%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU317+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:27:35 AM UTC 2025
% Result : Theorem 0.12s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU317+1 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.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 06:45:41 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.40 % SZS status Theorem
% 0.12/0.40 % SZS output start Proof
% 0.12/0.40 tff(in_type, type, (
% 0.12/0.40 in: ( $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_D_7_type, type, (
% 0.12/0.40 tptp_fun_D_7: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_A_8_type, type, (
% 0.12/0.40 tptp_fun_A_8: $i)).
% 0.12/0.40 tff(tptp_fun_B_9_type, type, (
% 0.12/0.40 tptp_fun_B_9: $i)).
% 0.12/0.40 tff(tptp_fun_C_0_type, type, (
% 0.12/0.40 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.12/0.40 tff(topstr_closure_type, type, (
% 0.12/0.40 topstr_closure: ( $i * $i ) > $i)).
% 0.12/0.40 tff(subset_type, type, (
% 0.12/0.40 subset: ( $i * $i ) > $o)).
% 0.12/0.40 tff(element_type, type, (
% 0.12/0.40 element: ( $i * $i ) > $o)).
% 0.12/0.40 tff(powerset_type, type, (
% 0.12/0.40 powerset: $i > $i)).
% 0.12/0.40 tff(the_carrier_type, type, (
% 0.12/0.40 the_carrier: $i > $i)).
% 0.12/0.40 tff(closed_subset_type, type, (
% 0.12/0.40 closed_subset: ( $i * $i ) > $o)).
% 0.12/0.40 tff(top_str_type, type, (
% 0.12/0.40 top_str: $i > $o)).
% 0.12/0.40 tff(1,plain,
% 0.12/0.40 (^[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))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(2,plain,
% 0.12/0.40 (![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)))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.40 tff(3,plain,
% 0.12/0.40 (^[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))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(4,plain,
% 0.12/0.40 (![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)))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.40 tff(5,plain,
% 0.12/0.40 (![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)))))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[4, 2])).
% 0.12/0.40 tff(6,plain,
% 0.12/0.40 (^[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)))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(7,plain,
% 0.12/0.40 (![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)))))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[6])).
% 0.12/0.41 tff(8,plain,
% 0.12/0.41 (![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)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(9,plain,
% 0.12/0.41 (^[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))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(10,plain,
% 0.12/0.41 (![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)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[9])).
% 0.12/0.41 tff(11,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')).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.19/0.41 tff(13,plain,
% 0.19/0.41 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.19/0.41 tff(14,plain,(
% 0.19/0.41 ![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)))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[13])).
% 0.19/0.41 tff(15,plain,
% 0.19/0.41 (![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)))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 (![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)))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 ((~![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(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | ![C: $i] : ((~in(C, B!9)) | in(C, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))) | (~(subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)) | (~((~in(tptp_fun_C_0(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), B!9), B!9)) | in(tptp_fun_C_0(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 (~((~((~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | ![C: $i] : ((~in(C, B!9)) | in(C, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))) | (~(subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)) | (~((~in(tptp_fun_C_0(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), B!9), B!9)) | in(tptp_fun_C_0(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 (((~((~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | ![C: $i] : ((~in(C, B!9)) | in(C, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))) | (~(subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)) | (~((~in(tptp_fun_C_0(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), B!9), B!9)) | in(tptp_fun_C_0(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))))) | ((~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | ![C: $i] : ((~in(C, B!9)) | in(C, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 ((~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | ![C: $i] : ((~in(C, B!9)) | in(C, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 ((~![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(B!9, the_carrier(A!8))) | ![C: $i] : ((~in(C, B!9)) | in(C, the_carrier(A!8))))) | (~(subset(B!9, the_carrier(A!8)) | (~((~in(tptp_fun_C_0(the_carrier(A!8), B!9), B!9)) | in(tptp_fun_C_0(the_carrier(A!8), B!9), the_carrier(A!8))))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(22,plain,
% 0.19/0.41 (~((~((~subset(B!9, the_carrier(A!8))) | ![C: $i] : ((~in(C, B!9)) | in(C, the_carrier(A!8))))) | (~(subset(B!9, the_carrier(A!8)) | (~((~in(tptp_fun_C_0(the_carrier(A!8), B!9), B!9)) | in(tptp_fun_C_0(the_carrier(A!8), B!9), the_carrier(A!8)))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[21, 16])).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 (((~((~subset(B!9, the_carrier(A!8))) | ![C: $i] : ((~in(C, B!9)) | in(C, the_carrier(A!8))))) | (~(subset(B!9, the_carrier(A!8)) | (~((~in(tptp_fun_C_0(the_carrier(A!8), B!9), B!9)) | in(tptp_fun_C_0(the_carrier(A!8), B!9), the_carrier(A!8))))))) | ((~subset(B!9, the_carrier(A!8))) | ![C: $i] : ((~in(C, B!9)) | in(C, the_carrier(A!8))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 ((~subset(B!9, the_carrier(A!8))) | ![C: $i] : ((~in(C, B!9)) | in(C, the_carrier(A!8)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 (^[A: $i, B: $i] : refl((element(A, powerset(B)) <=> subset(A, B)) <=> (element(A, powerset(B)) <=> subset(A, B)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(28,axiom,(![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t3_subset')).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.41 tff(30,plain,(
% 0.19/0.41 ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.19/0.41 inference(skolemize,[status(sab)],[29])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))) | (element(B!9, powerset(the_carrier(A!8))) <=> subset(B!9, the_carrier(A!8)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (element(B!9, powerset(the_carrier(A!8))) <=> subset(B!9, the_carrier(A!8))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))) <=> (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 ((~![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => subset(B, topstr_closure(A, B))))) <=> (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(36,axiom,(~![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => subset(B, topstr_closure(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t48_pre_topc')).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[37, 34])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[39, 34])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 (~((~element(B!9, powerset(the_carrier(A!8)))) | subset(B!9, topstr_closure(A!8, B!9)))),
% 0.19/0.41 inference(and_elim,[status(thm)],[40])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 (element(B!9, powerset(the_carrier(A!8)))),
% 0.19/0.41 inference(or_elim,[status(thm)],[41])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 ((~(element(B!9, powerset(the_carrier(A!8))) <=> subset(B!9, the_carrier(A!8)))) | (~element(B!9, powerset(the_carrier(A!8)))) | subset(B!9, the_carrier(A!8))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 ((~(element(B!9, powerset(the_carrier(A!8))) <=> subset(B!9, the_carrier(A!8)))) | subset(B!9, the_carrier(A!8))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 (subset(B!9, the_carrier(A!8))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[44, 33])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 ((~((~subset(B!9, the_carrier(A!8))) | ![C: $i] : ((~in(C, B!9)) | in(C, the_carrier(A!8))))) | (~subset(B!9, the_carrier(A!8))) | ![C: $i] : ((~in(C, B!9)) | in(C, the_carrier(A!8)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 ((~((~subset(B!9, the_carrier(A!8))) | ![C: $i] : ((~in(C, B!9)) | in(C, the_carrier(A!8))))) | ![C: $i] : ((~in(C, B!9)) | in(C, the_carrier(A!8)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (![C: $i] : ((~in(C, B!9)) | in(C, the_carrier(A!8)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[47, 24])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 ((~![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(B!9, topstr_closure(A!8, B!9))) | ![C: $i] : ((~in(C, B!9)) | in(C, topstr_closure(A!8, B!9))))) | (~(subset(B!9, topstr_closure(A!8, B!9)) | (~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 (~((~((~subset(B!9, topstr_closure(A!8, B!9))) | ![C: $i] : ((~in(C, B!9)) | in(C, topstr_closure(A!8, B!9))))) | (~(subset(B!9, topstr_closure(A!8, B!9)) | (~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[49, 16])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (((~((~subset(B!9, topstr_closure(A!8, B!9))) | ![C: $i] : ((~in(C, B!9)) | in(C, topstr_closure(A!8, B!9))))) | (~(subset(B!9, topstr_closure(A!8, B!9)) | (~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))))))) | (subset(B!9, topstr_closure(A!8, B!9)) | (~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 (subset(B!9, topstr_closure(A!8, B!9)) | (~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 (~subset(B!9, topstr_closure(A!8, B!9))),
% 0.19/0.41 inference(or_elim,[status(thm)],[41])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 ((~(subset(B!9, topstr_closure(A!8, B!9)) | (~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)))))) | subset(B!9, topstr_closure(A!8, B!9)) | (~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(55,plain,
% 0.19/0.42 ((~(subset(B!9, topstr_closure(A!8, B!9)) | (~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)))))) | (~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.19/0.42 tff(56,plain,
% 0.19/0.42 (~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[55, 52])).
% 0.19/0.42 tff(57,plain,
% 0.19/0.42 (((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(58,plain,
% 0.19/0.42 (in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.19/0.42 tff(59,plain,
% 0.19/0.42 (((~![C: $i] : ((~in(C, B!9)) | in(C, the_carrier(A!8)))) | ((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), the_carrier(A!8)))) <=> ((~![C: $i] : ((~in(C, B!9)) | in(C, the_carrier(A!8)))) | (~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), the_carrier(A!8)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(60,plain,
% 0.19/0.42 ((~![C: $i] : ((~in(C, B!9)) | in(C, the_carrier(A!8)))) | ((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), the_carrier(A!8)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(61,plain,
% 0.19/0.42 ((~![C: $i] : ((~in(C, B!9)) | in(C, the_carrier(A!8)))) | (~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), the_carrier(A!8))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.42 tff(62,plain,
% 0.19/0.42 (in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), the_carrier(A!8))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[61, 58, 48])).
% 0.19/0.42 tff(63,plain,
% 0.19/0.42 (top_str(A!8)),
% 0.19/0.42 inference(and_elim,[status(thm)],[40])).
% 0.19/0.42 tff(64,plain,
% 0.19/0.42 (^[A: $i] : refl(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A)))))))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A)))))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(65,plain,
% 0.19/0.42 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A)))))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A))))))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[64])).
% 0.19/0.42 tff(66,plain,
% 0.19/0.42 (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A)))))))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A)))))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(67,plain,
% 0.19/0.42 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A)))))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A))))))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[66])).
% 0.19/0.42 tff(68,plain,
% 0.19/0.42 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A)))))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A))))))))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[67, 65])).
% 0.19/0.42 tff(69,plain,
% 0.19/0.42 (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))) & (in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~(closed_subset(tptp_fun_D_7(C, B, A), A) & subset(B, tptp_fun_D_7(C, B, A)))) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A))))))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A)))))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(70,plain,
% 0.19/0.42 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))) & (in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~(closed_subset(tptp_fun_D_7(C, B, A), A) & subset(B, tptp_fun_D_7(C, B, A)))) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A))))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A))))))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[69])).
% 0.19/0.42 tff(71,plain,
% 0.19/0.42 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(72,plain,
% 0.19/0.42 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((in(C, topstr_closure(A, B)) <=> ![D: $i] : (element(D, powerset(the_carrier(A))) => ((closed_subset(D, A) & subset(B, D)) => in(C, D)))) <=> (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A))))))), ((in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (element(D, powerset(the_carrier(A))) => ((closed_subset(D, A) & subset(B, D)) => in(C, D))))) <=> (in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A))))))))), rewrite((in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A))))))) <=> ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))))), ((in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (element(D, powerset(the_carrier(A))) => ((closed_subset(D, A) & subset(B, D)) => in(C, D))))) <=> ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))))))), (![C: $i] : (in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (element(D, powerset(the_carrier(A))) => ((closed_subset(D, A) & subset(B, D)) => in(C, D))))) <=> ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A))))))))), ((element(B, powerset(the_carrier(A))) => ![C: $i] : (in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (element(D, powerset(the_carrier(A))) => ((closed_subset(D, A) & subset(B, D)) => in(C, D)))))) <=> (element(B, powerset(the_carrier(A))) => ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))))))), rewrite((element(B, powerset(the_carrier(A))) => ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))))) <=> ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A))))))))), ((element(B, powerset(the_carrier(A))) => ![C: $i] : (in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (element(D, powerset(the_carrier(A))) => ((closed_subset(D, A) & subset(B, D)) => in(C, D)))))) <=> ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A))))))))))), (![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (element(D, powerset(the_carrier(A))) => ((closed_subset(D, A) & subset(B, D)) => in(C, D)))))) <=> ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))))))), ((top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (element(D, powerset(the_carrier(A))) => ((closed_subset(D, A) & subset(B, D)) => in(C, D))))))) <=> (top_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A))))))))))), rewrite((top_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A))))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))))))), ((top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (element(D, powerset(the_carrier(A))) => ((closed_subset(D, A) & subset(B, D)) => in(C, D))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(73,plain,
% 0.19/0.42 (![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (element(D, powerset(the_carrier(A))) => ((closed_subset(D, A) & subset(B, D)) => in(C, D))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[72])).
% 0.19/0.42 tff(74,axiom,(![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (element(D, powerset(the_carrier(A))) => ((closed_subset(D, A) & subset(B, D)) => in(C, D)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t45_pre_topc')).
% 0.19/0.42 tff(75,plain,
% 0.19/0.42 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.19/0.42 tff(76,plain,
% 0.19/0.42 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.19/0.42 tff(77,plain,(
% 0.19/0.42 ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))) & (in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~(closed_subset(tptp_fun_D_7(C, B, A), A) & subset(B, tptp_fun_D_7(C, B, A)))) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))))))))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[76])).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A))))))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A))))))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[78, 68])).
% 0.19/0.42 tff(80,plain,
% 0.19/0.42 (((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A))))))))))))) | ((~top_str(A!8)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B)) | (~((~subset(B, tptp_fun_D_7(C, B, A!8))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | in(C, tptp_fun_D_7(C, B, A!8)))))))))))) <=> ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A))))))))))))) | (~top_str(A!8)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B)) | (~((~subset(B, tptp_fun_D_7(C, B, A!8))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | in(C, tptp_fun_D_7(C, B, A!8)))))))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(81,plain,
% 0.19/0.43 (((~top_str(A!8)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A!8, B)) | (~(in(C, tptp_fun_D_7(C, B, A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~subset(B, tptp_fun_D_7(C, B, A!8)))))))))))) <=> ((~top_str(A!8)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B)) | (~((~subset(B, tptp_fun_D_7(C, B, A!8))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | in(C, tptp_fun_D_7(C, B, A!8)))))))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(82,plain,
% 0.19/0.43 (((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A))))))))))))) | ((~top_str(A!8)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A!8, B)) | (~(in(C, tptp_fun_D_7(C, B, A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~subset(B, tptp_fun_D_7(C, B, A!8))))))))))))) <=> ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A))))))))))))) | ((~top_str(A!8)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B)) | (~((~subset(B, tptp_fun_D_7(C, B, A!8))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | in(C, tptp_fun_D_7(C, B, A!8))))))))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[81])).
% 0.19/0.43 tff(83,plain,
% 0.19/0.43 (((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A))))))))))))) | ((~top_str(A!8)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A!8, B)) | (~(in(C, tptp_fun_D_7(C, B, A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~subset(B, tptp_fun_D_7(C, B, A!8))))))))))))) <=> ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A))))))))))))) | (~top_str(A!8)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B)) | (~((~subset(B, tptp_fun_D_7(C, B, A!8))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | in(C, tptp_fun_D_7(C, B, A!8)))))))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[82, 80])).
% 0.19/0.43 tff(84,plain,
% 0.19/0.43 ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A))))))))))))) | ((~top_str(A!8)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A!8, B)) | (~(in(C, tptp_fun_D_7(C, B, A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~subset(B, tptp_fun_D_7(C, B, A!8))))))))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(85,plain,
% 0.19/0.43 ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A))))))))))))) | (~top_str(A!8)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B)) | (~((~subset(B, tptp_fun_D_7(C, B, A!8))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | in(C, tptp_fun_D_7(C, B, A!8))))))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.19/0.43 tff(86,plain,
% 0.19/0.43 (![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B)) | (~((~subset(B, tptp_fun_D_7(C, B, A!8))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | in(C, tptp_fun_D_7(C, B, A!8))))))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[85, 79, 63])).
% 0.19/0.43 tff(87,plain,
% 0.19/0.43 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B)) | (~((~subset(B, tptp_fun_D_7(C, B, A!8))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | in(C, tptp_fun_D_7(C, B, A!8))))))))))) | ((~element(B!9, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8)))))))))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B)) | (~((~subset(B, tptp_fun_D_7(C, B, A!8))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | in(C, tptp_fun_D_7(C, B, A!8))))))))))) | (~element(B!9, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8)))))))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(88,plain,
% 0.19/0.43 (((~element(B!9, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B!9, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~((~subset(B!9, tptp_fun_D_7(C, B!9, A!8))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | in(C, tptp_fun_D_7(C, B!9, A!8)))))))))) <=> ((~element(B!9, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8)))))))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(89,plain,
% 0.19/0.43 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B)) | (~((~subset(B, tptp_fun_D_7(C, B, A!8))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | in(C, tptp_fun_D_7(C, B, A!8))))))))))) | ((~element(B!9, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B!9, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~((~subset(B!9, tptp_fun_D_7(C, B!9, A!8))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | in(C, tptp_fun_D_7(C, B!9, A!8))))))))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B)) | (~((~subset(B, tptp_fun_D_7(C, B, A!8))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | in(C, tptp_fun_D_7(C, B, A!8))))))))))) | ((~element(B!9, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8))))))))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[88])).
% 0.19/0.43 tff(90,plain,
% 0.19/0.43 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B)) | (~((~subset(B, tptp_fun_D_7(C, B, A!8))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | in(C, tptp_fun_D_7(C, B, A!8))))))))))) | ((~element(B!9, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B!9, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~((~subset(B!9, tptp_fun_D_7(C, B!9, A!8))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | in(C, tptp_fun_D_7(C, B!9, A!8))))))))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B)) | (~((~subset(B, tptp_fun_D_7(C, B, A!8))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | in(C, tptp_fun_D_7(C, B, A!8))))))))))) | (~element(B!9, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8)))))))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[89, 87])).
% 0.19/0.43 tff(91,plain,
% 0.19/0.43 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B)) | (~((~subset(B, tptp_fun_D_7(C, B, A!8))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | in(C, tptp_fun_D_7(C, B, A!8))))))))))) | ((~element(B!9, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B!9, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~((~subset(B!9, tptp_fun_D_7(C, B!9, A!8))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | in(C, tptp_fun_D_7(C, B!9, A!8))))))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(92,plain,
% 0.19/0.44 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B)) | (~((~subset(B, tptp_fun_D_7(C, B, A!8))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | in(C, tptp_fun_D_7(C, B, A!8))))))))))) | (~element(B!9, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8))))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.19/0.44 tff(93,plain,
% 0.19/0.44 (![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8))))))))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[92, 42, 86])).
% 0.19/0.44 tff(94,plain,
% 0.19/0.44 (((~![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8))))))))))) | ((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), the_carrier(A!8))) | (~((~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), D)))) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~((~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))))))))) <=> ((~![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8))))))))))) | (~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), the_carrier(A!8))) | (~((~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), D)))) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~((~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(95,plain,
% 0.19/0.44 (((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), the_carrier(A!8))) | (~((~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))) | ![D: $i] : (in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))))))))) <=> ((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), the_carrier(A!8))) | (~((~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), D)))) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~((~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(96,plain,
% 0.19/0.44 (((~![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8))))))))))) | ((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), the_carrier(A!8))) | (~((~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))) | ![D: $i] : (in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))))))))) <=> ((~![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8))))))))))) | ((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), the_carrier(A!8))) | (~((~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), D)))) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~((~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[95])).
% 0.19/0.45 tff(97,plain,
% 0.19/0.45 (((~![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8))))))))))) | ((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), the_carrier(A!8))) | (~((~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))) | ![D: $i] : (in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))))))))) <=> ((~![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8))))))))))) | (~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), the_carrier(A!8))) | (~((~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), D)))) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~((~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[96, 94])).
% 0.19/0.45 tff(98,plain,
% 0.19/0.45 ((~![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8))))))))))) | ((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), the_carrier(A!8))) | (~((~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))) | ![D: $i] : (in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(99,plain,
% 0.19/0.45 ((~![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8))))))))))) | (~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), the_carrier(A!8))) | (~((~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), D)))) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~((~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.19/0.45 tff(100,plain,
% 0.19/0.45 (~((~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), D)))) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~((~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[99, 93, 62])).
% 0.19/0.45 tff(101,plain,
% 0.19/0.45 (((~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), D)))) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~((~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))))) | (in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~((~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(102,plain,
% 0.19/0.45 (in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~((~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.19/0.45 tff(103,plain,
% 0.19/0.45 (((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))) | (~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(104,plain,
% 0.19/0.45 (~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[103, 56])).
% 0.19/0.45 tff(105,plain,
% 0.19/0.45 ((~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~((~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))))) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~((~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(106,plain,
% 0.19/0.45 ((~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~((~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))))) | (~((~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.19/0.45 tff(107,plain,
% 0.19/0.45 (~((~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[106, 102])).
% 0.19/0.45 tff(108,plain,
% 0.19/0.45 (((~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(109,plain,
% 0.19/0.45 (subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.19/0.45 tff(110,plain,
% 0.19/0.45 ((~((~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | ![C: $i] : ((~in(C, B!9)) | in(C, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))) | (~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | ![C: $i] : ((~in(C, B!9)) | in(C, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(111,plain,
% 0.19/0.46 ((~((~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | ![C: $i] : ((~in(C, B!9)) | in(C, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))) | ![C: $i] : ((~in(C, B!9)) | in(C, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.19/0.46 tff(112,plain,
% 0.19/0.46 (![C: $i] : ((~in(C, B!9)) | in(C, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[111, 20])).
% 0.19/0.46 tff(113,plain,
% 0.19/0.46 (((~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | (~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(114,plain,
% 0.19/0.46 (~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[113, 107])).
% 0.19/0.46 tff(115,plain,
% 0.19/0.46 (((~![C: $i] : ((~in(C, B!9)) | in(C, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))) | ((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))) <=> ((~![C: $i] : ((~in(C, B!9)) | in(C, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))) | (~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(116,plain,
% 0.19/0.46 ((~![C: $i] : ((~in(C, B!9)) | in(C, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))) | ((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(117,plain,
% 0.19/0.46 ((~![C: $i] : ((~in(C, B!9)) | in(C, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))) | (~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.19/0.46 tff(118,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[117, 58, 114, 112])).
% 0.19/0.46 % SZS output end Proof
% 0.19/0.46 % E exiting
%------------------------------------------------------------------------------