%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU114+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 0.54s 0.75s
% Output : Proof 0.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU114+1 : TPTP v9.0.0. Released v3.2.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n013.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 06:05:53 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.54/0.75 % SZS status Theorem
% 0.54/0.75 % SZS output start Proof
% 0.54/0.75 tff(subset_type, type, (
% 0.54/0.75 subset: ( $i * $i ) > $o)).
% 0.54/0.75 tff(tptp_fun_A_11_type, type, (
% 0.54/0.75 tptp_fun_A_11: $i)).
% 0.54/0.75 tff(tptp_fun_C_0_type, type, (
% 0.54/0.75 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.54/0.75 tff(powerset_type, type, (
% 0.54/0.75 powerset: $i > $i)).
% 0.54/0.75 tff(finite_subsets_type, type, (
% 0.54/0.75 finite_subsets: $i > $i)).
% 0.54/0.75 tff(element_type, type, (
% 0.54/0.75 element: ( $i * $i ) > $o)).
% 0.54/0.75 tff(finite_type, type, (
% 0.54/0.75 finite: $i > $o)).
% 0.54/0.75 tff(in_type, type, (
% 0.54/0.75 in: ( $i * $i ) > $o)).
% 0.54/0.75 tff(preboolean_type, type, (
% 0.54/0.75 preboolean: $i > $o)).
% 0.54/0.75 tff(tptp_fun_C_1_type, type, (
% 0.54/0.75 tptp_fun_C_1: ( $i * $i ) > $i)).
% 0.54/0.75 tff(1,plain,
% 0.54/0.75 (^[A: $i, B: $i] : refl((element(A, powerset(B)) <=> subset(A, B)) <=> (element(A, powerset(B)) <=> subset(A, B)))),
% 0.54/0.75 inference(bind,[status(th)],[])).
% 0.54/0.75 tff(2,plain,
% 0.54/0.75 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.54/0.75 inference(quant_intro,[status(thm)],[1])).
% 0.54/0.75 tff(3,plain,
% 0.54/0.75 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(4,axiom,(![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t3_subset')).
% 0.54/0.75 tff(5,plain,
% 0.54/0.75 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.54/0.75 tff(6,plain,(
% 0.54/0.75 ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.54/0.75 inference(skolemize,[status(sab)],[5])).
% 0.54/0.75 tff(7,plain,
% 0.54/0.75 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.54/0.75 tff(8,plain,
% 0.54/0.75 ((~![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))) | (element(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11)) <=> subset(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), A!11))),
% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
% 0.54/0.75 tff(9,plain,
% 0.54/0.75 (element(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11)) <=> subset(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), A!11)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.54/0.75 tff(10,plain,
% 0.54/0.75 (^[A: $i] : refl(preboolean(finite_subsets(A)) <=> preboolean(finite_subsets(A)))),
% 0.54/0.75 inference(bind,[status(th)],[])).
% 0.54/0.75 tff(11,plain,
% 0.54/0.75 (![A: $i] : preboolean(finite_subsets(A)) <=> ![A: $i] : preboolean(finite_subsets(A))),
% 0.54/0.75 inference(quant_intro,[status(thm)],[10])).
% 0.54/0.75 tff(12,plain,
% 0.54/0.75 (![A: $i] : preboolean(finite_subsets(A)) <=> ![A: $i] : preboolean(finite_subsets(A))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(13,axiom,(![A: $i] : preboolean(finite_subsets(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k5_finsub_1')).
% 0.54/0.75 tff(14,plain,
% 0.54/0.75 (![A: $i] : preboolean(finite_subsets(A))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.54/0.75 tff(15,plain,(
% 0.54/0.75 ![A: $i] : preboolean(finite_subsets(A))),
% 0.54/0.75 inference(skolemize,[status(sab)],[14])).
% 0.54/0.75 tff(16,plain,
% 0.54/0.75 (![A: $i] : preboolean(finite_subsets(A))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.54/0.75 tff(17,plain,
% 0.54/0.75 ((~![A: $i] : preboolean(finite_subsets(A))) | preboolean(finite_subsets(A!11))),
% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
% 0.54/0.75 tff(18,plain,
% 0.54/0.75 (preboolean(finite_subsets(A!11))),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.54/0.75 tff(19,plain,
% 0.54/0.75 (^[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)))))))))),
% 0.54/0.75 inference(bind,[status(th)],[])).
% 0.54/0.75 tff(20,plain,
% 0.54/0.75 (![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))))))))),
% 0.54/0.75 inference(quant_intro,[status(thm)],[19])).
% 0.54/0.75 tff(21,plain,
% 0.54/0.75 (^[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))))))))),
% 0.54/0.75 inference(bind,[status(th)],[])).
% 0.54/0.75 tff(22,plain,
% 0.54/0.75 (![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)))))))),
% 0.54/0.75 inference(quant_intro,[status(thm)],[21])).
% 0.54/0.75 tff(23,plain,
% 0.54/0.75 (^[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))))))))),
% 0.54/0.75 inference(bind,[status(th)],[])).
% 0.54/0.75 tff(24,plain,
% 0.54/0.75 (![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)))))))),
% 0.54/0.75 inference(quant_intro,[status(thm)],[23])).
% 0.54/0.75 tff(25,plain,
% 0.54/0.75 (![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)))))))),
% 0.54/0.75 inference(transitivity,[status(thm)],[24, 22])).
% 0.54/0.75 tff(26,plain,
% 0.54/0.75 (^[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))))))))),
% 0.54/0.75 inference(bind,[status(th)],[])).
% 0.54/0.76 tff(27,plain,
% 0.54/0.76 (![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)))))))),
% 0.54/0.76 inference(quant_intro,[status(thm)],[26])).
% 0.54/0.76 tff(28,plain,
% 0.54/0.76 (![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)))))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(29,plain,
% 0.54/0.76 (^[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)))))))),
% 0.54/0.76 inference(bind,[status(th)],[])).
% 0.54/0.76 tff(30,plain,
% 0.54/0.76 (![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)))))),
% 0.54/0.76 inference(quant_intro,[status(thm)],[29])).
% 0.54/0.76 tff(31,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')).
% 0.54/0.76 tff(32,plain,
% 0.54/0.76 (![A: $i, B: $i] : ((~preboolean(B)) | ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.54/0.76 tff(33,plain,
% 0.54/0.76 (![A: $i, B: $i] : ((~preboolean(B)) | ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.54/0.76 tff(34,plain,(
% 0.54/0.76 ![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))))))))),
% 0.54/0.76 inference(skolemize,[status(sab)],[33])).
% 0.54/0.76 tff(35,plain,
% 0.54/0.76 (![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)))))))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.54/0.76 tff(36,plain,
% 0.54/0.76 (![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)))))))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[35, 25])).
% 0.54/0.76 tff(37,plain,
% 0.54/0.76 (![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))))))))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[36, 20])).
% 0.54/0.76 tff(38,plain,
% 0.54/0.76 (((~![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)))))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(39,plain,
% 0.54/0.76 (((~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)))))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(40,plain,
% 0.54/0.76 (((~![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))))))),
% 0.54/0.76 inference(monotonicity,[status(thm)],[39])).
% 0.54/0.76 tff(41,plain,
% 0.54/0.76 (((~![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)))))),
% 0.54/0.76 inference(transitivity,[status(thm)],[40, 38])).
% 0.54/0.76 tff(42,plain,
% 0.54/0.76 ((~![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)))))))))),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(43,plain,
% 0.54/0.76 ((~![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))))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.54/0.76 tff(44,plain,
% 0.54/0.76 (![C: $i] : (~(((~finite(C)) | (~subset(C, A!11))) <=> in(C, finite_subsets(A!11))))),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[43, 37, 18])).
% 0.54/0.76 tff(45,plain,
% 0.54/0.76 ((~![C: $i] : (~(((~finite(C)) | (~subset(C, A!11))) <=> in(C, finite_subsets(A!11))))) | (~(((~finite(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)))) | (~subset(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), A!11))) <=> in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11))))),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(46,plain,
% 0.54/0.76 (~(((~finite(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)))) | (~subset(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), A!11))) <=> in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11)))),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.54/0.76 tff(47,plain,
% 0.54/0.76 (^[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))))))))),
% 0.54/0.76 inference(bind,[status(th)],[])).
% 0.54/0.76 tff(48,plain,
% 0.54/0.76 (![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)))))))),
% 0.54/0.76 inference(quant_intro,[status(thm)],[47])).
% 0.54/0.76 tff(49,plain,
% 0.54/0.76 (^[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))))))))),
% 0.54/0.76 inference(bind,[status(th)],[])).
% 0.54/0.76 tff(50,plain,
% 0.54/0.76 (![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)))))))),
% 0.54/0.76 inference(quant_intro,[status(thm)],[49])).
% 0.54/0.76 tff(51,plain,
% 0.54/0.76 (![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)))))))),
% 0.54/0.76 inference(transitivity,[status(thm)],[50, 48])).
% 0.54/0.76 tff(52,plain,
% 0.54/0.76 (^[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)))))))))),
% 0.54/0.76 inference(bind,[status(th)],[])).
% 0.54/0.76 tff(53,plain,
% 0.54/0.76 (![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)))))))),
% 0.54/0.76 inference(quant_intro,[status(thm)],[52])).
% 0.54/0.76 tff(54,plain,
% 0.54/0.76 (![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)))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(55,plain,
% 0.54/0.76 (^[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))))),
% 0.54/0.76 inference(bind,[status(th)],[])).
% 0.54/0.76 tff(56,plain,
% 0.54/0.76 (![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)))),
% 0.54/0.76 inference(quant_intro,[status(thm)],[55])).
% 0.54/0.76 tff(57,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_tarski')).
% 0.54/0.76 tff(58,plain,
% 0.54/0.76 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.54/0.76 tff(59,plain,
% 0.54/0.76 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.54/0.76 tff(60,plain,(
% 0.54/0.76 ![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)))))),
% 0.54/0.76 inference(skolemize,[status(sab)],[59])).
% 0.54/0.76 tff(61,plain,
% 0.54/0.76 (![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)))))))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.54/0.76 tff(62,plain,
% 0.54/0.76 (![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)))))))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[61, 51])).
% 0.54/0.76 tff(63,plain,
% 0.54/0.76 ((~![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(powerset(A!11), finite_subsets(A!11))) | ![C: $i] : ((~in(C, powerset(A!11))) | in(C, finite_subsets(A!11))))) | (~(subset(powerset(A!11), finite_subsets(A!11)) | (~((~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11))))))))),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(64,plain,
% 0.54/0.76 (~((~((~subset(powerset(A!11), finite_subsets(A!11))) | ![C: $i] : ((~in(C, powerset(A!11))) | in(C, finite_subsets(A!11))))) | (~(subset(powerset(A!11), finite_subsets(A!11)) | (~((~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11)))))))),
% 0.61/0.76 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.61/0.76 tff(65,plain,
% 0.61/0.76 (((~((~subset(powerset(A!11), finite_subsets(A!11))) | ![C: $i] : ((~in(C, powerset(A!11))) | in(C, finite_subsets(A!11))))) | (~(subset(powerset(A!11), finite_subsets(A!11)) | (~((~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11))))))) | (subset(powerset(A!11), finite_subsets(A!11)) | (~((~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11)))))),
% 0.61/0.76 inference(tautology,[status(thm)],[])).
% 0.61/0.76 tff(66,plain,
% 0.61/0.76 (subset(powerset(A!11), finite_subsets(A!11)) | (~((~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11))))),
% 0.61/0.76 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.61/0.76 tff(67,plain,
% 0.61/0.76 (^[A: $i, B: $i] : refl((~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))))),
% 0.61/0.76 inference(bind,[status(th)],[])).
% 0.61/0.76 tff(68,plain,
% 0.61/0.76 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.61/0.76 inference(quant_intro,[status(thm)],[67])).
% 0.61/0.76 tff(69,plain,
% 0.61/0.76 (^[A: $i, B: $i] : trans(trans(monotonicity(rewrite((subset(A, B) & subset(B, A)) <=> (~((~subset(A, B)) | (~subset(B, A))))), (((A = B) <=> (subset(A, B) & subset(B, A))) <=> ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))))), rewrite(((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))), (((A = B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))))), rewrite((~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))), (((A = B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))))),
% 0.61/0.76 inference(bind,[status(th)],[])).
% 0.61/0.76 tff(70,plain,
% 0.61/0.76 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.61/0.76 inference(quant_intro,[status(thm)],[69])).
% 0.61/0.76 tff(71,plain,
% 0.61/0.76 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.61/0.76 inference(rewrite,[status(thm)],[])).
% 0.61/0.76 tff(72,axiom,(![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d10_xboole_0')).
% 0.61/0.76 tff(73,plain,
% 0.61/0.76 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.61/0.76 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.61/0.76 tff(74,plain,(
% 0.61/0.76 ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.61/0.76 inference(skolemize,[status(sab)],[73])).
% 0.61/0.76 tff(75,plain,
% 0.61/0.76 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.61/0.76 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.61/0.76 tff(76,plain,
% 0.61/0.76 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.61/0.76 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.61/0.76 tff(77,plain,
% 0.61/0.76 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))) | (~(((~subset(finite_subsets(A!11), powerset(A!11))) | (~subset(powerset(A!11), finite_subsets(A!11)))) <=> (finite_subsets(A!11) = powerset(A!11))))),
% 0.61/0.76 inference(quant_inst,[status(thm)],[])).
% 0.61/0.76 tff(78,plain,
% 0.61/0.76 (~(((~subset(finite_subsets(A!11), powerset(A!11))) | (~subset(powerset(A!11), finite_subsets(A!11)))) <=> (finite_subsets(A!11) = powerset(A!11)))),
% 0.61/0.76 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.61/0.76 tff(79,plain,
% 0.61/0.76 ((~![A: $i] : ((~finite(A)) | (finite_subsets(A) = powerset(A)))) <=> (~![A: $i] : ((~finite(A)) | (finite_subsets(A) = powerset(A))))),
% 0.61/0.76 inference(rewrite,[status(thm)],[])).
% 0.61/0.76 tff(80,plain,
% 0.61/0.76 ((~![A: $i] : (finite(A) => (finite_subsets(A) = powerset(A)))) <=> (~![A: $i] : ((~finite(A)) | (finite_subsets(A) = powerset(A))))),
% 0.61/0.76 inference(rewrite,[status(thm)],[])).
% 0.61/0.76 tff(81,axiom,(~![A: $i] : (finite(A) => (finite_subsets(A) = powerset(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t27_finsub_1')).
% 0.61/0.76 tff(82,plain,
% 0.61/0.76 (~![A: $i] : ((~finite(A)) | (finite_subsets(A) = powerset(A)))),
% 0.61/0.76 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.61/0.76 tff(83,plain,
% 0.61/0.76 (~![A: $i] : ((~finite(A)) | (finite_subsets(A) = powerset(A)))),
% 0.61/0.76 inference(modus_ponens,[status(thm)],[82, 79])).
% 0.61/0.76 tff(84,plain,
% 0.61/0.76 (~![A: $i] : ((~finite(A)) | (finite_subsets(A) = powerset(A)))),
% 0.61/0.76 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.61/0.76 tff(85,plain,
% 0.61/0.76 (~![A: $i] : ((~finite(A)) | (finite_subsets(A) = powerset(A)))),
% 0.61/0.76 inference(modus_ponens,[status(thm)],[84, 79])).
% 0.61/0.76 tff(86,plain,(
% 0.61/0.76 ~((~finite(A!11)) | (finite_subsets(A!11) = powerset(A!11)))),
% 0.61/0.76 inference(skolemize,[status(sab)],[85])).
% 0.61/0.76 tff(87,plain,
% 0.61/0.76 (~(finite_subsets(A!11) = powerset(A!11))),
% 0.61/0.76 inference(or_elim,[status(thm)],[86])).
% 0.61/0.76 tff(88,plain,
% 0.61/0.76 ((((~subset(finite_subsets(A!11), powerset(A!11))) | (~subset(powerset(A!11), finite_subsets(A!11)))) <=> (finite_subsets(A!11) = powerset(A!11))) | ((~subset(finite_subsets(A!11), powerset(A!11))) | (~subset(powerset(A!11), finite_subsets(A!11)))) | (finite_subsets(A!11) = powerset(A!11))),
% 0.61/0.76 inference(tautology,[status(thm)],[])).
% 0.61/0.76 tff(89,plain,
% 0.61/0.76 ((((~subset(finite_subsets(A!11), powerset(A!11))) | (~subset(powerset(A!11), finite_subsets(A!11)))) <=> (finite_subsets(A!11) = powerset(A!11))) | ((~subset(finite_subsets(A!11), powerset(A!11))) | (~subset(powerset(A!11), finite_subsets(A!11))))),
% 0.61/0.76 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.61/0.76 tff(90,plain,
% 0.61/0.76 ((~subset(finite_subsets(A!11), powerset(A!11))) | (~subset(powerset(A!11), finite_subsets(A!11)))),
% 0.61/0.76 inference(unit_resolution,[status(thm)],[89, 78])).
% 0.61/0.76 tff(91,plain,
% 0.61/0.76 (^[A: $i] : refl(subset(finite_subsets(A), powerset(A)) <=> subset(finite_subsets(A), powerset(A)))),
% 0.61/0.76 inference(bind,[status(th)],[])).
% 0.61/0.76 tff(92,plain,
% 0.61/0.76 (![A: $i] : subset(finite_subsets(A), powerset(A)) <=> ![A: $i] : subset(finite_subsets(A), powerset(A))),
% 0.61/0.76 inference(quant_intro,[status(thm)],[91])).
% 0.61/0.76 tff(93,plain,
% 0.61/0.76 (![A: $i] : subset(finite_subsets(A), powerset(A)) <=> ![A: $i] : subset(finite_subsets(A), powerset(A))),
% 0.61/0.76 inference(rewrite,[status(thm)],[])).
% 0.61/0.76 tff(94,axiom,(![A: $i] : subset(finite_subsets(A), powerset(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t26_finsub_1')).
% 0.61/0.76 tff(95,plain,
% 0.61/0.76 (![A: $i] : subset(finite_subsets(A), powerset(A))),
% 0.61/0.76 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.61/0.76 tff(96,plain,(
% 0.61/0.76 ![A: $i] : subset(finite_subsets(A), powerset(A))),
% 0.61/0.76 inference(skolemize,[status(sab)],[95])).
% 0.61/0.76 tff(97,plain,
% 0.61/0.76 (![A: $i] : subset(finite_subsets(A), powerset(A))),
% 0.61/0.76 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.61/0.76 tff(98,plain,
% 0.61/0.76 ((~![A: $i] : subset(finite_subsets(A), powerset(A))) | subset(finite_subsets(A!11), powerset(A!11))),
% 0.61/0.76 inference(quant_inst,[status(thm)],[])).
% 0.61/0.76 tff(99,plain,
% 0.61/0.76 (subset(finite_subsets(A!11), powerset(A!11))),
% 0.61/0.76 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.61/0.76 tff(100,plain,
% 0.61/0.76 ((~((~subset(finite_subsets(A!11), powerset(A!11))) | (~subset(powerset(A!11), finite_subsets(A!11))))) | (~subset(finite_subsets(A!11), powerset(A!11))) | (~subset(powerset(A!11), finite_subsets(A!11)))),
% 0.61/0.76 inference(tautology,[status(thm)],[])).
% 0.61/0.76 tff(101,plain,
% 0.61/0.76 ((~((~subset(finite_subsets(A!11), powerset(A!11))) | (~subset(powerset(A!11), finite_subsets(A!11))))) | (~subset(powerset(A!11), finite_subsets(A!11)))),
% 0.61/0.76 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.61/0.76 tff(102,plain,
% 0.61/0.76 (~subset(powerset(A!11), finite_subsets(A!11))),
% 0.61/0.76 inference(unit_resolution,[status(thm)],[101, 90])).
% 0.61/0.76 tff(103,plain,
% 0.61/0.76 ((~(subset(powerset(A!11), finite_subsets(A!11)) | (~((~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11)))))) | subset(powerset(A!11), finite_subsets(A!11)) | (~((~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11))))),
% 0.61/0.76 inference(tautology,[status(thm)],[])).
% 0.61/0.76 tff(104,plain,
% 0.61/0.76 ((~(subset(powerset(A!11), finite_subsets(A!11)) | (~((~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11)))))) | (~((~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11))))),
% 0.61/0.76 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.61/0.76 tff(105,plain,
% 0.61/0.76 (~((~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11)))),
% 0.61/0.76 inference(unit_resolution,[status(thm)],[104, 66])).
% 0.61/0.76 tff(106,plain,
% 0.61/0.76 (((~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11))) | (~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11)))),
% 0.61/0.76 inference(tautology,[status(thm)],[])).
% 0.61/0.76 tff(107,plain,
% 0.61/0.76 (~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11))),
% 0.61/0.76 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.61/0.76 tff(108,plain,
% 0.61/0.76 ((((~finite(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)))) | (~subset(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), A!11))) <=> in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11))) | ((~finite(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)))) | (~subset(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), A!11))) | in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11))),
% 0.61/0.76 inference(tautology,[status(thm)],[])).
% 0.61/0.76 tff(109,plain,
% 0.61/0.76 ((((~finite(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)))) | (~subset(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), A!11))) <=> in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11))) | ((~finite(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)))) | (~subset(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), A!11)))),
% 0.61/0.76 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.61/0.76 tff(110,plain,
% 0.61/0.76 ((~finite(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)))) | (~subset(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), A!11))),
% 0.61/0.76 inference(unit_resolution,[status(thm)],[109, 46])).
% 0.61/0.76 tff(111,plain,
% 0.61/0.76 (((~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11))) | in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))),
% 0.61/0.76 inference(tautology,[status(thm)],[])).
% 0.61/0.76 tff(112,plain,
% 0.61/0.76 (in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))),
% 0.61/0.76 inference(unit_resolution,[status(thm)],[111, 105])).
% 0.61/0.76 tff(113,plain,
% 0.61/0.76 (^[A: $i, B: $i] : refl(((~in(A, B)) | element(A, B)) <=> ((~in(A, B)) | element(A, B)))),
% 0.61/0.76 inference(bind,[status(th)],[])).
% 0.61/0.76 tff(114,plain,
% 0.61/0.76 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.61/0.76 inference(quant_intro,[status(thm)],[113])).
% 0.61/0.76 tff(115,plain,
% 0.61/0.76 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.61/0.76 inference(rewrite,[status(thm)],[])).
% 0.61/0.76 tff(116,plain,
% 0.61/0.76 (^[A: $i, B: $i] : rewrite((in(A, B) => element(A, B)) <=> ((~in(A, B)) | element(A, B)))),
% 0.61/0.76 inference(bind,[status(th)],[])).
% 0.61/0.76 tff(117,plain,
% 0.61/0.76 (![A: $i, B: $i] : (in(A, B) => element(A, B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.61/0.76 inference(quant_intro,[status(thm)],[116])).
% 0.61/0.76 tff(118,axiom,(![A: $i, B: $i] : (in(A, B) => element(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t1_subset')).
% 0.61/0.76 tff(119,plain,
% 0.61/0.76 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.61/0.76 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.61/0.76 tff(120,plain,
% 0.61/0.76 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.61/0.76 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.61/0.76 tff(121,plain,(
% 0.61/0.76 ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.61/0.76 inference(skolemize,[status(sab)],[120])).
% 0.61/0.76 tff(122,plain,
% 0.61/0.76 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.61/0.76 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.61/0.76 tff(123,plain,
% 0.61/0.76 (((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | ((~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | element(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11)))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | (~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | element(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11)))),
% 0.61/0.76 inference(rewrite,[status(thm)],[])).
% 0.61/0.76 tff(124,plain,
% 0.61/0.76 ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | ((~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | element(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11)))),
% 0.61/0.76 inference(quant_inst,[status(thm)],[])).
% 0.61/0.76 tff(125,plain,
% 0.61/0.76 ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | (~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | element(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))),
% 0.61/0.76 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.61/0.76 tff(126,plain,
% 0.61/0.76 (element(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))),
% 0.61/0.76 inference(unit_resolution,[status(thm)],[125, 122, 112])).
% 0.61/0.76 tff(127,plain,
% 0.61/0.76 (finite(A!11)),
% 0.61/0.76 inference(or_elim,[status(thm)],[86])).
% 0.61/0.76 tff(128,plain,
% 0.61/0.76 (^[A: $i] : refl(((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A))))) <=> ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A))))))),
% 0.61/0.76 inference(bind,[status(th)],[])).
% 0.61/0.76 tff(129,plain,
% 0.61/0.76 (![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A))))) <=> ![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.61/0.76 inference(quant_intro,[status(thm)],[128])).
% 0.61/0.76 tff(130,plain,
% 0.61/0.76 (^[A: $i] : rewrite(((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A))))) <=> ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A))))))),
% 0.61/0.76 inference(bind,[status(th)],[])).
% 0.61/0.76 tff(131,plain,
% 0.61/0.76 (![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A))))) <=> ![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.61/0.76 inference(quant_intro,[status(thm)],[130])).
% 0.61/0.76 tff(132,plain,
% 0.61/0.76 (![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A))))) <=> ![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.61/0.76 inference(transitivity,[status(thm)],[131, 129])).
% 0.61/0.76 tff(133,plain,
% 0.61/0.76 (![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A))))) <=> ![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.61/0.76 inference(rewrite,[status(thm)],[])).
% 0.61/0.76 tff(134,plain,
% 0.61/0.76 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((element(B, powerset(A)) => finite(B)) <=> (finite(B) | (~element(B, powerset(A)))))), (![B: $i] : (element(B, powerset(A)) => finite(B)) <=> ![B: $i] : (finite(B) | (~element(B, powerset(A)))))), ((finite(A) => ![B: $i] : (element(B, powerset(A)) => finite(B))) <=> (finite(A) => ![B: $i] : (finite(B) | (~element(B, powerset(A))))))), rewrite((finite(A) => ![B: $i] : (finite(B) | (~element(B, powerset(A))))) <=> ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))), ((finite(A) => ![B: $i] : (element(B, powerset(A)) => finite(B))) <=> ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))))),
% 0.61/0.76 inference(bind,[status(th)],[])).
% 0.61/0.76 tff(135,plain,
% 0.61/0.76 (![A: $i] : (finite(A) => ![B: $i] : (element(B, powerset(A)) => finite(B))) <=> ![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.61/0.76 inference(quant_intro,[status(thm)],[134])).
% 0.61/0.76 tff(136,axiom,(![A: $i] : (finite(A) => ![B: $i] : (element(B, powerset(A)) => finite(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cc2_finset_1')).
% 0.61/0.76 tff(137,plain,
% 0.61/0.76 (![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.61/0.77 tff(138,plain,
% 0.61/0.77 (![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.61/0.77 tff(139,plain,(
% 0.61/0.77 ![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.61/0.77 inference(skolemize,[status(sab)],[138])).
% 0.61/0.77 tff(140,plain,
% 0.61/0.77 (![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[139, 132])).
% 0.61/0.77 tff(141,plain,
% 0.61/0.77 (((~![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))) | ((~finite(A!11)) | ![B: $i] : (finite(B) | (~element(B, powerset(A!11)))))) <=> ((~![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))) | (~finite(A!11)) | ![B: $i] : (finite(B) | (~element(B, powerset(A!11)))))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(142,plain,
% 0.61/0.77 ((~![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))) | ((~finite(A!11)) | ![B: $i] : (finite(B) | (~element(B, powerset(A!11)))))),
% 0.61/0.77 inference(quant_inst,[status(thm)],[])).
% 0.61/0.77 tff(143,plain,
% 0.61/0.77 ((~![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))) | (~finite(A!11)) | ![B: $i] : (finite(B) | (~element(B, powerset(A!11))))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.61/0.77 tff(144,plain,
% 0.61/0.77 (![B: $i] : (finite(B) | (~element(B, powerset(A!11))))),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[143, 140, 127])).
% 0.61/0.77 tff(145,plain,
% 0.61/0.77 (((~![B: $i] : (finite(B) | (~element(B, powerset(A!11))))) | (finite(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11))) | (~element(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))))) <=> ((~![B: $i] : (finite(B) | (~element(B, powerset(A!11))))) | finite(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11))) | (~element(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(146,plain,
% 0.61/0.77 ((~![B: $i] : (finite(B) | (~element(B, powerset(A!11))))) | (finite(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11))) | (~element(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))))),
% 0.61/0.77 inference(quant_inst,[status(thm)],[])).
% 0.61/0.77 tff(147,plain,
% 0.61/0.77 ((~![B: $i] : (finite(B) | (~element(B, powerset(A!11))))) | finite(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11))) | (~element(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11)))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.61/0.77 tff(148,plain,
% 0.61/0.77 (finite(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)))),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[147, 144, 126])).
% 0.61/0.77 tff(149,plain,
% 0.61/0.77 ((~((~finite(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)))) | (~subset(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), A!11)))) | (~finite(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)))) | (~subset(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), A!11))),
% 0.61/0.77 inference(tautology,[status(thm)],[])).
% 0.61/0.77 tff(150,plain,
% 0.61/0.77 (~subset(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), A!11)),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[149, 148, 110])).
% 0.61/0.77 tff(151,plain,
% 0.61/0.77 ((~(element(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11)) <=> subset(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), A!11))) | (~element(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | subset(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), A!11)),
% 0.61/0.77 inference(tautology,[status(thm)],[])).
% 0.61/0.77 tff(152,plain,
% 0.61/0.77 ((~(element(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11)) <=> subset(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), A!11))) | subset(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), A!11)),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[151, 126])).
% 0.61/0.77 tff(153,plain,
% 0.61/0.77 ($false),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[152, 150, 9])).
% 0.61/0.77 % SZS output end Proof
% 0.61/0.77 % E exiting
%------------------------------------------------------------------------------