%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU118+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 : Sat Jun 21 05:26:55 AM UTC 2025
% Result : Theorem 0.14s 0.40s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU118+1 : TPTP v9.0.0. Released v3.2.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 06:05:38 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.40 % SZS status Theorem
% 0.14/0.40 % SZS output start Proof
% 0.14/0.40 tff(in_type, type, (
% 0.14/0.40 in: ( $i * $i ) > $o)).
% 0.14/0.40 tff(finite_subsets_type, type, (
% 0.14/0.40 finite_subsets: $i > $i)).
% 0.14/0.40 tff(tptp_fun_A_11_type, type, (
% 0.14/0.40 tptp_fun_A_11: $i)).
% 0.14/0.40 tff(tptp_fun_B_10_type, type, (
% 0.14/0.40 tptp_fun_B_10: $i)).
% 0.14/0.40 tff(subset_type, type, (
% 0.14/0.40 subset: ( $i * $i ) > $o)).
% 0.14/0.40 tff(finite_type, type, (
% 0.14/0.40 finite: $i > $o)).
% 0.14/0.40 tff(element_type, type, (
% 0.14/0.40 element: ( $i * $i ) > $o)).
% 0.14/0.40 tff(powerset_type, type, (
% 0.14/0.40 powerset: $i > $i)).
% 0.14/0.40 tff(preboolean_type, type, (
% 0.14/0.40 preboolean: $i > $o)).
% 0.14/0.40 tff(tptp_fun_C_0_type, type, (
% 0.14/0.40 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.14/0.40 tff(1,plain,
% 0.14/0.40 (^[A: $i, B: $i] : refl((element(A, powerset(B)) <=> subset(A, B)) <=> (element(A, powerset(B)) <=> subset(A, B)))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(2,plain,
% 0.14/0.40 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.40 tff(3,plain,
% 0.14/0.40 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(4,axiom,(![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t3_subset')).
% 0.14/0.40 tff(5,plain,
% 0.14/0.40 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.14/0.40 tff(6,plain,(
% 0.14/0.40 ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.14/0.40 inference(skolemize,[status(sab)],[5])).
% 0.14/0.40 tff(7,plain,
% 0.14/0.40 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.14/0.40 tff(8,plain,
% 0.14/0.40 ((~![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))) | (element(B!10, powerset(A!11)) <=> subset(B!10, A!11))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(9,plain,
% 0.14/0.40 (element(B!10, powerset(A!11)) <=> subset(B!10, A!11)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.14/0.40 tff(10,plain,
% 0.14/0.40 ((~(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))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(11,plain,
% 0.14/0.40 ((~![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))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(12,plain,
% 0.14/0.40 ((~![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))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(13,axiom,(~![A: $i, B: $i] : (element(B, powerset(A)) => (finite(A) => element(B, finite_subsets(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t34_finsub_1')).
% 0.14/0.40 tff(14,plain,
% 0.14/0.40 (~![A: $i, B: $i] : (element(B, finite_subsets(A)) | (~element(B, powerset(A))) | (~finite(A)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.14/0.40 tff(15,plain,
% 0.14/0.40 (~![A: $i, B: $i] : (element(B, finite_subsets(A)) | (~element(B, powerset(A))) | (~finite(A)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.14/0.40 tff(16,plain,
% 0.14/0.40 (~![A: $i, B: $i] : (element(B, finite_subsets(A)) | (~element(B, powerset(A))) | (~finite(A)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.14/0.40 tff(17,plain,
% 0.14/0.40 (~![A: $i, B: $i] : (element(B, finite_subsets(A)) | (~element(B, powerset(A))) | (~finite(A)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.14/0.40 tff(18,plain,(
% 0.14/0.40 ~(element(B!10, finite_subsets(A!11)) | (~element(B!10, powerset(A!11))) | (~finite(A!11)))),
% 0.14/0.40 inference(skolemize,[status(sab)],[17])).
% 0.14/0.40 tff(19,plain,
% 0.14/0.40 (~(element(B!10, finite_subsets(A!11)) | (~element(B!10, powerset(A!11))) | (~finite(A!11)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.14/0.40 tff(20,plain,
% 0.14/0.40 (element(B!10, powerset(A!11))),
% 0.14/0.40 inference(or_elim,[status(thm)],[19])).
% 0.14/0.40 tff(21,plain,
% 0.14/0.40 ((~(element(B!10, powerset(A!11)) <=> subset(B!10, A!11))) | (~element(B!10, powerset(A!11))) | subset(B!10, A!11)),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(22,plain,
% 0.14/0.41 ((~(element(B!10, powerset(A!11)) <=> subset(B!10, A!11))) | subset(B!10, A!11)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.14/0.41 tff(23,plain,
% 0.14/0.41 (subset(B!10, A!11)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[22, 9])).
% 0.14/0.41 tff(24,plain,
% 0.14/0.41 (finite(A!11)),
% 0.14/0.41 inference(or_elim,[status(thm)],[19])).
% 0.14/0.41 tff(25,plain,
% 0.14/0.41 (^[A: $i, B: $i] : refl((finite(A) | (~finite(B)) | (~subset(A, B))) <=> (finite(A) | (~finite(B)) | (~subset(A, B))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(26,plain,
% 0.14/0.41 (![A: $i, B: $i] : (finite(A) | (~finite(B)) | (~subset(A, B))) <=> ![A: $i, B: $i] : (finite(A) | (~finite(B)) | (~subset(A, B)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[25])).
% 0.14/0.41 tff(27,plain,
% 0.14/0.41 (^[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)))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(28,plain,
% 0.14/0.41 (![A: $i, B: $i] : (finite(A) | (~(subset(A, B) & finite(B)))) <=> ![A: $i, B: $i] : (finite(A) | (~finite(B)) | (~subset(A, B)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[27])).
% 0.14/0.41 tff(29,plain,
% 0.14/0.41 (![A: $i, B: $i] : (finite(A) | (~(subset(A, B) & finite(B)))) <=> ![A: $i, B: $i] : (finite(A) | (~(subset(A, B) & finite(B))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(30,plain,
% 0.14/0.41 (^[A: $i, B: $i] : rewrite(((subset(A, B) & finite(B)) => finite(A)) <=> (finite(A) | (~(subset(A, B) & finite(B)))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(31,plain,
% 0.14/0.41 (![A: $i, B: $i] : ((subset(A, B) & finite(B)) => finite(A)) <=> ![A: $i, B: $i] : (finite(A) | (~(subset(A, B) & finite(B))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[30])).
% 0.14/0.41 tff(32,axiom,(![A: $i, B: $i] : ((subset(A, B) & finite(B)) => finite(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t13_finset_1')).
% 0.14/0.41 tff(33,plain,
% 0.14/0.41 (![A: $i, B: $i] : (finite(A) | (~(subset(A, B) & finite(B))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.14/0.41 tff(34,plain,
% 0.14/0.41 (![A: $i, B: $i] : (finite(A) | (~(subset(A, B) & finite(B))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.14/0.41 tff(35,plain,(
% 0.14/0.41 ![A: $i, B: $i] : (finite(A) | (~(subset(A, B) & finite(B))))),
% 0.14/0.41 inference(skolemize,[status(sab)],[34])).
% 0.14/0.41 tff(36,plain,
% 0.14/0.41 (![A: $i, B: $i] : (finite(A) | (~finite(B)) | (~subset(A, B)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.14/0.41 tff(37,plain,
% 0.14/0.41 (![A: $i, B: $i] : (finite(A) | (~finite(B)) | (~subset(A, B)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[36, 26])).
% 0.14/0.41 tff(38,plain,
% 0.14/0.41 (((~![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)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(39,plain,
% 0.14/0.41 ((~![A: $i, B: $i] : (finite(A) | (~finite(B)) | (~subset(A, B)))) | (finite(B!10) | (~finite(A!11)) | (~subset(B!10, A!11)))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(40,plain,
% 0.14/0.41 ((~![A: $i, B: $i] : (finite(A) | (~finite(B)) | (~subset(A, B)))) | finite(B!10) | (~finite(A!11)) | (~subset(B!10, A!11))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.14/0.41 tff(41,plain,
% 0.14/0.41 (finite(B!10)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[40, 37, 24, 23])).
% 0.14/0.41 tff(42,plain,
% 0.14/0.41 ((~((~finite(B!10)) | (~subset(B!10, A!11)))) | (~finite(B!10)) | (~subset(B!10, A!11))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(43,plain,
% 0.14/0.41 (~((~finite(B!10)) | (~subset(B!10, A!11)))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[42, 23, 41])).
% 0.14/0.41 tff(44,plain,
% 0.14/0.41 (~element(B!10, finite_subsets(A!11))),
% 0.14/0.41 inference(or_elim,[status(thm)],[19])).
% 0.14/0.41 tff(45,plain,
% 0.14/0.41 (^[A: $i, B: $i] : refl(((~in(A, B)) | element(A, B)) <=> ((~in(A, B)) | element(A, B)))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(46,plain,
% 0.14/0.41 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[45])).
% 0.14/0.41 tff(47,plain,
% 0.14/0.41 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(48,plain,
% 0.14/0.41 (^[A: $i, B: $i] : rewrite((in(A, B) => element(A, B)) <=> ((~in(A, B)) | element(A, B)))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(49,plain,
% 0.14/0.41 (![A: $i, B: $i] : (in(A, B) => element(A, B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[48])).
% 0.14/0.41 tff(50,axiom,(![A: $i, B: $i] : (in(A, B) => element(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t1_subset')).
% 0.14/0.41 tff(51,plain,
% 0.14/0.41 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.14/0.41 tff(52,plain,
% 0.14/0.41 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.14/0.41 tff(53,plain,(
% 0.14/0.41 ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.14/0.41 inference(skolemize,[status(sab)],[52])).
% 0.14/0.41 tff(54,plain,
% 0.14/0.41 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.14/0.41 tff(55,plain,
% 0.14/0.41 (((~![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)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(56,plain,
% 0.14/0.41 ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | ((~in(B!10, finite_subsets(A!11))) | element(B!10, finite_subsets(A!11)))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(57,plain,
% 0.14/0.41 ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | (~in(B!10, finite_subsets(A!11))) | element(B!10, finite_subsets(A!11))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.14/0.41 tff(58,plain,
% 0.14/0.41 (~in(B!10, finite_subsets(A!11))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[57, 54, 44])).
% 0.14/0.41 tff(59,plain,
% 0.14/0.41 ((((~finite(B!10)) | (~subset(B!10, A!11))) <=> in(B!10, finite_subsets(A!11))) | ((~finite(B!10)) | (~subset(B!10, A!11))) | in(B!10, finite_subsets(A!11))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(60,plain,
% 0.14/0.41 (((~finite(B!10)) | (~subset(B!10, A!11))) <=> in(B!10, finite_subsets(A!11))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[59, 58, 43])).
% 0.14/0.41 tff(61,plain,
% 0.14/0.41 (^[A: $i] : refl(preboolean(finite_subsets(A)) <=> preboolean(finite_subsets(A)))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(62,plain,
% 0.14/0.41 (![A: $i] : preboolean(finite_subsets(A)) <=> ![A: $i] : preboolean(finite_subsets(A))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[61])).
% 0.14/0.41 tff(63,plain,
% 0.14/0.41 (![A: $i] : preboolean(finite_subsets(A)) <=> ![A: $i] : preboolean(finite_subsets(A))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(64,axiom,(![A: $i] : preboolean(finite_subsets(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k5_finsub_1')).
% 0.14/0.41 tff(65,plain,
% 0.14/0.41 (![A: $i] : preboolean(finite_subsets(A))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.14/0.41 tff(66,plain,(
% 0.14/0.41 ![A: $i] : preboolean(finite_subsets(A))),
% 0.14/0.41 inference(skolemize,[status(sab)],[65])).
% 0.14/0.41 tff(67,plain,
% 0.14/0.41 (![A: $i] : preboolean(finite_subsets(A))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.14/0.41 tff(68,plain,
% 0.14/0.41 ((~![A: $i] : preboolean(finite_subsets(A))) | preboolean(finite_subsets(A!11))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(69,plain,
% 0.14/0.41 (preboolean(finite_subsets(A!11))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.14/0.41 tff(70,plain,
% 0.14/0.41 (^[A: $i, B: $i] : rewrite(((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A)))) <=> in(tptp_fun_C_0(B, A), B))))))) <=> ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A)))) <=> in(tptp_fun_C_0(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B)))))))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(71,plain,
% 0.14/0.41 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A)))) <=> in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A)))) <=> in(tptp_fun_C_0(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[70])).
% 0.14/0.41 tff(72,plain,
% 0.14/0.41 (^[A: $i, B: $i] : refl(((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A)))) <=> in(tptp_fun_C_0(B, A), B))))))) <=> ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A)))) <=> in(tptp_fun_C_0(B, A), B))))))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(73,plain,
% 0.14/0.41 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A)))) <=> in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A)))) <=> in(tptp_fun_C_0(B, A), B)))))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[72])).
% 0.14/0.41 tff(74,plain,
% 0.14/0.41 (^[A: $i, B: $i] : rewrite(((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A)))) <=> in(tptp_fun_C_0(B, A), B))))))) <=> ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A)))) <=> in(tptp_fun_C_0(B, A), B))))))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(75,plain,
% 0.14/0.41 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A)))) <=> in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A)))) <=> in(tptp_fun_C_0(B, A), B)))))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[74])).
% 0.14/0.41 tff(76,plain,
% 0.14/0.41 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A)))) <=> in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A)))) <=> in(tptp_fun_C_0(B, A), B)))))))),
% 0.14/0.41 inference(transitivity,[status(thm)],[75, 73])).
% 0.14/0.41 tff(77,plain,
% 0.14/0.41 (^[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] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A)))) <=> in(tptp_fun_C_0(B, A), B))))))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(78,plain,
% 0.14/0.41 (![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] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A)))) <=> in(tptp_fun_C_0(B, A), B)))))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[77])).
% 0.14/0.41 tff(79,plain,
% 0.14/0.41 (![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)))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(80,plain,
% 0.14/0.41 (^[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)))))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(81,plain,
% 0.14/0.41 (![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)))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[80])).
% 0.14/0.41 tff(82,axiom,(![A: $i, B: $i] : (preboolean(B) => ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d5_finsub_1')).
% 0.14/0.41 tff(83,plain,
% 0.14/0.41 (![A: $i, B: $i] : ((~preboolean(B)) | ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.14/0.41 tff(84,plain,
% 0.14/0.41 (![A: $i, B: $i] : ((~preboolean(B)) | ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.14/0.41 tff(85,plain,(
% 0.14/0.41 ![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))))))))),
% 0.14/0.41 inference(skolemize,[status(sab)],[84])).
% 0.14/0.41 tff(86,plain,
% 0.14/0.41 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A)))) <=> in(tptp_fun_C_0(B, A), B)))))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.14/0.41 tff(87,plain,
% 0.14/0.41 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A)))) <=> in(tptp_fun_C_0(B, A), B)))))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[86, 76])).
% 0.14/0.41 tff(88,plain,
% 0.14/0.41 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A)))) <=> in(tptp_fun_C_0(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[87, 71])).
% 0.14/0.41 tff(89,plain,
% 0.14/0.41 (((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A)))) <=> in(tptp_fun_C_0(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))) | ((~preboolean(finite_subsets(A!11))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A!11))) <=> in(C, finite_subsets(A!11)))))) <=> ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A)))) <=> in(tptp_fun_C_0(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))) | (~preboolean(finite_subsets(A!11))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A!11))) <=> in(C, finite_subsets(A!11)))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(90,plain,
% 0.14/0.41 (((~preboolean(finite_subsets(A!11))) | (~((~((finite_subsets(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)))) <=> in(tptp_fun_C_0(finite_subsets(A!11), A!11), finite_subsets(A!11))))) | (~((~(finite_subsets(A!11) = finite_subsets(A!11))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A!11))) <=> in(C, finite_subsets(A!11))))))))) <=> ((~preboolean(finite_subsets(A!11))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A!11))) <=> in(C, finite_subsets(A!11)))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(91,plain,
% 0.14/0.41 (((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A)))) <=> in(tptp_fun_C_0(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))) | ((~preboolean(finite_subsets(A!11))) | (~((~((finite_subsets(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)))) <=> in(tptp_fun_C_0(finite_subsets(A!11), A!11), finite_subsets(A!11))))) | (~((~(finite_subsets(A!11) = finite_subsets(A!11))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A!11))) <=> in(C, finite_subsets(A!11)))))))))) <=> ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A)))) <=> in(tptp_fun_C_0(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))) | ((~preboolean(finite_subsets(A!11))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A!11))) <=> in(C, finite_subsets(A!11))))))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[90])).
% 0.14/0.41 tff(92,plain,
% 0.14/0.41 (((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A)))) <=> in(tptp_fun_C_0(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))) | ((~preboolean(finite_subsets(A!11))) | (~((~((finite_subsets(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)))) <=> in(tptp_fun_C_0(finite_subsets(A!11), A!11), finite_subsets(A!11))))) | (~((~(finite_subsets(A!11) = finite_subsets(A!11))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A!11))) <=> in(C, finite_subsets(A!11)))))))))) <=> ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A)))) <=> in(tptp_fun_C_0(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))) | (~preboolean(finite_subsets(A!11))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A!11))) <=> in(C, finite_subsets(A!11)))))),
% 0.14/0.42 inference(transitivity,[status(thm)],[91, 89])).
% 0.14/0.42 tff(93,plain,
% 0.14/0.42 ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A)))) <=> in(tptp_fun_C_0(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))) | ((~preboolean(finite_subsets(A!11))) | (~((~((finite_subsets(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)))) <=> in(tptp_fun_C_0(finite_subsets(A!11), A!11), finite_subsets(A!11))))) | (~((~(finite_subsets(A!11) = finite_subsets(A!11))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A!11))) <=> in(C, finite_subsets(A!11)))))))))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(94,plain,
% 0.14/0.42 ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_0(B, A), A)) | (~finite(tptp_fun_C_0(B, A)))) <=> in(tptp_fun_C_0(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))) | (~preboolean(finite_subsets(A!11))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A!11))) <=> in(C, finite_subsets(A!11))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.14/0.42 tff(95,plain,
% 0.14/0.42 (![C: $i] : (~(((~finite(C)) | (~subset(C, A!11))) <=> in(C, finite_subsets(A!11))))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[94, 88, 69])).
% 0.14/0.42 tff(96,plain,
% 0.14/0.42 ((~![C: $i] : (~(((~finite(C)) | (~subset(C, A!11))) <=> in(C, finite_subsets(A!11))))) | (~(((~finite(B!10)) | (~subset(B!10, A!11))) <=> in(B!10, finite_subsets(A!11))))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(97,plain,
% 0.14/0.42 ($false),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[96, 95, 60])).
% 0.14/0.42 % SZS output end Proof
% 0.14/0.42 % E exiting
%------------------------------------------------------------------------------