TSTP Solution File: SEU118+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU118+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 0.11s 0.32s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SEU118+1 : TPTP v8.1.0. Released v3.2.0.
% 0.00/0.08 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.07/0.27 % Computer : n014.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 300
% 0.07/0.27 % DateTime : Sat Sep 3 09:32:15 EDT 2022
% 0.07/0.27 % CPUTime :
% 0.07/0.27 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.07/0.27 Usage: tptp [options] [-file:]file
% 0.07/0.27 -h, -? prints this message.
% 0.07/0.27 -smt2 print SMT-LIB2 benchmark.
% 0.07/0.27 -m, -model generate model.
% 0.07/0.27 -p, -proof generate proof.
% 0.07/0.27 -c, -core generate unsat core of named formulas.
% 0.07/0.27 -st, -statistics display statistics.
% 0.07/0.27 -t:timeout set timeout (in second).
% 0.07/0.27 -smt2status display status in smt2 format instead of SZS.
% 0.07/0.27 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.07/0.27 -<param>:<value> configuration parameter and value.
% 0.07/0.27 -o:<output-file> file to place output in.
% 0.11/0.32 % SZS status Theorem
% 0.11/0.32 % SZS output start Proof
% 0.11/0.32 tff(subset_type, type, (
% 0.11/0.32 subset: ( $i * $i ) > $o)).
% 0.11/0.32 tff(tptp_fun_A_11_type, type, (
% 0.11/0.32 tptp_fun_A_11: $i)).
% 0.11/0.32 tff(tptp_fun_B_10_type, type, (
% 0.11/0.32 tptp_fun_B_10: $i)).
% 0.11/0.32 tff(finite_type, type, (
% 0.11/0.32 finite: $i > $o)).
% 0.11/0.32 tff(in_type, type, (
% 0.11/0.32 in: ( $i * $i ) > $o)).
% 0.11/0.32 tff(finite_subsets_type, type, (
% 0.11/0.32 finite_subsets: $i > $i)).
% 0.11/0.32 tff(element_type, type, (
% 0.11/0.32 element: ( $i * $i ) > $o)).
% 0.11/0.32 tff(powerset_type, type, (
% 0.11/0.32 powerset: $i > $i)).
% 0.11/0.32 tff(preboolean_type, type, (
% 0.11/0.32 preboolean: $i > $o)).
% 0.11/0.32 tff(tptp_fun_C_0_type, type, (
% 0.11/0.32 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.11/0.32 tff(1,plain,
% 0.11/0.32 (^[A: $i, B: $i] : refl((element(A, powerset(B)) <=> subset(A, B)) <=> (element(A, powerset(B)) <=> subset(A, B)))),
% 0.11/0.32 inference(bind,[status(th)],[])).
% 0.11/0.32 tff(2,plain,
% 0.11/0.32 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.11/0.32 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.32 tff(3,plain,
% 0.11/0.32 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.11/0.32 inference(rewrite,[status(thm)],[])).
% 0.11/0.32 tff(4,axiom,(![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3_subset')).
% 0.11/0.32 tff(5,plain,
% 0.11/0.32 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.11/0.32 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.11/0.32 tff(6,plain,(
% 0.11/0.32 ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.11/0.32 inference(skolemize,[status(sab)],[5])).
% 0.11/0.32 tff(7,plain,
% 0.11/0.32 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.11/0.32 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.11/0.32 tff(8,plain,
% 0.11/0.32 ((~![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))) | (element(B!10, powerset(A!11)) <=> subset(B!10, A!11))),
% 0.11/0.32 inference(quant_inst,[status(thm)],[])).
% 0.11/0.32 tff(9,plain,
% 0.11/0.32 (element(B!10, powerset(A!11)) <=> subset(B!10, A!11)),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.11/0.32 tff(10,plain,
% 0.11/0.32 ((~(element(B!10, finite_subsets(A!11)) | (~element(B!10, powerset(A!11))) | (~finite(A!11)))) <=> (~(element(B!10, finite_subsets(A!11)) | (~element(B!10, powerset(A!11))) | (~finite(A!11))))),
% 0.11/0.33 inference(rewrite,[status(thm)],[])).
% 0.11/0.33 tff(11,plain,
% 0.11/0.33 ((~![A: $i, B: $i] : (element(B, finite_subsets(A)) | (~element(B, powerset(A))) | (~finite(A)))) <=> (~![A: $i, B: $i] : (element(B, finite_subsets(A)) | (~element(B, powerset(A))) | (~finite(A))))),
% 0.11/0.33 inference(rewrite,[status(thm)],[])).
% 0.11/0.33 tff(12,plain,
% 0.11/0.33 ((~![A: $i, B: $i] : (element(B, powerset(A)) => (finite(A) => element(B, finite_subsets(A))))) <=> (~![A: $i, B: $i] : (element(B, finite_subsets(A)) | (~element(B, powerset(A))) | (~finite(A))))),
% 0.11/0.33 inference(rewrite,[status(thm)],[])).
% 0.11/0.33 tff(13,axiom,(~![A: $i, B: $i] : (element(B, powerset(A)) => (finite(A) => element(B, finite_subsets(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t34_finsub_1')).
% 0.11/0.33 tff(14,plain,
% 0.11/0.33 (~![A: $i, B: $i] : (element(B, finite_subsets(A)) | (~element(B, powerset(A))) | (~finite(A)))),
% 0.11/0.33 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.11/0.33 tff(15,plain,
% 0.11/0.33 (~![A: $i, B: $i] : (element(B, finite_subsets(A)) | (~element(B, powerset(A))) | (~finite(A)))),
% 0.11/0.33 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.11/0.33 tff(16,plain,
% 0.11/0.33 (~![A: $i, B: $i] : (element(B, finite_subsets(A)) | (~element(B, powerset(A))) | (~finite(A)))),
% 0.11/0.33 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.11/0.33 tff(17,plain,
% 0.11/0.33 (~![A: $i, B: $i] : (element(B, finite_subsets(A)) | (~element(B, powerset(A))) | (~finite(A)))),
% 0.11/0.33 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.11/0.33 tff(18,plain,
% 0.11/0.33 (~![A: $i, B: $i] : (element(B, finite_subsets(A)) | (~element(B, powerset(A))) | (~finite(A)))),
% 0.11/0.33 inference(modus_ponens,[status(thm)],[17, 11])).
% 0.11/0.33 tff(19,plain,
% 0.11/0.33 (~![A: $i, B: $i] : (element(B, finite_subsets(A)) | (~element(B, powerset(A))) | (~finite(A)))),
% 0.11/0.33 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.11/0.33 tff(20,plain,
% 0.11/0.33 (~![A: $i, B: $i] : (element(B, finite_subsets(A)) | (~element(B, powerset(A))) | (~finite(A)))),
% 0.11/0.33 inference(modus_ponens,[status(thm)],[19, 11])).
% 0.11/0.33 tff(21,plain,(
% 0.11/0.33 ~(element(B!10, finite_subsets(A!11)) | (~element(B!10, powerset(A!11))) | (~finite(A!11)))),
% 0.11/0.33 inference(skolemize,[status(sab)],[20])).
% 0.11/0.33 tff(22,plain,
% 0.11/0.33 (~(element(B!10, finite_subsets(A!11)) | (~element(B!10, powerset(A!11))) | (~finite(A!11)))),
% 0.11/0.33 inference(modus_ponens,[status(thm)],[21, 10])).
% 0.11/0.33 tff(23,plain,
% 0.11/0.33 (element(B!10, powerset(A!11))),
% 0.11/0.33 inference(or_elim,[status(thm)],[22])).
% 0.11/0.33 tff(24,plain,
% 0.11/0.33 ((~(element(B!10, powerset(A!11)) <=> subset(B!10, A!11))) | (~element(B!10, powerset(A!11))) | subset(B!10, A!11)),
% 0.11/0.33 inference(tautology,[status(thm)],[])).
% 0.11/0.33 tff(25,plain,
% 0.11/0.33 ((~(element(B!10, powerset(A!11)) <=> subset(B!10, A!11))) | subset(B!10, A!11)),
% 0.11/0.33 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.11/0.33 tff(26,plain,
% 0.11/0.33 (subset(B!10, A!11)),
% 0.11/0.33 inference(unit_resolution,[status(thm)],[25, 9])).
% 0.11/0.33 tff(27,plain,
% 0.11/0.33 (finite(A!11)),
% 0.11/0.33 inference(or_elim,[status(thm)],[22])).
% 0.11/0.33 tff(28,plain,
% 0.11/0.33 (^[A: $i, B: $i] : refl((finite(A) | (~finite(B)) | (~subset(A, B))) <=> (finite(A) | (~finite(B)) | (~subset(A, B))))),
% 0.11/0.33 inference(bind,[status(th)],[])).
% 0.11/0.33 tff(29,plain,
% 0.11/0.33 (![A: $i, B: $i] : (finite(A) | (~finite(B)) | (~subset(A, B))) <=> ![A: $i, B: $i] : (finite(A) | (~finite(B)) | (~subset(A, B)))),
% 0.11/0.33 inference(quant_intro,[status(thm)],[28])).
% 0.11/0.33 tff(30,plain,
% 0.11/0.33 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(A, B) & finite(B)) <=> (~((~finite(B)) | (~subset(A, B))))), ((~(subset(A, B) & finite(B))) <=> (~(~((~finite(B)) | (~subset(A, B))))))), rewrite((~(~((~finite(B)) | (~subset(A, B))))) <=> ((~finite(B)) | (~subset(A, B)))), ((~(subset(A, B) & finite(B))) <=> ((~finite(B)) | (~subset(A, B))))), ((finite(A) | (~(subset(A, B) & finite(B)))) <=> (finite(A) | ((~finite(B)) | (~subset(A, B)))))), rewrite((finite(A) | ((~finite(B)) | (~subset(A, B)))) <=> (finite(A) | (~finite(B)) | (~subset(A, B)))), ((finite(A) | (~(subset(A, B) & finite(B)))) <=> (finite(A) | (~finite(B)) | (~subset(A, B)))))),
% 0.11/0.33 inference(bind,[status(th)],[])).
% 0.11/0.33 tff(31,plain,
% 0.11/0.33 (![A: $i, B: $i] : (finite(A) | (~(subset(A, B) & finite(B)))) <=> ![A: $i, B: $i] : (finite(A) | (~finite(B)) | (~subset(A, B)))),
% 0.11/0.33 inference(quant_intro,[status(thm)],[30])).
% 0.11/0.33 tff(32,plain,
% 0.11/0.33 (![A: $i, B: $i] : (finite(A) | (~(subset(A, B) & finite(B)))) <=> ![A: $i, B: $i] : (finite(A) | (~(subset(A, B) & finite(B))))),
% 0.11/0.33 inference(rewrite,[status(thm)],[])).
% 0.11/0.33 tff(33,plain,
% 0.11/0.33 (^[A: $i, B: $i] : rewrite(((subset(A, B) & finite(B)) => finite(A)) <=> (finite(A) | (~(subset(A, B) & finite(B)))))),
% 0.11/0.33 inference(bind,[status(th)],[])).
% 0.11/0.33 tff(34,plain,
% 0.11/0.33 (![A: $i, B: $i] : ((subset(A, B) & finite(B)) => finite(A)) <=> ![A: $i, B: $i] : (finite(A) | (~(subset(A, B) & finite(B))))),
% 0.11/0.33 inference(quant_intro,[status(thm)],[33])).
% 0.11/0.33 tff(35,axiom,(![A: $i, B: $i] : ((subset(A, B) & finite(B)) => finite(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t13_finset_1')).
% 0.11/0.33 tff(36,plain,
% 0.11/0.33 (![A: $i, B: $i] : (finite(A) | (~(subset(A, B) & finite(B))))),
% 0.11/0.33 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.11/0.33 tff(37,plain,
% 0.11/0.33 (![A: $i, B: $i] : (finite(A) | (~(subset(A, B) & finite(B))))),
% 0.11/0.33 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.11/0.33 tff(38,plain,(
% 0.11/0.33 ![A: $i, B: $i] : (finite(A) | (~(subset(A, B) & finite(B))))),
% 0.11/0.33 inference(skolemize,[status(sab)],[37])).
% 0.11/0.33 tff(39,plain,
% 0.11/0.33 (![A: $i, B: $i] : (finite(A) | (~finite(B)) | (~subset(A, B)))),
% 0.11/0.33 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.11/0.33 tff(40,plain,
% 0.11/0.33 (![A: $i, B: $i] : (finite(A) | (~finite(B)) | (~subset(A, B)))),
% 0.11/0.33 inference(modus_ponens,[status(thm)],[39, 29])).
% 0.11/0.33 tff(41,plain,
% 0.11/0.33 (((~![A: $i, B: $i] : (finite(A) | (~finite(B)) | (~subset(A, B)))) | (finite(B!10) | (~finite(A!11)) | (~subset(B!10, A!11)))) <=> ((~![A: $i, B: $i] : (finite(A) | (~finite(B)) | (~subset(A, B)))) | finite(B!10) | (~finite(A!11)) | (~subset(B!10, A!11)))),
% 0.11/0.33 inference(rewrite,[status(thm)],[])).
% 0.11/0.33 tff(42,plain,
% 0.11/0.33 ((~![A: $i, B: $i] : (finite(A) | (~finite(B)) | (~subset(A, B)))) | (finite(B!10) | (~finite(A!11)) | (~subset(B!10, A!11)))),
% 0.11/0.33 inference(quant_inst,[status(thm)],[])).
% 0.11/0.33 tff(43,plain,
% 0.11/0.33 ((~![A: $i, B: $i] : (finite(A) | (~finite(B)) | (~subset(A, B)))) | finite(B!10) | (~finite(A!11)) | (~subset(B!10, A!11))),
% 0.11/0.33 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.11/0.33 tff(44,plain,
% 0.11/0.33 (finite(B!10)),
% 0.11/0.33 inference(unit_resolution,[status(thm)],[43, 40, 27, 26])).
% 0.11/0.33 tff(45,plain,
% 0.11/0.33 ((~((~finite(B!10)) | (~subset(B!10, A!11)))) | (~finite(B!10)) | (~subset(B!10, A!11))),
% 0.11/0.33 inference(tautology,[status(thm)],[])).
% 0.11/0.33 tff(46,plain,
% 0.11/0.33 (~((~finite(B!10)) | (~subset(B!10, A!11)))),
% 0.11/0.33 inference(unit_resolution,[status(thm)],[45, 26, 44])).
% 0.11/0.33 tff(47,plain,
% 0.11/0.33 (~element(B!10, finite_subsets(A!11))),
% 0.11/0.33 inference(or_elim,[status(thm)],[22])).
% 0.11/0.33 tff(48,plain,
% 0.11/0.33 (^[A: $i, B: $i] : refl(((~in(A, B)) | element(A, B)) <=> ((~in(A, B)) | element(A, B)))),
% 0.11/0.33 inference(bind,[status(th)],[])).
% 0.11/0.33 tff(49,plain,
% 0.11/0.33 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.11/0.33 inference(quant_intro,[status(thm)],[48])).
% 0.11/0.33 tff(50,plain,
% 0.11/0.33 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.11/0.33 inference(rewrite,[status(thm)],[])).
% 0.11/0.33 tff(51,plain,
% 0.11/0.33 (^[A: $i, B: $i] : rewrite((in(A, B) => element(A, B)) <=> ((~in(A, B)) | element(A, B)))),
% 0.11/0.33 inference(bind,[status(th)],[])).
% 0.11/0.33 tff(52,plain,
% 0.11/0.33 (![A: $i, B: $i] : (in(A, B) => element(A, B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.11/0.33 inference(quant_intro,[status(thm)],[51])).
% 0.11/0.33 tff(53,axiom,(![A: $i, B: $i] : (in(A, B) => element(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_subset')).
% 0.11/0.33 tff(54,plain,
% 0.11/0.33 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.11/0.33 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.11/0.33 tff(55,plain,
% 0.11/0.33 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.11/0.33 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.11/0.33 tff(56,plain,(
% 0.11/0.33 ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.11/0.33 inference(skolemize,[status(sab)],[55])).
% 0.11/0.33 tff(57,plain,
% 0.11/0.33 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.11/0.33 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.11/0.33 tff(58,plain,
% 0.11/0.33 (((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | ((~in(B!10, finite_subsets(A!11))) | element(B!10, finite_subsets(A!11)))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | (~in(B!10, finite_subsets(A!11))) | element(B!10, finite_subsets(A!11)))),
% 0.11/0.33 inference(rewrite,[status(thm)],[])).
% 0.11/0.33 tff(59,plain,
% 0.11/0.33 ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | ((~in(B!10, finite_subsets(A!11))) | element(B!10, finite_subsets(A!11)))),
% 0.11/0.33 inference(quant_inst,[status(thm)],[])).
% 0.11/0.33 tff(60,plain,
% 0.11/0.33 ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | (~in(B!10, finite_subsets(A!11))) | element(B!10, finite_subsets(A!11))),
% 0.11/0.33 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.11/0.33 tff(61,plain,
% 0.11/0.33 (~in(B!10, finite_subsets(A!11))),
% 0.11/0.33 inference(unit_resolution,[status(thm)],[60, 57, 47])).
% 0.11/0.33 tff(62,plain,
% 0.11/0.33 ((~(in(B!10, finite_subsets(A!11)) <=> (~((~finite(B!10)) | (~subset(B!10, A!11)))))) | in(B!10, finite_subsets(A!11)) | ((~finite(B!10)) | (~subset(B!10, A!11)))),
% 0.11/0.33 inference(tautology,[status(thm)],[])).
% 0.11/0.33 tff(63,plain,
% 0.11/0.33 (~(in(B!10, finite_subsets(A!11)) <=> (~((~finite(B!10)) | (~subset(B!10, A!11)))))),
% 0.11/0.33 inference(unit_resolution,[status(thm)],[62, 61, 46])).
% 0.11/0.33 tff(64,plain,
% 0.11/0.33 (^[A: $i] : refl(preboolean(finite_subsets(A)) <=> preboolean(finite_subsets(A)))),
% 0.11/0.33 inference(bind,[status(th)],[])).
% 0.11/0.33 tff(65,plain,
% 0.11/0.33 (![A: $i] : preboolean(finite_subsets(A)) <=> ![A: $i] : preboolean(finite_subsets(A))),
% 0.11/0.33 inference(quant_intro,[status(thm)],[64])).
% 0.11/0.33 tff(66,plain,
% 0.11/0.33 (![A: $i] : preboolean(finite_subsets(A)) <=> ![A: $i] : preboolean(finite_subsets(A))),
% 0.11/0.33 inference(rewrite,[status(thm)],[])).
% 0.11/0.33 tff(67,axiom,(![A: $i] : preboolean(finite_subsets(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k5_finsub_1')).
% 0.11/0.33 tff(68,plain,
% 0.11/0.33 (![A: $i] : preboolean(finite_subsets(A))),
% 0.11/0.33 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.11/0.33 tff(69,plain,(
% 0.11/0.33 ![A: $i] : preboolean(finite_subsets(A))),
% 0.11/0.33 inference(skolemize,[status(sab)],[68])).
% 0.11/0.33 tff(70,plain,
% 0.11/0.33 (![A: $i] : preboolean(finite_subsets(A))),
% 0.11/0.33 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.11/0.33 tff(71,plain,
% 0.11/0.33 ((~![A: $i] : preboolean(finite_subsets(A))) | preboolean(finite_subsets(A!11))),
% 0.11/0.33 inference(quant_inst,[status(thm)],[])).
% 0.11/0.33 tff(72,plain,
% 0.11/0.33 (preboolean(finite_subsets(A!11))),
% 0.11/0.33 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.11/0.33 tff(73,plain,
% 0.11/0.33 (^[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_0(B, A), B) <=> ((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A)))))))))) <=> ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (in(tptp_fun_C_0(B, A), B) <=> ((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A))))))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A)))))))))))),
% 0.11/0.33 inference(bind,[status(th)],[])).
% 0.11/0.33 tff(74,plain,
% 0.11/0.33 (![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_0(B, A), B) <=> ((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A)))))))))) <=> ![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (in(tptp_fun_C_0(B, A), B) <=> ((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A))))))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))))))),
% 0.11/0.33 inference(quant_intro,[status(thm)],[73])).
% 0.11/0.33 tff(75,plain,
% 0.11/0.33 (^[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_0(B, A), B) <=> ((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(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_0(B, A), B) <=> ((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A)))))))))))),
% 0.11/0.33 inference(bind,[status(th)],[])).
% 0.11/0.33 tff(76,plain,
% 0.11/0.33 (![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_0(B, A), B) <=> ((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(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_0(B, A), B) <=> ((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A))))))))))),
% 0.11/0.33 inference(quant_intro,[status(thm)],[75])).
% 0.11/0.33 tff(77,plain,
% 0.11/0.33 (^[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_0(B, A), B) <=> ((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(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_0(B, A), B) <=> ((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A)))))))))))),
% 0.11/0.33 inference(bind,[status(th)],[])).
% 0.11/0.33 tff(78,plain,
% 0.11/0.33 (![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_0(B, A), B) <=> ((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(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_0(B, A), B) <=> ((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A))))))))))),
% 0.11/0.33 inference(quant_intro,[status(thm)],[77])).
% 0.11/0.33 tff(79,plain,
% 0.11/0.33 (![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_0(B, A), B) <=> ((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(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_0(B, A), B) <=> ((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A))))))))))),
% 0.11/0.33 inference(transitivity,[status(thm)],[78, 76])).
% 0.11/0.33 tff(80,plain,
% 0.11/0.33 (^[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_0(B, A), B)) <=> (subset(tptp_fun_C_0(B, A), A) & finite(tptp_fun_C_0(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_0(B, A), B) <=> ((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A)))))))))))),
% 0.11/0.33 inference(bind,[status(th)],[])).
% 0.11/0.33 tff(81,plain,
% 0.11/0.33 (![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_0(B, A), B)) <=> (subset(tptp_fun_C_0(B, A), A) & finite(tptp_fun_C_0(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_0(B, A), B) <=> ((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A))))))))))),
% 0.11/0.33 inference(quant_intro,[status(thm)],[80])).
% 0.11/0.33 tff(82,plain,
% 0.11/0.33 (^[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_0(B, A), B) <=> (subset(tptp_fun_C_0(B, A), A) & finite(tptp_fun_C_0(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_0(B, A), B)) <=> (subset(tptp_fun_C_0(B, A), A) & finite(tptp_fun_C_0(B, A))))))))),
% 0.11/0.33 inference(bind,[status(th)],[])).
% 0.11/0.33 tff(83,plain,
% 0.11/0.33 (![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_0(B, A), B) <=> (subset(tptp_fun_C_0(B, A), A) & finite(tptp_fun_C_0(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_0(B, A), B)) <=> (subset(tptp_fun_C_0(B, A), A) & finite(tptp_fun_C_0(B, A)))))))),
% 0.11/0.33 inference(quant_intro,[status(thm)],[82])).
% 0.11/0.33 tff(84,plain,
% 0.11/0.33 (![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)))))),
% 0.11/0.33 inference(rewrite,[status(thm)],[])).
% 0.11/0.33 tff(85,plain,
% 0.11/0.33 (^[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)))))))),
% 0.11/0.33 inference(bind,[status(th)],[])).
% 0.11/0.33 tff(86,plain,
% 0.11/0.33 (![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)))))),
% 0.11/0.33 inference(quant_intro,[status(thm)],[85])).
% 0.11/0.33 tff(87,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')).
% 0.11/0.33 tff(88,plain,
% 0.11/0.33 (![A: $i, B: $i] : ((~preboolean(B)) | ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))),
% 0.11/0.33 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.11/0.33 tff(89,plain,
% 0.11/0.33 (![A: $i, B: $i] : ((~preboolean(B)) | ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))),
% 0.11/0.33 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.11/0.33 tff(90,plain,(
% 0.11/0.33 ![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_0(B, A), B) <=> (subset(tptp_fun_C_0(B, A), A) & finite(tptp_fun_C_0(B, A))))))))),
% 0.11/0.33 inference(skolemize,[status(sab)],[89])).
% 0.11/0.33 tff(91,plain,
% 0.11/0.33 (![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_0(B, A), B)) <=> (subset(tptp_fun_C_0(B, A), A) & finite(tptp_fun_C_0(B, A)))))))),
% 0.11/0.33 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.11/0.33 tff(92,plain,
% 0.11/0.33 (![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_0(B, A), B) <=> ((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A))))))))))),
% 0.11/0.33 inference(modus_ponens,[status(thm)],[91, 81])).
% 0.11/0.33 tff(93,plain,
% 0.11/0.33 (![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_0(B, A), B) <=> ((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A))))))))))),
% 0.11/0.33 inference(modus_ponens,[status(thm)],[92, 79])).
% 0.11/0.33 tff(94,plain,
% 0.11/0.33 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (in(tptp_fun_C_0(B, A), B) <=> ((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A))))))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))))))),
% 0.11/0.33 inference(modus_ponens,[status(thm)],[93, 74])).
% 0.11/0.33 tff(95,plain,
% 0.11/0.33 (((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (in(tptp_fun_C_0(B, A), B) <=> ((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A))))))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))))))) | ((~preboolean(finite_subsets(A!11))) | ![C: $i] : (in(C, finite_subsets(A!11)) <=> (~((~finite(C)) | (~subset(C, A!11))))))) <=> ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (in(tptp_fun_C_0(B, A), B) <=> ((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A))))))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))))))) | (~preboolean(finite_subsets(A!11))) | ![C: $i] : (in(C, finite_subsets(A!11)) <=> (~((~finite(C)) | (~subset(C, A!11))))))),
% 0.11/0.33 inference(rewrite,[status(thm)],[])).
% 0.11/0.33 tff(96,plain,
% 0.11/0.33 (((~preboolean(finite_subsets(A!11))) | (~((~((finite_subsets(A!11) = finite_subsets(A!11)) | (in(tptp_fun_C_0(finite_subsets(A!11), A!11), finite_subsets(A!11)) <=> ((~subset(tptp_fun_C_0(finite_subsets(A!11), A!11), A!11)) | (~finite(tptp_fun_C_0(finite_subsets(A!11), A!11))))))) | (~((~(finite_subsets(A!11) = finite_subsets(A!11))) | ![C: $i] : (in(C, finite_subsets(A!11)) <=> (~((~finite(C)) | (~subset(C, A!11)))))))))) <=> ((~preboolean(finite_subsets(A!11))) | ![C: $i] : (in(C, finite_subsets(A!11)) <=> (~((~finite(C)) | (~subset(C, A!11))))))),
% 0.11/0.34 inference(rewrite,[status(thm)],[])).
% 0.11/0.34 tff(97,plain,
% 0.11/0.34 (((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (in(tptp_fun_C_0(B, A), B) <=> ((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A))))))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))))))) | ((~preboolean(finite_subsets(A!11))) | (~((~((finite_subsets(A!11) = finite_subsets(A!11)) | (in(tptp_fun_C_0(finite_subsets(A!11), A!11), finite_subsets(A!11)) <=> ((~subset(tptp_fun_C_0(finite_subsets(A!11), A!11), A!11)) | (~finite(tptp_fun_C_0(finite_subsets(A!11), A!11))))))) | (~((~(finite_subsets(A!11) = finite_subsets(A!11))) | ![C: $i] : (in(C, finite_subsets(A!11)) <=> (~((~finite(C)) | (~subset(C, A!11))))))))))) <=> ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (in(tptp_fun_C_0(B, A), B) <=> ((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A))))))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))))))) | ((~preboolean(finite_subsets(A!11))) | ![C: $i] : (in(C, finite_subsets(A!11)) <=> (~((~finite(C)) | (~subset(C, A!11)))))))),
% 0.11/0.34 inference(monotonicity,[status(thm)],[96])).
% 0.11/0.34 tff(98,plain,
% 0.11/0.34 (((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (in(tptp_fun_C_0(B, A), B) <=> ((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A))))))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))))))) | ((~preboolean(finite_subsets(A!11))) | (~((~((finite_subsets(A!11) = finite_subsets(A!11)) | (in(tptp_fun_C_0(finite_subsets(A!11), A!11), finite_subsets(A!11)) <=> ((~subset(tptp_fun_C_0(finite_subsets(A!11), A!11), A!11)) | (~finite(tptp_fun_C_0(finite_subsets(A!11), A!11))))))) | (~((~(finite_subsets(A!11) = finite_subsets(A!11))) | ![C: $i] : (in(C, finite_subsets(A!11)) <=> (~((~finite(C)) | (~subset(C, A!11))))))))))) <=> ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (in(tptp_fun_C_0(B, A), B) <=> ((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A))))))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))))))) | (~preboolean(finite_subsets(A!11))) | ![C: $i] : (in(C, finite_subsets(A!11)) <=> (~((~finite(C)) | (~subset(C, A!11))))))),
% 0.11/0.34 inference(transitivity,[status(thm)],[97, 95])).
% 0.11/0.34 tff(99,plain,
% 0.11/0.34 ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (in(tptp_fun_C_0(B, A), B) <=> ((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A))))))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))))))) | ((~preboolean(finite_subsets(A!11))) | (~((~((finite_subsets(A!11) = finite_subsets(A!11)) | (in(tptp_fun_C_0(finite_subsets(A!11), A!11), finite_subsets(A!11)) <=> ((~subset(tptp_fun_C_0(finite_subsets(A!11), A!11), A!11)) | (~finite(tptp_fun_C_0(finite_subsets(A!11), A!11))))))) | (~((~(finite_subsets(A!11) = finite_subsets(A!11))) | ![C: $i] : (in(C, finite_subsets(A!11)) <=> (~((~finite(C)) | (~subset(C, A!11))))))))))),
% 0.11/0.34 inference(quant_inst,[status(thm)],[])).
% 0.11/0.34 tff(100,plain,
% 0.11/0.34 ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (in(tptp_fun_C_0(B, A), B) <=> ((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A))))))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))))))) | (~preboolean(finite_subsets(A!11))) | ![C: $i] : (in(C, finite_subsets(A!11)) <=> (~((~finite(C)) | (~subset(C, A!11)))))),
% 0.11/0.34 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.11/0.34 tff(101,plain,
% 0.11/0.34 (![C: $i] : (in(C, finite_subsets(A!11)) <=> (~((~finite(C)) | (~subset(C, A!11)))))),
% 0.11/0.34 inference(unit_resolution,[status(thm)],[100, 94, 72])).
% 0.11/0.34 tff(102,plain,
% 0.11/0.34 ((~![C: $i] : (in(C, finite_subsets(A!11)) <=> (~((~finite(C)) | (~subset(C, A!11)))))) | (in(B!10, finite_subsets(A!11)) <=> (~((~finite(B!10)) | (~subset(B!10, A!11)))))),
% 0.11/0.34 inference(quant_inst,[status(thm)],[])).
% 0.11/0.34 tff(103,plain,
% 0.11/0.34 ($false),
% 0.11/0.34 inference(unit_resolution,[status(thm)],[102, 101, 63])).
% 0.11/0.34 % SZS output end Proof
%------------------------------------------------------------------------------