%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU113+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:26:54 AM UTC 2025
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU113+1 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:05:26 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(subset_type, type, (
% 0.12/0.39 subset: ( $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_A_11_type, type, (
% 0.12/0.39 tptp_fun_A_11: $i)).
% 0.12/0.39 tff(tptp_fun_C_0_type, type, (
% 0.12/0.39 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.12/0.39 tff(finite_subsets_type, type, (
% 0.12/0.39 finite_subsets: $i > $i)).
% 0.12/0.39 tff(powerset_type, type, (
% 0.12/0.39 powerset: $i > $i)).
% 0.12/0.39 tff(element_type, type, (
% 0.12/0.39 element: ( $i * $i ) > $o)).
% 0.12/0.39 tff(in_type, type, (
% 0.12/0.39 in: ( $i * $i ) > $o)).
% 0.12/0.39 tff(empty_type, type, (
% 0.12/0.39 empty: $i > $o)).
% 0.12/0.39 tff(finite_type, type, (
% 0.12/0.39 finite: $i > $o)).
% 0.12/0.39 tff(preboolean_type, type, (
% 0.12/0.39 preboolean: $i > $o)).
% 0.12/0.39 tff(tptp_fun_C_1_type, type, (
% 0.12/0.39 tptp_fun_C_1: ( $i * $i ) > $i)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 (^[A: $i, B: $i] : refl((element(A, powerset(B)) <=> subset(A, B)) <=> (element(A, powerset(B)) <=> subset(A, B)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(4,axiom,(![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3_subset')).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.39 tff(6,plain,(
% 0.12/0.39 ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.12/0.39 inference(skolemize,[status(sab)],[5])).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 ((~![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))) | (element(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), powerset(A!11)) <=> subset(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), A!11))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (element(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), powerset(A!11)) <=> subset(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), A!11)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[10])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[12])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[13, 11])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[15])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[18])).
% 0.12/0.39 tff(20,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_tarski')).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.12/0.39 tff(23,plain,(
% 0.12/0.39 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[22])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[24, 14])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(finite_subsets(A!11), powerset(A!11))) | ![C: $i] : ((~in(C, finite_subsets(A!11))) | in(C, powerset(A!11))))) | (~(subset(finite_subsets(A!11), powerset(A!11)) | (~((~in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), finite_subsets(A!11))) | in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), powerset(A!11))))))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(27,plain,
% 0.12/0.40 (~((~((~subset(finite_subsets(A!11), powerset(A!11))) | ![C: $i] : ((~in(C, finite_subsets(A!11))) | in(C, powerset(A!11))))) | (~(subset(finite_subsets(A!11), powerset(A!11)) | (~((~in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), finite_subsets(A!11))) | in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), powerset(A!11)))))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.12/0.40 tff(28,plain,
% 0.12/0.40 (((~((~subset(finite_subsets(A!11), powerset(A!11))) | ![C: $i] : ((~in(C, finite_subsets(A!11))) | in(C, powerset(A!11))))) | (~(subset(finite_subsets(A!11), powerset(A!11)) | (~((~in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), finite_subsets(A!11))) | in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), powerset(A!11))))))) | (subset(finite_subsets(A!11), powerset(A!11)) | (~((~in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), finite_subsets(A!11))) | in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), powerset(A!11)))))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(29,plain,
% 0.12/0.40 (subset(finite_subsets(A!11), powerset(A!11)) | (~((~in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), finite_subsets(A!11))) | in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), powerset(A!11))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.12/0.40 tff(30,plain,
% 0.12/0.40 ((~![A: $i] : subset(finite_subsets(A), powerset(A))) <=> (~![A: $i] : subset(finite_subsets(A), powerset(A)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(31,axiom,(~![A: $i] : subset(finite_subsets(A), powerset(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t26_finsub_1')).
% 0.12/0.40 tff(32,plain,
% 0.12/0.40 (~![A: $i] : subset(finite_subsets(A), powerset(A))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.12/0.40 tff(33,plain,
% 0.12/0.40 (~![A: $i] : subset(finite_subsets(A), powerset(A))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[32, 30])).
% 0.12/0.40 tff(34,plain,
% 0.12/0.40 (~![A: $i] : subset(finite_subsets(A), powerset(A))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[33, 30])).
% 0.12/0.40 tff(35,plain,
% 0.12/0.40 (~![A: $i] : subset(finite_subsets(A), powerset(A))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.12/0.40 tff(36,plain,(
% 0.12/0.40 ~subset(finite_subsets(A!11), powerset(A!11))),
% 0.12/0.40 inference(skolemize,[status(sab)],[35])).
% 0.12/0.40 tff(37,plain,
% 0.12/0.40 ((~(subset(finite_subsets(A!11), powerset(A!11)) | (~((~in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), finite_subsets(A!11))) | in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), powerset(A!11)))))) | subset(finite_subsets(A!11), powerset(A!11)) | (~((~in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), finite_subsets(A!11))) | in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), powerset(A!11))))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(38,plain,
% 0.12/0.40 ((~(subset(finite_subsets(A!11), powerset(A!11)) | (~((~in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), finite_subsets(A!11))) | in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), powerset(A!11)))))) | (~((~in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), finite_subsets(A!11))) | in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), powerset(A!11))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.12/0.40 tff(39,plain,
% 0.12/0.40 (~((~in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), finite_subsets(A!11))) | in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), powerset(A!11)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[38, 29])).
% 0.12/0.40 tff(40,plain,
% 0.12/0.40 (((~in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), finite_subsets(A!11))) | in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), powerset(A!11))) | (~in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), powerset(A!11)))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(41,plain,
% 0.12/0.40 (~in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), powerset(A!11))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.12/0.40 tff(42,plain,
% 0.12/0.40 (^[A: $i] : refl((~empty(powerset(A))) <=> (~empty(powerset(A))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(43,plain,
% 0.12/0.40 (![A: $i] : (~empty(powerset(A))) <=> ![A: $i] : (~empty(powerset(A)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[42])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 (![A: $i] : (~empty(powerset(A))) <=> ![A: $i] : (~empty(powerset(A)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(45,axiom,(![A: $i] : (~empty(powerset(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_subset_1')).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (![A: $i] : (~empty(powerset(A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.40 tff(47,plain,(
% 0.19/0.40 ![A: $i] : (~empty(powerset(A)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[46])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (![A: $i] : (~empty(powerset(A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 ((~![A: $i] : (~empty(powerset(A)))) | (~empty(powerset(A!11)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (~empty(powerset(A!11))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 (^[A: $i, B: $i] : refl((empty(B) | in(A, B) | (~element(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[51])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 (^[A: $i, B: $i] : rewrite((element(A, B) => (empty(B) | in(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 (![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.40 tff(56,axiom,(![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2_subset')).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.19/0.40 tff(59,plain,(
% 0.19/0.40 ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[58])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(powerset(A!11)) | in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), powerset(A!11)) | (~element(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), powerset(A!11))))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(powerset(A!11)) | in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), powerset(A!11)) | (~element(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), powerset(A!11))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(powerset(A!11)) | in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), powerset(A!11)) | (~element(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), powerset(A!11))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(powerset(A!11)) | in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), powerset(A!11)) | (~element(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), powerset(A!11)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (~element(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), powerset(A!11))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[63, 60, 50, 41])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 ((~(element(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), powerset(A!11)) <=> subset(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), A!11))) | element(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), powerset(A!11)) | (~subset(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), A!11))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 ((~(element(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), powerset(A!11)) <=> subset(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), A!11))) | (~subset(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), A!11))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 (~subset(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), A!11)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[66, 9])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (^[A: $i] : refl(preboolean(finite_subsets(A)) <=> preboolean(finite_subsets(A)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 (![A: $i] : preboolean(finite_subsets(A)) <=> ![A: $i] : preboolean(finite_subsets(A))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[68])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (![A: $i] : preboolean(finite_subsets(A)) <=> ![A: $i] : preboolean(finite_subsets(A))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(71,axiom,(![A: $i] : preboolean(finite_subsets(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k5_finsub_1')).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 (![A: $i] : preboolean(finite_subsets(A))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.19/0.40 tff(73,plain,(
% 0.19/0.40 ![A: $i] : preboolean(finite_subsets(A))),
% 0.19/0.40 inference(skolemize,[status(sab)],[72])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 (![A: $i] : preboolean(finite_subsets(A))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 ((~![A: $i] : preboolean(finite_subsets(A))) | preboolean(finite_subsets(A!11))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 (preboolean(finite_subsets(A!11))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 (^[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_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B))))))) <=> ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B)))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 (![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_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B))))))) <=> ![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[77])).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 (^[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_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(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_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 (![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_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(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_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[79])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 (^[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_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(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_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(82,plain,
% 0.19/0.40 (![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_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(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_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[81])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 (![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_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(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_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[82, 80])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 (^[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_1(B, A), B) <=> (subset(tptp_fun_C_1(B, A), A) & finite(tptp_fun_C_1(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_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(85,plain,
% 0.19/0.40 (![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_1(B, A), B) <=> (subset(tptp_fun_C_1(B, A), A) & finite(tptp_fun_C_1(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_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[84])).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 (![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)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 (^[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)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(88,plain,
% 0.19/0.40 (![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)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[87])).
% 0.19/0.40 tff(89,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')).
% 0.19/0.40 tff(90,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((~preboolean(B)) | ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.19/0.40 tff(91,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((~preboolean(B)) | ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.19/0.40 tff(92,plain,(
% 0.19/0.40 ![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_1(B, A), B) <=> (subset(tptp_fun_C_1(B, A), A) & finite(tptp_fun_C_1(B, A))))))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[91])).
% 0.19/0.40 tff(93,plain,
% 0.19/0.40 (![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_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.19/0.40 tff(94,plain,
% 0.19/0.40 (![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_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[93, 83])).
% 0.19/0.40 tff(95,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[94, 78])).
% 0.19/0.40 tff(96,plain,
% 0.19/0.40 (((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(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_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(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)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(97,plain,
% 0.19/0.40 (((~preboolean(finite_subsets(A!11))) | (~((~((finite_subsets(A!11) = finite_subsets(A!11)) | (((~subset(tptp_fun_C_1(finite_subsets(A!11), A!11), A!11)) | (~finite(tptp_fun_C_1(finite_subsets(A!11), A!11)))) <=> in(tptp_fun_C_1(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)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 (((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(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_1(finite_subsets(A!11), A!11), A!11)) | (~finite(tptp_fun_C_1(finite_subsets(A!11), A!11)))) <=> in(tptp_fun_C_1(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_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(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))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[97])).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 (((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(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_1(finite_subsets(A!11), A!11), A!11)) | (~finite(tptp_fun_C_1(finite_subsets(A!11), A!11)))) <=> in(tptp_fun_C_1(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_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(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)))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[98, 96])).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(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_1(finite_subsets(A!11), A!11), A!11)) | (~finite(tptp_fun_C_1(finite_subsets(A!11), A!11)))) <=> in(tptp_fun_C_1(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)))))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(101,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(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))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 (![C: $i] : (~(((~finite(C)) | (~subset(C, A!11))) <=> in(C, finite_subsets(A!11))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[101, 95, 76])).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 ((~![C: $i] : (~(((~finite(C)) | (~subset(C, A!11))) <=> in(C, finite_subsets(A!11))))) | (~(((~finite(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)))) | (~subset(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), A!11))) <=> in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), finite_subsets(A!11))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(104,plain,
% 0.19/0.41 (~(((~finite(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)))) | (~subset(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), A!11))) <=> in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), finite_subsets(A!11)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.19/0.41 tff(105,plain,
% 0.19/0.41 (((~in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), finite_subsets(A!11))) | in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), powerset(A!11))) | in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), finite_subsets(A!11))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 (in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), finite_subsets(A!11))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[105, 39])).
% 0.19/0.41 tff(107,plain,
% 0.19/0.41 ((((~finite(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)))) | (~subset(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), A!11))) <=> in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), finite_subsets(A!11))) | (~((~finite(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)))) | (~subset(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), A!11)))) | (~in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), finite_subsets(A!11)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 ((((~finite(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)))) | (~subset(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), A!11))) <=> in(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), finite_subsets(A!11))) | (~((~finite(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)))) | (~subset(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), A!11))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 (~((~finite(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)))) | (~subset(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), A!11)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[108, 104])).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 (((~finite(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)))) | (~subset(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), A!11))) | subset(tptp_fun_C_0(powerset(A!11), finite_subsets(A!11)), A!11)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[110, 109, 67])).
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------