TSTP Solution File: SEU117+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU117+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 07:27:32 EDT 2022
% Result : Theorem 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU117+1 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 09:30:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(subset_type, type, (
% 0.19/0.41 subset: ( $i * $i ) > $o)).
% 0.19/0.41 tff(tptp_fun_A_10_type, type, (
% 0.19/0.41 tptp_fun_A_10: $i)).
% 0.19/0.41 tff(tptp_fun_B_9_type, type, (
% 0.19/0.41 tptp_fun_B_9: $i)).
% 0.19/0.41 tff(finite_type, type, (
% 0.19/0.41 finite: $i > $o)).
% 0.19/0.41 tff(in_type, type, (
% 0.19/0.41 in: ( $i * $i ) > $o)).
% 0.19/0.41 tff(finite_subsets_type, type, (
% 0.19/0.41 finite_subsets: $i > $i)).
% 0.19/0.41 tff(element_type, type, (
% 0.19/0.41 element: ( $i * $i ) > $o)).
% 0.19/0.41 tff(powerset_type, type, (
% 0.19/0.41 powerset: $i > $i)).
% 0.19/0.41 tff(empty_type, type, (
% 0.19/0.41 empty: $i > $o)).
% 0.19/0.41 tff(preboolean_type, type, (
% 0.19/0.41 preboolean: $i > $o)).
% 0.19/0.41 tff(diff_closed_type, type, (
% 0.19/0.41 diff_closed: $i > $o)).
% 0.19/0.41 tff(cup_closed_type, type, (
% 0.19/0.41 cup_closed: $i > $o)).
% 0.19/0.41 tff(tptp_fun_C_11_type, type, (
% 0.19/0.41 tptp_fun_C_11: ( $i * $i ) > $i)).
% 0.19/0.41 tff(1,plain,
% 0.19/0.41 (^[A: $i, B: $i] : refl((element(A, powerset(B)) <=> subset(A, B)) <=> (element(A, powerset(B)) <=> subset(A, B)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(2,plain,
% 0.19/0.41 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.41 tff(3,plain,
% 0.19/0.41 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(4,axiom,(![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3_subset')).
% 0.19/0.41 tff(5,plain,
% 0.19/0.41 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.41 tff(6,plain,(
% 0.19/0.41 ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.19/0.41 inference(skolemize,[status(sab)],[5])).
% 0.19/0.41 tff(7,plain,
% 0.19/0.41 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))) | (element(B!9, powerset(A!10)) <=> subset(B!9, A!10))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(9,plain,
% 0.19/0.41 (element(B!9, powerset(A!10)) <=> subset(B!9, A!10)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : ((~element(B, finite_subsets(A))) | element(B, powerset(A)))) <=> (~![A: $i, B: $i] : ((~element(B, finite_subsets(A))) | element(B, powerset(A))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(11,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : (element(B, finite_subsets(A)) => element(B, powerset(A)))) <=> (~![A: $i, B: $i] : ((~element(B, finite_subsets(A))) | element(B, powerset(A))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(12,axiom,(~![A: $i, B: $i] : (element(B, finite_subsets(A)) => element(B, powerset(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t32_finsub_1')).
% 0.19/0.41 tff(13,plain,
% 0.19/0.41 (~![A: $i, B: $i] : ((~element(B, finite_subsets(A))) | element(B, powerset(A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 (~![A: $i, B: $i] : ((~element(B, finite_subsets(A))) | element(B, powerset(A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.19/0.41 tff(15,plain,
% 0.19/0.41 (~![A: $i, B: $i] : ((~element(B, finite_subsets(A))) | element(B, powerset(A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 (~![A: $i, B: $i] : ((~element(B, finite_subsets(A))) | element(B, powerset(A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 (~![A: $i, B: $i] : ((~element(B, finite_subsets(A))) | element(B, powerset(A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[16, 10])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 (~![A: $i, B: $i] : ((~element(B, finite_subsets(A))) | element(B, powerset(A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 (~![A: $i, B: $i] : ((~element(B, finite_subsets(A))) | element(B, powerset(A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.19/0.41 tff(20,plain,(
% 0.19/0.41 ~((~element(B!9, finite_subsets(A!10))) | element(B!9, powerset(A!10)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[19])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 (~element(B!9, powerset(A!10))),
% 0.19/0.41 inference(or_elim,[status(thm)],[20])).
% 0.19/0.41 tff(22,plain,
% 0.19/0.41 ((~(element(B!9, powerset(A!10)) <=> subset(B!9, A!10))) | element(B!9, powerset(A!10)) | (~subset(B!9, A!10))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 ((~(element(B!9, powerset(A!10)) <=> subset(B!9, A!10))) | (~subset(B!9, A!10))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 (~subset(B!9, A!10)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[23, 9])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 (((~finite(B!9)) | (~subset(B!9, A!10))) | subset(B!9, A!10)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 ((~finite(B!9)) | (~subset(B!9, A!10))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 (^[A: $i] : refl((~(empty(finite_subsets(A)) | (~cup_closed(finite_subsets(A))) | (~diff_closed(finite_subsets(A))) | (~preboolean(finite_subsets(A))))) <=> (~(empty(finite_subsets(A)) | (~cup_closed(finite_subsets(A))) | (~diff_closed(finite_subsets(A))) | (~preboolean(finite_subsets(A))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (![A: $i] : (~(empty(finite_subsets(A)) | (~cup_closed(finite_subsets(A))) | (~diff_closed(finite_subsets(A))) | (~preboolean(finite_subsets(A))))) <=> ![A: $i] : (~(empty(finite_subsets(A)) | (~cup_closed(finite_subsets(A))) | (~diff_closed(finite_subsets(A))) | (~preboolean(finite_subsets(A)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 (^[A: $i] : rewrite(((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A)) & diff_closed(finite_subsets(A)) & preboolean(finite_subsets(A))) <=> (~(empty(finite_subsets(A)) | (~cup_closed(finite_subsets(A))) | (~diff_closed(finite_subsets(A))) | (~preboolean(finite_subsets(A))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 (![A: $i] : ((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A)) & diff_closed(finite_subsets(A)) & preboolean(finite_subsets(A))) <=> ![A: $i] : (~(empty(finite_subsets(A)) | (~cup_closed(finite_subsets(A))) | (~diff_closed(finite_subsets(A))) | (~preboolean(finite_subsets(A)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 (![A: $i] : ((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A)) & diff_closed(finite_subsets(A)) & preboolean(finite_subsets(A))) <=> ![A: $i] : ((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A)) & diff_closed(finite_subsets(A)) & preboolean(finite_subsets(A)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 (^[A: $i] : trans(monotonicity(rewrite((((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A))) & diff_closed(finite_subsets(A))) <=> ((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A)) & diff_closed(finite_subsets(A)))), (((((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A))) & diff_closed(finite_subsets(A))) & preboolean(finite_subsets(A))) <=> (((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A)) & diff_closed(finite_subsets(A))) & preboolean(finite_subsets(A))))), rewrite((((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A)) & diff_closed(finite_subsets(A))) & preboolean(finite_subsets(A))) <=> ((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A)) & diff_closed(finite_subsets(A)) & preboolean(finite_subsets(A)))), (((((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A))) & diff_closed(finite_subsets(A))) & preboolean(finite_subsets(A))) <=> ((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A)) & diff_closed(finite_subsets(A)) & preboolean(finite_subsets(A)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (![A: $i] : ((((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A))) & diff_closed(finite_subsets(A))) & preboolean(finite_subsets(A))) <=> ![A: $i] : ((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A)) & diff_closed(finite_subsets(A)) & preboolean(finite_subsets(A)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.41 tff(34,axiom,(![A: $i] : ((((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A))) & diff_closed(finite_subsets(A))) & preboolean(finite_subsets(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc2_finsub_1')).
% 0.19/0.42 tff(35,plain,
% 0.19/0.42 (![A: $i] : ((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A)) & diff_closed(finite_subsets(A)) & preboolean(finite_subsets(A)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.42 tff(36,plain,
% 0.19/0.42 (![A: $i] : ((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A)) & diff_closed(finite_subsets(A)) & preboolean(finite_subsets(A)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.19/0.42 tff(37,plain,(
% 0.19/0.42 ![A: $i] : ((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A)) & diff_closed(finite_subsets(A)) & preboolean(finite_subsets(A)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[36])).
% 0.19/0.42 tff(38,plain,
% 0.19/0.42 (![A: $i] : (~(empty(finite_subsets(A)) | (~cup_closed(finite_subsets(A))) | (~diff_closed(finite_subsets(A))) | (~preboolean(finite_subsets(A)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.19/0.42 tff(39,plain,
% 0.19/0.42 (![A: $i] : (~(empty(finite_subsets(A)) | (~cup_closed(finite_subsets(A))) | (~diff_closed(finite_subsets(A))) | (~preboolean(finite_subsets(A)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[38, 28])).
% 0.19/0.42 tff(40,plain,
% 0.19/0.42 ((~![A: $i] : (~(empty(finite_subsets(A)) | (~cup_closed(finite_subsets(A))) | (~diff_closed(finite_subsets(A))) | (~preboolean(finite_subsets(A)))))) | (~(empty(finite_subsets(A!10)) | (~cup_closed(finite_subsets(A!10))) | (~diff_closed(finite_subsets(A!10))) | (~preboolean(finite_subsets(A!10)))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(41,plain,
% 0.19/0.42 (~(empty(finite_subsets(A!10)) | (~cup_closed(finite_subsets(A!10))) | (~diff_closed(finite_subsets(A!10))) | (~preboolean(finite_subsets(A!10))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.19/0.42 tff(42,plain,
% 0.19/0.42 ((empty(finite_subsets(A!10)) | (~cup_closed(finite_subsets(A!10))) | (~diff_closed(finite_subsets(A!10))) | (~preboolean(finite_subsets(A!10)))) | (~empty(finite_subsets(A!10)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(43,plain,
% 0.19/0.42 (~empty(finite_subsets(A!10))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.19/0.42 tff(44,plain,
% 0.19/0.42 (element(B!9, finite_subsets(A!10))),
% 0.19/0.42 inference(or_elim,[status(thm)],[20])).
% 0.19/0.42 tff(45,plain,
% 0.19/0.42 (^[A: $i, B: $i] : refl((empty(B) | in(A, B) | (~element(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(46,plain,
% 0.19/0.42 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[45])).
% 0.19/0.42 tff(47,plain,
% 0.19/0.42 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(48,plain,
% 0.19/0.42 (^[A: $i, B: $i] : rewrite((element(A, B) => (empty(B) | in(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(49,plain,
% 0.19/0.42 (![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[48])).
% 0.19/0.42 tff(50,axiom,(![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2_subset')).
% 0.19/0.42 tff(51,plain,
% 0.19/0.42 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.42 tff(52,plain,
% 0.19/0.42 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.19/0.42 tff(53,plain,(
% 0.19/0.42 ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[52])).
% 0.19/0.42 tff(54,plain,
% 0.19/0.42 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.19/0.42 tff(55,plain,
% 0.19/0.42 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | ((~element(B!9, finite_subsets(A!10))) | empty(finite_subsets(A!10)) | in(B!9, finite_subsets(A!10)))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (~element(B!9, finite_subsets(A!10))) | empty(finite_subsets(A!10)) | in(B!9, finite_subsets(A!10)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(56,plain,
% 0.19/0.42 ((empty(finite_subsets(A!10)) | in(B!9, finite_subsets(A!10)) | (~element(B!9, finite_subsets(A!10)))) <=> ((~element(B!9, finite_subsets(A!10))) | empty(finite_subsets(A!10)) | in(B!9, finite_subsets(A!10)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(57,plain,
% 0.19/0.42 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(finite_subsets(A!10)) | in(B!9, finite_subsets(A!10)) | (~element(B!9, finite_subsets(A!10))))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | ((~element(B!9, finite_subsets(A!10))) | empty(finite_subsets(A!10)) | in(B!9, finite_subsets(A!10))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[56])).
% 0.19/0.42 tff(58,plain,
% 0.19/0.42 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(finite_subsets(A!10)) | in(B!9, finite_subsets(A!10)) | (~element(B!9, finite_subsets(A!10))))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (~element(B!9, finite_subsets(A!10))) | empty(finite_subsets(A!10)) | in(B!9, finite_subsets(A!10)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[57, 55])).
% 0.19/0.42 tff(59,plain,
% 0.19/0.42 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(finite_subsets(A!10)) | in(B!9, finite_subsets(A!10)) | (~element(B!9, finite_subsets(A!10))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(60,plain,
% 0.19/0.42 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (~element(B!9, finite_subsets(A!10))) | empty(finite_subsets(A!10)) | in(B!9, finite_subsets(A!10))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.19/0.42 tff(61,plain,
% 0.19/0.42 (empty(finite_subsets(A!10)) | in(B!9, finite_subsets(A!10))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[60, 54, 44])).
% 0.19/0.42 tff(62,plain,
% 0.19/0.42 (in(B!9, finite_subsets(A!10))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[61, 43])).
% 0.19/0.42 tff(63,plain,
% 0.19/0.42 ((~(in(B!9, finite_subsets(A!10)) <=> (~((~finite(B!9)) | (~subset(B!9, A!10)))))) | (~in(B!9, finite_subsets(A!10))) | (~((~finite(B!9)) | (~subset(B!9, A!10))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(64,plain,
% 0.19/0.42 (~(in(B!9, finite_subsets(A!10)) <=> (~((~finite(B!9)) | (~subset(B!9, A!10)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[63, 62, 26])).
% 0.19/0.42 tff(65,plain,
% 0.19/0.42 (^[A: $i] : refl(preboolean(finite_subsets(A)) <=> preboolean(finite_subsets(A)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(66,plain,
% 0.19/0.42 (![A: $i] : preboolean(finite_subsets(A)) <=> ![A: $i] : preboolean(finite_subsets(A))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.42 tff(67,plain,
% 0.19/0.42 (![A: $i] : preboolean(finite_subsets(A)) <=> ![A: $i] : preboolean(finite_subsets(A))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(68,axiom,(![A: $i] : preboolean(finite_subsets(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k5_finsub_1')).
% 0.19/0.42 tff(69,plain,
% 0.19/0.42 (![A: $i] : preboolean(finite_subsets(A))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.19/0.42 tff(70,plain,(
% 0.19/0.42 ![A: $i] : preboolean(finite_subsets(A))),
% 0.19/0.42 inference(skolemize,[status(sab)],[69])).
% 0.19/0.42 tff(71,plain,
% 0.19/0.42 (![A: $i] : preboolean(finite_subsets(A))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.19/0.42 tff(72,plain,
% 0.19/0.42 ((~![A: $i] : preboolean(finite_subsets(A))) | preboolean(finite_subsets(A!10))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(73,plain,
% 0.19/0.42 (preboolean(finite_subsets(A!10))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.19/0.42 tff(74,plain,
% 0.19/0.42 (^[A: $i, B: $i] : rewrite(((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))) | (~((B = finite_subsets(A)) | (in(tptp_fun_C_11(B, A), B) <=> ((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))))))))) <=> ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (in(tptp_fun_C_11(B, A), B) <=> ((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A))))))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A)))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(75,plain,
% 0.19/0.42 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))) | (~((B = finite_subsets(A)) | (in(tptp_fun_C_11(B, A), B) <=> ((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))))))))) <=> ![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (in(tptp_fun_C_11(B, A), B) <=> ((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A))))))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[74])).
% 0.19/0.42 tff(76,plain,
% 0.19/0.42 (^[A: $i, B: $i] : refl(((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))) | (~((B = finite_subsets(A)) | (in(tptp_fun_C_11(B, A), B) <=> ((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))))))))) <=> ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))) | (~((B = finite_subsets(A)) | (in(tptp_fun_C_11(B, A), B) <=> ((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(77,plain,
% 0.19/0.42 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))) | (~((B = finite_subsets(A)) | (in(tptp_fun_C_11(B, A), B) <=> ((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))))))))) <=> ![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))) | (~((B = finite_subsets(A)) | (in(tptp_fun_C_11(B, A), B) <=> ((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A))))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[76])).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 (^[A: $i, B: $i] : rewrite(((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))) | (~((B = finite_subsets(A)) | (in(tptp_fun_C_11(B, A), B) <=> ((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))))))))) <=> ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))) | (~((B = finite_subsets(A)) | (in(tptp_fun_C_11(B, A), B) <=> ((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))) | (~((B = finite_subsets(A)) | (in(tptp_fun_C_11(B, A), B) <=> ((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))))))))) <=> ![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))) | (~((B = finite_subsets(A)) | (in(tptp_fun_C_11(B, A), B) <=> ((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A))))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[78])).
% 0.19/0.42 tff(80,plain,
% 0.19/0.42 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))) | (~((B = finite_subsets(A)) | (in(tptp_fun_C_11(B, A), B) <=> ((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))))))))) <=> ![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))) | (~((B = finite_subsets(A)) | (in(tptp_fun_C_11(B, A), B) <=> ((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A))))))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[79, 77])).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 (^[A: $i, B: $i] : rewrite(((~preboolean(B)) | (((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))) & ((B = finite_subsets(A)) | ((~in(tptp_fun_C_11(B, A), B)) <=> (subset(tptp_fun_C_11(B, A), A) & finite(tptp_fun_C_11(B, A))))))) <=> ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))) | (~((B = finite_subsets(A)) | (in(tptp_fun_C_11(B, A), B) <=> ((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 (![A: $i, B: $i] : ((~preboolean(B)) | (((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))) & ((B = finite_subsets(A)) | ((~in(tptp_fun_C_11(B, A), B)) <=> (subset(tptp_fun_C_11(B, A), A) & finite(tptp_fun_C_11(B, A))))))) <=> ![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))) | (~((B = finite_subsets(A)) | (in(tptp_fun_C_11(B, A), B) <=> ((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A))))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[81])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 (^[A: $i, B: $i] : rewrite(((~preboolean(B)) | (((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))) & ((B = finite_subsets(A)) | (~(in(tptp_fun_C_11(B, A), B) <=> (subset(tptp_fun_C_11(B, A), A) & finite(tptp_fun_C_11(B, A)))))))) <=> ((~preboolean(B)) | (((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))) & ((B = finite_subsets(A)) | ((~in(tptp_fun_C_11(B, A), B)) <=> (subset(tptp_fun_C_11(B, A), A) & finite(tptp_fun_C_11(B, A))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 (![A: $i, B: $i] : ((~preboolean(B)) | (((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))) & ((B = finite_subsets(A)) | (~(in(tptp_fun_C_11(B, A), B) <=> (subset(tptp_fun_C_11(B, A), A) & finite(tptp_fun_C_11(B, A)))))))) <=> ![A: $i, B: $i] : ((~preboolean(B)) | (((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))) & ((B = finite_subsets(A)) | ((~in(tptp_fun_C_11(B, A), B)) <=> (subset(tptp_fun_C_11(B, A), A) & finite(tptp_fun_C_11(B, A)))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[83])).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 (![A: $i, B: $i] : ((~preboolean(B)) | ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C))))) <=> ![A: $i, B: $i] : ((~preboolean(B)) | ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))) <=> ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C))))), ((preboolean(B) => ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C))))) <=> (preboolean(B) => ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C))))))), rewrite((preboolean(B) => ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C))))) <=> ((~preboolean(B)) | ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))), ((preboolean(B) => ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C))))) <=> ((~preboolean(B)) | ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 (![A: $i, B: $i] : (preboolean(B) => ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C))))) <=> ![A: $i, B: $i] : ((~preboolean(B)) | ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[86])).
% 0.19/0.42 tff(88,axiom,(![A: $i, B: $i] : (preboolean(B) => ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d5_finsub_1')).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 (![A: $i, B: $i] : ((~preboolean(B)) | ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 (![A: $i, B: $i] : ((~preboolean(B)) | ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.19/0.42 tff(91,plain,(
% 0.19/0.42 ![A: $i, B: $i] : ((~preboolean(B)) | (((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))) & ((B = finite_subsets(A)) | (~(in(tptp_fun_C_11(B, A), B) <=> (subset(tptp_fun_C_11(B, A), A) & finite(tptp_fun_C_11(B, A))))))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[90])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 (![A: $i, B: $i] : ((~preboolean(B)) | (((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))) & ((B = finite_subsets(A)) | ((~in(tptp_fun_C_11(B, A), B)) <=> (subset(tptp_fun_C_11(B, A), A) & finite(tptp_fun_C_11(B, A)))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))) | (~((B = finite_subsets(A)) | (in(tptp_fun_C_11(B, A), B) <=> ((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A))))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[92, 82])).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))) | (~((B = finite_subsets(A)) | (in(tptp_fun_C_11(B, A), B) <=> ((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A))))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[93, 80])).
% 0.19/0.42 tff(95,plain,
% 0.19/0.42 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (in(tptp_fun_C_11(B, A), B) <=> ((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A))))))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[94, 75])).
% 0.19/0.42 tff(96,plain,
% 0.19/0.42 (((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (in(tptp_fun_C_11(B, A), B) <=> ((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A))))))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))))))) | ((~preboolean(finite_subsets(A!10))) | ![C: $i] : (in(C, finite_subsets(A!10)) <=> (~((~finite(C)) | (~subset(C, A!10))))))) <=> ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (in(tptp_fun_C_11(B, A), B) <=> ((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A))))))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))))))) | (~preboolean(finite_subsets(A!10))) | ![C: $i] : (in(C, finite_subsets(A!10)) <=> (~((~finite(C)) | (~subset(C, A!10))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(97,plain,
% 0.19/0.42 (((~preboolean(finite_subsets(A!10))) | (~((~((finite_subsets(A!10) = finite_subsets(A!10)) | (in(tptp_fun_C_11(finite_subsets(A!10), A!10), finite_subsets(A!10)) <=> ((~subset(tptp_fun_C_11(finite_subsets(A!10), A!10), A!10)) | (~finite(tptp_fun_C_11(finite_subsets(A!10), A!10))))))) | (~((~(finite_subsets(A!10) = finite_subsets(A!10))) | ![C: $i] : (in(C, finite_subsets(A!10)) <=> (~((~finite(C)) | (~subset(C, A!10)))))))))) <=> ((~preboolean(finite_subsets(A!10))) | ![C: $i] : (in(C, finite_subsets(A!10)) <=> (~((~finite(C)) | (~subset(C, A!10))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(98,plain,
% 0.19/0.42 (((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (in(tptp_fun_C_11(B, A), B) <=> ((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A))))))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))))))) | ((~preboolean(finite_subsets(A!10))) | (~((~((finite_subsets(A!10) = finite_subsets(A!10)) | (in(tptp_fun_C_11(finite_subsets(A!10), A!10), finite_subsets(A!10)) <=> ((~subset(tptp_fun_C_11(finite_subsets(A!10), A!10), A!10)) | (~finite(tptp_fun_C_11(finite_subsets(A!10), A!10))))))) | (~((~(finite_subsets(A!10) = finite_subsets(A!10))) | ![C: $i] : (in(C, finite_subsets(A!10)) <=> (~((~finite(C)) | (~subset(C, A!10))))))))))) <=> ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (in(tptp_fun_C_11(B, A), B) <=> ((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A))))))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))))))) | ((~preboolean(finite_subsets(A!10))) | ![C: $i] : (in(C, finite_subsets(A!10)) <=> (~((~finite(C)) | (~subset(C, A!10)))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[97])).
% 0.19/0.43 tff(99,plain,
% 0.19/0.43 (((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (in(tptp_fun_C_11(B, A), B) <=> ((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A))))))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))))))) | ((~preboolean(finite_subsets(A!10))) | (~((~((finite_subsets(A!10) = finite_subsets(A!10)) | (in(tptp_fun_C_11(finite_subsets(A!10), A!10), finite_subsets(A!10)) <=> ((~subset(tptp_fun_C_11(finite_subsets(A!10), A!10), A!10)) | (~finite(tptp_fun_C_11(finite_subsets(A!10), A!10))))))) | (~((~(finite_subsets(A!10) = finite_subsets(A!10))) | ![C: $i] : (in(C, finite_subsets(A!10)) <=> (~((~finite(C)) | (~subset(C, A!10))))))))))) <=> ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (in(tptp_fun_C_11(B, A), B) <=> ((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A))))))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))))))) | (~preboolean(finite_subsets(A!10))) | ![C: $i] : (in(C, finite_subsets(A!10)) <=> (~((~finite(C)) | (~subset(C, A!10))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[98, 96])).
% 0.19/0.43 tff(100,plain,
% 0.19/0.43 ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (in(tptp_fun_C_11(B, A), B) <=> ((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A))))))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))))))) | ((~preboolean(finite_subsets(A!10))) | (~((~((finite_subsets(A!10) = finite_subsets(A!10)) | (in(tptp_fun_C_11(finite_subsets(A!10), A!10), finite_subsets(A!10)) <=> ((~subset(tptp_fun_C_11(finite_subsets(A!10), A!10), A!10)) | (~finite(tptp_fun_C_11(finite_subsets(A!10), A!10))))))) | (~((~(finite_subsets(A!10) = finite_subsets(A!10))) | ![C: $i] : (in(C, finite_subsets(A!10)) <=> (~((~finite(C)) | (~subset(C, A!10))))))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(101,plain,
% 0.19/0.43 ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (in(tptp_fun_C_11(B, A), B) <=> ((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A))))))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))))))) | (~preboolean(finite_subsets(A!10))) | ![C: $i] : (in(C, finite_subsets(A!10)) <=> (~((~finite(C)) | (~subset(C, A!10)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.19/0.43 tff(102,plain,
% 0.19/0.43 (![C: $i] : (in(C, finite_subsets(A!10)) <=> (~((~finite(C)) | (~subset(C, A!10)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[101, 95, 73])).
% 0.19/0.43 tff(103,plain,
% 0.19/0.43 ((~![C: $i] : (in(C, finite_subsets(A!10)) <=> (~((~finite(C)) | (~subset(C, A!10)))))) | (in(B!9, finite_subsets(A!10)) <=> (~((~finite(B!9)) | (~subset(B!9, A!10)))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(104,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[103, 102, 64])).
% 0.19/0.43 % SZS output end Proof
%------------------------------------------------------------------------------