/0.72 inference(quant_intro,[status(thm)],[42])).
% 0.41/0.72 tff(44,plain,
% 0.41/0.72 (![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)))),
% 0.41/0.72 inference(rewrite,[status(thm)],[])).
% 0.41/0.72 tff(45,plain,
% 0.41/0.72 (^[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))))),
% 0.41/0.72 inference(bind,[status(th)],[])).
% 0.41/0.72 tff(46,plain,
% 0.41/0.72 (![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)))),
% 0.41/0.72 inference(quant_intro,[status(thm)],[45])).
% 0.41/0.72 tff(47,axiom,(![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, B) | member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','union_defn')).
% 0.41/0.72 tff(48,plain,
% 0.41/0.72 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.41/0.72 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.41/0.72 tff(49,plain,
% 0.41/0.72 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.41/0.72 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.41/0.72 tff(50,plain,(
% 0.41/0.72 ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.41/0.72 inference(skolemize,[status(sab)],[49])).
% 0.41/0.72 tff(51,plain,
% 0.41/0.72 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.41/0.72 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.41/0.72 tff(52,plain,
% 0.41/0.72 (((~![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(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(C!2, B!3))) <=> (member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2)) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3))))) <=> ((~![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(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(C!2, B!3))) <=> (member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2)) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3)))))),
% 0.41/0.72 inference(rewrite,[status(thm)],[])).
% 0.41/0.72 tff(53,plain,
% 0.41/0.72 ((member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(C!2, B!3))) <=> (member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3)) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2)))) <=> (member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(C!2, B!3))) <=> (member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2)) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3))))),
% 0.41/0.72 inference(rewrite,[status(thm)],[])).
% 0.41/0.72 tff(54,plain,
% 0.41/0.72 (((~![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(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(C!2, B!3))) <=> (member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3)) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2))))) <=> ((~![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(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(C!2, B!3))) <=> (member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2)) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3)))))),
% 0.41/0.72 inference(monotonicity,[status(thm)],[53])).
% 0.41/0.72 tff(55,plain,
% 0.41/0.72 (((~![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(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(C!2, B!3))) <=> (member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3)) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2))))) <=> ((~![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(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(C!2, B!3))) <=> (member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2)) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3)))))),
% 0.41/0.72 inference(transitivity,[status(thm)],[54, 52])).
% 0.41/0.72 tff(56,plain,
% 0.41/0.72 ((~![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(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(C!2, B!3))) <=> (member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3)) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2))))),
% 0.41/0.72 inference(quant_inst,[status(thm)],[])).
% 0.41/0.72 tff(57,plain,
% 0.41/0.72 ((~![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(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(C!2, B!3))) <=> (member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2)) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3))))),
% 0.41/0.72 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.41/0.72 tff(58,plain,
% 0.41/0.72 (member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(C!2, B!3))) <=> (member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2)) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3)))),
% 0.41/0.72 inference(unit_resolution,[status(thm)],[57, 51])).
% 0.41/0.72 tff(59,plain,
% 0.41/0.72 (^[B: $i, C: $i, D: $i] : refl((member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))) <=> (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))))),
% 0.41/0.72 inference(bind,[status(th)],[])).
% 0.41/0.72 tff(60,plain,
% 0.41/0.72 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))) <=> ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 0.41/0.72 inference(quant_intro,[status(thm)],[59])).
% 0.41/0.72 tff(61,plain,
% 0.41/0.72 (^[B: $i, C: $i, D: $i] : rewrite((member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))))),
% 0.41/0.72 inference(bind,[status(th)],[])).
% 0.41/0.72 tff(62,plain,
% 0.41/0.72 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 0.41/0.72 inference(quant_intro,[status(thm)],[61])).
% 0.41/0.72 tff(63,plain,
% 0.41/0.72 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.41/0.73 inference(rewrite,[status(thm)],[])).
% 0.41/0.73 tff(64,axiom,(![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','difference_defn')).
% 0.41/0.73 tff(65,plain,
% 0.41/0.73 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.41/0.73 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.41/0.73 tff(66,plain,(
% 0.41/0.73 ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.41/0.73 inference(skolemize,[status(sab)],[65])).
% 0.41/0.73 tff(67,plain,
% 0.41/0.73 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 0.41/0.73 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.41/0.73 tff(68,plain,
% 0.41/0.73 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 0.41/0.73 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.41/0.73 tff(69,plain,
% 0.41/0.73 ((~![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))) | (member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2)) <=> (~((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), C!2))))),
% 0.41/0.73 inference(quant_inst,[status(thm)],[])).
% 0.41/0.73 tff(70,plain,
% 0.41/0.73 (member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2)) <=> (~((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), C!2)))),
% 0.41/0.73 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.41/0.73 tff(71,assumption,(~(member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2)) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3)))), introduced(assumption)).
% 0.41/0.73 tff(72,plain,
% 0.41/0.73 ((member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2)) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3))) | (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2)))),
% 0.41/0.73 inference(tautology,[status(thm)],[])).
% 0.41/0.73 tff(73,plain,
% 0.41/0.73 (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2))),
% 0.41/0.73 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.41/0.73 tff(74,plain,
% 0.41/0.73 ((~(member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2)) <=> (~((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), C!2))))) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2)) | ((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), C!2))),
% 0.41/0.73 inference(tautology,[status(thm)],[])).
% 0.41/0.73 tff(75,plain,
% 0.41/0.73 ((~(member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2)) <=> (~((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), C!2))))) | ((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), C!2))),
% 0.41/0.73 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.41/0.73 tff(76,plain,
% 0.41/0.73 ((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), C!2)),
% 0.41/0.73 inference(unit_resolution,[status(thm)],[75, 70])).
% 0.41/0.73 tff(77,plain,
% 0.41/0.73 ((~![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(difference(B!3, C!2), intersection(B!3, C!2)) = B!3)) | (member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), intersection(C!2, B!3)), union(difference(B!3, C!2), intersection(B!3, C!2))) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), intersection(C!2, B!3)), B!3)))) | (~((union(difference(B!3, C!2), intersection(B!3, C!2)) = B!3) | ((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(B!3, C!2)))) <=> member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3))))))),
% 0.41/0.73 inference(quant_inst,[status(thm)],[])).
% 0.41/0.73 tff(78,plain,
% 0.41/0.73 (~((~((~(union(difference(B!3, C!2), intersection(B!3, C!2)) = B!3)) | (member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), intersection(C!2, B!3)), union(difference(B!3, C!2), intersection(B!3, C!2))) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), intersection(C!2, B!3)), B!3)))) | (~((union(difference(B!3, C!2), intersection(B!3, C!2)) = B!3) | ((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(B!3, C!2)))) <=> member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)))))),
% 0.41/0.73 inference(unit_resolution,[status(thm)],[77, 21])).
% 0.41/0.73 tff(79,plain,
% 0.41/0.73 (((~((~(union(difference(B!3, C!2), intersection(B!3, C!2)) = B!3)) | (member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), intersection(C!2, B!3)), union(difference(B!3, C!2), intersection(B!3, C!2))) <=> member(tptp_fun_D_1(union(difference(B!3, C!2), intersection(B!3, C!2)), intersection(C!2, B!3)), B!3)))) | (~((union(difference(B!3, C!2), intersection(B!3, C!2)) = B!3) | ((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(B!3, C!2)))) <=> member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3))))) | ((union(difference(B!3, C!2), intersection(B!3, C!2)) = B!3) | ((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(B!3, C!2)))) <=> member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)))),
% 0.41/0.73 inference(tautology,[status(thm)],[])).
% 0.41/0.73 tff(80,plain,
% 0.41/0.73 ((union(difference(B!3, C!2), intersection(B!3, C!2)) = B!3) | ((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(B!3, C!2)))) <=> member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3))),
% 0.41/0.73 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.41/0.73 tff(81,plain,
% 0.41/0.73 (^[B: $i, C: $i] : refl((union(B, C) = union(C, B)) <=> (union(B, C) = union(C, B)))),
% 0.41/0.73 inference(bind,[status(th)],[])).
% 0.41/0.73 tff(82,plain,
% 0.41/0.73 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.41/0.73 inference(quant_intro,[status(thm)],[81])).
% 0.41/0.73 tff(83,plain,
% 0.41/0.73 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.41/0.73 inference(rewrite,[status(thm)],[])).
% 0.41/0.73 tff(84,axiom,(![B: $i, C: $i] : (union(B, C) = union(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_of_union')).
% 0.41/0.73 tff(85,plain,
% 0.41/0.73 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.41/0.73 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.41/0.73 tff(86,plain,(
% 0.41/0.73 ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.41/0.73 inference(skolemize,[status(sab)],[85])).
% 0.41/0.73 tff(87,plain,
% 0.41/0.73 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.41/0.73 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.41/0.73 tff(88,plain,
% 0.41/0.73 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(intersection(B!3, C!2), difference(B!3, C!2)) = union(difference(B!3, C!2), intersection(B!3, C!2)))),
% 0.41/0.73 inference(quant_inst,[status(thm)],[])).
% 0.41/0.73 tff(89,plain,
% 0.41/0.73 (union(intersection(B!3, C!2), difference(B!3, C!2)) = union(difference(B!3, C!2), intersection(B!3, C!2))),
% 0.41/0.74 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.41/0.74 tff(90,plain,
% 0.41/0.74 (union(difference(B!3, C!2), intersection(B!3, C!2)) = union(intersection(B!3, C!2), difference(B!3, C!2))),
% 0.41/0.74 inference(symmetry,[status(thm)],[89])).
% 0.41/0.74 tff(91,plain,
% 0.41/0.74 ((union(difference(B!3, C!2), intersection(B!3, C!2)) = B!3) <=> (union(intersection(B!3, C!2), difference(B!3, C!2)) = B!3)),
% 0.41/0.74 inference(monotonicity,[status(thm)],[90])).
% 0.41/0.74 tff(92,plain,
% 0.41/0.74 ((union(intersection(B!3, C!2), difference(B!3, C!2)) = B!3) <=> (union(difference(B!3, C!2), intersection(B!3, C!2)) = B!3)),
% 0.41/0.74 inference(symmetry,[status(thm)],[91])).
% 0.41/0.74 tff(93,plain,
% 0.41/0.74 ((~(union(intersection(B!3, C!2), difference(B!3, C!2)) = B!3)) <=> (~(union(difference(B!3, C!2), intersection(B!3, C!2)) = B!3))),
% 0.41/0.74 inference(monotonicity,[status(thm)],[92])).
% 0.41/0.74 tff(94,plain,
% 0.41/0.74 ((~![B: $i, C: $i] : (union(intersection(B, C), difference(B, C)) = B)) <=> (~![B: $i, C: $i] : (union(intersection(B, C), difference(B, C)) = B))),
% 0.41/0.74 inference(rewrite,[status(thm)],[])).
% 0.41/0.74 tff(95,axiom,(~![B: $i, C: $i] : (union(intersection(B, C), difference(B, C)) = B)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_union_intersection_difference')).
% 0.41/0.74 tff(96,plain,
% 0.41/0.74 (~![B: $i, C: $i] : (union(intersection(B, C), difference(B, C)) = B)),
% 0.41/0.74 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.41/0.74 tff(97,plain,
% 0.41/0.74 (~![B: $i, C: $i] : (union(intersection(B, C), difference(B, C)) = B)),
% 0.41/0.74 inference(modus_ponens,[status(thm)],[96, 94])).
% 0.41/0.74 tff(98,plain,
% 0.41/0.74 (~![B: $i, C: $i] : (union(intersection(B, C), difference(B, C)) = B)),
% 0.41/0.74 inference(modus_ponens,[status(thm)],[97, 94])).
% 0.41/0.74 tff(99,plain,
% 0.41/0.74 (~![B: $i, C: $i] : (union(intersection(B, C), difference(B, C)) = B)),
% 0.41/0.74 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.41/0.74 tff(100,plain,
% 0.41/0.74 (~![B: $i, C: $i] : (union(intersection(B, C), difference(B, C)) = B)),
% 0.41/0.74 inference(modus_ponens,[status(thm)],[99, 94])).
% 0.41/0.74 tff(101,plain,
% 0.41/0.74 (~![B: $i, C: $i] : (union(intersection(B, C), difference(B, C)) = B)),
% 0.41/0.74 inference(modus_ponens,[status(thm)],[100, 94])).
% 0.41/0.74 tff(102,plain,
% 0.41/0.74 (~![B: $i, C: $i] : (union(intersection(B, C), difference(B, C)) = B)),
% 0.41/0.74 inference(modus_ponens,[status(thm)],[101, 94])).
% 0.41/0.74 tff(103,plain,(
% 0.41/0.74 ~(union(intersection(B!3, C!2), difference(B!3, C!2)) = B!3)),
% 0.41/0.74 inference(skolemize,[status(sab)],[102])).
% 0.41/0.74 tff(104,plain,
% 0.41/0.74 (~(union(difference(B!3, C!2), intersection(B!3, C!2)) = B!3)),
% 0.41/0.74 inference(modus_ponens,[status(thm)],[103, 93])).
% 0.41/0.74 tff(105,plain,
% 0.41/0.74 ((~((union(difference(B!3, C!2), intersection(B!3, C!2)) = B!3) | ((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(B!3, C!2)))) <=> member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)))) | (union(difference(B!3, C!2), intersection(B!3, C!2)) = B!3) | ((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(B!3, C!2)))) <=> member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3))),
% 0.41/0.74 inference(tautology,[status(thm)],[])).
% 0.41/0.74 tff(106,plain,
% 0.41/0.74 ((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(B!3, C!2)))) <=> member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)),
% 0.41/0.74 inference(unit_resolution,[status(thm)],[105, 104, 80])).
% 0.41/0.74 tff(107,plain,
% 0.41/0.74 ((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(C!2, B!3)))) <=> (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(B!3, C!2))))),
% 0.41/0.74 inference(monotonicity,[status(thm)],[37])).
% 0.41/0.74 tff(108,plain,
% 0.41/0.74 ((~(member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(C!2, B!3))) <=> (member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2)) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3))))) | (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(C!2, B!3)))) | (member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2)) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3)))),
% 0.41/0.74 inference(tautology,[status(thm)],[])).
% 0.41/0.74 tff(109,plain,
% 0.41/0.74 (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(C!2, B!3)))),
% 0.41/0.74 inference(unit_resolution,[status(thm)],[108, 71, 58])).
% 0.41/0.74 tff(110,plain,
% 0.41/0.74 (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(B!3, C!2)))),
% 0.41/0.74 inference(modus_ponens,[status(thm)],[109, 107])).
% 0.41/0.74 tff(111,plain,
% 0.41/0.74 ((~((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(B!3, C!2)))) <=> member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3))) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(B!3, C!2))) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)),
% 0.41/0.74 inference(tautology,[status(thm)],[])).
% 0.41/0.74 tff(112,plain,
% 0.41/0.74 (member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)),
% 0.41/0.74 inference(unit_resolution,[status(thm)],[111, 110, 106])).
% 0.41/0.74 tff(113,plain,
% 0.41/0.74 (^[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))))))),
% 0.41/0.74 inference(bind,[status(th)],[])).
% 0.41/0.74 tff(114,plain,
% 0.41/0.74 (![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)))))),
% 0.41/0.74 inference(quant_intro,[status(thm)],[113])).
% 0.41/0.74 tff(115,plain,
% 0.41/0.74 (^[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))))))),
% 0.41/0.74 inference(bind,[status(th)],[])).
% 0.41/0.74 tff(116,plain,
% 0.41/0.74 (![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)))))),
% 0.41/0.74 inference(quant_intro,[status(thm)],[115])).
% 0.41/0.74 tff(117,plain,
% 0.41/0.74 (![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)))),
% 0.41/0.74 inference(rewrite,[status(thm)],[])).
% 0.41/0.74 tff(118,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')).
% 0.41/0.74 tff(119,plain,
% 0.41/0.74 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.41/0.74 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.41/0.74 tff(120,plain,(
% 0.41/0.74 ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.41/0.74 inference(skolemize,[status(sab)],[119])).
% 0.41/0.74 tff(121,plain,
% 0.41/0.74 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))),
% 0.41/0.74 inference(modus_ponens,[status(thm)],[120, 116])).
% 0.41/0.74 tff(122,plain,
% 0.41/0.74 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))),
% 0.41/0.74 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.41/0.74 tff(123,plain,
% 0.41/0.74 ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3)) <=> (~((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)) | (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), C!2)))))),
% 0.41/0.74 inference(quant_inst,[status(thm)],[])).
% 0.41/0.74 tff(124,plain,
% 0.41/0.74 (member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3)) <=> (~((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)) | (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), C!2))))),
% 0.41/0.74 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.41/0.74 tff(125,plain,
% 0.41/0.74 ((member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2)) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3))) | (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3)))),
% 0.41/0.74 inference(tautology,[status(thm)],[])).
% 0.41/0.74 tff(126,plain,
% 0.41/0.74 (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3))),
% 0.41/0.74 inference(unit_resolution,[status(thm)],[125, 71])).
% 0.41/0.74 tff(127,plain,
% 0.41/0.74 ((~(member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3)) <=> (~((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)) | (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), C!2)))))) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3)) | ((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)) | (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), C!2)))),
% 0.41/0.74 inference(tautology,[status(thm)],[])).
% 0.41/0.74 tff(128,plain,
% 0.41/0.74 ((~(member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3)) <=> (~((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)) | (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), C!2)))))) | ((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)) | (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), C!2)))),
% 0.41/0.74 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.41/0.74 tff(129,plain,
% 0.41/0.74 ((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)) | (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), C!2))),
% 0.41/0.74 inference(unit_resolution,[status(thm)],[128, 124])).
% 0.41/0.74 tff(130,plain,
% 0.41/0.74 ((~((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)) | (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), C!2)))) | (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)) | (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), C!2))),
% 0.41/0.74 inference(tautology,[status(thm)],[])).
% 0.41/0.74 tff(131,plain,
% 0.41/0.74 (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), C!2)),
% 0.41/0.74 inference(unit_resolution,[status(thm)],[130, 112, 129])).
% 0.41/0.74 tff(132,plain,
% 0.41/0.74 ((~((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), C!2))) | (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), C!2)),
% 0.41/0.74 inference(tautology,[status(thm)],[])).
% 0.41/0.74 tff(133,plain,
% 0.41/0.74 ($false),
% 0.41/0.74 inference(unit_resolution,[status(thm)],[132, 131, 112, 76])).
% 0.41/0.74 tff(134,plain,(member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2)) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3))), inference(lemma,lemma(discharge,[]))).
% 0.41/0.74 tff(135,plain,
% 0.41/0.74 ((~(member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(C!2, B!3))) <=> (member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2)) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3))))) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(C!2, B!3))) | (~(member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2)) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3))))),
% 0.41/0.75 inference(tautology,[status(thm)],[])).
% 0.41/0.75 tff(136,plain,
% 0.41/0.75 ((~(member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(C!2, B!3))) <=> (member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2)) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3))))) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(C!2, B!3)))),
% 0.41/0.75 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.41/0.75 tff(137,plain,
% 0.41/0.75 (member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(C!2, B!3)))),
% 0.41/0.75 inference(unit_resolution,[status(thm)],[136, 58])).
% 0.41/0.75 tff(138,plain,
% 0.41/0.75 ($false),
% 0.41/0.75 inference(unit_resolution,[status(thm)],[137, 41])).
% 0.41/0.75 tff(139,plain,(member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(B!3, C!2)))), inference(lemma,lemma(discharge,[]))).
% 0.41/0.75 tff(140,assumption,(~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)), introduced(assumption)).
% 0.41/0.75 tff(141,assumption,(~((~member(tptp_fun_D_0(B!3, difference(B!3, C!2)), difference(B!3, C!2))) | member(tptp_fun_D_0(B!3, difference(B!3, C!2)), B!3))), introduced(assumption)).
% 0.41/0.75 tff(142,plain,
% 0.41/0.75 (((~member(tptp_fun_D_0(B!3, difference(B!3, C!2)), difference(B!3, C!2))) | member(tptp_fun_D_0(B!3, difference(B!3, C!2)), B!3)) | (~member(tptp_fun_D_0(B!3, difference(B!3, C!2)), B!3))),
% 0.41/0.75 inference(tautology,[status(thm)],[])).
% 0.41/0.75 tff(143,plain,
% 0.41/0.75 (~member(tptp_fun_D_0(B!3, difference(B!3, C!2)), B!3)),
% 0.41/0.75 inference(unit_resolution,[status(thm)],[142, 141])).
% 0.41/0.75 tff(144,assumption,(~(member(tptp_fun_D_0(B!3, difference(B!3, C!2)), difference(B!3, C!2)) <=> (~((~member(tptp_fun_D_0(B!3, difference(B!3, C!2)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, C!2)), C!2))))), introduced(assumption)).
% 0.41/0.75 tff(145,plain,
% 0.41/0.75 ((~![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))) | (member(tptp_fun_D_0(B!3, difference(B!3, C!2)), difference(B!3, C!2)) <=> (~((~member(tptp_fun_D_0(B!3, difference(B!3, C!2)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, C!2)), C!2))))),
% 0.41/0.75 inference(quant_inst,[status(thm)],[])).
% 0.41/0.75 tff(146,plain,
% 0.41/0.75 ($false),
% 0.41/0.75 inference(unit_resolution,[status(thm)],[145, 68, 144])).
% 0.41/0.75 tff(147,plain,(member(tptp_fun_D_0(B!3, difference(B!3, C!2)), difference(B!3, C!2)) <=> (~((~member(tptp_fun_D_0(B!3, difference(B!3, C!2)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, C!2)), C!2)))), inference(lemma,lemma(discharge,[]))).
% 0.41/0.75 tff(148,plain,
% 0.41/0.75 (((~member(tptp_fun_D_0(B!3, difference(B!3, C!2)), difference(B!3, C!2))) | member(tptp_fun_D_0(B!3, difference(B!3, C!2)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, C!2)), difference(B!3, C!2))),
% 0.41/0.75 inference(tautology,[status(thm)],[])).
% 0.41/0.75 tff(149,plain,
% 0.41/0.75 (member(tptp_fun_D_0(B!3, difference(B!3, C!2)), difference(B!3, C!2))),
% 0.41/0.75 inference(unit_resolution,[status(thm)],[148, 141])).
% 0.41/0.75 tff(150,plain,
% 0.41/0.75 ((~(member(tptp_fun_D_0(B!3, difference(B!3, C!2)), difference(B!3, C!2)) <=> (~((~member(tptp_fun_D_0(B!3, difference(B!3, C!2)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, C!2)), C!2))))) | (~member(tptp_fun_D_0(B!3, difference(B!3, C!2)), difference(B!3, C!2))) | (~((~member(tptp_fun_D_0(B!3, difference(B!3, C!2)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, C!2)), C!2)))),
% 0.41/0.75 inference(tautology,[status(thm)],[])).
% 0.41/0.75 tff(151,plain,
% 0.41/0.75 (~((~member(tptp_fun_D_0(B!3, difference(B!3, C!2)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, C!2)), C!2))),
% 0.41/0.75 inference(unit_resolution,[status(thm)],[150, 149, 147])).
% 0.41/0.75 tff(152,plain,
% 0.41/0.75 (((~member(tptp_fun_D_0(B!3, difference(B!3, C!2)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, C!2)), C!2)) | member(tptp_fun_D_0(B!3, difference(B!3, C!2)), B!3)),
% 0.41/0.75 inference(tautology,[status(thm)],[])).
% 0.41/0.75 tff(153,plain,
% 0.41/0.75 ($false),
% 0.41/0.75 inference(unit_resolution,[status(thm)],[152, 151, 143])).
% 0.41/0.75 tff(154,plain,((~member(tptp_fun_D_0(B!3, difference(B!3, C!2)), difference(B!3, C!2))) | member(tptp_fun_D_0(B!3, difference(B!3, C!2)), B!3)), inference(lemma,lemma(discharge,[]))).
% 0.41/0.75 tff(155,plain,
% 0.41/0.75 (^[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))))))))),
% 0.41/0.75 inference(bind,[status(th)],[])).
% 0.41/0.75 tff(156,plain,
% 0.41/0.75 (![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)))))))),
% 0.41/0.75 inference(quant_intro,[status(thm)],[155])).
% 0.41/0.75 tff(157,plain,
% 0.41/0.75 (^[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))))))))),
% 0.41/0.75 inference(bind,[status(th)],[])).
% 0.41/0.75 tff(158,plain,
% 0.41/0.75 (![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)))))))),
% 0.41/0.75 inference(quant_intro,[status(thm)],[157])).
% 0.41/0.75 tff(159,plain,
% 0.41/0.75 (![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)))))))),
% 0.41/0.75 inference(transitivity,[status(thm)],[158, 156])).
% 0.41/0.75 tff(160,plain,
% 0.41/0.75 (^[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)))))))))),
% 0.41/0.75 inference(bind,[status(th)],[])).
% 0.41/0.75 tff(161,plain,
% 0.41/0.75 (![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)))))))),
% 0.41/0.75 inference(quant_intro,[status(thm)],[160])).
% 0.41/0.75 tff(162,plain,
% 0.41/0.75 (![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)))),
% 0.41/0.75 inference(rewrite,[status(thm)],[])).
% 0.41/0.75 tff(163,plain,
% 0.41/0.75 (^[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))))),
% 0.41/0.75 inference(bind,[status(th)],[])).
% 0.41/0.75 tff(164,plain,
% 0.41/0.75 (![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)))),
% 0.41/0.75 inference(quant_intro,[status(thm)],[163])).
% 0.41/0.75 tff(165,axiom,(![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','subset_defn')).
% 0.41/0.75 tff(166,plain,
% 0.41/0.75 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.41/0.75 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.41/0.75 tff(167,plain,
% 0.41/0.75 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.41/0.75 inference(modus_ponens,[status(thm)],[166, 162])).
% 0.41/0.75 tff(168,plain,(
% 0.41/0.75 ![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)))))),
% 0.41/0.75 inference(skolemize,[status(sab)],[167])).
% 0.41/0.75 tff(169,plain,
% 0.41/0.75 (![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)))))))),
% 0.41/0.75 inference(modus_ponens,[status(thm)],[168, 161])).
% 0.41/0.75 tff(170,plain,
% 0.41/0.75 (![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)))))))),
% 0.41/0.75 inference(modus_ponens,[status(thm)],[169, 159])).
% 0.41/0.75 tff(171,plain,
% 0.41/0.75 ((~![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(difference(B!3, C!2), B!3)) | ![D: $i] : ((~member(D, difference(B!3, C!2))) | member(D, B!3)))) | (~(subset(difference(B!3, C!2), B!3) | (~((~member(tptp_fun_D_0(B!3, difference(B!3, C!2)), difference(B!3, C!2))) | member(tptp_fun_D_0(B!3, difference(B!3, C!2)), B!3)))))))),
% 0.41/0.75 inference(quant_inst,[status(thm)],[])).
% 0.41/0.75 tff(172,plain,
% 0.41/0.75 (~((~((~subset(difference(B!3, C!2), B!3)) | ![D: $i] : ((~member(D, difference(B!3, C!2))) | member(D, B!3)))) | (~(subset(difference(B!3, C!2), B!3) | (~((~member(tptp_fun_D_0(B!3, difference(B!3, C!2)), difference(B!3, C!2))) | member(tptp_fun_D_0(B!3, difference(B!3, C!2)), B!3))))))),
% 0.41/0.75 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.41/0.75 tff(173,plain,
% 0.41/0.75 (((~((~subset(difference(B!3, C!2), B!3)) | ![D: $i] : ((~member(D, difference(B!3, C!2))) | member(D, B!3)))) | (~(subset(difference(B!3, C!2), B!3) | (~((~member(tptp_fun_D_0(B!3, difference(B!3, C!2)), difference(B!3, C!2))) | member(tptp_fun_D_0(B!3, difference(B!3, C!2)), B!3)))))) | (subset(difference(B!3, C!2), B!3) | (~((~member(tptp_fun_D_0(B!3, difference(B!3, C!2)), difference(B!3, C!2))) | member(tptp_fun_D_0(B!3, difference(B!3, C!2)), B!3))))),
% 0.41/0.75 inference(tautology,[status(thm)],[])).
% 0.41/0.75 tff(174,plain,
% 0.41/0.75 (subset(difference(B!3, C!2), B!3) | (~((~member(tptp_fun_D_0(B!3, difference(B!3, C!2)), difference(B!3, C!2))) | member(tptp_fun_D_0(B!3, difference(B!3, C!2)), B!3)))),
% 0.41/0.75 inference(unit_resolution,[status(thm)],[173, 172])).
% 0.41/0.75 tff(175,plain,
% 0.41/0.75 ((~(subset(difference(B!3, C!2), B!3) | (~((~member(tptp_fun_D_0(B!3, difference(B!3, C!2)), difference(B!3, C!2))) | member(tptp_fun_D_0(B!3, difference(B!3, C!2)), B!3))))) | subset(difference(B!3, C!2), B!3) | (~((~member(tptp_fun_D_0(B!3, difference(B!3, C!2)), difference(B!3, C!2))) | member(tptp_fun_D_0(B!3, difference(B!3, C!2)), B!3)))),
% 0.41/0.75 inference(tautology,[status(thm)],[])).
% 0.41/0.75 tff(176,plain,
% 0.41/0.75 (subset(difference(B!3, C!2), B!3) | (~((~member(tptp_fun_D_0(B!3, difference(B!3, C!2)), difference(B!3, C!2))) | member(tptp_fun_D_0(B!3, difference(B!3, C!2)), B!3)))),
% 0.41/0.75 inference(unit_resolution,[status(thm)],[175, 174])).
% 0.41/0.75 tff(177,plain,
% 0.41/0.75 (subset(difference(B!3, C!2), B!3)),
% 0.41/0.75 inference(unit_resolution,[status(thm)],[176, 154])).
% 0.41/0.75 tff(178,plain,
% 0.41/0.75 (((~((~subset(difference(B!3, C!2), B!3)) | ![D: $i] : ((~member(D, difference(B!3, C!2))) | member(D, B!3)))) | (~(subset(difference(B!3, C!2), B!3) | (~((~member(tptp_fun_D_0(B!3, difference(B!3, C!2)), difference(B!3, C!2))) | member(tptp_fun_D_0(B!3, difference(B!3, C!2)), B!3)))))) | ((~subset(difference(B!3, C!2), B!3)) | ![D: $i] : ((~member(D, difference(B!3, C!2))) | member(D, B!3)))),
% 0.41/0.75 inference(tautology,[status(thm)],[])).
% 0.41/0.75 tff(179,plain,
% 0.41/0.75 ((~subset(difference(B!3, C!2), B!3)) | ![D: $i] : ((~member(D, difference(B!3, C!2))) | member(D, B!3))),
% 0.41/0.75 inference(unit_resolution,[status(thm)],[178, 172])).
% 0.41/0.75 tff(180,plain,
% 0.41/0.75 ((~((~subset(difference(B!3, C!2), B!3)) | ![D: $i] : ((~member(D, difference(B!3, C!2))) | member(D, B!3)))) | (~subset(difference(B!3, C!2), B!3)) | ![D: $i] : ((~member(D, difference(B!3, C!2))) | member(D, B!3))),
% 0.41/0.75 inference(tautology,[status(thm)],[])).
% 0.41/0.75 tff(181,plain,
% 0.41/0.75 ((~subset(difference(B!3, C!2), B!3)) | ![D: $i] : ((~member(D, difference(B!3, C!2))) | member(D, B!3))),
% 0.41/0.75 inference(unit_resolution,[status(thm)],[180, 179])).
% 0.41/0.75 tff(182,plain,
% 0.41/0.75 (![D: $i] : ((~member(D, difference(B!3, C!2))) | member(D, B!3))),
% 0.41/0.75 inference(unit_resolution,[status(thm)],[181, 177])).
% 0.41/0.75 tff(183,plain,
% 0.41/0.75 (((~![D: $i] : ((~member(D, difference(B!3, C!2))) | member(D, B!3))) | ((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2))) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3))) <=> ((~![D: $i] : ((~member(D, difference(B!3, C!2))) | member(D, B!3))) | (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2))) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3))),
% 0.41/0.75 inference(rewrite,[status(thm)],[])).
% 0.41/0.75 tff(184,plain,
% 0.41/0.75 ((~![D: $i] : ((~member(D, difference(B!3, C!2))) | member(D, B!3))) | ((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2))) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3))),
% 0.41/0.75 inference(quant_inst,[status(thm)],[])).
% 0.41/0.75 tff(185,plain,
% 0.41/0.75 ((~![D: $i] : ((~member(D, difference(B!3, C!2))) | member(D, B!3))) | (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2))) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)),
% 0.41/0.75 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.41/0.75 tff(186,plain,
% 0.41/0.75 ((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2))) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)),
% 0.41/0.75 inference(unit_resolution,[status(thm)],[185, 182])).
% 0.41/0.75 tff(187,plain,
% 0.41/0.75 (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2))),
% 0.41/0.75 inference(unit_resolution,[status(thm)],[186, 140])).
% 0.41/0.75 tff(188,assumption,(~(member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3)) <=> (~((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)) | (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), C!2)))))), introduced(assumption)).
% 0.41/0.76 tff(189,plain,
% 0.41/0.76 ($false),
% 0.41/0.76 inference(unit_resolution,[status(thm)],[123, 122, 188])).
% 0.41/0.76 tff(190,plain,(member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3)) <=> (~((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)) | (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), C!2))))), inference(lemma,lemma(discharge,[]))).
% 0.41/0.76 tff(191,plain,
% 0.41/0.76 (((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)) | (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), C!2))) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)),
% 0.41/0.76 inference(tautology,[status(thm)],[])).
% 0.41/0.76 tff(192,plain,
% 0.41/0.76 ((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)) | (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), C!2))),
% 0.41/0.76 inference(unit_resolution,[status(thm)],[191, 140])).
% 0.41/0.76 tff(193,plain,
% 0.41/0.76 ((~(member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3)) <=> (~((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)) | (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), C!2)))))) | (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3))) | (~((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)) | (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), C!2))))),
% 0.41/0.76 inference(tautology,[status(thm)],[])).
% 0.41/0.76 tff(194,plain,
% 0.41/0.76 (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3))),
% 0.41/0.76 inference(unit_resolution,[status(thm)],[193, 192, 190])).
% 0.41/0.76 tff(195,plain,
% 0.41/0.76 ((~(member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2)) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3)))) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2)) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3))),
% 0.41/0.76 inference(tautology,[status(thm)],[])).
% 0.41/0.76 tff(196,plain,
% 0.41/0.76 (member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), difference(B!3, C!2)) | member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), intersection(C!2, B!3))),
% 0.41/0.76 inference(unit_resolution,[status(thm)],[195, 134])).
% 0.41/0.76 tff(197,plain,
% 0.41/0.76 ($false),
% 0.41/0.76 inference(unit_resolution,[status(thm)],[196, 194, 187])).
% 0.41/0.76 tff(198,plain,(member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)), inference(lemma,lemma(discharge,[]))).
% 0.41/0.76 tff(199,plain,
% 0.41/0.76 ((~((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(B!3, C!2)))) <=> member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3))) | (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(B!3, C!2)))) | (~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3))),
% 0.41/0.76 inference(tautology,[status(thm)],[])).
% 0.41/0.76 tff(200,plain,
% 0.41/0.76 (~((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(B!3, C!2)))) <=> member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3))),
% 0.41/0.76 inference(unit_resolution,[status(thm)],[199, 198, 139])).
% 0.41/0.76 tff(201,plain,
% 0.41/0.76 ((~((union(difference(B!3, C!2), intersection(B!3, C!2)) = B!3) | ((~member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), union(difference(B!3, C!2), intersection(B!3, C!2)))) <=> member(tptp_fun_D_1(B!3, union(difference(B!3, C!2), intersection(B!3, C!2))), B!3)))) | (union(difference(B!3, C!2), intersection(B!3, C!2)) = B!3)),
% 0.41/0.76 inference(unit_resolution,[status(thm)],[105, 200])).
% 0.41/0.76 tff(202,plain,
% 0.41/0.76 (union(difference(B!3, C!2), intersection(B!3, C!2)) = B!3),
% 0.41/0.76 inference(unit_resolution,[status(thm)],[201, 25])).
% 0.41/0.76 tff(203,plain,
% 0.41/0.76 (union(intersection(B!3, C!2), difference(B!3, C!2)) = B!3),
% 0.41/0.76 inference(transitivity,[status(thm)],[89, 202])).
% 0.41/0.76 tff(204,plain,
% 0.41/0.76 ($false),
% 0.41/0.76 inference(unit_resolution,[status(thm)],[103, 203])).
% 0.41/0.76 % SZS output end Proof
%------------------------------------------------------------------------------