TSTP Solution File: SET607+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET607+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 05:07:16 EDT 2022
% Result : Theorem 0.64s 0.63s
% Output : Proof 0.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET607+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n027.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 07:09:20 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.64/0.63 % SZS status Theorem
% 0.64/0.63 % SZS output start Proof
% 0.64/0.63 tff(member_type, type, (
% 0.64/0.63 member: ( $i * $i ) > $o)).
% 0.64/0.63 tff(union_type, type, (
% 0.64/0.63 union: ( $i * $i ) > $i)).
% 0.64/0.63 tff(tptp_fun_B_3_type, type, (
% 0.64/0.63 tptp_fun_B_3: $i)).
% 0.64/0.63 tff(tptp_fun_C_2_type, type, (
% 0.64/0.63 tptp_fun_C_2: $i)).
% 0.64/0.63 tff(tptp_fun_D_1_type, type, (
% 0.64/0.63 tptp_fun_D_1: ( $i * $i ) > $i)).
% 0.64/0.63 tff(difference_type, type, (
% 0.64/0.63 difference: ( $i * $i ) > $i)).
% 0.64/0.63 tff(1,plain,
% 0.64/0.63 (^[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))))),
% 0.64/0.63 inference(bind,[status(th)],[])).
% 0.64/0.63 tff(2,plain,
% 0.64/0.63 (![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)))),
% 0.64/0.63 inference(quant_intro,[status(thm)],[1])).
% 0.64/0.63 tff(3,plain,
% 0.64/0.63 (![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)))),
% 0.64/0.63 inference(rewrite,[status(thm)],[])).
% 0.64/0.63 tff(4,plain,
% 0.64/0.63 (^[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))))),
% 0.64/0.63 inference(bind,[status(th)],[])).
% 0.64/0.63 tff(5,plain,
% 0.64/0.63 (![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)))),
% 0.64/0.63 inference(quant_intro,[status(thm)],[4])).
% 0.64/0.63 tff(6,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')).
% 0.64/0.63 tff(7,plain,
% 0.64/0.63 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.64/0.63 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.64/0.63 tff(8,plain,
% 0.64/0.63 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.64/0.63 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.64/0.63 tff(9,plain,(
% 0.64/0.63 ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.64/0.63 inference(skolemize,[status(sab)],[8])).
% 0.64/0.63 tff(10,plain,
% 0.64/0.63 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.64/0.63 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.64/0.63 tff(11,plain,
% 0.64/0.63 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), union(C!2, difference(C!2, B!3))) <=> (member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2) | member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), difference(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(union(C!2, difference(C!2, B!3)), C!2), union(C!2, difference(C!2, B!3))) <=> (member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2) | member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), difference(C!2, B!3)))))),
% 0.64/0.63 inference(rewrite,[status(thm)],[])).
% 0.64/0.63 tff(12,plain,
% 0.64/0.63 ((member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), union(C!2, difference(C!2, B!3))) <=> (member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), difference(C!2, B!3)) | member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2))) <=> (member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), union(C!2, difference(C!2, B!3))) <=> (member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2) | member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), difference(C!2, B!3))))),
% 0.64/0.63 inference(rewrite,[status(thm)],[])).
% 0.64/0.63 tff(13,plain,
% 0.64/0.63 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), union(C!2, difference(C!2, B!3))) <=> (member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), difference(C!2, B!3)) | member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), union(C!2, difference(C!2, B!3))) <=> (member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2) | member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), difference(C!2, B!3)))))),
% 0.64/0.63 inference(monotonicity,[status(thm)],[12])).
% 0.64/0.63 tff(14,plain,
% 0.64/0.63 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), union(C!2, difference(C!2, B!3))) <=> (member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), difference(C!2, B!3)) | member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), union(C!2, difference(C!2, B!3))) <=> (member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2) | member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), difference(C!2, B!3)))))),
% 0.64/0.63 inference(transitivity,[status(thm)],[13, 11])).
% 0.64/0.63 tff(15,plain,
% 0.64/0.63 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), union(C!2, difference(C!2, B!3))) <=> (member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), difference(C!2, B!3)) | member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2)))),
% 0.64/0.63 inference(quant_inst,[status(thm)],[])).
% 0.64/0.63 tff(16,plain,
% 0.64/0.63 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), union(C!2, difference(C!2, B!3))) <=> (member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2) | member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), difference(C!2, B!3))))),
% 0.64/0.63 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.64/0.63 tff(17,plain,
% 0.64/0.63 (member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), union(C!2, difference(C!2, B!3))) <=> (member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2) | member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), difference(C!2, B!3)))),
% 0.64/0.63 inference(unit_resolution,[status(thm)],[16, 10])).
% 0.64/0.63 tff(18,assumption,((~member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2)) <=> member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), union(C!2, difference(C!2, B!3)))), introduced(assumption)).
% 0.64/0.63 tff(19,assumption,(~member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2)), introduced(assumption)).
% 0.64/0.63 tff(20,plain,
% 0.64/0.63 ((~((~member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2)) <=> member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), union(C!2, difference(C!2, B!3))))) | member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2) | member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), union(C!2, difference(C!2, B!3)))),
% 0.64/0.63 inference(tautology,[status(thm)],[])).
% 0.64/0.63 tff(21,plain,
% 0.64/0.63 (member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), union(C!2, difference(C!2, B!3)))),
% 0.64/0.63 inference(unit_resolution,[status(thm)],[20, 19, 18])).
% 0.64/0.63 tff(22,plain,
% 0.64/0.63 ((~(member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), union(C!2, difference(C!2, B!3))) <=> (member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2) | member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), difference(C!2, B!3))))) | (~member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), union(C!2, difference(C!2, B!3)))) | (member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2) | member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), difference(C!2, B!3)))),
% 0.64/0.63 inference(tautology,[status(thm)],[])).
% 0.64/0.63 tff(23,plain,
% 0.64/0.63 (member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2) | member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), difference(C!2, B!3))),
% 0.64/0.63 inference(unit_resolution,[status(thm)],[22, 21, 17])).
% 0.64/0.63 tff(24,assumption,(~(member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), difference(C!2, B!3)) <=> (~((~member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2)) | member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), B!3))))), introduced(assumption)).
% 0.64/0.63 tff(25,plain,
% 0.64/0.63 (^[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)))))),
% 0.64/0.63 inference(bind,[status(th)],[])).
% 0.64/0.63 tff(26,plain,
% 0.64/0.63 (![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))))),
% 0.64/0.63 inference(quant_intro,[status(thm)],[25])).
% 0.64/0.63 tff(27,plain,
% 0.64/0.63 (^[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)))))),
% 0.64/0.63 inference(bind,[status(th)],[])).
% 0.64/0.63 tff(28,plain,
% 0.64/0.63 (![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))))),
% 0.64/0.63 inference(quant_intro,[status(thm)],[27])).
% 0.64/0.63 tff(29,plain,
% 0.64/0.63 (![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))))),
% 0.64/0.63 inference(rewrite,[status(thm)],[])).
% 0.64/0.63 tff(30,axiom,(![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','difference_defn')).
% 0.64/0.63 tff(31,plain,
% 0.64/0.63 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.64/0.63 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.64/0.63 tff(32,plain,(
% 0.64/0.63 ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.64/0.63 inference(skolemize,[status(sab)],[31])).
% 0.64/0.63 tff(33,plain,
% 0.64/0.63 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 0.64/0.63 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.64/0.63 tff(34,plain,
% 0.64/0.63 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 0.64/0.63 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.64/0.63 tff(35,plain,
% 0.64/0.63 ((~![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))) | (member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), difference(C!2, B!3)) <=> (~((~member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2)) | member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), B!3))))),
% 0.64/0.63 inference(quant_inst,[status(thm)],[])).
% 0.64/0.63 tff(36,plain,
% 0.64/0.63 ($false),
% 0.64/0.63 inference(unit_resolution,[status(thm)],[35, 34, 24])).
% 0.64/0.63 tff(37,plain,(member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), difference(C!2, B!3)) <=> (~((~member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2)) | member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), B!3)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.63 tff(38,plain,
% 0.64/0.63 (((~member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2)) | member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), B!3)) | member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2)),
% 0.64/0.64 inference(tautology,[status(thm)],[])).
% 0.64/0.64 tff(39,plain,
% 0.64/0.64 ((~member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2)) | member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), B!3)),
% 0.64/0.64 inference(unit_resolution,[status(thm)],[38, 19])).
% 0.64/0.64 tff(40,plain,
% 0.64/0.64 ((~(member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), difference(C!2, B!3)) <=> (~((~member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2)) | member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), B!3))))) | (~member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), difference(C!2, B!3))) | (~((~member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2)) | member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), B!3)))),
% 0.64/0.64 inference(tautology,[status(thm)],[])).
% 0.64/0.64 tff(41,plain,
% 0.64/0.64 (~member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), difference(C!2, B!3))),
% 0.64/0.64 inference(unit_resolution,[status(thm)],[40, 39, 37])).
% 0.64/0.64 tff(42,plain,
% 0.64/0.64 ((~(member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2) | member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), difference(C!2, B!3)))) | member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2) | member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), difference(C!2, B!3))),
% 0.64/0.64 inference(tautology,[status(thm)],[])).
% 0.64/0.64 tff(43,plain,
% 0.64/0.64 ($false),
% 0.64/0.64 inference(unit_resolution,[status(thm)],[42, 41, 23, 19])).
% 0.64/0.64 tff(44,plain,(member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2) | (~((~member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2)) <=> member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), union(C!2, difference(C!2, B!3)))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.64 tff(45,plain,
% 0.64/0.64 (member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2)),
% 0.64/0.64 inference(unit_resolution,[status(thm)],[44, 18])).
% 0.64/0.64 tff(46,plain,
% 0.64/0.64 ((~((~member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2)) <=> member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), union(C!2, difference(C!2, B!3))))) | (~member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2)) | (~member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), union(C!2, difference(C!2, B!3))))),
% 0.64/0.64 inference(tautology,[status(thm)],[])).
% 0.64/0.64 tff(47,plain,
% 0.64/0.64 (~member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), union(C!2, difference(C!2, B!3)))),
% 0.64/0.64 inference(unit_resolution,[status(thm)],[46, 45, 18])).
% 0.64/0.64 tff(48,plain,
% 0.64/0.64 ((member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2) | member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), difference(C!2, B!3))) | (~member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2))),
% 0.64/0.64 inference(tautology,[status(thm)],[])).
% 0.64/0.64 tff(49,plain,
% 0.64/0.64 (member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2) | member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), difference(C!2, B!3))),
% 0.64/0.64 inference(unit_resolution,[status(thm)],[48, 45])).
% 0.64/0.64 tff(50,plain,
% 0.64/0.64 ((~(member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), union(C!2, difference(C!2, B!3))) <=> (member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2) | member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), difference(C!2, B!3))))) | member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), union(C!2, difference(C!2, B!3))) | (~(member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2) | member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), difference(C!2, B!3))))),
% 0.64/0.64 inference(tautology,[status(thm)],[])).
% 0.64/0.64 tff(51,plain,
% 0.64/0.64 ($false),
% 0.64/0.64 inference(unit_resolution,[status(thm)],[50, 49, 47, 17])).
% 0.64/0.64 tff(52,plain,(~((~member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2)) <=> member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), union(C!2, difference(C!2, B!3))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.64 tff(53,plain,
% 0.64/0.64 (^[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)))))))),
% 0.64/0.64 inference(bind,[status(th)],[])).
% 0.64/0.64 tff(54,plain,
% 0.64/0.64 (![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))))))),
% 0.64/0.64 inference(quant_intro,[status(thm)],[53])).
% 0.64/0.64 tff(55,plain,
% 0.64/0.64 (![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))))))),
% 0.64/0.64 inference(pull_quant,[status(thm)],[])).
% 0.64/0.64 tff(56,plain,
% 0.64/0.64 (^[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))))))))),
% 0.64/0.64 inference(bind,[status(th)],[])).
% 0.64/0.64 tff(57,plain,
% 0.64/0.64 (![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))))))),
% 0.64/0.64 inference(quant_intro,[status(thm)],[56])).
% 0.64/0.64 tff(58,plain,
% 0.64/0.64 (![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))))))),
% 0.64/0.64 inference(transitivity,[status(thm)],[57, 55])).
% 0.64/0.64 tff(59,plain,
% 0.64/0.64 (![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))))))),
% 0.64/0.64 inference(transitivity,[status(thm)],[58, 54])).
% 0.64/0.64 tff(60,plain,
% 0.64/0.64 (^[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)))))))),
% 0.64/0.64 inference(bind,[status(th)],[])).
% 0.64/0.64 tff(61,plain,
% 0.64/0.64 (![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))))))),
% 0.64/0.64 inference(quant_intro,[status(thm)],[60])).
% 0.64/0.64 tff(62,plain,
% 0.64/0.64 (![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))))))),
% 0.64/0.64 inference(transitivity,[status(thm)],[61, 59])).
% 0.64/0.64 tff(63,plain,
% 0.64/0.64 (^[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))))))))),
% 0.64/0.64 inference(bind,[status(th)],[])).
% 0.64/0.64 tff(64,plain,
% 0.64/0.64 (![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))))))),
% 0.64/0.64 inference(quant_intro,[status(thm)],[63])).
% 0.64/0.64 tff(65,plain,
% 0.64/0.64 (^[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)))))),
% 0.64/0.64 inference(bind,[status(th)],[])).
% 0.64/0.64 tff(66,plain,
% 0.64/0.64 (![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))))),
% 0.64/0.64 inference(quant_intro,[status(thm)],[65])).
% 0.64/0.64 tff(67,plain,
% 0.64/0.64 (![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)))),
% 0.64/0.64 inference(rewrite,[status(thm)],[])).
% 0.64/0.64 tff(68,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')).
% 0.64/0.64 tff(69,plain,
% 0.64/0.64 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.64/0.64 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.64/0.64 tff(70,plain,(
% 0.64/0.64 ![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)))))),
% 0.64/0.64 inference(skolemize,[status(sab)],[69])).
% 0.64/0.64 tff(71,plain,
% 0.64/0.64 (![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))))),
% 0.64/0.64 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.64/0.64 tff(72,plain,
% 0.64/0.64 (![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))))))),
% 0.64/0.64 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.64/0.64 tff(73,plain,
% 0.64/0.64 (![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))))))),
% 0.64/0.64 inference(modus_ponens,[status(thm)],[72, 62])).
% 0.64/0.64 tff(74,plain,
% 0.64/0.64 ((~![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))))))) | (~((~((~(C!2 = union(C!2, difference(C!2, B!3)))) | (member(tptp_fun_D_1(difference(C!2, B!3), union(C!2, difference(C!2, B!3))), C!2) <=> member(tptp_fun_D_1(difference(C!2, B!3), union(C!2, difference(C!2, B!3))), union(C!2, difference(C!2, B!3)))))) | (~((C!2 = union(C!2, difference(C!2, B!3))) | ((~member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2)) <=> member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), union(C!2, difference(C!2, B!3))))))))),
% 0.64/0.64 inference(quant_inst,[status(thm)],[])).
% 0.64/0.64 tff(75,plain,
% 0.64/0.64 (~((~((~(C!2 = union(C!2, difference(C!2, B!3)))) | (member(tptp_fun_D_1(difference(C!2, B!3), union(C!2, difference(C!2, B!3))), C!2) <=> member(tptp_fun_D_1(difference(C!2, B!3), union(C!2, difference(C!2, B!3))), union(C!2, difference(C!2, B!3)))))) | (~((C!2 = union(C!2, difference(C!2, B!3))) | ((~member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2)) <=> member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), union(C!2, difference(C!2, B!3)))))))),
% 0.64/0.64 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.64/0.64 tff(76,plain,
% 0.64/0.64 (((~((~(C!2 = union(C!2, difference(C!2, B!3)))) | (member(tptp_fun_D_1(difference(C!2, B!3), union(C!2, difference(C!2, B!3))), C!2) <=> member(tptp_fun_D_1(difference(C!2, B!3), union(C!2, difference(C!2, B!3))), union(C!2, difference(C!2, B!3)))))) | (~((C!2 = union(C!2, difference(C!2, B!3))) | ((~member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2)) <=> member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), union(C!2, difference(C!2, B!3))))))) | ((C!2 = union(C!2, difference(C!2, B!3))) | ((~member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2)) <=> member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), union(C!2, difference(C!2, B!3)))))),
% 0.64/0.64 inference(tautology,[status(thm)],[])).
% 0.64/0.64 tff(77,plain,
% 0.64/0.64 ((C!2 = union(C!2, difference(C!2, B!3))) | ((~member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2)) <=> member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), union(C!2, difference(C!2, B!3))))),
% 0.64/0.64 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.64/0.64 tff(78,plain,
% 0.64/0.64 ((~((C!2 = union(C!2, difference(C!2, B!3))) | ((~member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2)) <=> member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), union(C!2, difference(C!2, B!3)))))) | (C!2 = union(C!2, difference(C!2, B!3))) | ((~member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2)) <=> member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), union(C!2, difference(C!2, B!3))))),
% 0.64/0.64 inference(tautology,[status(thm)],[])).
% 0.64/0.64 tff(79,plain,
% 0.64/0.64 ((C!2 = union(C!2, difference(C!2, B!3))) | ((~member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), C!2)) <=> member(tptp_fun_D_1(union(C!2, difference(C!2, B!3)), C!2), union(C!2, difference(C!2, B!3))))),
% 0.64/0.64 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.64/0.64 tff(80,plain,
% 0.64/0.64 (C!2 = union(C!2, difference(C!2, B!3))),
% 0.64/0.64 inference(unit_resolution,[status(thm)],[79, 52])).
% 0.64/0.64 tff(81,plain,
% 0.64/0.64 (union(C!2, difference(C!2, B!3)) = C!2),
% 0.64/0.64 inference(symmetry,[status(thm)],[80])).
% 0.64/0.64 tff(82,plain,
% 0.64/0.64 (union(union(C!2, difference(C!2, B!3)), B!3) = union(C!2, B!3)),
% 0.64/0.64 inference(monotonicity,[status(thm)],[81])).
% 0.64/0.64 tff(83,plain,
% 0.64/0.64 (union(C!2, B!3) = union(union(C!2, difference(C!2, B!3)), B!3)),
% 0.64/0.64 inference(symmetry,[status(thm)],[82])).
% 0.64/0.64 tff(84,plain,
% 0.64/0.64 (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, B!3)) <=> member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(union(C!2, difference(C!2, B!3)), B!3))),
% 0.64/0.64 inference(monotonicity,[status(thm)],[83])).
% 0.64/0.64 tff(85,plain,
% 0.64/0.64 (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(union(C!2, difference(C!2, B!3)), B!3)) <=> member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, B!3))),
% 0.64/0.64 inference(symmetry,[status(thm)],[84])).
% 0.64/0.64 tff(86,plain,
% 0.64/0.64 (union(union(C!2, difference(C!2, B!3)), difference(C!2, B!3)) = union(C!2, difference(C!2, B!3))),
% 0.64/0.64 inference(monotonicity,[status(thm)],[81])).
% 0.64/0.64 tff(87,plain,
% 0.64/0.64 (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(union(C!2, difference(C!2, B!3)), difference(C!2, B!3))) <=> member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3)))),
% 0.64/0.64 inference(monotonicity,[status(thm)],[86])).
% 0.64/0.64 tff(88,plain,
% 0.64/0.64 (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3))) <=> member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(union(C!2, difference(C!2, B!3)), difference(C!2, B!3)))),
% 0.64/0.64 inference(symmetry,[status(thm)],[87])).
% 0.64/0.64 tff(89,plain,
% 0.64/0.64 ((~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3)))) <=> (~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(union(C!2, difference(C!2, B!3)), difference(C!2, B!3))))),
% 0.64/0.64 inference(monotonicity,[status(thm)],[88])).
% 0.64/0.64 tff(90,plain,
% 0.64/0.64 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(union(C!2, difference(C!2, B!3)), B!3)) <=> (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3)))))),
% 0.64/0.64 inference(quant_inst,[status(thm)],[])).
% 0.64/0.64 tff(91,plain,
% 0.64/0.64 (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(union(C!2, difference(C!2, B!3)), B!3)) <=> (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3))))),
% 0.64/0.64 inference(unit_resolution,[status(thm)],[90, 10])).
% 0.64/0.64 tff(92,assumption,(~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(union(C!2, difference(C!2, B!3)), B!3))), introduced(assumption)).
% 0.64/0.64 tff(93,plain,
% 0.64/0.64 ((~(member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(union(C!2, difference(C!2, B!3)), B!3)) <=> (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3)))))) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(union(C!2, difference(C!2, B!3)), B!3)) | (~(member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3)))))),
% 0.64/0.64 inference(tautology,[status(thm)],[])).
% 0.64/0.64 tff(94,plain,
% 0.64/0.64 (~(member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3))))),
% 0.64/0.64 inference(unit_resolution,[status(thm)],[93, 92, 91])).
% 0.64/0.64 tff(95,plain,
% 0.64/0.64 ((member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3)))) | (~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3))))),
% 0.64/0.64 inference(tautology,[status(thm)],[])).
% 0.64/0.64 tff(96,plain,
% 0.64/0.64 (~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3)))),
% 0.64/0.65 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.64/0.65 tff(97,plain,
% 0.64/0.65 (~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(union(C!2, difference(C!2, B!3)), difference(C!2, B!3)))),
% 0.64/0.65 inference(modus_ponens,[status(thm)],[96, 89])).
% 0.64/0.65 tff(98,plain,
% 0.64/0.65 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(union(C!2, difference(C!2, B!3)), difference(C!2, B!3))) <=> (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(C!2, B!3)) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3)))))),
% 0.64/0.65 inference(quant_inst,[status(thm)],[])).
% 0.64/0.65 tff(99,plain,
% 0.64/0.65 (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(union(C!2, difference(C!2, B!3)), difference(C!2, B!3))) <=> (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(C!2, B!3)) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3))))),
% 0.64/0.65 inference(unit_resolution,[status(thm)],[98, 10])).
% 0.64/0.65 tff(100,plain,
% 0.64/0.65 ((member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3)))) | (~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3))),
% 0.64/0.65 inference(tautology,[status(thm)],[])).
% 0.64/0.65 tff(101,plain,
% 0.64/0.65 (~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3)),
% 0.64/0.65 inference(unit_resolution,[status(thm)],[100, 94])).
% 0.64/0.65 tff(102,plain,
% 0.64/0.65 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3)) <=> (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(C!2, B!3))))),
% 0.64/0.65 inference(quant_inst,[status(thm)],[])).
% 0.64/0.65 tff(103,plain,
% 0.64/0.65 (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3)) <=> (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(C!2, B!3)))),
% 0.64/0.65 inference(unit_resolution,[status(thm)],[102, 10])).
% 0.64/0.65 tff(104,plain,
% 0.64/0.65 ((~![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(C!2, B!3) = union(difference(C!2, B!3), B!3))) | (member(tptp_fun_D_1(B!3, union(difference(C!2, B!3), B!3)), union(C!2, B!3)) <=> member(tptp_fun_D_1(B!3, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3))))) | (~((union(C!2, B!3) = union(difference(C!2, B!3), B!3)) | ((~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, B!3))) <=> member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3)))))))),
% 0.64/0.65 inference(quant_inst,[status(thm)],[])).
% 0.64/0.65 tff(105,plain,
% 0.64/0.65 (~((~((~(union(C!2, B!3) = union(difference(C!2, B!3), B!3))) | (member(tptp_fun_D_1(B!3, union(difference(C!2, B!3), B!3)), union(C!2, B!3)) <=> member(tptp_fun_D_1(B!3, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3))))) | (~((union(C!2, B!3) = union(difference(C!2, B!3), B!3)) | ((~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, B!3))) <=> member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3))))))),
% 0.64/0.65 inference(unit_resolution,[status(thm)],[104, 73])).
% 0.64/0.65 tff(106,plain,
% 0.64/0.65 (((~((~(union(C!2, B!3) = union(difference(C!2, B!3), B!3))) | (member(tptp_fun_D_1(B!3, union(difference(C!2, B!3), B!3)), union(C!2, B!3)) <=> member(tptp_fun_D_1(B!3, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3))))) | (~((union(C!2, B!3) = union(difference(C!2, B!3), B!3)) | ((~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, B!3))) <=> member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3)))))) | ((union(C!2, B!3) = union(difference(C!2, B!3), B!3)) | ((~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, B!3))) <=> member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3))))),
% 0.64/0.65 inference(tautology,[status(thm)],[])).
% 0.64/0.65 tff(107,plain,
% 0.64/0.65 ((union(C!2, B!3) = union(difference(C!2, B!3), B!3)) | ((~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, B!3))) <=> member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3)))),
% 0.64/0.65 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.64/0.65 tff(108,plain,
% 0.64/0.65 ((union(B!3, C!2) = union(B!3, difference(C!2, B!3))) <=> (union(B!3, difference(C!2, B!3)) = union(B!3, C!2))),
% 0.64/0.65 inference(commutativity,[status(thm)],[])).
% 0.64/0.65 tff(109,plain,
% 0.64/0.65 (^[B: $i, C: $i] : refl((union(B, C) = union(C, B)) <=> (union(B, C) = union(C, B)))),
% 0.64/0.65 inference(bind,[status(th)],[])).
% 0.64/0.65 tff(110,plain,
% 0.64/0.65 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.64/0.65 inference(quant_intro,[status(thm)],[109])).
% 0.64/0.65 tff(111,plain,
% 0.64/0.65 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.64/0.65 inference(rewrite,[status(thm)],[])).
% 0.64/0.65 tff(112,axiom,(![B: $i, C: $i] : (union(B, C) = union(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_union')).
% 0.64/0.65 tff(113,plain,
% 0.64/0.65 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.64/0.65 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.64/0.65 tff(114,plain,(
% 0.64/0.65 ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.64/0.65 inference(skolemize,[status(sab)],[113])).
% 0.64/0.65 tff(115,plain,
% 0.64/0.65 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.64/0.65 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.64/0.65 tff(116,plain,
% 0.64/0.65 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(B!3, difference(C!2, B!3)) = union(difference(C!2, B!3), B!3))),
% 0.64/0.65 inference(quant_inst,[status(thm)],[])).
% 0.64/0.65 tff(117,plain,
% 0.64/0.65 (union(B!3, difference(C!2, B!3)) = union(difference(C!2, B!3), B!3)),
% 0.64/0.65 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.64/0.65 tff(118,plain,
% 0.64/0.65 (union(difference(C!2, B!3), B!3) = union(B!3, difference(C!2, B!3))),
% 0.64/0.65 inference(symmetry,[status(thm)],[117])).
% 0.64/0.65 tff(119,plain,
% 0.64/0.65 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(B!3, C!2) = union(C!2, B!3))),
% 0.64/0.65 inference(quant_inst,[status(thm)],[])).
% 0.64/0.65 tff(120,plain,
% 0.64/0.65 (union(B!3, C!2) = union(C!2, B!3)),
% 0.64/0.65 inference(unit_resolution,[status(thm)],[119, 115])).
% 0.64/0.65 tff(121,plain,
% 0.64/0.65 (union(C!2, B!3) = union(B!3, C!2)),
% 0.64/0.65 inference(symmetry,[status(thm)],[120])).
% 0.64/0.65 tff(122,plain,
% 0.64/0.65 ((union(C!2, B!3) = union(difference(C!2, B!3), B!3)) <=> (union(B!3, C!2) = union(B!3, difference(C!2, B!3)))),
% 0.64/0.65 inference(monotonicity,[status(thm)],[121, 118])).
% 0.64/0.65 tff(123,plain,
% 0.64/0.65 ((union(C!2, B!3) = union(difference(C!2, B!3), B!3)) <=> (union(B!3, difference(C!2, B!3)) = union(B!3, C!2))),
% 0.64/0.65 inference(transitivity,[status(thm)],[122, 108])).
% 0.64/0.65 tff(124,plain,
% 0.64/0.65 ((union(B!3, difference(C!2, B!3)) = union(B!3, C!2)) <=> (union(C!2, B!3) = union(difference(C!2, B!3), B!3))),
% 0.64/0.65 inference(symmetry,[status(thm)],[123])).
% 0.64/0.65 tff(125,plain,
% 0.64/0.65 ((~(union(B!3, difference(C!2, B!3)) = union(B!3, C!2))) <=> (~(union(C!2, B!3) = union(difference(C!2, B!3), B!3)))),
% 0.64/0.65 inference(monotonicity,[status(thm)],[124])).
% 0.64/0.65 tff(126,plain,
% 0.64/0.65 ((~![B: $i, C: $i] : (union(B, difference(C, B)) = union(B, C))) <=> (~![B: $i, C: $i] : (union(B, difference(C, B)) = union(B, C)))),
% 0.64/0.65 inference(rewrite,[status(thm)],[])).
% 0.64/0.65 tff(127,axiom,(~![B: $i, C: $i] : (union(B, difference(C, B)) = union(B, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_th79')).
% 0.64/0.65 tff(128,plain,
% 0.64/0.65 (~![B: $i, C: $i] : (union(B, difference(C, B)) = union(B, C))),
% 0.64/0.65 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.64/0.65 tff(129,plain,
% 0.64/0.65 (~![B: $i, C: $i] : (union(B, difference(C, B)) = union(B, C))),
% 0.64/0.65 inference(modus_ponens,[status(thm)],[128, 126])).
% 0.64/0.65 tff(130,plain,
% 0.64/0.65 (~![B: $i, C: $i] : (union(B, difference(C, B)) = union(B, C))),
% 0.64/0.65 inference(modus_ponens,[status(thm)],[129, 126])).
% 0.64/0.65 tff(131,plain,
% 0.64/0.65 (~![B: $i, C: $i] : (union(B, difference(C, B)) = union(B, C))),
% 0.64/0.65 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.64/0.65 tff(132,plain,
% 0.64/0.65 (~![B: $i, C: $i] : (union(B, difference(C, B)) = union(B, C))),
% 0.64/0.65 inference(modus_ponens,[status(thm)],[131, 126])).
% 0.64/0.65 tff(133,plain,
% 0.64/0.65 (~![B: $i, C: $i] : (union(B, difference(C, B)) = union(B, C))),
% 0.64/0.65 inference(modus_ponens,[status(thm)],[132, 126])).
% 0.64/0.65 tff(134,plain,
% 0.64/0.65 (~![B: $i, C: $i] : (union(B, difference(C, B)) = union(B, C))),
% 0.64/0.65 inference(modus_ponens,[status(thm)],[133, 126])).
% 0.64/0.65 tff(135,plain,(
% 0.64/0.65 ~(union(B!3, difference(C!2, B!3)) = union(B!3, C!2))),
% 0.64/0.65 inference(skolemize,[status(sab)],[134])).
% 0.64/0.65 tff(136,plain,
% 0.64/0.65 (~(union(C!2, B!3) = union(difference(C!2, B!3), B!3))),
% 0.64/0.65 inference(modus_ponens,[status(thm)],[135, 125])).
% 0.64/0.65 tff(137,plain,
% 0.64/0.65 ((~((union(C!2, B!3) = union(difference(C!2, B!3), B!3)) | ((~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, B!3))) <=> member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3))))) | (union(C!2, B!3) = union(difference(C!2, B!3), B!3)) | ((~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, B!3))) <=> member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3)))),
% 0.64/0.65 inference(tautology,[status(thm)],[])).
% 0.64/0.65 tff(138,plain,
% 0.64/0.65 ((~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, B!3))) <=> member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3))),
% 0.64/0.65 inference(unit_resolution,[status(thm)],[137, 136, 107])).
% 0.64/0.65 tff(139,plain,
% 0.64/0.65 (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(union(C!2, difference(C!2, B!3)), B!3)) <=> member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, B!3))),
% 0.64/0.65 inference(monotonicity,[status(thm)],[82])).
% 0.64/0.65 tff(140,plain,
% 0.64/0.65 ((~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(union(C!2, difference(C!2, B!3)), B!3))) <=> (~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, B!3)))),
% 0.64/0.65 inference(monotonicity,[status(thm)],[139])).
% 0.64/0.65 tff(141,plain,
% 0.64/0.65 (~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, B!3))),
% 0.64/0.65 inference(modus_ponens,[status(thm)],[92, 140])).
% 0.64/0.65 tff(142,plain,
% 0.64/0.65 ((~((~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, B!3))) <=> member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3)))) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, B!3)) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3))),
% 0.64/0.65 inference(tautology,[status(thm)],[])).
% 0.64/0.65 tff(143,plain,
% 0.64/0.65 (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3))),
% 0.64/0.65 inference(unit_resolution,[status(thm)],[142, 141, 138])).
% 0.64/0.65 tff(144,plain,
% 0.64/0.65 ((~(member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3)) <=> (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(C!2, B!3))))) | (~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3))) | (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(C!2, B!3)))),
% 0.64/0.65 inference(tautology,[status(thm)],[])).
% 0.64/0.65 tff(145,plain,
% 0.64/0.65 (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(C!2, B!3))),
% 0.64/0.65 inference(unit_resolution,[status(thm)],[144, 143, 103])).
% 0.64/0.65 tff(146,plain,
% 0.64/0.65 ((~(member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(C!2, B!3)))) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(C!2, B!3))),
% 0.64/0.65 inference(tautology,[status(thm)],[])).
% 0.64/0.65 tff(147,plain,
% 0.64/0.65 (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(C!2, B!3))),
% 0.64/0.65 inference(unit_resolution,[status(thm)],[146, 145, 101])).
% 0.64/0.65 tff(148,plain,
% 0.64/0.65 ((member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(C!2, B!3)) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3)))) | (~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(C!2, B!3)))),
% 0.64/0.65 inference(tautology,[status(thm)],[])).
% 0.64/0.65 tff(149,plain,
% 0.64/0.65 (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(C!2, B!3)) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3)))),
% 0.64/0.65 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.64/0.65 tff(150,plain,
% 0.64/0.65 ((~(member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(union(C!2, difference(C!2, B!3)), difference(C!2, B!3))) <=> (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(C!2, B!3)) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3)))))) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(union(C!2, difference(C!2, B!3)), difference(C!2, B!3))) | (~(member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(C!2, B!3)) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3)))))),
% 0.64/0.65 inference(tautology,[status(thm)],[])).
% 0.64/0.65 tff(151,plain,
% 0.64/0.65 (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(union(C!2, difference(C!2, B!3)), difference(C!2, B!3)))),
% 0.64/0.65 inference(unit_resolution,[status(thm)],[150, 149, 99])).
% 0.64/0.65 tff(152,plain,
% 0.64/0.65 ($false),
% 0.64/0.65 inference(unit_resolution,[status(thm)],[151, 97])).
% 0.64/0.65 tff(153,plain,(member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(union(C!2, difference(C!2, B!3)), B!3))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.65 tff(154,plain,
% 0.64/0.65 (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, B!3))),
% 0.64/0.65 inference(modus_ponens,[status(thm)],[153, 85])).
% 0.64/0.65 tff(155,assumption,((~((~(union(C!2, B!3) = union(difference(C!2, B!3), B!3))) | (member(tptp_fun_D_1(B!3, union(difference(C!2, B!3), B!3)), union(C!2, B!3)) <=> member(tptp_fun_D_1(B!3, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3))))) | (~((union(C!2, B!3) = union(difference(C!2, B!3), B!3)) | ((~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, B!3))) <=> member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3)))))), introduced(assumption)).
% 0.64/0.65 tff(156,plain,
% 0.64/0.65 ($false),
% 0.64/0.65 inference(unit_resolution,[status(thm)],[104, 73, 155])).
% 0.64/0.65 tff(157,plain,(~((~((~(union(C!2, B!3) = union(difference(C!2, B!3), B!3))) | (member(tptp_fun_D_1(B!3, union(difference(C!2, B!3), B!3)), union(C!2, B!3)) <=> member(tptp_fun_D_1(B!3, union(difference(C!2, B!3), B!3)), union(difference(C!2, B!3), B!3))))) | (~((union(C!2, B!3) = union(difference(C!2, B!3), B!3)) | ((~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, B!3))) <=> member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3))))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.66 tff(158,plain,
% 0.64/0.66 ((union(C!2, B!3) = union(difference(C!2, B!3), B!3)) | ((~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, B!3))) <=> member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3)))),
% 0.64/0.66 inference(unit_resolution,[status(thm)],[106, 157])).
% 0.64/0.66 tff(159,assumption,(union(C!2, B!3) = union(difference(C!2, B!3), B!3)), introduced(assumption)).
% 0.64/0.66 tff(160,plain,
% 0.64/0.66 (union(difference(C!2, B!3), B!3) = union(C!2, B!3)),
% 0.64/0.66 inference(symmetry,[status(thm)],[159])).
% 0.64/0.66 tff(161,plain,
% 0.64/0.66 (union(B!3, difference(C!2, B!3)) = union(B!3, C!2)),
% 0.64/0.66 inference(transitivity,[status(thm)],[117, 160, 121])).
% 0.64/0.66 tff(162,plain,
% 0.64/0.66 ($false),
% 0.64/0.66 inference(unit_resolution,[status(thm)],[135, 161])).
% 0.64/0.66 tff(163,plain,(~(union(C!2, B!3) = union(difference(C!2, B!3), B!3))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.66 tff(164,plain,
% 0.64/0.66 ((~((union(C!2, B!3) = union(difference(C!2, B!3), B!3)) | ((~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, B!3))) <=> member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3))))) | ((~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, B!3))) <=> member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3)))),
% 0.64/0.66 inference(unit_resolution,[status(thm)],[137, 163])).
% 0.64/0.66 tff(165,plain,
% 0.64/0.66 ((~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, B!3))) <=> member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3))),
% 0.64/0.66 inference(unit_resolution,[status(thm)],[164, 158])).
% 0.64/0.66 tff(166,assumption,(~(member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3)) <=> (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(C!2, B!3))))), introduced(assumption)).
% 0.64/0.66 tff(167,plain,
% 0.64/0.66 ($false),
% 0.64/0.66 inference(unit_resolution,[status(thm)],[102, 10, 166])).
% 0.64/0.66 tff(168,plain,(member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3)) <=> (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(C!2, B!3)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.66 tff(169,plain,
% 0.64/0.66 (difference(union(C!2, difference(C!2, B!3)), B!3) = difference(C!2, B!3)),
% 0.64/0.66 inference(monotonicity,[status(thm)],[81])).
% 0.64/0.66 tff(170,plain,
% 0.64/0.66 (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(union(C!2, difference(C!2, B!3)), B!3)) <=> member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(C!2, B!3))),
% 0.64/0.66 inference(monotonicity,[status(thm)],[169])).
% 0.64/0.66 tff(171,plain,
% 0.64/0.66 (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(C!2, B!3)) <=> member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(union(C!2, difference(C!2, B!3)), B!3))),
% 0.64/0.66 inference(symmetry,[status(thm)],[170])).
% 0.64/0.66 tff(172,plain,
% 0.64/0.66 ((~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(C!2, B!3))) <=> (~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(union(C!2, difference(C!2, B!3)), B!3)))),
% 0.64/0.66 inference(monotonicity,[status(thm)],[171])).
% 0.64/0.66 tff(173,assumption,(~(member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(C!2, B!3)))), introduced(assumption)).
% 0.64/0.66 tff(174,plain,
% 0.64/0.66 ((member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(C!2, B!3))) | (~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(C!2, B!3)))),
% 0.64/0.66 inference(tautology,[status(thm)],[])).
% 0.64/0.66 tff(175,plain,
% 0.64/0.66 (~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(C!2, B!3))),
% 0.64/0.66 inference(unit_resolution,[status(thm)],[174, 173])).
% 0.64/0.66 tff(176,plain,
% 0.64/0.66 (~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(union(C!2, difference(C!2, B!3)), B!3))),
% 0.64/0.66 inference(modus_ponens,[status(thm)],[175, 172])).
% 0.64/0.66 tff(177,plain,
% 0.64/0.66 ((~![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))) | (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(union(C!2, difference(C!2, B!3)), B!3)) <=> (~((~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3)))) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3))))),
% 0.64/0.66 inference(quant_inst,[status(thm)],[])).
% 0.64/0.66 tff(178,plain,
% 0.64/0.66 (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(union(C!2, difference(C!2, B!3)), B!3)) <=> (~((~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3)))) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3)))),
% 0.64/0.66 inference(unit_resolution,[status(thm)],[177, 34])).
% 0.64/0.66 tff(179,plain,
% 0.64/0.66 ((member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(C!2, B!3))) | (~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3))),
% 0.64/0.66 inference(tautology,[status(thm)],[])).
% 0.64/0.66 tff(180,plain,
% 0.64/0.66 (~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3)),
% 0.64/0.66 inference(unit_resolution,[status(thm)],[179, 173])).
% 0.64/0.66 tff(181,plain,
% 0.64/0.66 ((~(member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(union(C!2, difference(C!2, B!3)), B!3)) <=> (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3)))))) | (~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(union(C!2, difference(C!2, B!3)), B!3))) | (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3))))),
% 0.64/0.66 inference(tautology,[status(thm)],[])).
% 0.64/0.66 tff(182,plain,
% 0.64/0.66 ((~(member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(union(C!2, difference(C!2, B!3)), B!3)) <=> (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3)))))) | (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3))))),
% 0.64/0.66 inference(unit_resolution,[status(thm)],[181, 153])).
% 0.64/0.66 tff(183,plain,
% 0.64/0.66 (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3)))),
% 0.64/0.66 inference(unit_resolution,[status(thm)],[182, 91])).
% 0.64/0.66 tff(184,plain,
% 0.64/0.66 ((~(member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3))))) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3)))),
% 0.64/0.66 inference(tautology,[status(thm)],[])).
% 0.64/0.66 tff(185,plain,
% 0.64/0.66 (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3)))),
% 0.64/0.66 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.64/0.66 tff(186,plain,
% 0.64/0.66 (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3)))),
% 0.64/0.66 inference(unit_resolution,[status(thm)],[185, 180])).
% 0.64/0.66 tff(187,plain,
% 0.64/0.66 ((~((~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3)))) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3))) | (~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3)))) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3)),
% 0.64/0.66 inference(tautology,[status(thm)],[])).
% 0.64/0.66 tff(188,plain,
% 0.64/0.66 (~((~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3)))) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3))),
% 0.64/0.66 inference(unit_resolution,[status(thm)],[187, 180, 186])).
% 0.64/0.66 tff(189,plain,
% 0.64/0.66 ((~(member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(union(C!2, difference(C!2, B!3)), B!3)) <=> (~((~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3)))) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3))))) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(union(C!2, difference(C!2, B!3)), B!3)) | ((~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3)))) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3))),
% 0.64/0.66 inference(tautology,[status(thm)],[])).
% 0.64/0.66 tff(190,plain,
% 0.64/0.66 ((~(member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(union(C!2, difference(C!2, B!3)), B!3)) <=> (~((~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, difference(C!2, B!3)))) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3))))) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(union(C!2, difference(C!2, B!3)), B!3))),
% 0.64/0.66 inference(unit_resolution,[status(thm)],[189, 188])).
% 0.64/0.66 tff(191,plain,
% 0.64/0.66 (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(union(C!2, difference(C!2, B!3)), B!3))),
% 0.64/0.66 inference(unit_resolution,[status(thm)],[190, 178])).
% 0.64/0.66 tff(192,plain,
% 0.64/0.66 ($false),
% 0.64/0.66 inference(unit_resolution,[status(thm)],[191, 176])).
% 0.64/0.66 tff(193,plain,(member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(C!2, B!3))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.66 tff(194,plain,
% 0.64/0.66 ((~(member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3)) <=> (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(C!2, B!3))))) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3)) | (~(member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(C!2, B!3))))),
% 0.64/0.66 inference(tautology,[status(thm)],[])).
% 0.64/0.66 tff(195,plain,
% 0.64/0.66 ((~(member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3)) <=> (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), B!3) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), difference(C!2, B!3))))) | member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3))),
% 0.64/0.66 inference(unit_resolution,[status(thm)],[194, 193])).
% 0.64/0.66 tff(196,plain,
% 0.64/0.66 (member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3))),
% 0.64/0.66 inference(unit_resolution,[status(thm)],[195, 168])).
% 0.64/0.66 tff(197,plain,
% 0.64/0.66 ((~((~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, B!3))) <=> member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3)))) | (~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, B!3))) | (~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3)))),
% 0.64/0.66 inference(tautology,[status(thm)],[])).
% 0.64/0.66 tff(198,plain,
% 0.64/0.66 ((~((~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, B!3))) <=> member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(difference(C!2, B!3), B!3)))) | (~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, B!3)))),
% 0.64/0.66 inference(unit_resolution,[status(thm)],[197, 196])).
% 0.64/0.66 tff(199,plain,
% 0.64/0.66 (~member(tptp_fun_D_1(union(difference(C!2, B!3), B!3), union(C!2, B!3)), union(C!2, B!3))),
% 0.64/0.66 inference(unit_resolution,[status(thm)],[198, 165])).
% 0.64/0.66 tff(200,plain,
% 0.64/0.66 ($false),
% 0.64/0.66 inference(unit_resolution,[status(thm)],[199, 154])).
% 0.64/0.66 % SZS output end Proof
%------------------------------------------------------------------------------