TSTP Solution File: SET588+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET588+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 05:07:09 EDT 2022
% Result : Theorem 0.18s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET588+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n016.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 07:11:21 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.
% 0.18/0.38 % SZS status Theorem
% 0.18/0.38 % SZS output start Proof
% 0.18/0.38 tff(member_type, type, (
% 0.18/0.38 member: ( $i * $i ) > $o)).
% 0.18/0.38 tff(tptp_fun_B_3_type, type, (
% 0.18/0.38 tptp_fun_B_3: $i)).
% 0.18/0.38 tff(tptp_fun_D_0_type, type, (
% 0.18/0.38 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.18/0.38 tff(difference_type, type, (
% 0.18/0.38 difference: ( $i * $i ) > $i)).
% 0.18/0.38 tff(tptp_fun_D_1_type, type, (
% 0.18/0.38 tptp_fun_D_1: $i)).
% 0.18/0.38 tff(tptp_fun_C_2_type, type, (
% 0.18/0.38 tptp_fun_C_2: $i)).
% 0.18/0.38 tff(subset_type, type, (
% 0.18/0.38 subset: ( $i * $i ) > $o)).
% 0.18/0.38 tff(1,plain,
% 0.18/0.38 (^[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)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(2,plain,
% 0.18/0.38 (![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))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.38 tff(3,plain,
% 0.18/0.38 (^[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)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(4,plain,
% 0.18/0.38 (![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))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.18/0.38 tff(5,plain,
% 0.18/0.38 (![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))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(6,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')).
% 0.18/0.38 tff(7,plain,
% 0.18/0.38 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.18/0.38 tff(8,plain,(
% 0.18/0.38 ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.18/0.38 inference(skolemize,[status(sab)],[7])).
% 0.18/0.38 tff(9,plain,
% 0.18/0.38 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.18/0.38 tff(10,plain,
% 0.18/0.38 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.18/0.38 tff(11,plain,
% 0.18/0.38 ((~![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))) | (member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(B!3, D!1)) <=> (~((~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), B!3)) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), D!1))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(12,plain,
% 0.18/0.38 (member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(B!3, D!1)) <=> (~((~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), B!3)) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), D!1)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.18/0.38 tff(13,plain,
% 0.18/0.38 (^[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))))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(14,plain,
% 0.18/0.38 (![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)))))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.18/0.38 tff(15,plain,
% 0.18/0.38 (^[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))))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(16,plain,
% 0.18/0.38 (![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)))))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.18/0.38 tff(17,plain,
% 0.18/0.38 (![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)))))))),
% 0.18/0.38 inference(transitivity,[status(thm)],[16, 14])).
% 0.18/0.38 tff(18,plain,
% 0.18/0.38 (^[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)))))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(19,plain,
% 0.18/0.38 (![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)))))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[18])).
% 0.18/0.38 tff(20,plain,
% 0.18/0.38 (![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)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(21,plain,
% 0.18/0.38 (^[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))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(22,plain,
% 0.18/0.38 (![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)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[21])).
% 0.18/0.38 tff(23,axiom,(![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','subset_defn')).
% 0.18/0.38 tff(24,plain,
% 0.18/0.38 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.18/0.38 tff(25,plain,
% 0.18/0.38 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.18/0.38 tff(26,plain,(
% 0.18/0.38 ![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)))))),
% 0.18/0.38 inference(skolemize,[status(sab)],[25])).
% 0.18/0.38 tff(27,plain,
% 0.18/0.38 (![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)))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.18/0.38 tff(28,plain,
% 0.18/0.38 (![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)))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.18/0.38 tff(29,plain,
% 0.18/0.38 ((~![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, D!1), difference(C!2, D!1))) | ![D: $i] : ((~member(D, difference(B!3, D!1))) | member(D, difference(C!2, D!1))))) | (~(subset(difference(B!3, D!1), difference(C!2, D!1)) | (~((~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(B!3, D!1))) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(C!2, D!1))))))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(30,plain,
% 0.18/0.38 (~((~((~subset(difference(B!3, D!1), difference(C!2, D!1))) | ![D: $i] : ((~member(D, difference(B!3, D!1))) | member(D, difference(C!2, D!1))))) | (~(subset(difference(B!3, D!1), difference(C!2, D!1)) | (~((~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(B!3, D!1))) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(C!2, D!1)))))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.18/0.38 tff(31,plain,
% 0.18/0.38 (((~((~subset(difference(B!3, D!1), difference(C!2, D!1))) | ![D: $i] : ((~member(D, difference(B!3, D!1))) | member(D, difference(C!2, D!1))))) | (~(subset(difference(B!3, D!1), difference(C!2, D!1)) | (~((~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(B!3, D!1))) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(C!2, D!1))))))) | (subset(difference(B!3, D!1), difference(C!2, D!1)) | (~((~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(B!3, D!1))) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(C!2, D!1)))))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(32,plain,
% 0.18/0.38 (subset(difference(B!3, D!1), difference(C!2, D!1)) | (~((~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(B!3, D!1))) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(C!2, D!1))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.18/0.38 tff(33,plain,
% 0.18/0.38 ((~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(difference(B, D), difference(C, D)))) <=> (~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(difference(B, D), difference(C, D))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(34,plain,
% 0.18/0.38 ((~![B: $i, C: $i, D: $i] : (subset(B, C) => subset(difference(B, D), difference(C, D)))) <=> (~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(difference(B, D), difference(C, D))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(35,axiom,(~![B: $i, C: $i, D: $i] : (subset(B, C) => subset(difference(B, D), difference(C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_difference_subset1')).
% 0.18/0.38 tff(36,plain,
% 0.18/0.38 (~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(difference(B, D), difference(C, D)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.18/0.38 tff(37,plain,
% 0.18/0.38 (~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(difference(B, D), difference(C, D)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[36, 33])).
% 0.18/0.38 tff(38,plain,
% 0.18/0.39 (~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(difference(B, D), difference(C, D)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.18/0.39 tff(39,plain,
% 0.18/0.39 (~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(difference(B, D), difference(C, D)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[38, 33])).
% 0.18/0.39 tff(40,plain,
% 0.18/0.39 (~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(difference(B, D), difference(C, D)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[39, 33])).
% 0.18/0.39 tff(41,plain,
% 0.18/0.39 (~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(difference(B, D), difference(C, D)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.18/0.39 tff(42,plain,
% 0.18/0.39 (~![B: $i, C: $i, D: $i] : ((~subset(B, C)) | subset(difference(B, D), difference(C, D)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[41, 33])).
% 0.18/0.39 tff(43,plain,(
% 0.18/0.39 ~((~subset(B!3, C!2)) | subset(difference(B!3, D!1), difference(C!2, D!1)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[42])).
% 0.18/0.39 tff(44,plain,
% 0.18/0.39 (~subset(difference(B!3, D!1), difference(C!2, D!1))),
% 0.18/0.39 inference(or_elim,[status(thm)],[43])).
% 0.18/0.39 tff(45,plain,
% 0.18/0.39 ((~(subset(difference(B!3, D!1), difference(C!2, D!1)) | (~((~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(B!3, D!1))) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(C!2, D!1)))))) | subset(difference(B!3, D!1), difference(C!2, D!1)) | (~((~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(B!3, D!1))) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(C!2, D!1))))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(46,plain,
% 0.18/0.39 ((~(subset(difference(B!3, D!1), difference(C!2, D!1)) | (~((~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(B!3, D!1))) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(C!2, D!1)))))) | (~((~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(B!3, D!1))) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(C!2, D!1))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.18/0.39 tff(47,plain,
% 0.18/0.39 (~((~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(B!3, D!1))) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(C!2, D!1)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[46, 32])).
% 0.18/0.39 tff(48,plain,
% 0.18/0.39 (((~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(B!3, D!1))) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(C!2, D!1))) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(B!3, D!1))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(49,plain,
% 0.18/0.39 (member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(B!3, D!1))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.18/0.39 tff(50,plain,
% 0.18/0.39 ((~(member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(B!3, D!1)) <=> (~((~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), B!3)) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), D!1))))) | (~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(B!3, D!1))) | (~((~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), B!3)) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), D!1)))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(51,plain,
% 0.18/0.39 ((~(member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(B!3, D!1)) <=> (~((~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), B!3)) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), D!1))))) | (~((~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), B!3)) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), D!1)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.18/0.39 tff(52,plain,
% 0.18/0.39 (~((~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), B!3)) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), D!1))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[51, 12])).
% 0.18/0.39 tff(53,plain,
% 0.18/0.39 (((~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), B!3)) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), D!1)) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), B!3)),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(54,plain,
% 0.18/0.39 (member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), B!3)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.18/0.39 tff(55,plain,
% 0.18/0.39 ((~![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))) | (member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(C!2, D!1)) <=> (~((~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), C!2)) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), D!1))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(56,plain,
% 0.18/0.39 (member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(C!2, D!1)) <=> (~((~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), C!2)) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), D!1)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[55, 10])).
% 0.18/0.39 tff(57,plain,
% 0.18/0.39 (((~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(B!3, D!1))) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(C!2, D!1))) | (~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(C!2, D!1)))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(58,plain,
% 0.18/0.39 (~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(C!2, D!1))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[57, 47])).
% 0.18/0.39 tff(59,plain,
% 0.18/0.39 ((~(member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(C!2, D!1)) <=> (~((~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), C!2)) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), D!1))))) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(C!2, D!1)) | ((~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), C!2)) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), D!1))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(60,plain,
% 0.18/0.39 ((~(member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), difference(C!2, D!1)) <=> (~((~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), C!2)) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), D!1))))) | ((~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), C!2)) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), D!1))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.18/0.39 tff(61,plain,
% 0.18/0.39 ((~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), C!2)) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), D!1)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[60, 56])).
% 0.18/0.39 tff(62,plain,
% 0.18/0.39 (((~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), B!3)) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), D!1)) | (~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), D!1))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(63,plain,
% 0.18/0.39 (~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), D!1)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[62, 52])).
% 0.18/0.39 tff(64,plain,
% 0.18/0.39 ((~((~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), C!2)) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), D!1))) | (~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), C!2)) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), D!1)),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(65,plain,
% 0.18/0.39 (~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), C!2)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[64, 63, 61])).
% 0.18/0.39 tff(66,plain,
% 0.18/0.39 ((~![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(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2)))) | (~(subset(B!3, C!2) | (~((~member(tptp_fun_D_0(C!2, B!3), B!3)) | member(tptp_fun_D_0(C!2, B!3), C!2)))))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(67,plain,
% 0.18/0.40 (~((~((~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2)))) | (~(subset(B!3, C!2) | (~((~member(tptp_fun_D_0(C!2, B!3), B!3)) | member(tptp_fun_D_0(C!2, B!3), C!2))))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[66, 28])).
% 0.18/0.40 tff(68,plain,
% 0.18/0.40 (((~((~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2)))) | (~(subset(B!3, C!2) | (~((~member(tptp_fun_D_0(C!2, B!3), B!3)) | member(tptp_fun_D_0(C!2, B!3), C!2)))))) | ((~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2)))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(69,plain,
% 0.18/0.40 ((~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.18/0.40 tff(70,plain,
% 0.18/0.40 (subset(B!3, C!2)),
% 0.18/0.40 inference(or_elim,[status(thm)],[43])).
% 0.18/0.40 tff(71,plain,
% 0.18/0.40 ((~((~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2)))) | (~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(72,plain,
% 0.18/0.40 ((~((~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2)))) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.18/0.40 tff(73,plain,
% 0.18/0.40 (![D: $i] : ((~member(D, B!3)) | member(D, C!2))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[72, 69])).
% 0.18/0.40 tff(74,plain,
% 0.18/0.40 (((~![D: $i] : ((~member(D, B!3)) | member(D, C!2))) | ((~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), B!3)) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), C!2))) <=> ((~![D: $i] : ((~member(D, B!3)) | member(D, C!2))) | (~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), B!3)) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), C!2))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(75,plain,
% 0.18/0.40 ((~![D: $i] : ((~member(D, B!3)) | member(D, C!2))) | ((~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), B!3)) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), C!2))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(76,plain,
% 0.18/0.40 ((~![D: $i] : ((~member(D, B!3)) | member(D, C!2))) | (~member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), B!3)) | member(tptp_fun_D_0(difference(C!2, D!1), difference(B!3, D!1)), C!2)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.18/0.40 tff(77,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[76, 73, 65, 54])).
% 0.18/0.40 % SZS output end Proof
%------------------------------------------------------------------------------