%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU313+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:27:34 AM UTC 2025
% Result : Theorem 22.65s 22.88s
% Output : Proof 22.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU313+1 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.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 06:41:48 EDT 2025
% 0.12/0.33 % CPUTime :
% 22.65/22.88 % SZS status Theorem
% 22.65/22.88 % SZS output start Proof
% 22.65/22.88 tff(in_type, type, (
% 22.65/22.88 in: ( $i * $i ) > $o)).
% 22.65/22.88 tff(subset_difference_type, type, (
% 22.65/22.88 subset_difference: ( $i * $i * $i ) > $i)).
% 22.65/22.88 tff(tptp_fun_E_0_type, type, (
% 22.65/22.88 tptp_fun_E_0: ( $i * $i * $i ) > $i)).
% 22.65/22.88 tff(tptp_fun_A_10_type, type, (
% 22.65/22.88 tptp_fun_A_10: $i)).
% 22.65/22.88 tff(tptp_fun_B_11_type, type, (
% 22.65/22.88 tptp_fun_B_11: $i)).
% 22.65/22.88 tff(tptp_fun_C_12_type, type, (
% 22.65/22.88 tptp_fun_C_12: $i)).
% 22.65/22.88 tff(cast_as_carrier_subset_type, type, (
% 22.65/22.88 cast_as_carrier_subset: $i > $i)).
% 22.65/22.88 tff(the_carrier_type, type, (
% 22.65/22.88 the_carrier: $i > $i)).
% 22.65/22.88 tff(tptp_fun_D_3_type, type, (
% 22.65/22.88 tptp_fun_D_3: ( $i * $i * $i ) > $i)).
% 22.65/22.88 tff(set_difference_type, type, (
% 22.65/22.88 set_difference: ( $i * $i ) > $i)).
% 22.65/22.88 tff(element_type, type, (
% 22.65/22.88 element: ( $i * $i ) > $o)).
% 22.65/22.88 tff(powerset_type, type, (
% 22.65/22.88 powerset: $i > $i)).
% 22.65/22.88 tff(open_subset_type, type, (
% 22.65/22.88 open_subset: ( $i * $i ) > $o)).
% 22.65/22.88 tff(disjoint_type, type, (
% 22.65/22.88 disjoint: ( $i * $i ) > $o)).
% 22.65/22.88 tff(topstr_closure_type, type, (
% 22.65/22.88 topstr_closure: ( $i * $i ) > $i)).
% 22.65/22.88 tff(tptp_fun_D_13_type, type, (
% 22.65/22.88 tptp_fun_D_13: $i)).
% 22.65/22.88 tff(subset_type, type, (
% 22.65/22.88 subset: ( $i * $i ) > $o)).
% 22.65/22.88 tff(closed_subset_type, type, (
% 22.65/22.88 closed_subset: ( $i * $i ) > $o)).
% 22.65/22.88 tff(top_str_type, type, (
% 22.65/22.88 top_str: $i > $o)).
% 22.65/22.88 tff(tptp_fun_D_1_type, type, (
% 22.65/22.88 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 22.65/22.88 tff(tptp_fun_E_2_type, type, (
% 22.65/22.88 tptp_fun_E_2: ( $i * $i * $i ) > $i)).
% 22.65/22.88 tff(subset_complement_type, type, (
% 22.65/22.88 subset_complement: ( $i * $i ) > $i)).
% 22.65/22.88 tff(one_sorted_str_type, type, (
% 22.65/22.88 one_sorted_str: $i > $o)).
% 22.65/22.88 tff(tptp_fun_B_9_type, type, (
% 22.65/22.88 tptp_fun_B_9: $i > $i)).
% 22.65/22.88 tff(empty_set_type, type, (
% 22.65/22.88 empty_set: $i)).
% 22.65/22.88 tff(empty_type, type, (
% 22.65/22.88 empty: $i > $o)).
% 22.65/22.88 tff(v1_membered_type, type, (
% 22.65/22.88 v1_membered: $i > $o)).
% 22.65/22.88 tff(v2_membered_type, type, (
% 22.65/22.88 v2_membered: $i > $o)).
% 22.65/22.88 tff(v3_membered_type, type, (
% 22.65/22.88 v3_membered: $i > $o)).
% 22.65/22.88 tff(v4_membered_type, type, (
% 22.65/22.88 v4_membered: $i > $o)).
% 22.65/22.88 tff(v5_membered_type, type, (
% 22.65/22.88 v5_membered: $i > $o)).
% 22.65/22.88 tff(1,plain,
% 22.65/22.88 ((top_str(A!10) & (element(B!11, powerset(the_carrier(A!10))) & in(C!12, the_carrier(A!10)) & (in(C!12, topstr_closure(A!10, B!11)) | ![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | (~(closed_subset(D, A!10) & subset(B!11, D))) | in(C!12, D))) & ((~in(C!12, topstr_closure(A!10, B!11))) | (~(in(C!12, D!13) | (~(closed_subset(D!13, A!10) & subset(B!11, D!13))) | (~element(D!13, powerset(the_carrier(A!10))))))))) <=> (top_str(A!10) & element(B!11, powerset(the_carrier(A!10))) & in(C!12, the_carrier(A!10)) & (in(C!12, topstr_closure(A!10, B!11)) | ![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | (~(closed_subset(D, A!10) & subset(B!11, D))) | in(C!12, D))) & ((~in(C!12, topstr_closure(A!10, B!11))) | (~(in(C!12, D!13) | (~(closed_subset(D!13, A!10) & subset(B!11, D!13))) | (~element(D!13, powerset(the_carrier(A!10))))))))),
% 22.65/22.88 inference(rewrite,[status(thm)],[])).
% 22.65/22.88 tff(2,plain,
% 22.65/22.88 ((element(B!11, powerset(the_carrier(A!10))) & (in(C!12, the_carrier(A!10)) & (in(C!12, topstr_closure(A!10, B!11)) | ![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | (~(closed_subset(D, A!10) & subset(B!11, D))) | in(C!12, D))) & ((~in(C!12, topstr_closure(A!10, B!11))) | (~(in(C!12, D!13) | (~(closed_subset(D!13, A!10) & subset(B!11, D!13))) | (~element(D!13, powerset(the_carrier(A!10))))))))) <=> (element(B!11, powerset(the_carrier(A!10))) & in(C!12, the_carrier(A!10)) & (in(C!12, topstr_closure(A!10, B!11)) | ![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | (~(closed_subset(D, A!10) & subset(B!11, D))) | in(C!12, D))) & ((~in(C!12, topstr_closure(A!10, B!11))) | (~(in(C!12, D!13) | (~(closed_subset(D!13, A!10) & subset(B!11, D!13))) | (~element(D!13, powerset(the_carrier(A!10))))))))),
% 22.65/22.88 inference(rewrite,[status(thm)],[])).
% 22.65/22.88 tff(3,plain,
% 22.65/22.88 ((in(C!12, the_carrier(A!10)) & ((in(C!12, topstr_closure(A!10, B!11)) | ![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | (~(closed_subset(D, A!10) & subset(B!11, D))) | in(C!12, D))) & ((~in(C!12, topstr_closure(A!10, B!11))) | (~(in(C!12, D!13) | (~(closed_subset(D!13, A!10) & subset(B!11, D!13))) | (~element(D!13, powerset(the_carrier(A!10))))))))) <=> (in(C!12, the_carrier(A!10)) & (in(C!12, topstr_closure(A!10, B!11)) | ![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | (~(closed_subset(D, A!10) & subset(B!11, D))) | in(C!12, D))) & ((~in(C!12, topstr_closure(A!10, B!11))) | (~(in(C!12, D!13) | (~(closed_subset(D!13, A!10) & subset(B!11, D!13))) | (~element(D!13, powerset(the_carrier(A!10))))))))),
% 22.65/22.89 inference(rewrite,[status(thm)],[])).
% 22.65/22.89 tff(4,plain,
% 22.65/22.89 (((in(C!12, topstr_closure(A!10, B!11)) | ![D: $i] : (in(C!12, D) | (~(closed_subset(D, A!10) & subset(B!11, D))) | (~element(D, powerset(the_carrier(A!10)))))) & ((~in(C!12, topstr_closure(A!10, B!11))) | (~(in(C!12, D!13) | (~(closed_subset(D!13, A!10) & subset(B!11, D!13))) | (~element(D!13, powerset(the_carrier(A!10)))))))) <=> ((in(C!12, topstr_closure(A!10, B!11)) | ![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | (~(closed_subset(D, A!10) & subset(B!11, D))) | in(C!12, D))) & ((~in(C!12, topstr_closure(A!10, B!11))) | (~(in(C!12, D!13) | (~(closed_subset(D!13, A!10) & subset(B!11, D!13))) | (~element(D!13, powerset(the_carrier(A!10))))))))),
% 22.65/22.89 inference(rewrite,[status(thm)],[])).
% 22.65/22.89 tff(5,plain,
% 22.65/22.89 ((in(C!12, the_carrier(A!10)) & ((in(C!12, topstr_closure(A!10, B!11)) | ![D: $i] : (in(C!12, D) | (~(closed_subset(D, A!10) & subset(B!11, D))) | (~element(D, powerset(the_carrier(A!10)))))) & ((~in(C!12, topstr_closure(A!10, B!11))) | (~(in(C!12, D!13) | (~(closed_subset(D!13, A!10) & subset(B!11, D!13))) | (~element(D!13, powerset(the_carrier(A!10))))))))) <=> (in(C!12, the_carrier(A!10)) & ((in(C!12, topstr_closure(A!10, B!11)) | ![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | (~(closed_subset(D, A!10) & subset(B!11, D))) | in(C!12, D))) & ((~in(C!12, topstr_closure(A!10, B!11))) | (~(in(C!12, D!13) | (~(closed_subset(D!13, A!10) & subset(B!11, D!13))) | (~element(D!13, powerset(the_carrier(A!10)))))))))),
% 22.65/22.89 inference(monotonicity,[status(thm)],[4])).
% 22.65/22.89 tff(6,plain,
% 22.65/22.89 ((in(C!12, the_carrier(A!10)) & ((in(C!12, topstr_closure(A!10, B!11)) | ![D: $i] : (in(C!12, D) | (~(closed_subset(D, A!10) & subset(B!11, D))) | (~element(D, powerset(the_carrier(A!10)))))) & ((~in(C!12, topstr_closure(A!10, B!11))) | (~(in(C!12, D!13) | (~(closed_subset(D!13, A!10) & subset(B!11, D!13))) | (~element(D!13, powerset(the_carrier(A!10))))))))) <=> (in(C!12, the_carrier(A!10)) & (in(C!12, topstr_closure(A!10, B!11)) | ![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | (~(closed_subset(D, A!10) & subset(B!11, D))) | in(C!12, D))) & ((~in(C!12, topstr_closure(A!10, B!11))) | (~(in(C!12, D!13) | (~(closed_subset(D!13, A!10) & subset(B!11, D!13))) | (~element(D!13, powerset(the_carrier(A!10))))))))),
% 22.65/22.89 inference(transitivity,[status(thm)],[5, 3])).
% 22.65/22.89 tff(7,plain,
% 22.65/22.89 ((element(B!11, powerset(the_carrier(A!10))) & (in(C!12, the_carrier(A!10)) & ((in(C!12, topstr_closure(A!10, B!11)) | ![D: $i] : (in(C!12, D) | (~(closed_subset(D, A!10) & subset(B!11, D))) | (~element(D, powerset(the_carrier(A!10)))))) & ((~in(C!12, topstr_closure(A!10, B!11))) | (~(in(C!12, D!13) | (~(closed_subset(D!13, A!10) & subset(B!11, D!13))) | (~element(D!13, powerset(the_carrier(A!10)))))))))) <=> (element(B!11, powerset(the_carrier(A!10))) & (in(C!12, the_carrier(A!10)) & (in(C!12, topstr_closure(A!10, B!11)) | ![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | (~(closed_subset(D, A!10) & subset(B!11, D))) | in(C!12, D))) & ((~in(C!12, topstr_closure(A!10, B!11))) | (~(in(C!12, D!13) | (~(closed_subset(D!13, A!10) & subset(B!11, D!13))) | (~element(D!13, powerset(the_carrier(A!10)))))))))),
% 22.65/22.89 inference(monotonicity,[status(thm)],[6])).
% 22.65/22.89 tff(8,plain,
% 22.65/22.89 ((element(B!11, powerset(the_carrier(A!10))) & (in(C!12, the_carrier(A!10)) & ((in(C!12, topstr_closure(A!10, B!11)) | ![D: $i] : (in(C!12, D) | (~(closed_subset(D, A!10) & subset(B!11, D))) | (~element(D, powerset(the_carrier(A!10)))))) & ((~in(C!12, topstr_closure(A!10, B!11))) | (~(in(C!12, D!13) | (~(closed_subset(D!13, A!10) & subset(B!11, D!13))) | (~element(D!13, powerset(the_carrier(A!10)))))))))) <=> (element(B!11, powerset(the_carrier(A!10))) & in(C!12, the_carrier(A!10)) & (in(C!12, topstr_closure(A!10, B!11)) | ![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | (~(closed_subset(D, A!10) & subset(B!11, D))) | in(C!12, D))) & ((~in(C!12, topstr_closure(A!10, B!11))) | (~(in(C!12, D!13) | (~(closed_subset(D!13, A!10) & subset(B!11, D!13))) | (~element(D!13, powerset(the_carrier(A!10))))))))),
% 22.65/22.89 inference(transitivity,[status(thm)],[7, 2])).
% 22.65/22.89 tff(9,plain,
% 22.65/22.89 ((top_str(A!10) & (element(B!11, powerset(the_carrier(A!10))) & (in(C!12, the_carrier(A!10)) & ((in(C!12, topstr_closure(A!10, B!11)) | ![D: $i] : (in(C!12, D) | (~(closed_subset(D, A!10) & subset(B!11, D))) | (~element(D, powerset(the_carrier(A!10)))))) & ((~in(C!12, topstr_closure(A!10, B!11))) | (~(in(C!12, D!13) | (~(closed_subset(D!13, A!10) & subset(B!11, D!13))) | (~element(D!13, powerset(the_carrier(A!10))))))))))) <=> (top_str(A!10) & (element(B!11, powerset(the_carrier(A!10))) & in(C!12, the_carrier(A!10)) & (in(C!12, topstr_closure(A!10, B!11)) | ![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | (~(closed_subset(D, A!10) & subset(B!11, D))) | in(C!12, D))) & ((~in(C!12, topstr_closure(A!10, B!11))) | (~(in(C!12, D!13) | (~(closed_subset(D!13, A!10) & subset(B!11, D!13))) | (~element(D!13, powerset(the_carrier(A!10)))))))))),
% 22.65/22.89 inference(monotonicity,[status(thm)],[8])).
% 22.65/22.89 tff(10,plain,
% 22.65/22.89 ((top_str(A!10) & (element(B!11, powerset(the_carrier(A!10))) & (in(C!12, the_carrier(A!10)) & ((in(C!12, topstr_closure(A!10, B!11)) | ![D: $i] : (in(C!12, D) | (~(closed_subset(D, A!10) & subset(B!11, D))) | (~element(D, powerset(the_carrier(A!10)))))) & ((~in(C!12, topstr_closure(A!10, B!11))) | (~(in(C!12, D!13) | (~(closed_subset(D!13, A!10) & subset(B!11, D!13))) | (~element(D!13, powerset(the_carrier(A!10))))))))))) <=> (top_str(A!10) & element(B!11, powerset(the_carrier(A!10))) & in(C!12, the_carrier(A!10)) & (in(C!12, topstr_closure(A!10, B!11)) | ![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | (~(closed_subset(D, A!10) & subset(B!11, D))) | in(C!12, D))) & ((~in(C!12, topstr_closure(A!10, B!11))) | (~(in(C!12, D!13) | (~(closed_subset(D!13, A!10) & subset(B!11, D!13))) | (~element(D!13, powerset(the_carrier(A!10))))))))),
% 22.65/22.89 inference(transitivity,[status(thm)],[9, 1])).
% 22.65/22.89 tff(11,plain,
% 22.65/22.89 ((~![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))))))))))),
% 22.65/22.89 inference(rewrite,[status(thm)],[])).
% 22.65/22.89 tff(12,plain,
% 22.65/22.89 ((~![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))))))))))),
% 22.65/22.89 inference(rewrite,[status(thm)],[])).
% 22.65/22.89 tff(13,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/sandbox/benchmark/theBenchmark.p','t45_pre_topc')).
% 22.65/22.89 tff(14,plain,
% 22.65/22.89 (~![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)))))))))),
% 22.65/22.89 inference(modus_ponens,[status(thm)],[13, 12])).
% 22.65/22.89 tff(15,plain,
% 22.65/22.89 (~![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)))))))))),
% 22.65/22.89 inference(modus_ponens,[status(thm)],[14, 11])).
% 22.65/22.89 tff(16,plain,
% 22.65/22.89 (~![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)))))))))),
% 22.65/22.89 inference(modus_ponens,[status(thm)],[15, 11])).
% 22.65/22.89 tff(17,plain,
% 22.65/22.89 (~![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)))))))))),
% 22.65/22.89 inference(modus_ponens,[status(thm)],[16, 11])).
% 22.65/22.89 tff(18,plain,
% 22.65/22.89 (top_str(A!10) & element(B!11, powerset(the_carrier(A!10))) & in(C!12, the_carrier(A!10)) & (in(C!12, topstr_closure(A!10, B!11)) | ![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | (~(closed_subset(D, A!10) & subset(B!11, D))) | in(C!12, D))) & ((~in(C!12, topstr_closure(A!10, B!11))) | (~(in(C!12, D!13) | (~(closed_subset(D!13, A!10) & subset(B!11, D!13))) | (~element(D!13, powerset(the_carrier(A!10)))))))),
% 22.65/22.89 inference(modus_ponens,[status(thm)],[17, 10])).
% 22.65/22.89 tff(19,plain,
% 22.65/22.89 (element(B!11, powerset(the_carrier(A!10)))),
% 22.65/22.89 inference(and_elim,[status(thm)],[18])).
% 22.65/22.89 tff(20,plain,
% 22.65/22.89 (top_str(A!10)),
% 22.65/22.89 inference(and_elim,[status(thm)],[18])).
% 22.65/22.89 tff(21,plain,
% 22.65/22.89 (^[A: $i, B: $i] : refl((element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A))) <=> (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A))))),
% 22.65/22.89 inference(bind,[status(th)],[])).
% 22.65/22.89 tff(22,plain,
% 22.65/22.89 (![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A))) <=> ![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 22.65/22.89 inference(quant_intro,[status(thm)],[21])).
% 22.65/22.89 tff(23,plain,
% 22.65/22.89 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((top_str(A) & element(B, powerset(the_carrier(A)))) <=> (~((~top_str(A)) | (~element(B, powerset(the_carrier(A))))))), ((~(top_str(A) & element(B, powerset(the_carrier(A))))) <=> (~(~((~top_str(A)) | (~element(B, powerset(the_carrier(A))))))))), rewrite((~(~((~top_str(A)) | (~element(B, powerset(the_carrier(A))))))) <=> ((~top_str(A)) | (~element(B, powerset(the_carrier(A)))))), ((~(top_str(A) & element(B, powerset(the_carrier(A))))) <=> ((~top_str(A)) | (~element(B, powerset(the_carrier(A))))))), (((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A)))) <=> (((~top_str(A)) | (~element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A)))))), rewrite((((~top_str(A)) | (~element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A)))) <=> (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))), (((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A)))) <=> (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))))),
% 22.65/22.89 inference(bind,[status(th)],[])).
% 22.65/22.89 tff(24,plain,
% 22.65/22.89 (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A)))) <=> ![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 22.65/22.89 inference(quant_intro,[status(thm)],[23])).
% 22.65/22.89 tff(25,plain,
% 22.65/22.89 (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A)))) <=> ![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A))))),
% 22.65/22.89 inference(rewrite,[status(thm)],[])).
% 22.65/22.89 tff(26,plain,
% 22.65/22.89 (^[A: $i, B: $i] : rewrite(((top_str(A) & element(B, powerset(the_carrier(A)))) => element(topstr_closure(A, B), powerset(the_carrier(A)))) <=> ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A)))))),
% 22.65/22.89 inference(bind,[status(th)],[])).
% 22.65/22.89 tff(27,plain,
% 22.65/22.89 (![A: $i, B: $i] : ((top_str(A) & element(B, powerset(the_carrier(A)))) => element(topstr_closure(A, B), powerset(the_carrier(A)))) <=> ![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A))))),
% 22.65/22.89 inference(quant_intro,[status(thm)],[26])).
% 22.65/22.89 tff(28,axiom,(![A: $i, B: $i] : ((top_str(A) & element(B, powerset(the_carrier(A)))) => element(topstr_closure(A, B), powerset(the_carrier(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k6_pre_topc')).
% 22.65/22.89 tff(29,plain,
% 22.65/22.89 (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A))))),
% 22.65/22.89 inference(modus_ponens,[status(thm)],[28, 27])).
% 22.65/22.89 tff(30,plain,
% 22.65/22.89 (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A))))),
% 22.65/22.89 inference(modus_ponens,[status(thm)],[29, 25])).
% 22.65/22.89 tff(31,plain,(
% 22.65/22.89 ![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A))))),
% 22.65/22.89 inference(skolemize,[status(sab)],[30])).
% 22.65/22.89 tff(32,plain,
% 22.65/22.89 (![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 22.65/22.89 inference(modus_ponens,[status(thm)],[31, 24])).
% 22.65/22.89 tff(33,plain,
% 22.65/22.89 (![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 22.65/22.89 inference(modus_ponens,[status(thm)],[32, 22])).
% 22.65/22.89 tff(34,plain,
% 22.65/22.89 (((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | ((~top_str(A!10)) | (~element(B!11, powerset(the_carrier(A!10)))) | element(topstr_closure(A!10, B!11), powerset(the_carrier(A!10))))) <=> ((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (~top_str(A!10)) | (~element(B!11, powerset(the_carrier(A!10)))) | element(topstr_closure(A!10, B!11), powerset(the_carrier(A!10))))),
% 22.65/22.89 inference(rewrite,[status(thm)],[])).
% 22.65/22.89 tff(35,plain,
% 22.65/22.89 ((element(topstr_closure(A!10, B!11), powerset(the_carrier(A!10))) | (~element(B!11, powerset(the_carrier(A!10)))) | (~top_str(A!10))) <=> ((~top_str(A!10)) | (~element(B!11, powerset(the_carrier(A!10)))) | element(topstr_closure(A!10, B!11), powerset(the_carrier(A!10))))),
% 22.65/22.89 inference(rewrite,[status(thm)],[])).
% 22.65/22.89 tff(36,plain,
% 22.65/22.89 (((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (element(topstr_closure(A!10, B!11), powerset(the_carrier(A!10))) | (~element(B!11, powerset(the_carrier(A!10)))) | (~top_str(A!10)))) <=> ((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | ((~top_str(A!10)) | (~element(B!11, powerset(the_carrier(A!10)))) | element(topstr_closure(A!10, B!11), powerset(the_carrier(A!10)))))),
% 22.65/22.89 inference(monotonicity,[status(thm)],[35])).
% 22.65/22.89 tff(37,plain,
% 22.65/22.89 (((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (element(topstr_closure(A!10, B!11), powerset(the_carrier(A!10))) | (~element(B!11, powerset(the_carrier(A!10)))) | (~top_str(A!10)))) <=> ((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (~top_str(A!10)) | (~element(B!11, powerset(the_carrier(A!10)))) | element(topstr_closure(A!10, B!11), powerset(the_carrier(A!10))))),
% 22.65/22.89 inference(transitivity,[status(thm)],[36, 34])).
% 22.65/22.89 tff(38,plain,
% 22.65/22.89 ((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (element(topstr_closure(A!10, B!11), powerset(the_carrier(A!10))) | (~element(B!11, powerset(the_carrier(A!10)))) | (~top_str(A!10)))),
% 22.65/22.89 inference(quant_inst,[status(thm)],[])).
% 22.65/22.89 tff(39,plain,
% 22.65/22.89 ((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (~top_str(A!10)) | (~element(B!11, powerset(the_carrier(A!10)))) | element(topstr_closure(A!10, B!11), powerset(the_carrier(A!10)))),
% 22.65/22.89 inference(modus_ponens,[status(thm)],[38, 37])).
% 22.65/22.89 tff(40,plain,
% 22.65/22.89 (element(topstr_closure(A!10, B!11), powerset(the_carrier(A!10)))),
% 22.65/22.89 inference(unit_resolution,[status(thm)],[39, 33, 20, 19])).
% 22.65/22.89 tff(41,plain,
% 22.65/22.89 (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A)))))))))))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E)))))))))))))))),
% 22.65/22.89 inference(bind,[status(th)],[])).
% 22.65/22.89 tff(42,plain,
% 22.65/22.89 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A)))))))))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))))))))))))),
% 22.65/22.89 inference(quant_intro,[status(thm)],[41])).
% 22.65/22.89 tff(43,plain,
% 22.65/22.89 (^[A: $i] : refl(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A)))))))))))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A)))))))))))))))))),
% 22.65/22.89 inference(bind,[status(th)],[])).
% 22.65/22.89 tff(44,plain,
% 22.65/22.89 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A)))))))))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))))))))))))),
% 22.65/22.89 inference(quant_intro,[status(thm)],[43])).
% 22.65/22.89 tff(45,plain,
% 22.65/22.89 (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A)))))))))))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A)))))))))))))))))),
% 22.65/22.89 inference(bind,[status(th)],[])).
% 22.65/22.89 tff(46,plain,
% 22.65/22.89 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A)))))))))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))))))))))))),
% 22.65/22.89 inference(quant_intro,[status(thm)],[45])).
% 22.65/22.89 tff(47,plain,
% 22.65/22.89 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A)))))))))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))))))))))))),
% 22.65/22.89 inference(transitivity,[status(thm)],[46, 44])).
% 22.65/22.89 tff(48,plain,
% 22.65/22.89 (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & (in(D, C) | (~((~(open_subset(tptp_fun_E_0(D, B, A), A) & in(D, tptp_fun_E_0(D, B, A)) & disjoint(B, tptp_fun_E_0(D, B, A)))) | (~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))))))))) & ((C = topstr_closure(A, B)) | (in(tptp_fun_D_1(C, B, A), the_carrier(A)) & (in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~(open_subset(E, A) & in(tptp_fun_D_1(C, B, A), E) & disjoint(B, E))))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~(open_subset(tptp_fun_E_2(C, B, A), A) & in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A)) & disjoint(B, tptp_fun_E_2(C, B, A)))) | (~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A))))))))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A)))))))))))))))))),
% 22.65/22.89 inference(bind,[status(th)],[])).
% 22.65/22.89 tff(49,plain,
% 22.65/22.89 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & (in(D, C) | (~((~(open_subset(tptp_fun_E_0(D, B, A), A) & in(D, tptp_fun_E_0(D, B, A)) & disjoint(B, tptp_fun_E_0(D, B, A)))) | (~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))))))))) & ((C = topstr_closure(A, B)) | (in(tptp_fun_D_1(C, B, A), the_carrier(A)) & (in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~(open_subset(E, A) & in(tptp_fun_D_1(C, B, A), E) & disjoint(B, E))))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~(open_subset(tptp_fun_E_2(C, B, A), A) & in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A)) & disjoint(B, tptp_fun_E_2(C, B, A)))) | (~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A))))))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))))))))))))),
% 22.65/22.89 inference(quant_intro,[status(thm)],[48])).
% 22.65/22.89 tff(50,plain,
% 22.65/22.89 (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & (in(D, C) | (~((~(open_subset(tptp_fun_E_0(D, B, A), A) & in(D, tptp_fun_E_0(D, B, A)) & disjoint(B, tptp_fun_E_0(D, B, A)))) | (~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))))))))) & ((C = topstr_closure(A, B)) | (in(tptp_fun_D_1(C, B, A), the_carrier(A)) & ((in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~(open_subset(E, A) & in(tptp_fun_D_1(C, B, A), E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~(open_subset(tptp_fun_E_2(C, B, A), A) & in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A)) & disjoint(B, tptp_fun_E_2(C, B, A)))) | (~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))))))))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & (in(D, C) | (~((~(open_subset(tptp_fun_E_0(D, B, A), A) & in(D, tptp_fun_E_0(D, B, A)) & disjoint(B, tptp_fun_E_0(D, B, A)))) | (~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))))))))) & ((C = topstr_closure(A, B)) | (in(tptp_fun_D_1(C, B, A), the_carrier(A)) & (in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~(open_subset(E, A) & in(tptp_fun_D_1(C, B, A), E) & disjoint(B, E))))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~(open_subset(tptp_fun_E_2(C, B, A), A) & in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A)) & disjoint(B, tptp_fun_E_2(C, B, A)))) | (~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A))))))))))))))),
% 22.65/22.89 inference(bind,[status(th)],[])).
% 22.65/22.89 tff(51,plain,
% 22.65/22.89 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & (in(D, C) | (~((~(open_subset(tptp_fun_E_0(D, B, A), A) & in(D, tptp_fun_E_0(D, B, A)) & disjoint(B, tptp_fun_E_0(D, B, A)))) | (~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))))))))) & ((C = topstr_closure(A, B)) | (in(tptp_fun_D_1(C, B, A), the_carrier(A)) & ((in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~(open_subset(E, A) & in(tptp_fun_D_1(C, B, A), E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~(open_subset(tptp_fun_E_2(C, B, A), A) & in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A)) & disjoint(B, tptp_fun_E_2(C, B, A)))) | (~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))))))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & (in(D, C) | (~((~(open_subset(tptp_fun_E_0(D, B, A), A) & in(D, tptp_fun_E_0(D, B, A)) & disjoint(B, tptp_fun_E_0(D, B, A)))) | (~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))))))))) & ((C = topstr_closure(A, B)) | (in(tptp_fun_D_1(C, B, A), the_carrier(A)) & (in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~(open_subset(E, A) & in(tptp_fun_D_1(C, B, A), E) & disjoint(B, E))))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~(open_subset(tptp_fun_E_2(C, B, A), A) & in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A)) & disjoint(B, tptp_fun_E_2(C, B, A)))) | (~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))))))))))))),
% 22.65/22.89 inference(quant_intro,[status(thm)],[50])).
% 22.65/22.89 tff(52,plain,
% 22.65/22.89 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A))))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))))))))),
% 22.65/22.89 inference(rewrite,[status(thm)],[])).
% 22.65/22.89 tff(53,plain,
% 22.65/22.89 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((C = topstr_closure(A, B)) <=> ![D: $i] : (in(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (element(E, powerset(the_carrier(A))) => (~((open_subset(E, A) & in(D, E)) & disjoint(B, E))))))) <=> ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A))))))))), ((element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : (in(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (element(E, powerset(the_carrier(A))) => (~((open_subset(E, A) & in(D, E)) & disjoint(B, E)))))))) <=> (element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A))))))))))), rewrite((element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A))))))))) <=> ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))))))), ((element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : (in(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (element(E, powerset(the_carrier(A))) => (~((open_subset(E, A) & in(D, E)) & disjoint(B, E)))))))) <=> ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))))))))), (![C: $i] : (element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : (in(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (element(E, powerset(the_carrier(A))) => (~((open_subset(E, A) & in(D, E)) & disjoint(B, E)))))))) <=> ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A))))))))))), ((element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : (in(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (element(E, powerset(the_carrier(A))) => (~((open_subset(E, A) & in(D, E)) & disjoint(B, E))))))))) <=> (element(B, powerset(the_carrier(A))) => ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))))))))), rewrite((element(B, powerset(the_carrier(A))) => ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))))))) <=> ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A))))))))))), ((element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : (in(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (element(E, powerset(the_carrier(A))) => (~((open_subset(E, A) & in(D, E)) & disjoint(B, E))))))))) <=> ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A))))))))))))), (![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : (in(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (element(E, powerset(the_carrier(A))) => (~((open_subset(E, A) & in(D, E)) & disjoint(B, E))))))))) <=> ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))))))))), ((top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : (in(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (element(E, powerset(the_carrier(A))) => (~((open_subset(E, A) & in(D, E)) & disjoint(B, E)))))))))) <=> (top_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A))))))))))))), rewrite((top_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A))))))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))))))))), ((top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : (in(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (element(E, powerset(the_carrier(A))) => (~((open_subset(E, A) & in(D, E)) & disjoint(B, E)))))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))))))))))),
% 22.65/22.89 inference(bind,[status(th)],[])).
% 22.65/22.89 tff(54,plain,
% 22.65/22.89 (![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : (in(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (element(E, powerset(the_carrier(A))) => (~((open_subset(E, A) & in(D, E)) & disjoint(B, E)))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))))))))),
% 22.65/22.90 inference(quant_intro,[status(thm)],[53])).
% 22.65/22.90 tff(55,axiom,(![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : (in(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (element(E, powerset(the_carrier(A))) => (~((open_subset(E, A) & in(D, E)) & disjoint(B, E))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d13_pre_topc')).
% 22.65/22.90 tff(56,plain,
% 22.65/22.90 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))))))))),
% 22.65/22.90 inference(modus_ponens,[status(thm)],[55, 54])).
% 22.65/22.90 tff(57,plain,
% 22.65/22.90 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))))))))),
% 22.65/22.90 inference(modus_ponens,[status(thm)],[56, 52])).
% 22.65/22.90 tff(58,plain,(
% 22.65/22.90 ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & (in(D, C) | (~((~(open_subset(tptp_fun_E_0(D, B, A), A) & in(D, tptp_fun_E_0(D, B, A)) & disjoint(B, tptp_fun_E_0(D, B, A)))) | (~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))))))))) & ((C = topstr_closure(A, B)) | (in(tptp_fun_D_1(C, B, A), the_carrier(A)) & ((in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~(open_subset(E, A) & in(tptp_fun_D_1(C, B, A), E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~(open_subset(tptp_fun_E_2(C, B, A), A) & in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A)) & disjoint(B, tptp_fun_E_2(C, B, A)))) | (~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A))))))))))))))),
% 22.65/22.90 inference(skolemize,[status(sab)],[57])).
% 22.65/22.90 tff(59,plain,
% 22.65/22.90 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & (in(D, C) | (~((~(open_subset(tptp_fun_E_0(D, B, A), A) & in(D, tptp_fun_E_0(D, B, A)) & disjoint(B, tptp_fun_E_0(D, B, A)))) | (~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))))))))) & ((C = topstr_closure(A, B)) | (in(tptp_fun_D_1(C, B, A), the_carrier(A)) & (in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~(open_subset(E, A) & in(tptp_fun_D_1(C, B, A), E) & disjoint(B, E))))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~(open_subset(tptp_fun_E_2(C, B, A), A) & in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A)) & disjoint(B, tptp_fun_E_2(C, B, A)))) | (~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))))))))))))),
% 22.65/22.90 inference(modus_ponens,[status(thm)],[58, 51])).
% 22.65/22.90 tff(60,plain,
% 22.65/22.90 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))))))))))))),
% 22.65/22.90 inference(modus_ponens,[status(thm)],[59, 49])).
% 22.65/22.90 tff(61,plain,
% 22.65/22.90 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))))))))))))),
% 22.65/22.90 inference(modus_ponens,[status(thm)],[60, 47])).
% 22.65/22.90 tff(62,plain,
% 22.65/22.90 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))))))))))))),
% 22.65/22.90 inference(modus_ponens,[status(thm)],[61, 42])).
% 22.65/22.90 tff(63,plain,
% 22.65/22.90 (((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))))))))))))) | ((~top_str(A!10)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B, E)) | (~open_subset(E, A!10))))) | (~(in(D, C) | (~((~disjoint(B, tptp_fun_E_0(D, B, A!10))) | (~in(D, tptp_fun_E_0(D, B, A!10))) | (~open_subset(tptp_fun_E_0(D, B, A!10), A!10)) | (~element(tptp_fun_E_0(D, B, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B)) | (~((~in(tptp_fun_D_1(C, B, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B, A!10), C)) | (~((~disjoint(B, tptp_fun_E_2(C, B, A!10))) | (~in(tptp_fun_D_1(C, B, A!10), tptp_fun_E_2(C, B, A!10))) | (~open_subset(tptp_fun_E_2(C, B, A!10), A!10)) | (~element(tptp_fun_E_2(C, B, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B, E)) | (~open_subset(E, A!10)) | (~in(tptp_fun_D_1(C, B, A!10), E))))))))))))))) <=> ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))))))))))))) | (~top_str(A!10)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B, E)) | (~open_subset(E, A!10))))) | (~(in(D, C) | (~((~disjoint(B, tptp_fun_E_0(D, B, A!10))) | (~in(D, tptp_fun_E_0(D, B, A!10))) | (~open_subset(tptp_fun_E_0(D, B, A!10), A!10)) | (~element(tptp_fun_E_0(D, B, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B)) | (~((~in(tptp_fun_D_1(C, B, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B, A!10), C)) | (~((~disjoint(B, tptp_fun_E_2(C, B, A!10))) | (~in(tptp_fun_D_1(C, B, A!10), tptp_fun_E_2(C, B, A!10))) | (~open_subset(tptp_fun_E_2(C, B, A!10), A!10)) | (~element(tptp_fun_E_2(C, B, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B, E)) | (~open_subset(E, A!10)) | (~in(tptp_fun_D_1(C, B, A!10), E))))))))))))))),
% 22.65/22.90 inference(rewrite,[status(thm)],[])).
% 22.65/22.90 tff(64,plain,
% 22.65/22.90 (((~top_str(A!10)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A!10), powerset(the_carrier(A!10)))) | (~open_subset(tptp_fun_E_0(D, B, A!10), A!10)) | (~in(D, tptp_fun_E_0(D, B, A!10))) | (~disjoint(B, tptp_fun_E_0(D, B, A!10)))))))))))) | (~((C = topstr_closure(A!10, B)) | (~((~in(tptp_fun_D_1(C, B, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B, A!10), C)) | (~((~element(tptp_fun_E_2(C, B, A!10), powerset(the_carrier(A!10)))) | (~open_subset(tptp_fun_E_2(C, B, A!10), A!10)) | (~in(tptp_fun_D_1(C, B, A!10), tptp_fun_E_2(C, B, A!10))) | (~disjoint(B, tptp_fun_E_2(C, B, A!10))))))) | (~(in(tptp_fun_D_1(C, B, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~in(tptp_fun_D_1(C, B, A!10), E)) | (~disjoint(B, E)))))))))))))) <=> ((~top_str(A!10)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B, E)) | (~open_subset(E, A!10))))) | (~(in(D, C) | (~((~disjoint(B, tptp_fun_E_0(D, B, A!10))) | (~in(D, tptp_fun_E_0(D, B, A!10))) | (~open_subset(tptp_fun_E_0(D, B, A!10), A!10)) | (~element(tptp_fun_E_0(D, B, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B)) | (~((~in(tptp_fun_D_1(C, B, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B, A!10), C)) | (~((~disjoint(B, tptp_fun_E_2(C, B, A!10))) | (~in(tptp_fun_D_1(C, B, A!10), tptp_fun_E_2(C, B, A!10))) | (~open_subset(tptp_fun_E_2(C, B, A!10), A!10)) | (~element(tptp_fun_E_2(C, B, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B, E)) | (~open_subset(E, A!10)) | (~in(tptp_fun_D_1(C, B, A!10), E))))))))))))))),
% 22.65/22.90 inference(rewrite,[status(thm)],[])).
% 22.65/22.90 tff(65,plain,
% 22.65/22.90 (((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))))))))))))) | ((~top_str(A!10)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A!10), powerset(the_carrier(A!10)))) | (~open_subset(tptp_fun_E_0(D, B, A!10), A!10)) | (~in(D, tptp_fun_E_0(D, B, A!10))) | (~disjoint(B, tptp_fun_E_0(D, B, A!10)))))))))))) | (~((C = topstr_closure(A!10, B)) | (~((~in(tptp_fun_D_1(C, B, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B, A!10), C)) | (~((~element(tptp_fun_E_2(C, B, A!10), powerset(the_carrier(A!10)))) | (~open_subset(tptp_fun_E_2(C, B, A!10), A!10)) | (~in(tptp_fun_D_1(C, B, A!10), tptp_fun_E_2(C, B, A!10))) | (~disjoint(B, tptp_fun_E_2(C, B, A!10))))))) | (~(in(tptp_fun_D_1(C, B, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~in(tptp_fun_D_1(C, B, A!10), E)) | (~disjoint(B, E))))))))))))))) <=> ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))))))))))))) | ((~top_str(A!10)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B, E)) | (~open_subset(E, A!10))))) | (~(in(D, C) | (~((~disjoint(B, tptp_fun_E_0(D, B, A!10))) | (~in(D, tptp_fun_E_0(D, B, A!10))) | (~open_subset(tptp_fun_E_0(D, B, A!10), A!10)) | (~element(tptp_fun_E_0(D, B, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B)) | (~((~in(tptp_fun_D_1(C, B, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B, A!10), C)) | (~((~disjoint(B, tptp_fun_E_2(C, B, A!10))) | (~in(tptp_fun_D_1(C, B, A!10), tptp_fun_E_2(C, B, A!10))) | (~open_subset(tptp_fun_E_2(C, B, A!10), A!10)) | (~element(tptp_fun_E_2(C, B, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B, E)) | (~open_subset(E, A!10)) | (~in(tptp_fun_D_1(C, B, A!10), E)))))))))))))))),
% 22.65/22.90 inference(monotonicity,[status(thm)],[64])).
% 22.65/22.90 tff(66,plain,
% 22.65/22.90 (((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))))))))))))) | ((~top_str(A!10)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A!10), powerset(the_carrier(A!10)))) | (~open_subset(tptp_fun_E_0(D, B, A!10), A!10)) | (~in(D, tptp_fun_E_0(D, B, A!10))) | (~disjoint(B, tptp_fun_E_0(D, B, A!10)))))))))))) | (~((C = topstr_closure(A!10, B)) | (~((~in(tptp_fun_D_1(C, B, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B, A!10), C)) | (~((~element(tptp_fun_E_2(C, B, A!10), powerset(the_carrier(A!10)))) | (~open_subset(tptp_fun_E_2(C, B, A!10), A!10)) | (~in(tptp_fun_D_1(C, B, A!10), tptp_fun_E_2(C, B, A!10))) | (~disjoint(B, tptp_fun_E_2(C, B, A!10))))))) | (~(in(tptp_fun_D_1(C, B, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~in(tptp_fun_D_1(C, B, A!10), E)) | (~disjoint(B, E))))))))))))))) <=> ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))))))))))))) | (~top_str(A!10)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B, E)) | (~open_subset(E, A!10))))) | (~(in(D, C) | (~((~disjoint(B, tptp_fun_E_0(D, B, A!10))) | (~in(D, tptp_fun_E_0(D, B, A!10))) | (~open_subset(tptp_fun_E_0(D, B, A!10), A!10)) | (~element(tptp_fun_E_0(D, B, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B)) | (~((~in(tptp_fun_D_1(C, B, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B, A!10), C)) | (~((~disjoint(B, tptp_fun_E_2(C, B, A!10))) | (~in(tptp_fun_D_1(C, B, A!10), tptp_fun_E_2(C, B, A!10))) | (~open_subset(tptp_fun_E_2(C, B, A!10), A!10)) | (~element(tptp_fun_E_2(C, B, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B, E)) | (~open_subset(E, A!10)) | (~in(tptp_fun_D_1(C, B, A!10), E))))))))))))))),
% 22.65/22.90 inference(transitivity,[status(thm)],[65, 63])).
% 22.65/22.90 tff(67,plain,
% 22.65/22.90 ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))))))))))))) | ((~top_str(A!10)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A!10), powerset(the_carrier(A!10)))) | (~open_subset(tptp_fun_E_0(D, B, A!10), A!10)) | (~in(D, tptp_fun_E_0(D, B, A!10))) | (~disjoint(B, tptp_fun_E_0(D, B, A!10)))))))))))) | (~((C = topstr_closure(A!10, B)) | (~((~in(tptp_fun_D_1(C, B, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B, A!10), C)) | (~((~element(tptp_fun_E_2(C, B, A!10), powerset(the_carrier(A!10)))) | (~open_subset(tptp_fun_E_2(C, B, A!10), A!10)) | (~in(tptp_fun_D_1(C, B, A!10), tptp_fun_E_2(C, B, A!10))) | (~disjoint(B, tptp_fun_E_2(C, B, A!10))))))) | (~(in(tptp_fun_D_1(C, B, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~in(tptp_fun_D_1(C, B, A!10), E)) | (~disjoint(B, E))))))))))))))),
% 22.65/22.90 inference(quant_inst,[status(thm)],[])).
% 22.65/22.90 tff(68,plain,
% 22.65/22.90 ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))))))))))))) | (~top_str(A!10)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B, E)) | (~open_subset(E, A!10))))) | (~(in(D, C) | (~((~disjoint(B, tptp_fun_E_0(D, B, A!10))) | (~in(D, tptp_fun_E_0(D, B, A!10))) | (~open_subset(tptp_fun_E_0(D, B, A!10), A!10)) | (~element(tptp_fun_E_0(D, B, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B)) | (~((~in(tptp_fun_D_1(C, B, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B, A!10), C)) | (~((~disjoint(B, tptp_fun_E_2(C, B, A!10))) | (~in(tptp_fun_D_1(C, B, A!10), tptp_fun_E_2(C, B, A!10))) | (~open_subset(tptp_fun_E_2(C, B, A!10), A!10)) | (~element(tptp_fun_E_2(C, B, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B, E)) | (~open_subset(E, A!10)) | (~in(tptp_fun_D_1(C, B, A!10), E)))))))))))))),
% 22.65/22.90 inference(modus_ponens,[status(thm)],[67, 66])).
% 22.65/22.90 tff(69,plain,
% 22.65/22.90 (![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B, E)) | (~open_subset(E, A!10))))) | (~(in(D, C) | (~((~disjoint(B, tptp_fun_E_0(D, B, A!10))) | (~in(D, tptp_fun_E_0(D, B, A!10))) | (~open_subset(tptp_fun_E_0(D, B, A!10), A!10)) | (~element(tptp_fun_E_0(D, B, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B)) | (~((~in(tptp_fun_D_1(C, B, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B, A!10), C)) | (~((~disjoint(B, tptp_fun_E_2(C, B, A!10))) | (~in(tptp_fun_D_1(C, B, A!10), tptp_fun_E_2(C, B, A!10))) | (~open_subset(tptp_fun_E_2(C, B, A!10), A!10)) | (~element(tptp_fun_E_2(C, B, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B, E)) | (~open_subset(E, A!10)) | (~in(tptp_fun_D_1(C, B, A!10), E)))))))))))))),
% 22.65/22.90 inference(unit_resolution,[status(thm)],[68, 62, 20])).
% 22.65/22.90 tff(70,plain,
% 22.65/22.90 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B, E)) | (~open_subset(E, A!10))))) | (~(in(D, C) | (~((~disjoint(B, tptp_fun_E_0(D, B, A!10))) | (~in(D, tptp_fun_E_0(D, B, A!10))) | (~open_subset(tptp_fun_E_0(D, B, A!10), A!10)) | (~element(tptp_fun_E_0(D, B, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B)) | (~((~in(tptp_fun_D_1(C, B, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B, A!10), C)) | (~((~disjoint(B, tptp_fun_E_2(C, B, A!10))) | (~in(tptp_fun_D_1(C, B, A!10), tptp_fun_E_2(C, B, A!10))) | (~open_subset(tptp_fun_E_2(C, B, A!10), A!10)) | (~element(tptp_fun_E_2(C, B, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B, E)) | (~open_subset(E, A!10)) | (~in(tptp_fun_D_1(C, B, A!10), E)))))))))))))) | ((~element(B!11, powerset(the_carrier(A!10)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B!11))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, C) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B!11)) | (~((~in(tptp_fun_D_1(C, B!11, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B!11, A!10), C)) | (~((~disjoint(B!11, tptp_fun_E_2(C, B!11, A!10))) | (~in(tptp_fun_D_1(C, B!11, A!10), tptp_fun_E_2(C, B!11, A!10))) | (~open_subset(tptp_fun_E_2(C, B!11, A!10), A!10)) | (~element(tptp_fun_E_2(C, B!11, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B!11, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(tptp_fun_D_1(C, B!11, A!10), E)))))))))))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B, E)) | (~open_subset(E, A!10))))) | (~(in(D, C) | (~((~disjoint(B, tptp_fun_E_0(D, B, A!10))) | (~in(D, tptp_fun_E_0(D, B, A!10))) | (~open_subset(tptp_fun_E_0(D, B, A!10), A!10)) | (~element(tptp_fun_E_0(D, B, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B)) | (~((~in(tptp_fun_D_1(C, B, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B, A!10), C)) | (~((~disjoint(B, tptp_fun_E_2(C, B, A!10))) | (~in(tptp_fun_D_1(C, B, A!10), tptp_fun_E_2(C, B, A!10))) | (~open_subset(tptp_fun_E_2(C, B, A!10), A!10)) | (~element(tptp_fun_E_2(C, B, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B, E)) | (~open_subset(E, A!10)) | (~in(tptp_fun_D_1(C, B, A!10), E)))))))))))))) | (~element(B!11, powerset(the_carrier(A!10)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B!11))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, C) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B!11)) | (~((~in(tptp_fun_D_1(C, B!11, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B!11, A!10), C)) | (~((~disjoint(B!11, tptp_fun_E_2(C, B!11, A!10))) | (~in(tptp_fun_D_1(C, B!11, A!10), tptp_fun_E_2(C, B!11, A!10))) | (~open_subset(tptp_fun_E_2(C, B!11, A!10), A!10)) | (~element(tptp_fun_E_2(C, B!11, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B!11, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(tptp_fun_D_1(C, B!11, A!10), E)))))))))))))),
% 22.74/22.91 inference(rewrite,[status(thm)],[])).
% 22.74/22.91 tff(71,plain,
% 22.74/22.91 (((~element(B!11, powerset(the_carrier(A!10)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B!11))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B!11, E)) | (~open_subset(E, A!10))))) | (~(in(D, C) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B!11)) | (~((~in(tptp_fun_D_1(C, B!11, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B!11, A!10), C)) | (~((~disjoint(B!11, tptp_fun_E_2(C, B!11, A!10))) | (~in(tptp_fun_D_1(C, B!11, A!10), tptp_fun_E_2(C, B!11, A!10))) | (~open_subset(tptp_fun_E_2(C, B!11, A!10), A!10)) | (~element(tptp_fun_E_2(C, B!11, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B!11, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B!11, E)) | (~open_subset(E, A!10)) | (~in(tptp_fun_D_1(C, B!11, A!10), E))))))))))))) <=> ((~element(B!11, powerset(the_carrier(A!10)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B!11))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, C) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B!11)) | (~((~in(tptp_fun_D_1(C, B!11, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B!11, A!10), C)) | (~((~disjoint(B!11, tptp_fun_E_2(C, B!11, A!10))) | (~in(tptp_fun_D_1(C, B!11, A!10), tptp_fun_E_2(C, B!11, A!10))) | (~open_subset(tptp_fun_E_2(C, B!11, A!10), A!10)) | (~element(tptp_fun_E_2(C, B!11, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B!11, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(tptp_fun_D_1(C, B!11, A!10), E)))))))))))))),
% 22.74/22.91 inference(rewrite,[status(thm)],[])).
% 22.74/22.91 tff(72,plain,
% 22.74/22.91 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B, E)) | (~open_subset(E, A!10))))) | (~(in(D, C) | (~((~disjoint(B, tptp_fun_E_0(D, B, A!10))) | (~in(D, tptp_fun_E_0(D, B, A!10))) | (~open_subset(tptp_fun_E_0(D, B, A!10), A!10)) | (~element(tptp_fun_E_0(D, B, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B)) | (~((~in(tptp_fun_D_1(C, B, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B, A!10), C)) | (~((~disjoint(B, tptp_fun_E_2(C, B, A!10))) | (~in(tptp_fun_D_1(C, B, A!10), tptp_fun_E_2(C, B, A!10))) | (~open_subset(tptp_fun_E_2(C, B, A!10), A!10)) | (~element(tptp_fun_E_2(C, B, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B, E)) | (~open_subset(E, A!10)) | (~in(tptp_fun_D_1(C, B, A!10), E)))))))))))))) | ((~element(B!11, powerset(the_carrier(A!10)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B!11))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B!11, E)) | (~open_subset(E, A!10))))) | (~(in(D, C) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B!11)) | (~((~in(tptp_fun_D_1(C, B!11, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B!11, A!10), C)) | (~((~disjoint(B!11, tptp_fun_E_2(C, B!11, A!10))) | (~in(tptp_fun_D_1(C, B!11, A!10), tptp_fun_E_2(C, B!11, A!10))) | (~open_subset(tptp_fun_E_2(C, B!11, A!10), A!10)) | (~element(tptp_fun_E_2(C, B!11, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B!11, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B!11, E)) | (~open_subset(E, A!10)) | (~in(tptp_fun_D_1(C, B!11, A!10), E)))))))))))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B, E)) | (~open_subset(E, A!10))))) | (~(in(D, C) | (~((~disjoint(B, tptp_fun_E_0(D, B, A!10))) | (~in(D, tptp_fun_E_0(D, B, A!10))) | (~open_subset(tptp_fun_E_0(D, B, A!10), A!10)) | (~element(tptp_fun_E_0(D, B, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B)) | (~((~in(tptp_fun_D_1(C, B, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B, A!10), C)) | (~((~disjoint(B, tptp_fun_E_2(C, B, A!10))) | (~in(tptp_fun_D_1(C, B, A!10), tptp_fun_E_2(C, B, A!10))) | (~open_subset(tptp_fun_E_2(C, B, A!10), A!10)) | (~element(tptp_fun_E_2(C, B, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B, E)) | (~open_subset(E, A!10)) | (~in(tptp_fun_D_1(C, B, A!10), E)))))))))))))) | ((~element(B!11, powerset(the_carrier(A!10)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B!11))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, C) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B!11)) | (~((~in(tptp_fun_D_1(C, B!11, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B!11, A!10), C)) | (~((~disjoint(B!11, tptp_fun_E_2(C, B!11, A!10))) | (~in(tptp_fun_D_1(C, B!11, A!10), tptp_fun_E_2(C, B!11, A!10))) | (~open_subset(tptp_fun_E_2(C, B!11, A!10), A!10)) | (~element(tptp_fun_E_2(C, B!11, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B!11, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(tptp_fun_D_1(C, B!11, A!10), E))))))))))))))),
% 22.74/22.91 inference(monotonicity,[status(thm)],[71])).
% 22.74/22.91 tff(73,plain,
% 22.74/22.91 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B, E)) | (~open_subset(E, A!10))))) | (~(in(D, C) | (~((~disjoint(B, tptp_fun_E_0(D, B, A!10))) | (~in(D, tptp_fun_E_0(D, B, A!10))) | (~open_subset(tptp_fun_E_0(D, B, A!10), A!10)) | (~element(tptp_fun_E_0(D, B, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B)) | (~((~in(tptp_fun_D_1(C, B, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B, A!10), C)) | (~((~disjoint(B, tptp_fun_E_2(C, B, A!10))) | (~in(tptp_fun_D_1(C, B, A!10), tptp_fun_E_2(C, B, A!10))) | (~open_subset(tptp_fun_E_2(C, B, A!10), A!10)) | (~element(tptp_fun_E_2(C, B, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B, E)) | (~open_subset(E, A!10)) | (~in(tptp_fun_D_1(C, B, A!10), E)))))))))))))) | ((~element(B!11, powerset(the_carrier(A!10)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B!11))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B!11, E)) | (~open_subset(E, A!10))))) | (~(in(D, C) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B!11)) | (~((~in(tptp_fun_D_1(C, B!11, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B!11, A!10), C)) | (~((~disjoint(B!11, tptp_fun_E_2(C, B!11, A!10))) | (~in(tptp_fun_D_1(C, B!11, A!10), tptp_fun_E_2(C, B!11, A!10))) | (~open_subset(tptp_fun_E_2(C, B!11, A!10), A!10)) | (~element(tptp_fun_E_2(C, B!11, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B!11, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B!11, E)) | (~open_subset(E, A!10)) | (~in(tptp_fun_D_1(C, B!11, A!10), E)))))))))))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B, E)) | (~open_subset(E, A!10))))) | (~(in(D, C) | (~((~disjoint(B, tptp_fun_E_0(D, B, A!10))) | (~in(D, tptp_fun_E_0(D, B, A!10))) | (~open_subset(tptp_fun_E_0(D, B, A!10), A!10)) | (~element(tptp_fun_E_0(D, B, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B)) | (~((~in(tptp_fun_D_1(C, B, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B, A!10), C)) | (~((~disjoint(B, tptp_fun_E_2(C, B, A!10))) | (~in(tptp_fun_D_1(C, B, A!10), tptp_fun_E_2(C, B, A!10))) | (~open_subset(tptp_fun_E_2(C, B, A!10), A!10)) | (~element(tptp_fun_E_2(C, B, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B, E)) | (~open_subset(E, A!10)) | (~in(tptp_fun_D_1(C, B, A!10), E)))))))))))))) | (~element(B!11, powerset(the_carrier(A!10)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B!11))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, C) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B!11)) | (~((~in(tptp_fun_D_1(C, B!11, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B!11, A!10), C)) | (~((~disjoint(B!11, tptp_fun_E_2(C, B!11, A!10))) | (~in(tptp_fun_D_1(C, B!11, A!10), tptp_fun_E_2(C, B!11, A!10))) | (~open_subset(tptp_fun_E_2(C, B!11, A!10), A!10)) | (~element(tptp_fun_E_2(C, B!11, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B!11, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(tptp_fun_D_1(C, B!11, A!10), E)))))))))))))),
% 22.74/22.91 inference(transitivity,[status(thm)],[72, 70])).
% 22.74/22.91 tff(74,plain,
% 22.74/22.91 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B, E)) | (~open_subset(E, A!10))))) | (~(in(D, C) | (~((~disjoint(B, tptp_fun_E_0(D, B, A!10))) | (~in(D, tptp_fun_E_0(D, B, A!10))) | (~open_subset(tptp_fun_E_0(D, B, A!10), A!10)) | (~element(tptp_fun_E_0(D, B, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B)) | (~((~in(tptp_fun_D_1(C, B, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B, A!10), C)) | (~((~disjoint(B, tptp_fun_E_2(C, B, A!10))) | (~in(tptp_fun_D_1(C, B, A!10), tptp_fun_E_2(C, B, A!10))) | (~open_subset(tptp_fun_E_2(C, B, A!10), A!10)) | (~element(tptp_fun_E_2(C, B, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B, E)) | (~open_subset(E, A!10)) | (~in(tptp_fun_D_1(C, B, A!10), E)))))))))))))) | ((~element(B!11, powerset(the_carrier(A!10)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B!11))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B!11, E)) | (~open_subset(E, A!10))))) | (~(in(D, C) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B!11)) | (~((~in(tptp_fun_D_1(C, B!11, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B!11, A!10), C)) | (~((~disjoint(B!11, tptp_fun_E_2(C, B!11, A!10))) | (~in(tptp_fun_D_1(C, B!11, A!10), tptp_fun_E_2(C, B!11, A!10))) | (~open_subset(tptp_fun_E_2(C, B!11, A!10), A!10)) | (~element(tptp_fun_E_2(C, B!11, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B!11, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B!11, E)) | (~open_subset(E, A!10)) | (~in(tptp_fun_D_1(C, B!11, A!10), E)))))))))))))),
% 22.74/22.91 inference(quant_inst,[status(thm)],[])).
% 22.74/22.91 tff(75,plain,
% 22.74/22.91 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B, E)) | (~open_subset(E, A!10))))) | (~(in(D, C) | (~((~disjoint(B, tptp_fun_E_0(D, B, A!10))) | (~in(D, tptp_fun_E_0(D, B, A!10))) | (~open_subset(tptp_fun_E_0(D, B, A!10), A!10)) | (~element(tptp_fun_E_0(D, B, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B)) | (~((~in(tptp_fun_D_1(C, B, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B, A!10), C)) | (~((~disjoint(B, tptp_fun_E_2(C, B, A!10))) | (~in(tptp_fun_D_1(C, B, A!10), tptp_fun_E_2(C, B, A!10))) | (~open_subset(tptp_fun_E_2(C, B, A!10), A!10)) | (~element(tptp_fun_E_2(C, B, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~disjoint(B, E)) | (~open_subset(E, A!10)) | (~in(tptp_fun_D_1(C, B, A!10), E)))))))))))))) | (~element(B!11, powerset(the_carrier(A!10)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B!11))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, C) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B!11)) | (~((~in(tptp_fun_D_1(C, B!11, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B!11, A!10), C)) | (~((~disjoint(B!11, tptp_fun_E_2(C, B!11, A!10))) | (~in(tptp_fun_D_1(C, B!11, A!10), tptp_fun_E_2(C, B!11, A!10))) | (~open_subset(tptp_fun_E_2(C, B!11, A!10), A!10)) | (~element(tptp_fun_E_2(C, B!11, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B!11, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(tptp_fun_D_1(C, B!11, A!10), E))))))))))))),
% 22.74/22.91 inference(modus_ponens,[status(thm)],[74, 73])).
% 22.74/22.91 tff(76,plain,
% 22.74/22.91 (![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B!11))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, C) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B!11)) | (~((~in(tptp_fun_D_1(C, B!11, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B!11, A!10), C)) | (~((~disjoint(B!11, tptp_fun_E_2(C, B!11, A!10))) | (~in(tptp_fun_D_1(C, B!11, A!10), tptp_fun_E_2(C, B!11, A!10))) | (~open_subset(tptp_fun_E_2(C, B!11, A!10), A!10)) | (~element(tptp_fun_E_2(C, B!11, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B!11, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(tptp_fun_D_1(C, B!11, A!10), E))))))))))))),
% 22.74/22.91 inference(unit_resolution,[status(thm)],[75, 19, 69])).
% 22.74/22.91 tff(77,plain,
% 22.74/22.91 (((~![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B!11))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, C) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B!11)) | (~((~in(tptp_fun_D_1(C, B!11, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B!11, A!10), C)) | (~((~disjoint(B!11, tptp_fun_E_2(C, B!11, A!10))) | (~in(tptp_fun_D_1(C, B!11, A!10), tptp_fun_E_2(C, B!11, A!10))) | (~open_subset(tptp_fun_E_2(C, B!11, A!10), A!10)) | (~element(tptp_fun_E_2(C, B!11, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B!11, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(tptp_fun_D_1(C, B!11, A!10), E))))))))))))) | ((~element(topstr_closure(A!10, B!11), powerset(the_carrier(A!10)))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, topstr_closure(A!10, B!11))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10))))))))))))) <=> ((~![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B!11))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, C) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B!11)) | (~((~in(tptp_fun_D_1(C, B!11, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B!11, A!10), C)) | (~((~disjoint(B!11, tptp_fun_E_2(C, B!11, A!10))) | (~in(tptp_fun_D_1(C, B!11, A!10), tptp_fun_E_2(C, B!11, A!10))) | (~open_subset(tptp_fun_E_2(C, B!11, A!10), A!10)) | (~element(tptp_fun_E_2(C, B!11, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B!11, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(tptp_fun_D_1(C, B!11, A!10), E))))))))))))) | (~element(topstr_closure(A!10, B!11), powerset(the_carrier(A!10)))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, topstr_closure(A!10, B!11))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10))))))))))))),
% 22.74/22.91 inference(rewrite,[status(thm)],[])).
% 22.74/22.91 tff(78,plain,
% 22.74/22.91 (((~element(topstr_closure(A!10, B!11), powerset(the_carrier(A!10)))) | (~((~((~(topstr_closure(A!10, B!11) = topstr_closure(A!10, B!11))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, topstr_closure(A!10, B!11))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10))))))))))))) | (~((topstr_closure(A!10, B!11) = topstr_closure(A!10, B!11)) | (~((~in(tptp_fun_D_1(topstr_closure(A!10, B!11), B!11, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(topstr_closure(A!10, B!11), B!11, A!10), topstr_closure(A!10, B!11))) | (~((~disjoint(B!11, tptp_fun_E_2(topstr_closure(A!10, B!11), B!11, A!10))) | (~in(tptp_fun_D_1(topstr_closure(A!10, B!11), B!11, A!10), tptp_fun_E_2(topstr_closure(A!10, B!11), B!11, A!10))) | (~open_subset(tptp_fun_E_2(topstr_closure(A!10, B!11), B!11, A!10), A!10)) | (~element(tptp_fun_E_2(topstr_closure(A!10, B!11), B!11, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(topstr_closure(A!10, B!11), B!11, A!10), topstr_closure(A!10, B!11)) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(tptp_fun_D_1(topstr_closure(A!10, B!11), B!11, A!10), E)))))))))))) <=> ((~element(topstr_closure(A!10, B!11), powerset(the_carrier(A!10)))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, topstr_closure(A!10, B!11))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10))))))))))))),
% 22.74/22.91 inference(rewrite,[status(thm)],[])).
% 22.74/22.91 tff(79,plain,
% 22.74/22.91 (((~![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B!11))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, C) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B!11)) | (~((~in(tptp_fun_D_1(C, B!11, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B!11, A!10), C)) | (~((~disjoint(B!11, tptp_fun_E_2(C, B!11, A!10))) | (~in(tptp_fun_D_1(C, B!11, A!10), tptp_fun_E_2(C, B!11, A!10))) | (~open_subset(tptp_fun_E_2(C, B!11, A!10), A!10)) | (~element(tptp_fun_E_2(C, B!11, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B!11, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(tptp_fun_D_1(C, B!11, A!10), E))))))))))))) | ((~element(topstr_closure(A!10, B!11), powerset(the_carrier(A!10)))) | (~((~((~(topstr_closure(A!10, B!11) = topstr_closure(A!10, B!11))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, topstr_closure(A!10, B!11))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10))))))))))))) | (~((topstr_closure(A!10, B!11) = topstr_closure(A!10, B!11)) | (~((~in(tptp_fun_D_1(topstr_closure(A!10, B!11), B!11, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(topstr_closure(A!10, B!11), B!11, A!10), topstr_closure(A!10, B!11))) | (~((~disjoint(B!11, tptp_fun_E_2(topstr_closure(A!10, B!11), B!11, A!10))) | (~in(tptp_fun_D_1(topstr_closure(A!10, B!11), B!11, A!10), tptp_fun_E_2(topstr_closure(A!10, B!11), B!11, A!10))) | (~open_subset(tptp_fun_E_2(topstr_closure(A!10, B!11), B!11, A!10), A!10)) | (~element(tptp_fun_E_2(topstr_closure(A!10, B!11), B!11, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(topstr_closure(A!10, B!11), B!11, A!10), topstr_closure(A!10, B!11)) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(tptp_fun_D_1(topstr_closure(A!10, B!11), B!11, A!10), E))))))))))))) <=> ((~![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B!11))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, C) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B!11)) | (~((~in(tptp_fun_D_1(C, B!11, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B!11, A!10), C)) | (~((~disjoint(B!11, tptp_fun_E_2(C, B!11, A!10))) | (~in(tptp_fun_D_1(C, B!11, A!10), tptp_fun_E_2(C, B!11, A!10))) | (~open_subset(tptp_fun_E_2(C, B!11, A!10), A!10)) | (~element(tptp_fun_E_2(C, B!11, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B!11, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(tptp_fun_D_1(C, B!11, A!10), E))))))))))))) | ((~element(topstr_closure(A!10, B!11), powerset(the_carrier(A!10)))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, topstr_closure(A!10, B!11))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10)))))))))))))),
% 22.74/22.91 inference(monotonicity,[status(thm)],[78])).
% 22.74/22.91 tff(80,plain,
% 22.74/22.91 (((~![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B!11))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, C) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B!11)) | (~((~in(tptp_fun_D_1(C, B!11, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B!11, A!10), C)) | (~((~disjoint(B!11, tptp_fun_E_2(C, B!11, A!10))) | (~in(tptp_fun_D_1(C, B!11, A!10), tptp_fun_E_2(C, B!11, A!10))) | (~open_subset(tptp_fun_E_2(C, B!11, A!10), A!10)) | (~element(tptp_fun_E_2(C, B!11, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B!11, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(tptp_fun_D_1(C, B!11, A!10), E))))))))))))) | ((~element(topstr_closure(A!10, B!11), powerset(the_carrier(A!10)))) | (~((~((~(topstr_closure(A!10, B!11) = topstr_closure(A!10, B!11))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, topstr_closure(A!10, B!11))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10))))))))))))) | (~((topstr_closure(A!10, B!11) = topstr_closure(A!10, B!11)) | (~((~in(tptp_fun_D_1(topstr_closure(A!10, B!11), B!11, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(topstr_closure(A!10, B!11), B!11, A!10), topstr_closure(A!10, B!11))) | (~((~disjoint(B!11, tptp_fun_E_2(topstr_closure(A!10, B!11), B!11, A!10))) | (~in(tptp_fun_D_1(topstr_closure(A!10, B!11), B!11, A!10), tptp_fun_E_2(topstr_closure(A!10, B!11), B!11, A!10))) | (~open_subset(tptp_fun_E_2(topstr_closure(A!10, B!11), B!11, A!10), A!10)) | (~element(tptp_fun_E_2(topstr_closure(A!10, B!11), B!11, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(topstr_closure(A!10, B!11), B!11, A!10), topstr_closure(A!10, B!11)) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(tptp_fun_D_1(topstr_closure(A!10, B!11), B!11, A!10), E))))))))))))) <=> ((~![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B!11))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, C) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B!11)) | (~((~in(tptp_fun_D_1(C, B!11, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B!11, A!10), C)) | (~((~disjoint(B!11, tptp_fun_E_2(C, B!11, A!10))) | (~in(tptp_fun_D_1(C, B!11, A!10), tptp_fun_E_2(C, B!11, A!10))) | (~open_subset(tptp_fun_E_2(C, B!11, A!10), A!10)) | (~element(tptp_fun_E_2(C, B!11, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B!11, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(tptp_fun_D_1(C, B!11, A!10), E))))))))))))) | (~element(topstr_closure(A!10, B!11), powerset(the_carrier(A!10)))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, topstr_closure(A!10, B!11))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10))))))))))))),
% 22.74/22.92 inference(transitivity,[status(thm)],[79, 77])).
% 22.74/22.92 tff(81,plain,
% 22.74/22.92 ((~![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B!11))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, C) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B!11)) | (~((~in(tptp_fun_D_1(C, B!11, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B!11, A!10), C)) | (~((~disjoint(B!11, tptp_fun_E_2(C, B!11, A!10))) | (~in(tptp_fun_D_1(C, B!11, A!10), tptp_fun_E_2(C, B!11, A!10))) | (~open_subset(tptp_fun_E_2(C, B!11, A!10), A!10)) | (~element(tptp_fun_E_2(C, B!11, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B!11, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(tptp_fun_D_1(C, B!11, A!10), E))))))))))))) | ((~element(topstr_closure(A!10, B!11), powerset(the_carrier(A!10)))) | (~((~((~(topstr_closure(A!10, B!11) = topstr_closure(A!10, B!11))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, topstr_closure(A!10, B!11))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10))))))))))))) | (~((topstr_closure(A!10, B!11) = topstr_closure(A!10, B!11)) | (~((~in(tptp_fun_D_1(topstr_closure(A!10, B!11), B!11, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(topstr_closure(A!10, B!11), B!11, A!10), topstr_closure(A!10, B!11))) | (~((~disjoint(B!11, tptp_fun_E_2(topstr_closure(A!10, B!11), B!11, A!10))) | (~in(tptp_fun_D_1(topstr_closure(A!10, B!11), B!11, A!10), tptp_fun_E_2(topstr_closure(A!10, B!11), B!11, A!10))) | (~open_subset(tptp_fun_E_2(topstr_closure(A!10, B!11), B!11, A!10), A!10)) | (~element(tptp_fun_E_2(topstr_closure(A!10, B!11), B!11, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(topstr_closure(A!10, B!11), B!11, A!10), topstr_closure(A!10, B!11)) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(tptp_fun_D_1(topstr_closure(A!10, B!11), B!11, A!10), E))))))))))))),
% 22.74/22.92 inference(quant_inst,[status(thm)],[])).
% 22.74/22.92 tff(82,plain,
% 22.74/22.92 ((~![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (~((~((~(C = topstr_closure(A!10, B!11))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, C) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10))))))))))))) | (~((C = topstr_closure(A!10, B!11)) | (~((~in(tptp_fun_D_1(C, B!11, A!10), the_carrier(A!10))) | (~((~in(tptp_fun_D_1(C, B!11, A!10), C)) | (~((~disjoint(B!11, tptp_fun_E_2(C, B!11, A!10))) | (~in(tptp_fun_D_1(C, B!11, A!10), tptp_fun_E_2(C, B!11, A!10))) | (~open_subset(tptp_fun_E_2(C, B!11, A!10), A!10)) | (~element(tptp_fun_E_2(C, B!11, A!10), powerset(the_carrier(A!10)))))))) | (~(in(tptp_fun_D_1(C, B!11, A!10), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(tptp_fun_D_1(C, B!11, A!10), E))))))))))))) | (~element(topstr_closure(A!10, B!11), powerset(the_carrier(A!10)))) | ![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, topstr_closure(A!10, B!11))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10)))))))))))),
% 22.74/22.92 inference(modus_ponens,[status(thm)],[81, 80])).
% 22.74/22.92 tff(83,plain,
% 22.74/22.92 (![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, topstr_closure(A!10, B!11))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10)))))))))))),
% 22.74/22.92 inference(unit_resolution,[status(thm)],[82, 76, 40])).
% 22.74/22.92 tff(84,plain,
% 22.74/22.92 (in(C!12, the_carrier(A!10))),
% 22.74/22.92 inference(and_elim,[status(thm)],[18])).
% 22.74/22.92 tff(85,plain,
% 22.74/22.92 (((~![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, topstr_closure(A!10, B!11))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10)))))))))))) | ((~in(C!12, the_carrier(A!10))) | (~((~((~in(C!12, topstr_closure(A!10, B!11))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(C!12, E))))) | (~(in(C!12, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10))) | (~in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) | (~open_subset(tptp_fun_E_0(C!12, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))))))))))) <=> ((~![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, topstr_closure(A!10, B!11))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10)))))))))))) | (~in(C!12, the_carrier(A!10))) | (~((~((~in(C!12, topstr_closure(A!10, B!11))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(C!12, E))))) | (~(in(C!12, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10))) | (~in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) | (~open_subset(tptp_fun_E_0(C!12, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))))))))))),
% 22.74/22.92 inference(rewrite,[status(thm)],[])).
% 22.74/22.92 tff(86,plain,
% 22.74/22.92 (((~in(C!12, the_carrier(A!10))) | (~((~((~in(C!12, topstr_closure(A!10, B!11))) | ![E: $i] : ((~in(C!12, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(C!12, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10))) | (~in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) | (~open_subset(tptp_fun_E_0(C!12, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10))))))))))) <=> ((~in(C!12, the_carrier(A!10))) | (~((~((~in(C!12, topstr_closure(A!10, B!11))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(C!12, E))))) | (~(in(C!12, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10))) | (~in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) | (~open_subset(tptp_fun_E_0(C!12, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))))))))))),
% 22.74/22.92 inference(rewrite,[status(thm)],[])).
% 22.74/22.92 tff(87,plain,
% 22.74/22.92 (((~![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, topstr_closure(A!10, B!11))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10)))))))))))) | ((~in(C!12, the_carrier(A!10))) | (~((~((~in(C!12, topstr_closure(A!10, B!11))) | ![E: $i] : ((~in(C!12, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(C!12, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10))) | (~in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) | (~open_subset(tptp_fun_E_0(C!12, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))))))))))) <=> ((~![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, topstr_closure(A!10, B!11))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10)))))))))))) | ((~in(C!12, the_carrier(A!10))) | (~((~((~in(C!12, topstr_closure(A!10, B!11))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(C!12, E))))) | (~(in(C!12, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10))) | (~in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) | (~open_subset(tptp_fun_E_0(C!12, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10))))))))))))),
% 22.74/22.92 inference(monotonicity,[status(thm)],[86])).
% 22.74/22.92 tff(88,plain,
% 22.74/22.92 (((~![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, topstr_closure(A!10, B!11))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10)))))))))))) | ((~in(C!12, the_carrier(A!10))) | (~((~((~in(C!12, topstr_closure(A!10, B!11))) | ![E: $i] : ((~in(C!12, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(C!12, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10))) | (~in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) | (~open_subset(tptp_fun_E_0(C!12, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))))))))))) <=> ((~![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, topstr_closure(A!10, B!11))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10)))))))))))) | (~in(C!12, the_carrier(A!10))) | (~((~((~in(C!12, topstr_closure(A!10, B!11))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(C!12, E))))) | (~(in(C!12, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10))) | (~in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) | (~open_subset(tptp_fun_E_0(C!12, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))))))))))),
% 22.74/22.92 inference(transitivity,[status(thm)],[87, 85])).
% 22.74/22.92 tff(89,plain,
% 22.74/22.92 ((~![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, topstr_closure(A!10, B!11))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10)))))))))))) | ((~in(C!12, the_carrier(A!10))) | (~((~((~in(C!12, topstr_closure(A!10, B!11))) | ![E: $i] : ((~in(C!12, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(C!12, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10))) | (~in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) | (~open_subset(tptp_fun_E_0(C!12, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))))))))))),
% 22.74/22.92 inference(quant_inst,[status(thm)],[])).
% 22.74/22.92 tff(90,plain,
% 22.74/22.92 ((~![D: $i] : ((~in(D, the_carrier(A!10))) | (~((~((~in(D, topstr_closure(A!10, B!11))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E))))) | (~(in(D, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(D, B!11, A!10))) | (~in(D, tptp_fun_E_0(D, B!11, A!10))) | (~open_subset(tptp_fun_E_0(D, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(D, B!11, A!10), powerset(the_carrier(A!10)))))))))))) | (~in(C!12, the_carrier(A!10))) | (~((~((~in(C!12, topstr_closure(A!10, B!11))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(C!12, E))))) | (~(in(C!12, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10))) | (~in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) | (~open_subset(tptp_fun_E_0(C!12, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10))))))))))),
% 22.74/22.92 inference(modus_ponens,[status(thm)],[89, 88])).
% 22.74/22.92 tff(91,plain,
% 22.74/22.92 (~((~((~in(C!12, topstr_closure(A!10, B!11))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(C!12, E))))) | (~(in(C!12, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10))) | (~in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) | (~open_subset(tptp_fun_E_0(C!12, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))))))))),
% 22.74/22.92 inference(unit_resolution,[status(thm)],[90, 84, 83])).
% 22.74/22.92 tff(92,plain,
% 22.74/22.92 (((~((~in(C!12, topstr_closure(A!10, B!11))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(C!12, E))))) | (~(in(C!12, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10))) | (~in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) | (~open_subset(tptp_fun_E_0(C!12, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10))))))))) | (in(C!12, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10))) | (~in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) | (~open_subset(tptp_fun_E_0(C!12, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))))))),
% 22.74/22.92 inference(tautology,[status(thm)],[])).
% 22.74/22.92 tff(93,plain,
% 22.74/22.92 (in(C!12, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10))) | (~in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) | (~open_subset(tptp_fun_E_0(C!12, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10))))))),
% 22.74/22.92 inference(unit_resolution,[status(thm)],[92, 91])).
% 22.74/22.92 tff(94,assumption,(~(in(C!12, D!13) | (~element(D!13, powerset(the_carrier(A!10)))) | (~closed_subset(D!13, A!10)) | (~subset(B!11, D!13)))), introduced(assumption)).
% 22.74/22.92 tff(95,plain,
% 22.74/22.92 ((in(C!12, D!13) | (~element(D!13, powerset(the_carrier(A!10)))) | (~closed_subset(D!13, A!10)) | (~subset(B!11, D!13))) | subset(B!11, D!13)),
% 22.74/22.92 inference(tautology,[status(thm)],[])).
% 22.74/22.92 tff(96,plain,
% 22.74/22.92 (subset(B!11, D!13)),
% 22.74/22.92 inference(unit_resolution,[status(thm)],[95, 94])).
% 22.74/22.92 tff(97,plain,
% 22.74/22.92 ((in(C!12, D!13) | (~element(D!13, powerset(the_carrier(A!10)))) | (~closed_subset(D!13, A!10)) | (~subset(B!11, D!13))) | closed_subset(D!13, A!10)),
% 22.74/22.92 inference(tautology,[status(thm)],[])).
% 22.74/22.92 tff(98,plain,
% 22.74/22.92 (closed_subset(D!13, A!10)),
% 22.74/22.92 inference(unit_resolution,[status(thm)],[97, 94])).
% 22.74/22.92 tff(99,plain,
% 22.74/22.92 ((in(C!12, D!13) | (~element(D!13, powerset(the_carrier(A!10)))) | (~closed_subset(D!13, A!10)) | (~subset(B!11, D!13))) | element(D!13, powerset(the_carrier(A!10)))),
% 22.74/22.92 inference(tautology,[status(thm)],[])).
% 22.74/22.92 tff(100,plain,
% 22.74/22.92 (element(D!13, powerset(the_carrier(A!10)))),
% 22.74/22.92 inference(unit_resolution,[status(thm)],[99, 94])).
% 22.74/22.92 tff(101,plain,
% 22.74/22.92 ((in(C!12, D!13) | (~element(D!13, powerset(the_carrier(A!10)))) | (~closed_subset(D!13, A!10)) | (~subset(B!11, D!13))) | (~in(C!12, D!13))),
% 22.74/22.92 inference(tautology,[status(thm)],[])).
% 22.74/22.92 tff(102,plain,
% 22.74/22.92 (~in(C!12, D!13)),
% 22.74/22.92 inference(unit_resolution,[status(thm)],[101, 94])).
% 22.74/22.92 tff(103,plain,
% 22.74/22.92 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C)))))) <=> (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C)))))))),
% 22.74/22.92 inference(bind,[status(th)],[])).
% 22.74/22.92 tff(104,plain,
% 22.74/22.92 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C))))))),
% 22.74/22.92 inference(quant_intro,[status(thm)],[103])).
% 22.74/22.92 tff(105,plain,
% 22.74/22.92 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C))))))),
% 22.74/22.92 inference(pull_quant,[status(thm)],[])).
% 22.74/22.92 tff(106,plain,
% 22.74/22.92 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))) <=> ![D: $i] : ((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) <=> (~![D: $i] : ((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))))), pull_quant((~![D: $i] : ((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))))), (((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C))))) <=> (?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C))))))), pull_quant((?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C)))))), (((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C))))))), ((~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C)))))) <=> (~?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C)))))))), pull_quant((~?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C))))))), ((~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C))))))))),
% 22.74/22.92 inference(bind,[status(th)],[])).
% 22.74/22.92 tff(107,plain,
% 22.74/22.92 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C))))))),
% 22.74/22.92 inference(quant_intro,[status(thm)],[106])).
% 22.74/22.92 tff(108,plain,
% 22.74/22.92 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C))))))),
% 22.74/22.92 inference(transitivity,[status(thm)],[107, 105])).
% 22.74/22.92 tff(109,plain,
% 22.74/22.92 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C))))))),
% 22.74/22.92 inference(transitivity,[status(thm)],[108, 104])).
% 22.74/22.92 tff(110,plain,
% 22.74/22.92 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C)))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C)))))))),
% 22.74/22.92 inference(bind,[status(th)],[])).
% 22.74/22.92 tff(111,plain,
% 22.74/22.92 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C))))))),
% 22.74/22.93 inference(quant_intro,[status(thm)],[110])).
% 22.74/22.93 tff(112,plain,
% 22.74/22.93 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C))))))),
% 22.74/22.93 inference(transitivity,[status(thm)],[111, 109])).
% 22.74/22.93 tff(113,plain,
% 22.74/22.93 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) <=> ((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))), rewrite(((C = set_difference(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) & (~in(tptp_fun_D_3(C, B, A), B)))))) <=> ((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C)))), ((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) & (~in(tptp_fun_D_3(C, B, A), B))))))) <=> (((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))) & ((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C)))))), rewrite((((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))) & ((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C)))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C))))))), ((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) & (~in(tptp_fun_D_3(C, B, A), B))))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C))))))))),
% 22.74/22.93 inference(bind,[status(th)],[])).
% 22.74/22.93 tff(114,plain,
% 22.74/22.93 (![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) & (~in(tptp_fun_D_3(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C))))))),
% 22.74/22.93 inference(quant_intro,[status(thm)],[113])).
% 22.74/22.93 tff(115,plain,
% 22.74/22.93 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) <=> ![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 22.74/22.93 inference(rewrite,[status(thm)],[])).
% 22.74/22.93 tff(116,axiom,(![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_xboole_0')).
% 22.74/22.93 tff(117,plain,
% 22.74/22.93 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 22.74/22.93 inference(modus_ponens,[status(thm)],[116, 115])).
% 22.74/22.93 tff(118,plain,(
% 22.74/22.93 ![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) & (~in(tptp_fun_D_3(C, B, A), B)))))))),
% 22.74/22.93 inference(skolemize,[status(sab)],[117])).
% 22.74/22.93 tff(119,plain,
% 22.74/22.93 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C))))))),
% 22.74/22.93 inference(modus_ponens,[status(thm)],[118, 114])).
% 22.74/22.93 tff(120,plain,
% 22.74/22.93 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C))))))),
% 22.74/22.93 inference(modus_ponens,[status(thm)],[119, 112])).
% 22.74/22.93 tff(121,plain,
% 22.74/22.93 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C))))))) | (~((~((~(D!13 = set_difference(the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)))) | (~(((~in(C!12, the_carrier(A!10))) | in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) <=> in(C!12, D!13))))) | (~((D!13 = set_difference(the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) | (((~in(tptp_fun_D_3(D!13, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), the_carrier(A!10)), the_carrier(A!10))) | in(tptp_fun_D_3(D!13, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), the_carrier(A!10)), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) <=> in(tptp_fun_D_3(D!13, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), the_carrier(A!10)), D!13))))))),
% 22.74/22.93 inference(quant_inst,[status(thm)],[])).
% 22.74/22.93 tff(122,plain,
% 22.74/22.93 (~((~((~(D!13 = set_difference(the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)))) | (~(((~in(C!12, the_carrier(A!10))) | in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) <=> in(C!12, D!13))))) | (~((D!13 = set_difference(the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) | (((~in(tptp_fun_D_3(D!13, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), the_carrier(A!10)), the_carrier(A!10))) | in(tptp_fun_D_3(D!13, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), the_carrier(A!10)), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) <=> in(tptp_fun_D_3(D!13, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), the_carrier(A!10)), D!13)))))),
% 22.74/22.93 inference(unit_resolution,[status(thm)],[121, 120])).
% 22.74/22.93 tff(123,plain,
% 22.74/22.93 (((~((~(D!13 = set_difference(the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)))) | (~(((~in(C!12, the_carrier(A!10))) | in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) <=> in(C!12, D!13))))) | (~((D!13 = set_difference(the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) | (((~in(tptp_fun_D_3(D!13, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), the_carrier(A!10)), the_carrier(A!10))) | in(tptp_fun_D_3(D!13, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), the_carrier(A!10)), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) <=> in(tptp_fun_D_3(D!13, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), the_carrier(A!10)), D!13))))) | ((~(D!13 = set_difference(the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)))) | (~(((~in(C!12, the_carrier(A!10))) | in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) <=> in(C!12, D!13))))),
% 22.74/22.93 inference(tautology,[status(thm)],[])).
% 22.74/22.93 tff(124,plain,
% 22.74/22.93 ((~(D!13 = set_difference(the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)))) | (~(((~in(C!12, the_carrier(A!10))) | in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) <=> in(C!12, D!13)))),
% 22.74/22.93 inference(unit_resolution,[status(thm)],[123, 122])).
% 22.74/22.93 tff(125,plain,
% 22.74/22.93 (^[A: $i] : refl((one_sorted_str(A) | (~top_str(A))) <=> (one_sorted_str(A) | (~top_str(A))))),
% 22.74/22.93 inference(bind,[status(th)],[])).
% 22.74/22.93 tff(126,plain,
% 22.74/22.93 (![A: $i] : (one_sorted_str(A) | (~top_str(A))) <=> ![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 22.74/22.93 inference(quant_intro,[status(thm)],[125])).
% 22.74/22.93 tff(127,plain,
% 22.74/22.93 (![A: $i] : (one_sorted_str(A) | (~top_str(A))) <=> ![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 22.74/22.93 inference(rewrite,[status(thm)],[])).
% 22.74/22.93 tff(128,plain,
% 22.74/22.93 (^[A: $i] : rewrite((top_str(A) => one_sorted_str(A)) <=> (one_sorted_str(A) | (~top_str(A))))),
% 22.74/22.93 inference(bind,[status(th)],[])).
% 22.74/22.93 tff(129,plain,
% 22.74/22.93 (![A: $i] : (top_str(A) => one_sorted_str(A)) <=> ![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 22.74/22.93 inference(quant_intro,[status(thm)],[128])).
% 22.74/22.93 tff(130,axiom,(![A: $i] : (top_str(A) => one_sorted_str(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l1_pre_topc')).
% 22.74/22.93 tff(131,plain,
% 22.74/22.93 (![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 22.74/22.93 inference(modus_ponens,[status(thm)],[130, 129])).
% 22.74/22.93 tff(132,plain,
% 22.74/22.93 (![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 22.74/22.93 inference(modus_ponens,[status(thm)],[131, 127])).
% 22.74/22.93 tff(133,plain,(
% 22.74/22.93 ![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 22.74/22.93 inference(skolemize,[status(sab)],[132])).
% 22.74/22.93 tff(134,plain,
% 22.74/22.93 (![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 22.74/22.93 inference(modus_ponens,[status(thm)],[133, 126])).
% 22.74/22.93 tff(135,plain,
% 22.74/22.93 (((~![A: $i] : (one_sorted_str(A) | (~top_str(A)))) | (one_sorted_str(A!10) | (~top_str(A!10)))) <=> ((~![A: $i] : (one_sorted_str(A) | (~top_str(A)))) | one_sorted_str(A!10) | (~top_str(A!10)))),
% 22.74/22.93 inference(rewrite,[status(thm)],[])).
% 22.74/22.93 tff(136,plain,
% 22.74/22.93 ((~![A: $i] : (one_sorted_str(A) | (~top_str(A)))) | (one_sorted_str(A!10) | (~top_str(A!10)))),
% 22.74/22.93 inference(quant_inst,[status(thm)],[])).
% 22.74/22.93 tff(137,plain,
% 22.74/22.93 ((~![A: $i] : (one_sorted_str(A) | (~top_str(A)))) | one_sorted_str(A!10) | (~top_str(A!10))),
% 22.74/22.93 inference(modus_ponens,[status(thm)],[136, 135])).
% 22.74/22.93 tff(138,plain,
% 22.74/22.93 (one_sorted_str(A!10)),
% 22.74/22.93 inference(unit_resolution,[status(thm)],[137, 134, 20])).
% 22.74/22.93 tff(139,plain,
% 22.74/22.93 (^[A: $i] : refl(((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)))) <=> ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)))))),
% 22.74/22.93 inference(bind,[status(th)],[])).
% 22.74/22.93 tff(140,plain,
% 22.74/22.93 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)))) <=> ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))),
% 22.74/22.93 inference(quant_intro,[status(thm)],[139])).
% 22.74/22.93 tff(141,plain,
% 22.74/22.93 (^[A: $i] : rewrite(((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)))) <=> ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)))))),
% 22.74/22.93 inference(bind,[status(th)],[])).
% 22.74/22.93 tff(142,plain,
% 22.74/22.93 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)))) <=> ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))),
% 22.74/22.93 inference(quant_intro,[status(thm)],[141])).
% 22.74/22.93 tff(143,plain,
% 22.74/22.93 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)))) <=> ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))),
% 22.74/22.93 inference(transitivity,[status(thm)],[142, 140])).
% 22.74/22.93 tff(144,plain,
% 22.74/22.93 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)))) <=> ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))),
% 22.74/22.93 inference(rewrite,[status(thm)],[])).
% 22.74/22.93 tff(145,plain,
% 22.74/22.93 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((element(B, powerset(the_carrier(A))) => (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))) <=> ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))), (![B: $i] : (element(B, powerset(the_carrier(A))) => (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))) <=> ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))), ((one_sorted_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)))) <=> (one_sorted_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)))))), rewrite((one_sorted_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)))) <=> ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))), ((one_sorted_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)))) <=> ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))))),
% 22.74/22.93 inference(bind,[status(th)],[])).
% 22.74/22.93 tff(146,plain,
% 22.74/22.93 (![A: $i] : (one_sorted_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)))) <=> ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))),
% 22.74/22.93 inference(quant_intro,[status(thm)],[145])).
% 22.74/22.93 tff(147,axiom,(![A: $i] : (one_sorted_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t17_pre_topc')).
% 22.74/22.93 tff(148,plain,
% 22.74/22.93 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))),
% 22.74/22.93 inference(modus_ponens,[status(thm)],[147, 146])).
% 22.74/22.93 tff(149,plain,
% 22.74/22.93 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))),
% 22.74/22.93 inference(modus_ponens,[status(thm)],[148, 144])).
% 22.74/22.93 tff(150,plain,(
% 22.74/22.93 ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))),
% 22.74/22.93 inference(skolemize,[status(sab)],[149])).
% 22.74/22.93 tff(151,plain,
% 22.74/22.93 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))),
% 22.74/22.93 inference(modus_ponens,[status(thm)],[150, 143])).
% 22.74/22.93 tff(152,plain,
% 22.74/22.93 (((~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))) | ((~one_sorted_str(A!10)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (subset_complement(the_carrier(A!10), B) = subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B))))) <=> ((~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))) | (~one_sorted_str(A!10)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (subset_complement(the_carrier(A!10), B) = subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B))))),
% 22.74/22.93 inference(rewrite,[status(thm)],[])).
% 22.74/22.93 tff(153,plain,
% 22.74/22.93 ((~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))) | ((~one_sorted_str(A!10)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (subset_complement(the_carrier(A!10), B) = subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B))))),
% 22.74/22.93 inference(quant_inst,[status(thm)],[])).
% 22.74/22.93 tff(154,plain,
% 22.74/22.93 ((~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_complement(the_carrier(A), B) = subset_difference(the_carrier(A), cast_as_carrier_subset(A), B))))) | (~one_sorted_str(A!10)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (subset_complement(the_carrier(A!10), B) = subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B)))),
% 22.74/22.93 inference(modus_ponens,[status(thm)],[153, 152])).
% 22.74/22.93 tff(155,plain,
% 22.74/22.93 (![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (subset_complement(the_carrier(A!10), B) = subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B)))),
% 22.74/22.93 inference(unit_resolution,[status(thm)],[154, 151, 138])).
% 22.74/22.93 tff(156,plain,
% 22.74/22.93 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (subset_complement(the_carrier(A!10), B) = subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B)))) | ((~element(D!13, powerset(the_carrier(A!10)))) | (subset_complement(the_carrier(A!10), D!13) = subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (subset_complement(the_carrier(A!10), B) = subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B)))) | (~element(D!13, powerset(the_carrier(A!10)))) | (subset_complement(the_carrier(A!10), D!13) = subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)))),
% 22.74/22.93 inference(rewrite,[status(thm)],[])).
% 22.74/22.93 tff(157,plain,
% 22.74/22.93 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (subset_complement(the_carrier(A!10), B) = subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B)))) | ((~element(D!13, powerset(the_carrier(A!10)))) | (subset_complement(the_carrier(A!10), D!13) = subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)))),
% 22.74/22.93 inference(quant_inst,[status(thm)],[])).
% 22.74/22.93 tff(158,plain,
% 22.74/22.93 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (subset_complement(the_carrier(A!10), B) = subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B)))) | (~element(D!13, powerset(the_carrier(A!10)))) | (subset_complement(the_carrier(A!10), D!13) = subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))),
% 22.74/22.93 inference(modus_ponens,[status(thm)],[157, 156])).
% 22.74/22.93 tff(159,plain,
% 22.74/22.93 (subset_complement(the_carrier(A!10), D!13) = subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)),
% 22.74/22.93 inference(unit_resolution,[status(thm)],[158, 100, 155])).
% 22.74/22.93 tff(160,plain,
% 22.74/22.93 (element(subset_complement(the_carrier(A!10), D!13), powerset(the_carrier(A!10))) <=> element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(the_carrier(A!10)))),
% 22.74/22.93 inference(monotonicity,[status(thm)],[159])).
% 22.74/22.93 tff(161,plain,
% 22.74/22.93 (^[A: $i, B: $i] : refl(((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A))) <=> ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A))))),
% 22.74/22.93 inference(bind,[status(th)],[])).
% 22.74/22.93 tff(162,plain,
% 22.74/22.93 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 22.74/22.93 inference(quant_intro,[status(thm)],[161])).
% 22.74/22.93 tff(163,plain,
% 22.74/22.93 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 22.74/22.93 inference(rewrite,[status(thm)],[])).
% 22.74/22.93 tff(164,plain,
% 22.74/22.93 (^[A: $i, B: $i] : rewrite((element(B, powerset(A)) => element(subset_complement(A, B), powerset(A))) <=> ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A))))),
% 22.74/22.93 inference(bind,[status(th)],[])).
% 22.74/22.93 tff(165,plain,
% 22.74/22.93 (![A: $i, B: $i] : (element(B, powerset(A)) => element(subset_complement(A, B), powerset(A))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 22.74/22.93 inference(quant_intro,[status(thm)],[164])).
% 22.74/22.93 tff(166,axiom,(![A: $i, B: $i] : (element(B, powerset(A)) => element(subset_complement(A, B), powerset(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k3_subset_1')).
% 22.74/22.93 tff(167,plain,
% 22.74/22.93 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 22.74/22.93 inference(modus_ponens,[status(thm)],[166, 165])).
% 22.74/22.93 tff(168,plain,
% 22.74/22.93 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 22.74/22.93 inference(modus_ponens,[status(thm)],[167, 163])).
% 22.74/22.93 tff(169,plain,(
% 22.74/22.93 ![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 22.74/22.93 inference(skolemize,[status(sab)],[168])).
% 22.74/22.93 tff(170,plain,
% 22.74/22.93 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 22.74/22.93 inference(modus_ponens,[status(thm)],[169, 162])).
% 22.74/22.93 tff(171,plain,
% 22.74/22.93 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | ((~element(D!13, powerset(the_carrier(A!10)))) | element(subset_complement(the_carrier(A!10), D!13), powerset(the_carrier(A!10))))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | (~element(D!13, powerset(the_carrier(A!10)))) | element(subset_complement(the_carrier(A!10), D!13), powerset(the_carrier(A!10))))),
% 22.74/22.93 inference(rewrite,[status(thm)],[])).
% 22.74/22.93 tff(172,plain,
% 22.74/22.93 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | ((~element(D!13, powerset(the_carrier(A!10)))) | element(subset_complement(the_carrier(A!10), D!13), powerset(the_carrier(A!10))))),
% 22.74/22.93 inference(quant_inst,[status(thm)],[])).
% 22.74/22.93 tff(173,plain,
% 22.74/22.93 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | (~element(D!13, powerset(the_carrier(A!10)))) | element(subset_complement(the_carrier(A!10), D!13), powerset(the_carrier(A!10)))),
% 22.74/22.93 inference(modus_ponens,[status(thm)],[172, 171])).
% 22.74/22.93 tff(174,plain,
% 22.74/22.93 (element(subset_complement(the_carrier(A!10), D!13), powerset(the_carrier(A!10)))),
% 22.74/22.93 inference(unit_resolution,[status(thm)],[173, 170, 100])).
% 22.74/22.93 tff(175,plain,
% 22.74/22.93 (element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(the_carrier(A!10)))),
% 22.74/22.93 inference(modus_ponens,[status(thm)],[174, 160])).
% 22.74/22.93 tff(176,plain,
% 22.74/22.93 (^[A: $i] : refl(((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A))) <=> ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A))))),
% 22.74/22.93 inference(bind,[status(th)],[])).
% 22.74/22.93 tff(177,plain,
% 22.74/22.93 (![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A))) <=> ![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 22.74/22.93 inference(quant_intro,[status(thm)],[176])).
% 22.74/22.93 tff(178,plain,
% 22.74/22.93 (![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A))) <=> ![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 22.74/22.93 inference(rewrite,[status(thm)],[])).
% 22.74/22.93 tff(179,plain,
% 22.74/22.93 (^[A: $i] : rewrite((one_sorted_str(A) => (cast_as_carrier_subset(A) = the_carrier(A))) <=> ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A))))),
% 22.74/22.93 inference(bind,[status(th)],[])).
% 22.74/22.93 tff(180,plain,
% 22.74/22.93 (![A: $i] : (one_sorted_str(A) => (cast_as_carrier_subset(A) = the_carrier(A))) <=> ![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 22.74/22.93 inference(quant_intro,[status(thm)],[179])).
% 22.74/22.93 tff(181,axiom,(![A: $i] : (one_sorted_str(A) => (cast_as_carrier_subset(A) = the_carrier(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_pre_topc')).
% 22.74/22.93 tff(182,plain,
% 22.74/22.93 (![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 22.74/22.93 inference(modus_ponens,[status(thm)],[181, 180])).
% 22.74/22.93 tff(183,plain,
% 22.74/22.93 (![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 22.74/22.93 inference(modus_ponens,[status(thm)],[182, 178])).
% 22.74/22.93 tff(184,plain,(
% 22.74/22.93 ![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 22.74/22.93 inference(skolemize,[status(sab)],[183])).
% 22.74/22.93 tff(185,plain,
% 22.74/22.93 (![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))),
% 22.74/22.93 inference(modus_ponens,[status(thm)],[184, 177])).
% 22.74/22.93 tff(186,plain,
% 22.74/22.93 (((~![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))) | ((~one_sorted_str(A!10)) | (cast_as_carrier_subset(A!10) = the_carrier(A!10)))) <=> ((~![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))) | (~one_sorted_str(A!10)) | (cast_as_carrier_subset(A!10) = the_carrier(A!10)))),
% 22.74/22.93 inference(rewrite,[status(thm)],[])).
% 22.74/22.93 tff(187,plain,
% 22.74/22.93 ((~![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))) | ((~one_sorted_str(A!10)) | (cast_as_carrier_subset(A!10) = the_carrier(A!10)))),
% 22.74/22.93 inference(quant_inst,[status(thm)],[])).
% 22.74/22.93 tff(188,plain,
% 22.74/22.93 ((~![A: $i] : ((~one_sorted_str(A)) | (cast_as_carrier_subset(A) = the_carrier(A)))) | (~one_sorted_str(A!10)) | (cast_as_carrier_subset(A!10) = the_carrier(A!10))),
% 22.74/22.93 inference(modus_ponens,[status(thm)],[187, 186])).
% 22.74/22.93 tff(189,plain,
% 22.74/22.93 (cast_as_carrier_subset(A!10) = the_carrier(A!10)),
% 22.74/22.93 inference(unit_resolution,[status(thm)],[188, 185, 138])).
% 22.74/22.93 tff(190,plain,
% 22.74/22.93 (the_carrier(A!10) = cast_as_carrier_subset(A!10)),
% 22.74/22.93 inference(symmetry,[status(thm)],[189])).
% 22.74/22.93 tff(191,plain,
% 22.74/22.93 (element(the_carrier(A!10), powerset(the_carrier(A!10))) <=> element(cast_as_carrier_subset(A!10), powerset(the_carrier(A!10)))),
% 22.74/22.93 inference(monotonicity,[status(thm)],[190])).
% 22.74/22.93 tff(192,plain,
% 22.74/22.93 (element(cast_as_carrier_subset(A!10), powerset(the_carrier(A!10))) <=> element(the_carrier(A!10), powerset(the_carrier(A!10)))),
% 22.74/22.93 inference(symmetry,[status(thm)],[191])).
% 22.74/22.93 tff(193,plain,
% 22.74/22.93 (^[A: $i] : refl(((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A)))) <=> ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A)))))),
% 22.74/22.93 inference(bind,[status(th)],[])).
% 22.74/22.93 tff(194,plain,
% 22.74/22.93 (![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A)))) <=> ![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 22.74/22.93 inference(quant_intro,[status(thm)],[193])).
% 22.74/22.93 tff(195,plain,
% 22.74/22.93 (![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A)))) <=> ![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 22.74/22.93 inference(rewrite,[status(thm)],[])).
% 22.74/22.93 tff(196,plain,
% 22.74/22.93 (^[A: $i] : rewrite((one_sorted_str(A) => element(cast_as_carrier_subset(A), powerset(the_carrier(A)))) <=> ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A)))))),
% 22.74/22.93 inference(bind,[status(th)],[])).
% 22.74/22.93 tff(197,plain,
% 22.74/22.93 (![A: $i] : (one_sorted_str(A) => element(cast_as_carrier_subset(A), powerset(the_carrier(A)))) <=> ![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 22.74/22.93 inference(quant_intro,[status(thm)],[196])).
% 22.74/22.93 tff(198,axiom,(![A: $i] : (one_sorted_str(A) => element(cast_as_carrier_subset(A), powerset(the_carrier(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k2_pre_topc')).
% 22.74/22.93 tff(199,plain,
% 22.74/22.93 (![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 22.74/22.93 inference(modus_ponens,[status(thm)],[198, 197])).
% 22.74/22.93 tff(200,plain,
% 22.74/22.93 (![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 22.74/22.93 inference(modus_ponens,[status(thm)],[199, 195])).
% 22.74/22.93 tff(201,plain,(
% 22.74/22.93 ![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 22.74/22.93 inference(skolemize,[status(sab)],[200])).
% 22.74/22.93 tff(202,plain,
% 22.74/22.93 (![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))),
% 22.74/22.93 inference(modus_ponens,[status(thm)],[201, 194])).
% 22.74/22.93 tff(203,plain,
% 22.74/22.93 (((~![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))) | ((~one_sorted_str(A!10)) | element(cast_as_carrier_subset(A!10), powerset(the_carrier(A!10))))) <=> ((~![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))) | (~one_sorted_str(A!10)) | element(cast_as_carrier_subset(A!10), powerset(the_carrier(A!10))))),
% 22.74/22.93 inference(rewrite,[status(thm)],[])).
% 22.74/22.93 tff(204,plain,
% 22.74/22.93 ((~![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))) | ((~one_sorted_str(A!10)) | element(cast_as_carrier_subset(A!10), powerset(the_carrier(A!10))))),
% 22.74/22.93 inference(quant_inst,[status(thm)],[])).
% 22.74/22.93 tff(205,plain,
% 22.74/22.93 ((~![A: $i] : ((~one_sorted_str(A)) | element(cast_as_carrier_subset(A), powerset(the_carrier(A))))) | (~one_sorted_str(A!10)) | element(cast_as_carrier_subset(A!10), powerset(the_carrier(A!10)))),
% 22.74/22.93 inference(modus_ponens,[status(thm)],[204, 203])).
% 22.74/22.93 tff(206,plain,
% 22.74/22.93 (element(cast_as_carrier_subset(A!10), powerset(the_carrier(A!10)))),
% 22.74/22.93 inference(unit_resolution,[status(thm)],[205, 202, 138])).
% 22.74/22.93 tff(207,plain,
% 22.74/22.93 (element(the_carrier(A!10), powerset(the_carrier(A!10)))),
% 22.74/22.93 inference(modus_ponens,[status(thm)],[206, 192])).
% 22.74/22.93 tff(208,plain,
% 22.74/22.93 (^[A: $i, B: $i, C: $i] : refl(((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A)))) <=> ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A)))))),
% 22.74/22.93 inference(bind,[status(th)],[])).
% 22.74/22.93 tff(209,plain,
% 22.74/22.93 (![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A)))) <=> ![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))),
% 22.74/22.93 inference(quant_intro,[status(thm)],[208])).
% 22.74/22.93 tff(210,plain,
% 22.74/22.93 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((element(B, powerset(A)) & element(C, powerset(A))) <=> (~((~element(C, powerset(A))) | (~element(B, powerset(A)))))), ((~(element(B, powerset(A)) & element(C, powerset(A)))) <=> (~(~((~element(C, powerset(A))) | (~element(B, powerset(A)))))))), rewrite((~(~((~element(C, powerset(A))) | (~element(B, powerset(A)))))) <=> ((~element(C, powerset(A))) | (~element(B, powerset(A))))), ((~(element(B, powerset(A)) & element(C, powerset(A)))) <=> ((~element(C, powerset(A))) | (~element(B, powerset(A)))))), (((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C))) <=> (((~element(C, powerset(A))) | (~element(B, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C))))), rewrite((((~element(C, powerset(A))) | (~element(B, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C))) <=> ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))), (((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C))) <=> ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))))),
% 22.74/22.93 inference(bind,[status(th)],[])).
% 22.74/22.93 tff(211,plain,
% 22.74/22.93 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C))) <=> ![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))),
% 22.74/22.93 inference(quant_intro,[status(thm)],[210])).
% 22.74/22.93 tff(212,plain,
% 22.74/22.93 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C)))),
% 22.74/22.93 inference(rewrite,[status(thm)],[])).
% 22.74/22.93 tff(213,plain,
% 22.74/22.93 (^[A: $i, B: $i, C: $i] : rewrite(((element(B, powerset(A)) & element(C, powerset(A))) => (subset_difference(A, B, C) = set_difference(B, C))) <=> ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C))))),
% 22.74/22.93 inference(bind,[status(th)],[])).
% 22.74/22.93 tff(214,plain,
% 22.74/22.93 (![A: $i, B: $i, C: $i] : ((element(B, powerset(A)) & element(C, powerset(A))) => (subset_difference(A, B, C) = set_difference(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C)))),
% 22.74/22.93 inference(quant_intro,[status(thm)],[213])).
% 22.74/22.93 tff(215,axiom,(![A: $i, B: $i, C: $i] : ((element(B, powerset(A)) & element(C, powerset(A))) => (subset_difference(A, B, C) = set_difference(B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k6_subset_1')).
% 22.74/22.93 tff(216,plain,
% 22.74/22.93 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C)))),
% 22.74/22.93 inference(modus_ponens,[status(thm)],[215, 214])).
% 22.74/22.93 tff(217,plain,
% 22.74/22.93 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C)))),
% 22.74/22.93 inference(modus_ponens,[status(thm)],[216, 212])).
% 22.74/22.93 tff(218,plain,(
% 22.74/22.93 ![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_difference(A, B, C) = set_difference(B, C)))),
% 22.74/22.93 inference(skolemize,[status(sab)],[217])).
% 22.74/22.93 tff(219,plain,
% 22.74/22.93 (![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))),
% 22.74/22.93 inference(modus_ponens,[status(thm)],[218, 211])).
% 22.74/22.93 tff(220,plain,
% 22.74/22.93 (![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))),
% 22.74/22.93 inference(modus_ponens,[status(thm)],[219, 209])).
% 22.74/22.93 tff(221,plain,
% 22.74/22.93 (((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((~element(the_carrier(A!10), powerset(the_carrier(A!10)))) | (~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)) = set_difference(the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | (~element(the_carrier(A!10), powerset(the_carrier(A!10)))) | (~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)) = set_difference(the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))))),
% 22.74/22.93 inference(rewrite,[status(thm)],[])).
% 22.74/22.93 tff(222,plain,
% 22.74/22.93 (((subset_difference(the_carrier(A!10), the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)) = set_difference(the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) | (~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(the_carrier(A!10)))) | (~element(the_carrier(A!10), powerset(the_carrier(A!10))))) <=> ((~element(the_carrier(A!10), powerset(the_carrier(A!10)))) | (~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)) = set_difference(the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))))),
% 22.74/22.93 inference(rewrite,[status(thm)],[])).
% 22.74/22.93 tff(223,plain,
% 22.74/22.93 (((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((subset_difference(the_carrier(A!10), the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)) = set_difference(the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) | (~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(the_carrier(A!10)))) | (~element(the_carrier(A!10), powerset(the_carrier(A!10)))))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((~element(the_carrier(A!10), powerset(the_carrier(A!10)))) | (~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)) = set_difference(the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)))))),
% 22.74/22.93 inference(monotonicity,[status(thm)],[222])).
% 22.74/22.93 tff(224,plain,
% 22.74/22.93 (((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((subset_difference(the_carrier(A!10), the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)) = set_difference(the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) | (~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(the_carrier(A!10)))) | (~element(the_carrier(A!10), powerset(the_carrier(A!10)))))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | (~element(the_carrier(A!10), powerset(the_carrier(A!10)))) | (~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)) = set_difference(the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))))),
% 22.74/22.93 inference(transitivity,[status(thm)],[223, 221])).
% 22.74/22.93 tff(225,plain,
% 22.74/22.93 ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((subset_difference(the_carrier(A!10), the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)) = set_difference(the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) | (~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(the_carrier(A!10)))) | (~element(the_carrier(A!10), powerset(the_carrier(A!10)))))),
% 22.74/22.93 inference(quant_inst,[status(thm)],[])).
% 22.74/22.93 tff(226,plain,
% 22.74/22.93 ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | (~element(the_carrier(A!10), powerset(the_carrier(A!10)))) | (~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)) = set_difference(the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)))),
% 22.74/22.93 inference(modus_ponens,[status(thm)],[225, 224])).
% 22.74/22.93 tff(227,plain,
% 22.74/22.93 ((~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)) = set_difference(the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)))),
% 22.74/22.93 inference(unit_resolution,[status(thm)],[226, 220, 207])).
% 22.74/22.93 tff(228,plain,
% 22.74/22.93 (subset_difference(the_carrier(A!10), the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)) = set_difference(the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))),
% 22.74/22.93 inference(unit_resolution,[status(thm)],[227, 175])).
% 22.74/22.93 tff(229,plain,
% 22.74/22.93 (subset_difference(the_carrier(A!10), the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)) = subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))),
% 22.74/22.93 inference(monotonicity,[status(thm)],[190])).
% 22.74/22.93 tff(230,plain,
% 22.74/22.93 (subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)) = subset_difference(the_carrier(A!10), the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))),
% 22.74/22.93 inference(symmetry,[status(thm)],[229])).
% 22.74/22.93 tff(231,plain,
% 22.74/22.93 (^[A: $i] : refl(((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B))) <=> ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B))))),
% 22.74/22.93 inference(bind,[status(th)],[])).
% 22.74/22.93 tff(232,plain,
% 22.74/22.93 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B))) <=> ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B)))),
% 22.74/22.93 inference(quant_intro,[status(thm)],[231])).
% 22.74/22.93 tff(233,plain,
% 22.74/22.93 (^[A: $i] : rewrite(((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B))) <=> ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B))))),
% 22.74/22.94 inference(bind,[status(th)],[])).
% 22.74/22.94 tff(234,plain,
% 22.74/22.94 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B))) <=> ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B)))),
% 22.74/22.94 inference(quant_intro,[status(thm)],[233])).
% 22.74/22.94 tff(235,plain,
% 22.74/22.94 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B))) <=> ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B)))),
% 22.74/22.94 inference(transitivity,[status(thm)],[234, 232])).
% 22.74/22.94 tff(236,plain,
% 22.74/22.94 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B))) <=> ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B)))),
% 22.74/22.94 inference(rewrite,[status(thm)],[])).
% 22.74/22.94 tff(237,plain,
% 22.74/22.94 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((element(B, powerset(the_carrier(A))) => (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B)) <=> ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B)))), (![B: $i] : (element(B, powerset(the_carrier(A))) => (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B)) <=> ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B)))), ((one_sorted_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B))) <=> (one_sorted_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B))))), rewrite((one_sorted_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B))) <=> ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B)))), ((one_sorted_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B))) <=> ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B)))))),
% 22.74/22.94 inference(bind,[status(th)],[])).
% 22.74/22.94 tff(238,plain,
% 22.74/22.94 (![A: $i] : (one_sorted_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B))) <=> ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B)))),
% 22.74/22.94 inference(quant_intro,[status(thm)],[237])).
% 22.74/22.94 tff(239,axiom,(![A: $i] : (one_sorted_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t22_pre_topc')).
% 22.74/22.94 tff(240,plain,
% 22.74/22.94 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B)))),
% 22.74/22.94 inference(modus_ponens,[status(thm)],[239, 238])).
% 22.74/22.94 tff(241,plain,
% 22.74/22.94 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B)))),
% 22.74/22.94 inference(modus_ponens,[status(thm)],[240, 236])).
% 22.74/22.94 tff(242,plain,(
% 22.74/22.94 ![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B)))),
% 22.74/22.94 inference(skolemize,[status(sab)],[241])).
% 22.74/22.94 tff(243,plain,
% 22.74/22.94 (![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B)))),
% 22.74/22.94 inference(modus_ponens,[status(thm)],[242, 235])).
% 22.74/22.94 tff(244,plain,
% 22.74/22.94 (((~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B)))) | ((~one_sorted_str(A!10)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B)) = B)))) <=> ((~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B)))) | (~one_sorted_str(A!10)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B)) = B)))),
% 22.74/22.94 inference(rewrite,[status(thm)],[])).
% 22.74/22.94 tff(245,plain,
% 22.74/22.94 ((~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B)))) | ((~one_sorted_str(A!10)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B)) = B)))),
% 22.74/22.94 inference(quant_inst,[status(thm)],[])).
% 22.74/22.94 tff(246,plain,
% 22.74/22.94 ((~![A: $i] : ((~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (subset_difference(the_carrier(A), cast_as_carrier_subset(A), subset_difference(the_carrier(A), cast_as_carrier_subset(A), B)) = B)))) | (~one_sorted_str(A!10)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B)) = B))),
% 22.74/22.94 inference(modus_ponens,[status(thm)],[245, 244])).
% 22.74/22.94 tff(247,plain,
% 22.74/22.94 (![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B)) = B))),
% 22.74/22.94 inference(unit_resolution,[status(thm)],[246, 243, 138])).
% 22.74/22.94 tff(248,plain,
% 22.74/22.94 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B)) = B))) | ((~element(D!13, powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)) = D!13))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B)) = B))) | (~element(D!13, powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)) = D!13))),
% 22.74/22.94 inference(rewrite,[status(thm)],[])).
% 22.74/22.94 tff(249,plain,
% 22.74/22.94 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B)) = B))) | ((~element(D!13, powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)) = D!13))),
% 22.74/22.94 inference(quant_inst,[status(thm)],[])).
% 22.74/22.94 tff(250,plain,
% 22.74/22.94 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B)) = B))) | (~element(D!13, powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)) = D!13)),
% 22.74/22.94 inference(modus_ponens,[status(thm)],[249, 248])).
% 22.74/22.94 tff(251,plain,
% 22.74/22.94 (subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)) = D!13),
% 22.74/22.94 inference(unit_resolution,[status(thm)],[250, 100, 247])).
% 22.74/22.94 tff(252,plain,
% 22.74/22.94 (D!13 = subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))),
% 22.74/22.94 inference(symmetry,[status(thm)],[251])).
% 22.74/22.94 tff(253,plain,
% 22.74/22.94 (D!13 = set_difference(the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))),
% 22.74/22.94 inference(transitivity,[status(thm)],[252, 230, 228])).
% 22.74/22.94 tff(254,plain,
% 22.74/22.94 ((~((~(D!13 = set_difference(the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)))) | (~(((~in(C!12, the_carrier(A!10))) | in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) <=> in(C!12, D!13))))) | (~(D!13 = set_difference(the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)))) | (~(((~in(C!12, the_carrier(A!10))) | in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) <=> in(C!12, D!13)))),
% 22.74/22.94 inference(tautology,[status(thm)],[])).
% 22.74/22.94 tff(255,plain,
% 22.74/22.94 ((~((~(D!13 = set_difference(the_carrier(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)))) | (~(((~in(C!12, the_carrier(A!10))) | in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) <=> in(C!12, D!13))))) | (~(((~in(C!12, the_carrier(A!10))) | in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) <=> in(C!12, D!13)))),
% 22.74/22.94 inference(unit_resolution,[status(thm)],[254, 253])).
% 22.74/22.94 tff(256,plain,
% 22.74/22.94 (~(((~in(C!12, the_carrier(A!10))) | in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) <=> in(C!12, D!13))),
% 22.74/22.94 inference(unit_resolution,[status(thm)],[255, 124])).
% 22.74/22.94 tff(257,plain,
% 22.74/22.94 ((((~in(C!12, the_carrier(A!10))) | in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) <=> in(C!12, D!13)) | ((~in(C!12, the_carrier(A!10))) | in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) | in(C!12, D!13)),
% 22.74/22.94 inference(tautology,[status(thm)],[])).
% 22.74/22.94 tff(258,plain,
% 22.74/22.94 ((((~in(C!12, the_carrier(A!10))) | in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) <=> in(C!12, D!13)) | ((~in(C!12, the_carrier(A!10))) | in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)))),
% 22.74/22.94 inference(unit_resolution,[status(thm)],[257, 102])).
% 22.74/22.94 tff(259,plain,
% 22.74/22.94 ((~in(C!12, the_carrier(A!10))) | in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))),
% 22.74/22.94 inference(unit_resolution,[status(thm)],[258, 256])).
% 22.74/22.94 tff(260,plain,
% 22.74/22.94 ((~((~in(C!12, the_carrier(A!10))) | in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)))) | (~in(C!12, the_carrier(A!10))) | in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))),
% 22.74/22.94 inference(tautology,[status(thm)],[])).
% 22.74/22.94 tff(261,plain,
% 22.74/22.94 ((~((~in(C!12, the_carrier(A!10))) | in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)))) | in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))),
% 22.74/22.94 inference(unit_resolution,[status(thm)],[260, 84])).
% 22.74/22.94 tff(262,plain,
% 22.74/22.94 (in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))),
% 22.74/22.94 inference(unit_resolution,[status(thm)],[261, 259])).
% 22.74/22.94 tff(263,plain,
% 22.74/22.94 (^[A: $i] : refl((set_difference(A, empty_set) = A) <=> (set_difference(A, empty_set) = A))),
% 22.74/22.94 inference(bind,[status(th)],[])).
% 22.74/22.94 tff(264,plain,
% 22.74/22.94 (![A: $i] : (set_difference(A, empty_set) = A) <=> ![A: $i] : (set_difference(A, empty_set) = A)),
% 22.74/22.94 inference(quant_intro,[status(thm)],[263])).
% 22.74/22.94 tff(265,plain,
% 22.74/22.94 (![A: $i] : (set_difference(A, empty_set) = A) <=> ![A: $i] : (set_difference(A, empty_set) = A)),
% 22.74/22.94 inference(rewrite,[status(thm)],[])).
% 22.74/22.94 tff(266,axiom,(![A: $i] : (set_difference(A, empty_set) = A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3_boole')).
% 22.74/22.94 tff(267,plain,
% 22.74/22.94 (![A: $i] : (set_difference(A, empty_set) = A)),
% 22.74/22.94 inference(modus_ponens,[status(thm)],[266, 265])).
% 22.74/22.94 tff(268,plain,(
% 22.74/22.94 ![A: $i] : (set_difference(A, empty_set) = A)),
% 22.74/22.94 inference(skolemize,[status(sab)],[267])).
% 22.74/22.94 tff(269,plain,
% 22.74/22.94 (![A: $i] : (set_difference(A, empty_set) = A)),
% 22.74/22.94 inference(modus_ponens,[status(thm)],[268, 264])).
% 22.74/22.94 tff(270,plain,
% 22.74/22.94 ((~![A: $i] : (set_difference(A, empty_set) = A)) | (set_difference(the_carrier(A!10), empty_set) = the_carrier(A!10))),
% 22.74/22.94 inference(quant_inst,[status(thm)],[])).
% 22.74/22.94 tff(271,plain,
% 22.74/22.94 (set_difference(the_carrier(A!10), empty_set) = the_carrier(A!10)),
% 22.74/22.94 inference(unit_resolution,[status(thm)],[270, 269])).
% 22.74/22.94 tff(272,plain,
% 22.74/22.94 (^[A: $i] : refl((~((~element(tptp_fun_B_9(A), powerset(A))) | (~empty(tptp_fun_B_9(A))))) <=> (~((~element(tptp_fun_B_9(A), powerset(A))) | (~empty(tptp_fun_B_9(A))))))),
% 22.74/22.94 inference(bind,[status(th)],[])).
% 22.74/22.94 tff(273,plain,
% 22.74/22.94 (![A: $i] : (~((~element(tptp_fun_B_9(A), powerset(A))) | (~empty(tptp_fun_B_9(A))))) <=> ![A: $i] : (~((~element(tptp_fun_B_9(A), powerset(A))) | (~empty(tptp_fun_B_9(A)))))),
% 22.74/22.94 inference(quant_intro,[status(thm)],[272])).
% 22.74/22.94 tff(274,plain,
% 22.74/22.94 (^[A: $i] : rewrite((element(tptp_fun_B_9(A), powerset(A)) & empty(tptp_fun_B_9(A))) <=> (~((~element(tptp_fun_B_9(A), powerset(A))) | (~empty(tptp_fun_B_9(A))))))),
% 22.74/22.94 inference(bind,[status(th)],[])).
% 22.74/22.94 tff(275,plain,
% 22.74/22.94 (![A: $i] : (element(tptp_fun_B_9(A), powerset(A)) & empty(tptp_fun_B_9(A))) <=> ![A: $i] : (~((~element(tptp_fun_B_9(A), powerset(A))) | (~empty(tptp_fun_B_9(A)))))),
% 22.74/22.94 inference(quant_intro,[status(thm)],[274])).
% 22.74/22.94 tff(276,plain,
% 22.74/22.94 (![A: $i] : ?[B: $i] : (element(B, powerset(A)) & empty(B)) <=> ![A: $i] : ?[B: $i] : (element(B, powerset(A)) & empty(B))),
% 22.74/22.94 inference(rewrite,[status(thm)],[])).
% 22.74/22.94 tff(277,axiom,(![A: $i] : ?[B: $i] : (element(B, powerset(A)) & empty(B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rc2_subset_1')).
% 22.74/22.94 tff(278,plain,
% 22.74/22.94 (![A: $i] : ?[B: $i] : (element(B, powerset(A)) & empty(B))),
% 22.74/22.94 inference(modus_ponens,[status(thm)],[277, 276])).
% 22.74/22.94 tff(279,plain,(
% 22.74/22.94 ![A: $i] : (element(tptp_fun_B_9(A), powerset(A)) & empty(tptp_fun_B_9(A)))),
% 22.74/22.94 inference(skolemize,[status(sab)],[278])).
% 22.74/22.94 tff(280,plain,
% 22.74/22.94 (![A: $i] : (~((~element(tptp_fun_B_9(A), powerset(A))) | (~empty(tptp_fun_B_9(A)))))),
% 22.74/22.94 inference(modus_ponens,[status(thm)],[279, 275])).
% 22.74/22.94 tff(281,plain,
% 22.74/22.94 (![A: $i] : (~((~element(tptp_fun_B_9(A), powerset(A))) | (~empty(tptp_fun_B_9(A)))))),
% 22.74/22.94 inference(modus_ponens,[status(thm)],[280, 273])).
% 22.74/22.94 tff(282,plain,
% 22.74/22.94 ((~![A: $i] : (~((~element(tptp_fun_B_9(A), powerset(A))) | (~empty(tptp_fun_B_9(A)))))) | (~((~element(tptp_fun_B_9(the_carrier(A!10)), powerset(the_carrier(A!10)))) | (~empty(tptp_fun_B_9(the_carrier(A!10))))))),
% 22.74/22.94 inference(quant_inst,[status(thm)],[])).
% 22.74/22.94 tff(283,plain,
% 22.74/22.94 (~((~element(tptp_fun_B_9(the_carrier(A!10)), powerset(the_carrier(A!10)))) | (~empty(tptp_fun_B_9(the_carrier(A!10)))))),
% 22.74/22.94 inference(unit_resolution,[status(thm)],[282, 281])).
% 22.74/22.94 tff(284,plain,
% 22.74/22.94 (((~element(tptp_fun_B_9(the_carrier(A!10)), powerset(the_carrier(A!10)))) | (~empty(tptp_fun_B_9(the_carrier(A!10))))) | empty(tptp_fun_B_9(the_carrier(A!10)))),
% 22.74/22.94 inference(tautology,[status(thm)],[])).
% 22.74/22.94 tff(285,plain,
% 22.74/22.94 (empty(tptp_fun_B_9(the_carrier(A!10)))),
% 22.74/22.94 inference(unit_resolution,[status(thm)],[284, 283])).
% 22.74/22.94 tff(286,plain,
% 22.74/22.94 (^[A: $i, B: $i] : refl(((~empty(B)) | (A = B) | (~empty(A))) <=> ((~empty(B)) | (A = B) | (~empty(A))))),
% 22.74/22.94 inference(bind,[status(th)],[])).
% 22.74/22.94 tff(287,plain,
% 22.74/22.94 (![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A))) <=> ![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))),
% 22.74/22.94 inference(quant_intro,[status(thm)],[286])).
% 22.74/22.94 tff(288,plain,
% 22.74/22.94 (^[A: $i, B: $i] : trans(monotonicity(rewrite((empty(A) & (~(A = B)) & empty(B)) <=> (~((~empty(B)) | (A = B) | (~empty(A))))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> (~(~((~empty(B)) | (A = B) | (~empty(A))))))), rewrite((~(~((~empty(B)) | (A = B) | (~empty(A))))) <=> ((~empty(B)) | (A = B) | (~empty(A)))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> ((~empty(B)) | (A = B) | (~empty(A)))))),
% 22.74/22.94 inference(bind,[status(th)],[])).
% 22.74/22.94 tff(289,plain,
% 22.74/22.94 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))),
% 22.74/22.94 inference(quant_intro,[status(thm)],[288])).
% 22.74/22.94 tff(290,plain,
% 22.74/22.94 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 22.74/22.94 inference(rewrite,[status(thm)],[])).
% 22.74/22.94 tff(291,plain,
% 22.74/22.94 (^[A: $i, B: $i] : rewrite((~((empty(A) & (~(A = B))) & empty(B))) <=> (~(empty(A) & (~(A = B)) & empty(B))))),
% 22.74/22.94 inference(bind,[status(th)],[])).
% 22.74/22.94 tff(292,plain,
% 22.74/22.94 (![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 22.74/22.94 inference(quant_intro,[status(thm)],[291])).
% 22.74/22.94 tff(293,axiom,(![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t8_boole')).
% 22.74/22.94 tff(294,plain,
% 22.74/22.94 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 22.74/22.94 inference(modus_ponens,[status(thm)],[293, 292])).
% 22.74/22.94 tff(295,plain,
% 22.74/22.94 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 22.74/22.94 inference(modus_ponens,[status(thm)],[294, 290])).
% 22.74/22.94 tff(296,plain,(
% 22.74/22.94 ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 22.74/22.94 inference(skolemize,[status(sab)],[295])).
% 22.74/22.94 tff(297,plain,
% 22.74/22.94 (![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))),
% 22.74/22.94 inference(modus_ponens,[status(thm)],[296, 289])).
% 22.74/22.94 tff(298,plain,
% 22.74/22.94 (![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))),
% 22.74/22.94 inference(modus_ponens,[status(thm)],[297, 287])).
% 22.74/22.94 tff(299,plain,
% 22.74/22.94 (empty(empty_set) <=> empty(empty_set)),
% 22.74/22.94 inference(rewrite,[status(thm)],[])).
% 22.74/22.94 tff(300,axiom,(((((empty(empty_set) & v1_membered(empty_set)) & v2_membered(empty_set)) & v3_membered(empty_set)) & v4_membered(empty_set)) & v5_membered(empty_set)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc6_membered')).
% 22.74/22.94 tff(301,plain,
% 22.74/22.94 ((((empty(empty_set) & v1_membered(empty_set)) & v2_membered(empty_set)) & v3_membered(empty_set)) & v4_membered(empty_set)),
% 22.74/22.94 inference(and_elim,[status(thm)],[300])).
% 22.74/22.94 tff(302,plain,
% 22.74/22.94 (((empty(empty_set) & v1_membered(empty_set)) & v2_membered(empty_set)) & v3_membered(empty_set)),
% 22.74/22.94 inference(and_elim,[status(thm)],[301])).
% 22.74/22.94 tff(303,plain,
% 22.74/22.94 ((empty(empty_set) & v1_membered(empty_set)) & v2_membered(empty_set)),
% 22.74/22.94 inference(and_elim,[status(thm)],[302])).
% 22.74/22.94 tff(304,plain,
% 22.74/22.94 (empty(empty_set) & v1_membered(empty_set)),
% 22.74/22.94 inference(and_elim,[status(thm)],[303])).
% 22.74/22.94 tff(305,plain,
% 22.74/22.94 (empty(empty_set)),
% 22.74/22.94 inference(and_elim,[status(thm)],[304])).
% 22.74/22.94 tff(306,plain,
% 22.74/22.94 (empty(empty_set)),
% 22.74/22.94 inference(modus_ponens,[status(thm)],[305, 299])).
% 22.74/22.94 tff(307,plain,
% 22.74/22.94 (((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | ((~empty(tptp_fun_B_9(the_carrier(A!10)))) | (~empty(empty_set)) | (tptp_fun_B_9(the_carrier(A!10)) = empty_set))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | (~empty(tptp_fun_B_9(the_carrier(A!10)))) | (~empty(empty_set)) | (tptp_fun_B_9(the_carrier(A!10)) = empty_set))),
% 22.74/22.94 inference(rewrite,[status(thm)],[])).
% 22.74/22.94 tff(308,plain,
% 22.74/22.94 (((~empty(empty_set)) | (tptp_fun_B_9(the_carrier(A!10)) = empty_set) | (~empty(tptp_fun_B_9(the_carrier(A!10))))) <=> ((~empty(tptp_fun_B_9(the_carrier(A!10)))) | (~empty(empty_set)) | (tptp_fun_B_9(the_carrier(A!10)) = empty_set))),
% 22.74/22.94 inference(rewrite,[status(thm)],[])).
% 22.74/22.94 tff(309,plain,
% 22.74/22.94 (((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | ((~empty(empty_set)) | (tptp_fun_B_9(the_carrier(A!10)) = empty_set) | (~empty(tptp_fun_B_9(the_carrier(A!10)))))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | ((~empty(tptp_fun_B_9(the_carrier(A!10)))) | (~empty(empty_set)) | (tptp_fun_B_9(the_carrier(A!10)) = empty_set)))),
% 22.74/22.94 inference(monotonicity,[status(thm)],[308])).
% 22.74/22.94 tff(310,plain,
% 22.74/22.94 (((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | ((~empty(empty_set)) | (tptp_fun_B_9(the_carrier(A!10)) = empty_set) | (~empty(tptp_fun_B_9(the_carrier(A!10)))))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | (~empty(tptp_fun_B_9(the_carrier(A!10)))) | (~empty(empty_set)) | (tptp_fun_B_9(the_carrier(A!10)) = empty_set))),
% 22.74/22.94 inference(transitivity,[status(thm)],[309, 307])).
% 22.74/22.94 tff(311,plain,
% 22.74/22.94 ((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | ((~empty(empty_set)) | (tptp_fun_B_9(the_carrier(A!10)) = empty_set) | (~empty(tptp_fun_B_9(the_carrier(A!10)))))),
% 22.74/22.94 inference(quant_inst,[status(thm)],[])).
% 22.74/22.94 tff(312,plain,
% 22.74/22.94 ((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | (~empty(tptp_fun_B_9(the_carrier(A!10)))) | (~empty(empty_set)) | (tptp_fun_B_9(the_carrier(A!10)) = empty_set)),
% 22.74/22.94 inference(modus_ponens,[status(thm)],[311, 310])).
% 22.74/22.94 tff(313,plain,
% 22.74/22.94 (tptp_fun_B_9(the_carrier(A!10)) = empty_set),
% 22.74/22.94 inference(unit_resolution,[status(thm)],[312, 306, 298, 285])).
% 22.74/22.94 tff(314,plain,
% 22.74/22.94 (empty_set = tptp_fun_B_9(the_carrier(A!10))),
% 22.74/22.94 inference(symmetry,[status(thm)],[313])).
% 22.74/22.94 tff(315,plain,
% 22.74/22.94 (element(empty_set, powerset(the_carrier(A!10))) <=> element(tptp_fun_B_9(the_carrier(A!10)), powerset(the_carrier(A!10)))),
% 22.74/22.94 inference(monotonicity,[status(thm)],[314])).
% 22.74/22.94 tff(316,plain,
% 22.74/22.94 (element(tptp_fun_B_9(the_carrier(A!10)), powerset(the_carrier(A!10))) <=> element(empty_set, powerset(the_carrier(A!10)))),
% 22.74/22.94 inference(symmetry,[status(thm)],[315])).
% 22.74/22.94 tff(317,plain,
% 22.74/22.94 (((~element(tptp_fun_B_9(the_carrier(A!10)), powerset(the_carrier(A!10)))) | (~empty(tptp_fun_B_9(the_carrier(A!10))))) | element(tptp_fun_B_9(the_carrier(A!10)), powerset(the_carrier(A!10)))),
% 22.74/22.94 inference(tautology,[status(thm)],[])).
% 22.74/22.94 tff(318,plain,
% 22.74/22.94 (element(tptp_fun_B_9(the_carrier(A!10)), powerset(the_carrier(A!10)))),
% 22.74/22.94 inference(unit_resolution,[status(thm)],[317, 283])).
% 22.74/22.94 tff(319,plain,
% 22.74/22.94 (element(empty_set, powerset(the_carrier(A!10)))),
% 22.74/22.94 inference(modus_ponens,[status(thm)],[318, 316])).
% 22.74/22.94 tff(320,plain,
% 22.74/22.94 (((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((~element(the_carrier(A!10), powerset(the_carrier(A!10)))) | (~element(empty_set, powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), the_carrier(A!10), empty_set) = set_difference(the_carrier(A!10), empty_set)))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | (~element(the_carrier(A!10), powerset(the_carrier(A!10)))) | (~element(empty_set, powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), the_carrier(A!10), empty_set) = set_difference(the_carrier(A!10), empty_set)))),
% 22.74/22.94 inference(rewrite,[status(thm)],[])).
% 22.74/22.94 tff(321,plain,
% 22.74/22.94 (((subset_difference(the_carrier(A!10), the_carrier(A!10), empty_set) = set_difference(the_carrier(A!10), empty_set)) | (~element(empty_set, powerset(the_carrier(A!10)))) | (~element(the_carrier(A!10), powerset(the_carrier(A!10))))) <=> ((~element(the_carrier(A!10), powerset(the_carrier(A!10)))) | (~element(empty_set, powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), the_carrier(A!10), empty_set) = set_difference(the_carrier(A!10), empty_set)))),
% 22.74/22.94 inference(rewrite,[status(thm)],[])).
% 22.74/22.94 tff(322,plain,
% 22.74/22.94 (((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((subset_difference(the_carrier(A!10), the_carrier(A!10), empty_set) = set_difference(the_carrier(A!10), empty_set)) | (~element(empty_set, powerset(the_carrier(A!10)))) | (~element(the_carrier(A!10), powerset(the_carrier(A!10)))))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((~element(the_carrier(A!10), powerset(the_carrier(A!10)))) | (~element(empty_set, powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), the_carrier(A!10), empty_set) = set_difference(the_carrier(A!10), empty_set))))),
% 22.74/22.94 inference(monotonicity,[status(thm)],[321])).
% 22.74/22.94 tff(323,plain,
% 22.74/22.94 (((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((subset_difference(the_carrier(A!10), the_carrier(A!10), empty_set) = set_difference(the_carrier(A!10), empty_set)) | (~element(empty_set, powerset(the_carrier(A!10)))) | (~element(the_carrier(A!10), powerset(the_carrier(A!10)))))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | (~element(the_carrier(A!10), powerset(the_carrier(A!10)))) | (~element(empty_set, powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), the_carrier(A!10), empty_set) = set_difference(the_carrier(A!10), empty_set)))),
% 22.74/22.94 inference(transitivity,[status(thm)],[322, 320])).
% 22.74/22.94 tff(324,plain,
% 22.74/22.94 ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((subset_difference(the_carrier(A!10), the_carrier(A!10), empty_set) = set_difference(the_carrier(A!10), empty_set)) | (~element(empty_set, powerset(the_carrier(A!10)))) | (~element(the_carrier(A!10), powerset(the_carrier(A!10)))))),
% 22.74/22.94 inference(quant_inst,[status(thm)],[])).
% 22.74/22.94 tff(325,plain,
% 22.74/22.94 ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | (~element(the_carrier(A!10), powerset(the_carrier(A!10)))) | (~element(empty_set, powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), the_carrier(A!10), empty_set) = set_difference(the_carrier(A!10), empty_set))),
% 22.74/22.94 inference(modus_ponens,[status(thm)],[324, 323])).
% 22.74/22.94 tff(326,plain,
% 22.74/22.94 ((~element(empty_set, powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), the_carrier(A!10), empty_set) = set_difference(the_carrier(A!10), empty_set))),
% 22.74/22.94 inference(unit_resolution,[status(thm)],[325, 220, 207])).
% 22.74/22.94 tff(327,plain,
% 22.74/22.94 (subset_difference(the_carrier(A!10), the_carrier(A!10), empty_set) = set_difference(the_carrier(A!10), empty_set)),
% 22.74/22.94 inference(unit_resolution,[status(thm)],[326, 319])).
% 22.74/22.94 tff(328,plain,
% 22.74/22.94 (subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10))) = subset_difference(the_carrier(A!10), the_carrier(A!10), empty_set)),
% 22.74/22.94 inference(monotonicity,[status(thm)],[189, 313])).
% 22.74/22.94 tff(329,plain,
% 22.74/22.94 (subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10))) = the_carrier(A!10)),
% 22.74/22.94 inference(transitivity,[status(thm)],[328, 327, 271])).
% 22.74/22.94 tff(330,plain,
% 22.74/22.94 (powerset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10)))) = powerset(the_carrier(A!10))),
% 22.74/22.94 inference(monotonicity,[status(thm)],[329])).
% 22.74/22.94 tff(331,plain,
% 22.74/22.94 (element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10))))) <=> element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(the_carrier(A!10)))),
% 22.74/22.94 inference(monotonicity,[status(thm)],[330])).
% 22.74/22.94 tff(332,plain,
% 22.74/22.94 (element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(the_carrier(A!10))) <=> element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10)))))),
% 22.74/22.94 inference(symmetry,[status(thm)],[331])).
% 22.74/22.94 tff(333,plain,
% 22.74/22.94 (element(subset_complement(the_carrier(A!10), D!13), powerset(the_carrier(A!10))) <=> element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10)))))),
% 22.74/22.94 inference(transitivity,[status(thm)],[160, 332])).
% 22.74/22.94 tff(334,plain,
% 22.74/22.94 (element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10)))))),
% 22.74/22.94 inference(modus_ponens,[status(thm)],[174, 333])).
% 22.74/22.94 tff(335,plain,
% 22.74/22.94 (element(B!11, powerset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10))))) <=> element(B!11, powerset(the_carrier(A!10)))),
% 22.74/22.94 inference(monotonicity,[status(thm)],[330])).
% 22.74/22.94 tff(336,plain,
% 22.74/22.94 (element(B!11, powerset(the_carrier(A!10))) <=> element(B!11, powerset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10)))))),
% 22.74/22.94 inference(symmetry,[status(thm)],[335])).
% 22.74/22.94 tff(337,plain,
% 22.74/22.94 (element(B!11, powerset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10)))))),
% 22.74/22.94 inference(modus_ponens,[status(thm)],[19, 336])).
% 22.74/22.94 tff(338,plain,
% 22.74/22.94 (^[A: $i, B: $i] : refl(((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C))))) <=> ((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C))))))),
% 22.74/22.94 inference(bind,[status(th)],[])).
% 22.74/22.94 tff(339,plain,
% 22.74/22.94 (![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C))))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C)))))),
% 22.74/22.94 inference(quant_intro,[status(thm)],[338])).
% 22.74/22.94 tff(340,plain,
% 22.74/22.94 (^[A: $i, B: $i] : rewrite(((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C))))) <=> ((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C))))))),
% 22.74/22.94 inference(bind,[status(th)],[])).
% 22.74/22.94 tff(341,plain,
% 22.74/22.94 (![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C))))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C)))))),
% 22.74/22.94 inference(quant_intro,[status(thm)],[340])).
% 22.74/22.94 tff(342,plain,
% 22.74/22.94 (![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C))))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C)))))),
% 22.74/22.94 inference(transitivity,[status(thm)],[341, 339])).
% 22.74/22.94 tff(343,plain,
% 22.74/22.94 (![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C))))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C)))))),
% 22.74/22.94 inference(rewrite,[status(thm)],[])).
% 22.74/22.94 tff(344,plain,
% 22.74/22.94 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((element(C, powerset(A)) => (disjoint(B, C) <=> subset(B, subset_complement(A, C)))) <=> ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C)))))), (![C: $i] : (element(C, powerset(A)) => (disjoint(B, C) <=> subset(B, subset_complement(A, C)))) <=> ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C)))))), ((element(B, powerset(A)) => ![C: $i] : (element(C, powerset(A)) => (disjoint(B, C) <=> subset(B, subset_complement(A, C))))) <=> (element(B, powerset(A)) => ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C))))))), rewrite((element(B, powerset(A)) => ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C))))) <=> ((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C)))))), ((element(B, powerset(A)) => ![C: $i] : (element(C, powerset(A)) => (disjoint(B, C) <=> subset(B, subset_complement(A, C))))) <=> ((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C)))))))),
% 22.74/22.94 inference(bind,[status(th)],[])).
% 22.74/22.94 tff(345,plain,
% 22.74/22.94 (![A: $i, B: $i] : (element(B, powerset(A)) => ![C: $i] : (element(C, powerset(A)) => (disjoint(B, C) <=> subset(B, subset_complement(A, C))))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C)))))),
% 22.74/22.94 inference(quant_intro,[status(thm)],[344])).
% 22.74/22.94 tff(346,axiom,(![A: $i, B: $i] : (element(B, powerset(A)) => ![C: $i] : (element(C, powerset(A)) => (disjoint(B, C) <=> subset(B, subset_complement(A, C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t43_subset_1')).
% 22.74/22.94 tff(347,plain,
% 22.74/22.94 (![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C)))))),
% 22.74/22.94 inference(modus_ponens,[status(thm)],[346, 345])).
% 22.74/22.94 tff(348,plain,
% 22.74/22.94 (![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C)))))),
% 22.74/22.94 inference(modus_ponens,[status(thm)],[347, 343])).
% 22.74/22.94 tff(349,plain,(
% 22.74/22.94 ![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C)))))),
% 22.74/22.94 inference(skolemize,[status(sab)],[348])).
% 22.74/22.94 tff(350,plain,
% 22.74/22.94 (![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C)))))),
% 22.74/22.94 inference(modus_ponens,[status(thm)],[349, 342])).
% 22.74/22.94 tff(351,plain,
% 22.74/22.94 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C)))))) | ((~element(B!11, powerset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10)))))) | ![C: $i] : ((~element(C, powerset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10)))))) | (disjoint(B!11, C) <=> subset(B!11, subset_complement(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10))), C)))))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C)))))) | (~element(B!11, powerset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10)))))) | ![C: $i] : ((~element(C, powerset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10)))))) | (disjoint(B!11, C) <=> subset(B!11, subset_complement(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10))), C)))))),
% 22.74/22.94 inference(rewrite,[status(thm)],[])).
% 22.74/22.94 tff(352,plain,
% 22.74/22.94 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C)))))) | ((~element(B!11, powerset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10)))))) | ![C: $i] : ((~element(C, powerset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10)))))) | (disjoint(B!11, C) <=> subset(B!11, subset_complement(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10))), C)))))),
% 22.74/22.94 inference(quant_inst,[status(thm)],[])).
% 22.74/22.94 tff(353,plain,
% 22.74/22.94 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C)))))) | (~element(B!11, powerset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10)))))) | ![C: $i] : ((~element(C, powerset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10)))))) | (disjoint(B!11, C) <=> subset(B!11, subset_complement(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10))), C))))),
% 22.74/22.94 inference(modus_ponens,[status(thm)],[352, 351])).
% 22.74/22.94 tff(354,plain,
% 22.74/22.94 ((~element(B!11, powerset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10)))))) | ![C: $i] : ((~element(C, powerset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10)))))) | (disjoint(B!11, C) <=> subset(B!11, subset_complement(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10))), C))))),
% 22.74/22.94 inference(unit_resolution,[status(thm)],[353, 350])).
% 22.74/22.94 tff(355,plain,
% 22.74/22.94 (![C: $i] : ((~element(C, powerset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10)))))) | (disjoint(B!11, C) <=> subset(B!11, subset_complement(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10))), C))))),
% 22.74/22.94 inference(unit_resolution,[status(thm)],[354, 337])).
% 22.74/22.94 tff(356,plain,
% 22.74/22.94 (((~![C: $i] : ((~element(C, powerset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10)))))) | (disjoint(B!11, C) <=> subset(B!11, subset_complement(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10))), C))))) | ((~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10)))))) | (disjoint(B!11, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)) <=> subset(B!11, subset_complement(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10))), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)))))) <=> ((~![C: $i] : ((~element(C, powerset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10)))))) | (disjoint(B!11, C) <=> subset(B!11, subset_complement(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10))), C))))) | (~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10)))))) | (disjoint(B!11, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)) <=> subset(B!11, subset_complement(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10))), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)))))),
% 22.74/22.95 inference(rewrite,[status(thm)],[])).
% 22.74/22.95 tff(357,plain,
% 22.74/22.95 ((~![C: $i] : ((~element(C, powerset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10)))))) | (disjoint(B!11, C) <=> subset(B!11, subset_complement(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10))), C))))) | ((~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10)))))) | (disjoint(B!11, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)) <=> subset(B!11, subset_complement(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10))), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)))))),
% 22.74/22.95 inference(quant_inst,[status(thm)],[])).
% 22.74/22.95 tff(358,plain,
% 22.74/22.95 ((~![C: $i] : ((~element(C, powerset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10)))))) | (disjoint(B!11, C) <=> subset(B!11, subset_complement(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10))), C))))) | (~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10)))))) | (disjoint(B!11, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)) <=> subset(B!11, subset_complement(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10))), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))))),
% 22.74/22.95 inference(modus_ponens,[status(thm)],[357, 356])).
% 22.74/22.95 tff(359,plain,
% 22.74/22.95 (disjoint(B!11, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)) <=> subset(B!11, subset_complement(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10))), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)))),
% 22.74/22.95 inference(unit_resolution,[status(thm)],[358, 355, 334])).
% 22.74/22.95 tff(360,plain,
% 22.74/22.95 (^[A: $i, B: $i] : refl(((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B)) <=> ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B)))),
% 22.74/22.95 inference(bind,[status(th)],[])).
% 22.74/22.95 tff(361,plain,
% 22.74/22.95 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B)) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 22.74/22.95 inference(quant_intro,[status(thm)],[360])).
% 22.74/22.95 tff(362,plain,
% 22.74/22.95 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B)) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 22.74/22.95 inference(rewrite,[status(thm)],[])).
% 22.74/22.95 tff(363,plain,
% 22.74/22.95 (^[A: $i, B: $i] : rewrite((element(B, powerset(A)) => (subset_complement(A, subset_complement(A, B)) = B)) <=> ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B)))),
% 22.74/22.95 inference(bind,[status(th)],[])).
% 22.74/22.95 tff(364,plain,
% 22.74/22.95 (![A: $i, B: $i] : (element(B, powerset(A)) => (subset_complement(A, subset_complement(A, B)) = B)) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 22.74/22.95 inference(quant_intro,[status(thm)],[363])).
% 22.74/22.95 tff(365,axiom,(![A: $i, B: $i] : (element(B, powerset(A)) => (subset_complement(A, subset_complement(A, B)) = B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','involutiveness_k3_subset_1')).
% 22.74/22.95 tff(366,plain,
% 22.74/22.95 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 22.74/22.95 inference(modus_ponens,[status(thm)],[365, 364])).
% 22.74/22.95 tff(367,plain,
% 22.74/22.95 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 22.74/22.95 inference(modus_ponens,[status(thm)],[366, 362])).
% 22.74/22.95 tff(368,plain,(
% 22.74/22.95 ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 22.74/22.95 inference(skolemize,[status(sab)],[367])).
% 22.74/22.95 tff(369,plain,
% 22.74/22.95 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 22.74/22.95 inference(modus_ponens,[status(thm)],[368, 361])).
% 22.74/22.95 tff(370,plain,
% 22.74/22.95 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | ((~element(D!13, powerset(the_carrier(A!10)))) | (subset_complement(the_carrier(A!10), subset_complement(the_carrier(A!10), D!13)) = D!13))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | (~element(D!13, powerset(the_carrier(A!10)))) | (subset_complement(the_carrier(A!10), subset_complement(the_carrier(A!10), D!13)) = D!13))),
% 22.74/22.95 inference(rewrite,[status(thm)],[])).
% 22.74/22.95 tff(371,plain,
% 22.74/22.95 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | ((~element(D!13, powerset(the_carrier(A!10)))) | (subset_complement(the_carrier(A!10), subset_complement(the_carrier(A!10), D!13)) = D!13))),
% 22.74/22.95 inference(quant_inst,[status(thm)],[])).
% 22.74/22.95 tff(372,plain,
% 22.74/22.95 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | (~element(D!13, powerset(the_carrier(A!10)))) | (subset_complement(the_carrier(A!10), subset_complement(the_carrier(A!10), D!13)) = D!13)),
% 22.74/22.95 inference(modus_ponens,[status(thm)],[371, 370])).
% 22.74/22.95 tff(373,plain,
% 22.74/22.95 (subset_complement(the_carrier(A!10), subset_complement(the_carrier(A!10), D!13)) = D!13),
% 22.74/22.95 inference(unit_resolution,[status(thm)],[372, 369, 100])).
% 22.74/22.95 tff(374,plain,
% 22.74/22.95 (subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13) = subset_complement(the_carrier(A!10), D!13)),
% 22.74/22.95 inference(symmetry,[status(thm)],[159])).
% 22.74/22.95 tff(375,plain,
% 22.74/22.95 (subset_complement(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10))), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)) = subset_complement(the_carrier(A!10), subset_complement(the_carrier(A!10), D!13))),
% 22.74/22.95 inference(monotonicity,[status(thm)],[329, 374])).
% 22.74/22.95 tff(376,plain,
% 22.74/22.95 (subset_complement(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10))), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)) = D!13),
% 22.74/22.95 inference(transitivity,[status(thm)],[375, 373])).
% 22.74/22.95 tff(377,plain,
% 22.74/22.95 (subset(B!11, subset_complement(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10))), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) <=> subset(B!11, D!13)),
% 22.74/22.95 inference(monotonicity,[status(thm)],[376])).
% 22.74/22.95 tff(378,plain,
% 22.74/22.95 (subset(B!11, D!13) <=> subset(B!11, subset_complement(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10))), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)))),
% 22.74/22.95 inference(symmetry,[status(thm)],[377])).
% 22.74/22.95 tff(379,plain,
% 22.74/22.95 (subset(B!11, subset_complement(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10))), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)))),
% 22.74/22.95 inference(modus_ponens,[status(thm)],[96, 378])).
% 22.74/22.95 tff(380,plain,
% 22.74/22.95 ((~(disjoint(B!11, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)) <=> subset(B!11, subset_complement(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10))), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))))) | disjoint(B!11, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)) | (~subset(B!11, subset_complement(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_B_9(the_carrier(A!10))), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))))),
% 22.74/22.95 inference(tautology,[status(thm)],[])).
% 22.74/22.95 tff(381,plain,
% 22.74/22.95 (disjoint(B!11, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))),
% 22.74/22.95 inference(unit_resolution,[status(thm)],[380, 379, 359])).
% 22.74/22.95 tff(382,plain,
% 22.74/22.95 (^[A: $i] : refl(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (closed_subset(B, A) <=> open_subset(subset_difference(the_carrier(A), cast_as_carrier_subset(A), B), A)))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (closed_subset(B, A) <=> open_subset(subset_difference(the_carrier(A), cast_as_carrier_subset(A), B), A)))))),
% 22.74/22.95 inference(bind,[status(th)],[])).
% 22.74/22.95 tff(383,plain,
% 22.74/22.95 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (closed_subset(B, A) <=> open_subset(subset_difference(the_carrier(A), cast_as_carrier_subset(A), B), A)))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (closed_subset(B, A) <=> open_subset(subset_difference(the_carrier(A), cast_as_carrier_subset(A), B), A))))),
% 22.74/22.95 inference(quant_intro,[status(thm)],[382])).
% 22.74/22.95 tff(384,plain,
% 22.74/22.95 (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (closed_subset(B, A) <=> open_subset(subset_difference(the_carrier(A), cast_as_carrier_subset(A), B), A)))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (closed_subset(B, A) <=> open_subset(subset_difference(the_carrier(A), cast_as_carrier_subset(A), B), A)))))),
% 22.74/22.95 inference(bind,[status(th)],[])).
% 22.74/22.95 tff(385,plain,
% 22.74/22.95 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (closed_subset(B, A) <=> open_subset(subset_difference(the_carrier(A), cast_as_carrier_subset(A), B), A)))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (closed_subset(B, A) <=> open_subset(subset_difference(the_carrier(A), cast_as_carrier_subset(A), B), A))))),
% 22.74/22.95 inference(quant_intro,[status(thm)],[384])).
% 22.74/22.95 tff(386,plain,
% 22.74/22.95 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (closed_subset(B, A) <=> open_subset(subset_difference(the_carrier(A), cast_as_carrier_subset(A), B), A)))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (closed_subset(B, A) <=> open_subset(subset_difference(the_carrier(A), cast_as_carrier_subset(A), B), A))))),
% 22.74/22.95 inference(transitivity,[status(thm)],[385, 383])).
% 22.74/22.95 tff(387,plain,
% 22.74/22.95 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (closed_subset(B, A) <=> open_subset(subset_difference(the_carrier(A), cast_as_carrier_subset(A), B), A)))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (closed_subset(B, A) <=> open_subset(subset_difference(the_carrier(A), cast_as_carrier_subset(A), B), A))))),
% 22.74/22.95 inference(rewrite,[status(thm)],[])).
% 22.74/22.95 tff(388,plain,
% 22.74/22.95 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((element(B, powerset(the_carrier(A))) => (closed_subset(B, A) <=> open_subset(subset_difference(the_carrier(A), cast_as_carrier_subset(A), B), A))) <=> ((~element(B, powerset(the_carrier(A)))) | (closed_subset(B, A) <=> open_subset(subset_difference(the_carrier(A), cast_as_carrier_subset(A), B), A))))), (![B: $i] : (element(B, powerset(the_carrier(A))) => (closed_subset(B, A) <=> open_subset(subset_difference(the_carrier(A), cast_as_carrier_subset(A), B), A))) <=> ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (closed_subset(B, A) <=> open_subset(subset_difference(the_carrier(A), cast_as_carrier_subset(A), B), A))))), ((top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (closed_subset(B, A) <=> open_subset(subset_difference(the_carrier(A), cast_as_carrier_subset(A), B), A)))) <=> (top_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (closed_subset(B, A) <=> open_subset(subset_difference(the_carrier(A), cast_as_carrier_subset(A), B), A)))))), rewrite((top_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (closed_subset(B, A) <=> open_subset(subset_difference(the_carrier(A), cast_as_carrier_subset(A), B), A)))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (closed_subset(B, A) <=> open_subset(subset_difference(the_carrier(A), cast_as_carrier_subset(A), B), A))))), ((top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (closed_subset(B, A) <=> open_subset(subset_difference(the_carrier(A), cast_as_carrier_subset(A), B), A)))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (closed_subset(B, A) <=> open_subset(subset_difference(the_carrier(A), cast_as_carrier_subset(A), B), A))))))),
% 22.74/22.95 inference(bind,[status(th)],[])).
% 22.74/22.95 tff(389,plain,
% 22.74/22.95 (![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (closed_subset(B, A) <=> open_subset(subset_difference(the_carrier(A), cast_as_carrier_subset(A), B), A)))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (closed_subset(B, A) <=> open_subset(subset_difference(the_carrier(A), cast_as_carrier_subset(A), B), A))))),
% 22.74/22.95 inference(quant_intro,[status(thm)],[388])).
% 22.74/22.95 tff(390,axiom,(![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (closed_subset(B, A) <=> open_subset(subset_difference(the_carrier(A), cast_as_carrier_subset(A), B), A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d6_pre_topc')).
% 22.74/22.95 tff(391,plain,
% 22.74/22.95 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (closed_subset(B, A) <=> open_subset(subset_difference(the_carrier(A), cast_as_carrier_subset(A), B), A))))),
% 22.74/22.95 inference(modus_ponens,[status(thm)],[390, 389])).
% 22.74/22.95 tff(392,plain,
% 22.74/22.95 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (closed_subset(B, A) <=> open_subset(subset_difference(the_carrier(A), cast_as_carrier_subset(A), B), A))))),
% 22.74/22.95 inference(modus_ponens,[status(thm)],[391, 387])).
% 22.74/22.95 tff(393,plain,(
% 22.74/22.95 ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (closed_subset(B, A) <=> open_subset(subset_difference(the_carrier(A), cast_as_carrier_subset(A), B), A))))),
% 22.74/22.95 inference(skolemize,[status(sab)],[392])).
% 22.74/22.95 tff(394,plain,
% 22.74/22.95 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (closed_subset(B, A) <=> open_subset(subset_difference(the_carrier(A), cast_as_carrier_subset(A), B), A))))),
% 22.74/22.95 inference(modus_ponens,[status(thm)],[393, 386])).
% 22.74/22.95 tff(395,plain,
% 22.74/22.95 (((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (closed_subset(B, A) <=> open_subset(subset_difference(the_carrier(A), cast_as_carrier_subset(A), B), A))))) | ((~top_str(A!10)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (closed_subset(B, A!10) <=> open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B), A!10))))) <=> ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (closed_subset(B, A) <=> open_subset(subset_difference(the_carrier(A), cast_as_carrier_subset(A), B), A))))) | (~top_str(A!10)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (closed_subset(B, A!10) <=> open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B), A!10))))),
% 22.74/22.95 inference(rewrite,[status(thm)],[])).
% 22.74/22.95 tff(396,plain,
% 22.74/22.95 ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (closed_subset(B, A) <=> open_subset(subset_difference(the_carrier(A), cast_as_carrier_subset(A), B), A))))) | ((~top_str(A!10)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (closed_subset(B, A!10) <=> open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B), A!10))))),
% 22.74/22.95 inference(quant_inst,[status(thm)],[])).
% 22.74/22.95 tff(397,plain,
% 22.74/22.95 ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (closed_subset(B, A) <=> open_subset(subset_difference(the_carrier(A), cast_as_carrier_subset(A), B), A))))) | (~top_str(A!10)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (closed_subset(B, A!10) <=> open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B), A!10)))),
% 22.74/22.95 inference(modus_ponens,[status(thm)],[396, 395])).
% 22.74/22.95 tff(398,plain,
% 22.74/22.95 (![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (closed_subset(B, A!10) <=> open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B), A!10)))),
% 22.74/22.95 inference(unit_resolution,[status(thm)],[397, 394, 20])).
% 22.74/22.95 tff(399,plain,
% 22.74/22.95 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (closed_subset(B, A!10) <=> open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B), A!10)))) | ((~element(D!13, powerset(the_carrier(A!10)))) | (closed_subset(D!13, A!10) <=> open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), A!10)))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (closed_subset(B, A!10) <=> open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B), A!10)))) | (~element(D!13, powerset(the_carrier(A!10)))) | (closed_subset(D!13, A!10) <=> open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), A!10)))),
% 22.74/22.95 inference(rewrite,[status(thm)],[])).
% 22.74/22.95 tff(400,plain,
% 22.74/22.95 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (closed_subset(B, A!10) <=> open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B), A!10)))) | ((~element(D!13, powerset(the_carrier(A!10)))) | (closed_subset(D!13, A!10) <=> open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), A!10)))),
% 22.74/22.95 inference(quant_inst,[status(thm)],[])).
% 22.74/22.95 tff(401,plain,
% 22.74/22.95 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (closed_subset(B, A!10) <=> open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B), A!10)))) | (~element(D!13, powerset(the_carrier(A!10)))) | (closed_subset(D!13, A!10) <=> open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), A!10))),
% 22.74/22.95 inference(modus_ponens,[status(thm)],[400, 399])).
% 22.74/22.95 tff(402,plain,
% 22.74/22.95 (closed_subset(D!13, A!10) <=> open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), A!10)),
% 22.74/22.95 inference(unit_resolution,[status(thm)],[401, 100, 398])).
% 22.74/22.95 tff(403,plain,
% 22.74/22.95 ((~(closed_subset(D!13, A!10) <=> open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), A!10))) | (~closed_subset(D!13, A!10)) | open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), A!10)),
% 22.74/22.95 inference(tautology,[status(thm)],[])).
% 22.74/22.95 tff(404,plain,
% 22.74/22.95 ((~(closed_subset(D!13, A!10) <=> open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), A!10))) | open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), A!10)),
% 22.74/22.95 inference(unit_resolution,[status(thm)],[403, 98])).
% 22.74/22.95 tff(405,plain,
% 22.74/22.95 (open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), A!10)),
% 22.74/22.95 inference(unit_resolution,[status(thm)],[404, 402])).
% 22.74/22.95 tff(406,assumption,(![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(C!12, E)))), introduced(assumption)).
% 22.74/22.95 tff(407,assumption,(in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))), introduced(assumption)).
% 22.74/22.95 tff(408,assumption,(disjoint(B!11, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))), introduced(assumption)).
% 22.74/22.95 tff(409,assumption,(element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(the_carrier(A!10)))), introduced(assumption)).
% 22.74/22.95 tff(410,assumption,(open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), A!10)), introduced(assumption)).
% 22.74/22.95 tff(411,plain,
% 22.74/22.95 (((~![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(C!12, E)))) | ((~open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), A!10)) | (~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(the_carrier(A!10)))) | (~disjoint(B!11, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) | (~in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))))) <=> ((~![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(C!12, E)))) | (~open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), A!10)) | (~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(the_carrier(A!10)))) | (~disjoint(B!11, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) | (~in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))))),
% 22.74/22.95 inference(rewrite,[status(thm)],[])).
% 22.74/22.95 tff(412,plain,
% 22.74/22.95 (((~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(the_carrier(A!10)))) | (~open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), A!10)) | (~disjoint(B!11, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) | (~in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)))) <=> ((~open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), A!10)) | (~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(the_carrier(A!10)))) | (~disjoint(B!11, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) | (~in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))))),
% 22.74/22.95 inference(rewrite,[status(thm)],[])).
% 22.74/22.95 tff(413,plain,
% 22.74/22.95 (((~![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(C!12, E)))) | ((~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(the_carrier(A!10)))) | (~open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), A!10)) | (~disjoint(B!11, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) | (~in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))))) <=> ((~![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(C!12, E)))) | ((~open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), A!10)) | (~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(the_carrier(A!10)))) | (~disjoint(B!11, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) | (~in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)))))),
% 22.74/22.95 inference(monotonicity,[status(thm)],[412])).
% 22.74/22.95 tff(414,plain,
% 22.74/22.95 (((~![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(C!12, E)))) | ((~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(the_carrier(A!10)))) | (~open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), A!10)) | (~disjoint(B!11, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) | (~in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))))) <=> ((~![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(C!12, E)))) | (~open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), A!10)) | (~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(the_carrier(A!10)))) | (~disjoint(B!11, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) | (~in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))))),
% 22.74/22.95 inference(transitivity,[status(thm)],[413, 411])).
% 22.74/22.95 tff(415,plain,
% 22.74/22.95 ((~![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(C!12, E)))) | ((~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(the_carrier(A!10)))) | (~open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), A!10)) | (~disjoint(B!11, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) | (~in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))))),
% 22.74/22.95 inference(quant_inst,[status(thm)],[])).
% 22.74/22.95 tff(416,plain,
% 22.74/22.95 ((~![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(C!12, E)))) | (~open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), A!10)) | (~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(the_carrier(A!10)))) | (~disjoint(B!11, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) | (~in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)))),
% 22.74/22.95 inference(modus_ponens,[status(thm)],[415, 414])).
% 22.74/22.95 tff(417,plain,
% 22.74/22.95 ($false),
% 22.74/22.95 inference(unit_resolution,[status(thm)],[416, 410, 409, 408, 407, 406])).
% 22.74/22.95 tff(418,plain,((~![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(C!12, E)))) | (~open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), A!10)) | (~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13), powerset(the_carrier(A!10)))) | (~disjoint(B!11, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13))) | (~in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), D!13)))), inference(lemma,lemma(discharge,[]))).
% 22.74/22.95 tff(419,plain,
% 22.74/22.95 (~![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(C!12, E)))),
% 22.74/22.95 inference(unit_resolution,[status(thm)],[418, 405, 175, 381, 262])).
% 22.74/22.95 tff(420,assumption,(~![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(C!12, E)))), introduced(assumption)).
% 22.74/22.95 tff(421,assumption,(in(C!12, topstr_closure(A!10, B!11))), introduced(assumption)).
% 22.74/22.95 tff(422,plain,
% 22.74/22.95 ((~((~in(C!12, topstr_closure(A!10, B!11))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(C!12, E))))) | (~in(C!12, topstr_closure(A!10, B!11))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(C!12, E)))),
% 22.74/22.95 inference(tautology,[status(thm)],[])).
% 22.74/22.95 tff(423,plain,
% 22.74/22.95 (~((~in(C!12, topstr_closure(A!10, B!11))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(C!12, E))))),
% 22.74/22.95 inference(unit_resolution,[status(thm)],[422, 421, 420])).
% 22.74/22.95 tff(424,plain,
% 22.74/22.95 (((~((~in(C!12, topstr_closure(A!10, B!11))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(C!12, E))))) | (~(in(C!12, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10))) | (~in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) | (~open_subset(tptp_fun_E_0(C!12, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10))))))))) | ((~in(C!12, topstr_closure(A!10, B!11))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(C!12, E))))),
% 22.74/22.95 inference(tautology,[status(thm)],[])).
% 22.74/22.95 tff(425,plain,
% 22.74/22.95 ((~((~in(C!12, topstr_closure(A!10, B!11))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(C!12, E))))) | (~(in(C!12, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10))) | (~in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) | (~open_subset(tptp_fun_E_0(C!12, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10))))))))),
% 22.74/22.95 inference(unit_resolution,[status(thm)],[424, 423])).
% 22.74/22.95 tff(426,plain,
% 22.74/22.95 ($false),
% 22.74/22.95 inference(unit_resolution,[status(thm)],[90, 84, 83, 425])).
% 22.74/22.95 tff(427,plain,((~in(C!12, topstr_closure(A!10, B!11))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!10)))) | (~open_subset(E, A!10)) | (~disjoint(B!11, E)) | (~in(C!12, E)))), inference(lemma,lemma(discharge,[]))).
% 22.74/22.95 tff(428,plain,
% 22.74/22.95 (~in(C!12, topstr_closure(A!10, B!11))),
% 22.74/22.95 inference(unit_resolution,[status(thm)],[427, 419])).
% 22.74/22.95 tff(429,plain,
% 22.74/22.95 ((in(C!12, topstr_closure(A!10, B!11)) | ![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | in(C!12, D) | (~closed_subset(D, A!10)) | (~subset(B!11, D)))) <=> (in(C!12, topstr_closure(A!10, B!11)) | ![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | in(C!12, D) | (~closed_subset(D, A!10)) | (~subset(B!11, D))))),
% 22.74/22.95 inference(rewrite,[status(thm)],[])).
% 22.74/22.95 tff(430,plain,
% 22.74/22.95 ((in(C!12, topstr_closure(A!10, B!11)) | ![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | (~(closed_subset(D, A!10) & subset(B!11, D))) | in(C!12, D))) <=> (in(C!12, topstr_closure(A!10, B!11)) | ![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | in(C!12, D) | (~closed_subset(D, A!10)) | (~subset(B!11, D))))),
% 22.74/22.95 inference(rewrite,[status(thm)],[])).
% 22.74/22.95 tff(431,plain,
% 22.74/22.95 (in(C!12, topstr_closure(A!10, B!11)) | ![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | (~(closed_subset(D, A!10) & subset(B!11, D))) | in(C!12, D))),
% 22.74/22.95 inference(and_elim,[status(thm)],[18])).
% 22.74/22.95 tff(432,plain,
% 22.74/22.95 (in(C!12, topstr_closure(A!10, B!11)) | ![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | in(C!12, D) | (~closed_subset(D, A!10)) | (~subset(B!11, D)))),
% 22.74/22.95 inference(modus_ponens,[status(thm)],[431, 430])).
% 22.74/22.95 tff(433,plain,
% 22.74/22.95 (in(C!12, topstr_closure(A!10, B!11)) | ![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | in(C!12, D) | (~closed_subset(D, A!10)) | (~subset(B!11, D)))),
% 22.74/22.95 inference(modus_ponens,[status(thm)],[432, 429])).
% 22.74/22.95 tff(434,plain,
% 22.74/22.95 (![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | in(C!12, D) | (~closed_subset(D, A!10)) | (~subset(B!11, D)))),
% 22.74/22.95 inference(unit_resolution,[status(thm)],[433, 428])).
% 22.74/22.95 tff(435,plain,
% 22.74/22.95 (((~![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | in(C!12, D) | (~closed_subset(D, A!10)) | (~subset(B!11, D)))) | (in(C!12, D!13) | (~element(D!13, powerset(the_carrier(A!10)))) | (~closed_subset(D!13, A!10)) | (~subset(B!11, D!13)))) <=> ((~![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | in(C!12, D) | (~closed_subset(D, A!10)) | (~subset(B!11, D)))) | in(C!12, D!13) | (~element(D!13, powerset(the_carrier(A!10)))) | (~closed_subset(D!13, A!10)) | (~subset(B!11, D!13)))),
% 22.74/22.95 inference(rewrite,[status(thm)],[])).
% 22.74/22.95 tff(436,plain,
% 22.74/22.95 (((~element(D!13, powerset(the_carrier(A!10)))) | in(C!12, D!13) | (~closed_subset(D!13, A!10)) | (~subset(B!11, D!13))) <=> (in(C!12, D!13) | (~element(D!13, powerset(the_carrier(A!10)))) | (~closed_subset(D!13, A!10)) | (~subset(B!11, D!13)))),
% 22.74/22.95 inference(rewrite,[status(thm)],[])).
% 22.74/22.95 tff(437,plain,
% 22.74/22.95 (((~![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | in(C!12, D) | (~closed_subset(D, A!10)) | (~subset(B!11, D)))) | ((~element(D!13, powerset(the_carrier(A!10)))) | in(C!12, D!13) | (~closed_subset(D!13, A!10)) | (~subset(B!11, D!13)))) <=> ((~![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | in(C!12, D) | (~closed_subset(D, A!10)) | (~subset(B!11, D)))) | (in(C!12, D!13) | (~element(D!13, powerset(the_carrier(A!10)))) | (~closed_subset(D!13, A!10)) | (~subset(B!11, D!13))))),
% 22.74/22.95 inference(monotonicity,[status(thm)],[436])).
% 22.74/22.95 tff(438,plain,
% 22.74/22.95 (((~![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | in(C!12, D) | (~closed_subset(D, A!10)) | (~subset(B!11, D)))) | ((~element(D!13, powerset(the_carrier(A!10)))) | in(C!12, D!13) | (~closed_subset(D!13, A!10)) | (~subset(B!11, D!13)))) <=> ((~![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | in(C!12, D) | (~closed_subset(D, A!10)) | (~subset(B!11, D)))) | in(C!12, D!13) | (~element(D!13, powerset(the_carrier(A!10)))) | (~closed_subset(D!13, A!10)) | (~subset(B!11, D!13)))),
% 22.74/22.96 inference(transitivity,[status(thm)],[437, 435])).
% 22.74/22.96 tff(439,plain,
% 22.74/22.96 ((~![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | in(C!12, D) | (~closed_subset(D, A!10)) | (~subset(B!11, D)))) | ((~element(D!13, powerset(the_carrier(A!10)))) | in(C!12, D!13) | (~closed_subset(D!13, A!10)) | (~subset(B!11, D!13)))),
% 22.74/22.96 inference(quant_inst,[status(thm)],[])).
% 22.74/22.96 tff(440,plain,
% 22.74/22.96 ((~![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | in(C!12, D) | (~closed_subset(D, A!10)) | (~subset(B!11, D)))) | in(C!12, D!13) | (~element(D!13, powerset(the_carrier(A!10)))) | (~closed_subset(D!13, A!10)) | (~subset(B!11, D!13))),
% 22.74/22.96 inference(modus_ponens,[status(thm)],[439, 438])).
% 22.74/22.96 tff(441,plain,
% 22.74/22.96 ($false),
% 22.74/22.96 inference(unit_resolution,[status(thm)],[440, 434, 102, 100, 98, 96])).
% 22.74/22.96 tff(442,plain,(in(C!12, D!13) | (~element(D!13, powerset(the_carrier(A!10)))) | (~closed_subset(D!13, A!10)) | (~subset(B!11, D!13))), inference(lemma,lemma(discharge,[]))).
% 22.74/22.96 tff(443,plain,
% 22.74/22.96 (((~in(C!12, topstr_closure(A!10, B!11))) | (~(in(C!12, D!13) | (~(closed_subset(D!13, A!10) & subset(B!11, D!13))) | (~element(D!13, powerset(the_carrier(A!10))))))) <=> ((~in(C!12, topstr_closure(A!10, B!11))) | (~(in(C!12, D!13) | (~element(D!13, powerset(the_carrier(A!10)))) | (~closed_subset(D!13, A!10)) | (~subset(B!11, D!13)))))),
% 22.74/22.96 inference(rewrite,[status(thm)],[])).
% 22.74/22.96 tff(444,plain,
% 22.74/22.96 ((~in(C!12, topstr_closure(A!10, B!11))) | (~(in(C!12, D!13) | (~(closed_subset(D!13, A!10) & subset(B!11, D!13))) | (~element(D!13, powerset(the_carrier(A!10))))))),
% 22.74/22.96 inference(and_elim,[status(thm)],[18])).
% 22.74/22.96 tff(445,plain,
% 22.74/22.96 ((~in(C!12, topstr_closure(A!10, B!11))) | (~(in(C!12, D!13) | (~element(D!13, powerset(the_carrier(A!10)))) | (~closed_subset(D!13, A!10)) | (~subset(B!11, D!13))))),
% 22.74/22.96 inference(modus_ponens,[status(thm)],[444, 443])).
% 22.74/22.96 tff(446,plain,
% 22.74/22.96 (~in(C!12, topstr_closure(A!10, B!11))),
% 22.74/22.96 inference(unit_resolution,[status(thm)],[445, 442])).
% 22.74/22.96 tff(447,plain,
% 22.74/22.96 ((~(in(C!12, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10))) | (~in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) | (~open_subset(tptp_fun_E_0(C!12, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))))))) | in(C!12, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10))) | (~in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) | (~open_subset(tptp_fun_E_0(C!12, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10))))))),
% 22.74/22.96 inference(tautology,[status(thm)],[])).
% 22.74/22.96 tff(448,plain,
% 22.74/22.96 ((~(in(C!12, topstr_closure(A!10, B!11)) | (~((~disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10))) | (~in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) | (~open_subset(tptp_fun_E_0(C!12, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))))))) | (~((~disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10))) | (~in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) | (~open_subset(tptp_fun_E_0(C!12, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10))))))),
% 22.74/22.96 inference(unit_resolution,[status(thm)],[447, 446])).
% 22.74/22.96 tff(449,plain,
% 22.74/22.96 (~((~disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10))) | (~in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) | (~open_subset(tptp_fun_E_0(C!12, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))))),
% 22.74/22.96 inference(unit_resolution,[status(thm)],[448, 93])).
% 22.74/22.96 tff(450,plain,
% 22.74/22.96 (((~disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10))) | (~in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) | (~open_subset(tptp_fun_E_0(C!12, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10))))) | in(C!12, tptp_fun_E_0(C!12, B!11, A!10))),
% 22.74/22.96 inference(tautology,[status(thm)],[])).
% 22.74/22.96 tff(451,plain,
% 22.74/22.96 (in(C!12, tptp_fun_E_0(C!12, B!11, A!10))),
% 22.74/22.96 inference(unit_resolution,[status(thm)],[450, 449])).
% 22.74/22.96 tff(452,plain,
% 22.74/22.96 (((~in(C!12, the_carrier(A!10))) | in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) | (~in(C!12, tptp_fun_E_0(C!12, B!11, A!10)))),
% 22.74/22.96 inference(tautology,[status(thm)],[])).
% 22.74/22.96 tff(453,plain,
% 22.74/22.96 ((~in(C!12, the_carrier(A!10))) | in(C!12, tptp_fun_E_0(C!12, B!11, A!10))),
% 22.74/22.96 inference(unit_resolution,[status(thm)],[452, 451])).
% 22.74/22.96 tff(454,plain,
% 22.74/22.96 (((~disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10))) | (~in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) | (~open_subset(tptp_fun_E_0(C!12, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10))))) | element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))),
% 22.74/22.96 inference(tautology,[status(thm)],[])).
% 22.74/22.96 tff(455,plain,
% 22.74/22.96 (element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))),
% 22.74/22.96 inference(unit_resolution,[status(thm)],[454, 449])).
% 22.74/22.96 tff(456,plain,
% 22.74/22.96 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (subset_complement(the_carrier(A!10), B) = subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B)))) | ((~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))) | (subset_complement(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)) = subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (subset_complement(the_carrier(A!10), B) = subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B)))) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))) | (subset_complement(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)) = subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))))),
% 22.74/22.96 inference(rewrite,[status(thm)],[])).
% 22.74/22.96 tff(457,plain,
% 22.74/22.96 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (subset_complement(the_carrier(A!10), B) = subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B)))) | ((~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))) | (subset_complement(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)) = subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))))),
% 22.74/22.96 inference(quant_inst,[status(thm)],[])).
% 22.74/22.96 tff(458,plain,
% 22.74/22.96 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (subset_complement(the_carrier(A!10), B) = subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B)))) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))) | (subset_complement(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)) = subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)))),
% 22.74/22.96 inference(modus_ponens,[status(thm)],[457, 456])).
% 22.74/22.96 tff(459,plain,
% 22.74/22.96 (subset_complement(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)) = subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))),
% 22.74/22.96 inference(unit_resolution,[status(thm)],[458, 155, 455])).
% 22.74/22.96 tff(460,plain,
% 22.74/22.96 (element(subset_complement(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)), powerset(the_carrier(A!10))) <=> element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), powerset(the_carrier(A!10)))),
% 22.74/22.96 inference(monotonicity,[status(thm)],[459])).
% 22.74/22.96 tff(461,plain,
% 22.74/22.96 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | ((~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))) | element(subset_complement(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)), powerset(the_carrier(A!10))))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))) | element(subset_complement(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)), powerset(the_carrier(A!10))))),
% 22.74/22.96 inference(rewrite,[status(thm)],[])).
% 22.74/22.96 tff(462,plain,
% 22.74/22.96 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | ((~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))) | element(subset_complement(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)), powerset(the_carrier(A!10))))),
% 22.74/22.96 inference(quant_inst,[status(thm)],[])).
% 22.74/22.96 tff(463,plain,
% 22.74/22.96 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))) | element(subset_complement(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)), powerset(the_carrier(A!10)))),
% 22.74/22.96 inference(modus_ponens,[status(thm)],[462, 461])).
% 22.74/22.96 tff(464,plain,
% 22.74/22.96 (element(subset_complement(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)), powerset(the_carrier(A!10)))),
% 22.74/22.96 inference(unit_resolution,[status(thm)],[463, 170, 455])).
% 22.74/22.96 tff(465,plain,
% 22.74/22.96 (element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), powerset(the_carrier(A!10)))),
% 22.74/22.96 inference(modus_ponens,[status(thm)],[464, 460])).
% 22.74/22.96 tff(466,plain,
% 22.74/22.96 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (closed_subset(B, A!10) <=> open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B), A!10)))) | ((~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), powerset(the_carrier(A!10)))) | (closed_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), A!10) <=> open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))), A!10)))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (closed_subset(B, A!10) <=> open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B), A!10)))) | (~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), powerset(the_carrier(A!10)))) | (closed_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), A!10) <=> open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))), A!10)))),
% 22.74/22.96 inference(rewrite,[status(thm)],[])).
% 22.74/22.96 tff(467,plain,
% 22.74/22.96 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (closed_subset(B, A!10) <=> open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B), A!10)))) | ((~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), powerset(the_carrier(A!10)))) | (closed_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), A!10) <=> open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))), A!10)))),
% 22.74/22.96 inference(quant_inst,[status(thm)],[])).
% 22.74/22.96 tff(468,plain,
% 22.74/22.96 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (closed_subset(B, A!10) <=> open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B), A!10)))) | (~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), powerset(the_carrier(A!10)))) | (closed_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), A!10) <=> open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))), A!10))),
% 22.74/22.96 inference(modus_ponens,[status(thm)],[467, 466])).
% 22.74/22.96 tff(469,plain,
% 22.74/22.96 ((~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), powerset(the_carrier(A!10)))) | (closed_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), A!10) <=> open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))), A!10))),
% 22.74/22.96 inference(unit_resolution,[status(thm)],[468, 398])).
% 22.74/22.96 tff(470,plain,
% 22.74/22.96 (closed_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), A!10) <=> open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))), A!10)),
% 22.74/22.96 inference(unit_resolution,[status(thm)],[469, 465])).
% 22.74/22.96 tff(471,plain,
% 22.74/22.96 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B)) = B))) | ((~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))) = tptp_fun_E_0(C!12, B!11, A!10)))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B)) = B))) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))) = tptp_fun_E_0(C!12, B!11, A!10)))),
% 22.74/22.96 inference(rewrite,[status(thm)],[])).
% 22.74/22.96 tff(472,plain,
% 22.74/22.96 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B)) = B))) | ((~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))) = tptp_fun_E_0(C!12, B!11, A!10)))),
% 22.74/22.96 inference(quant_inst,[status(thm)],[])).
% 22.74/22.96 tff(473,plain,
% 22.74/22.96 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), B)) = B))) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))) = tptp_fun_E_0(C!12, B!11, A!10))),
% 22.74/22.96 inference(modus_ponens,[status(thm)],[472, 471])).
% 22.74/22.96 tff(474,plain,
% 22.74/22.96 (subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))) = tptp_fun_E_0(C!12, B!11, A!10)),
% 22.74/22.96 inference(unit_resolution,[status(thm)],[473, 247, 455])).
% 22.74/22.96 tff(475,plain,
% 22.74/22.96 (open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))), A!10) <=> open_subset(tptp_fun_E_0(C!12, B!11, A!10), A!10)),
% 22.74/22.96 inference(monotonicity,[status(thm)],[474])).
% 22.74/22.96 tff(476,plain,
% 22.74/22.96 (open_subset(tptp_fun_E_0(C!12, B!11, A!10), A!10) <=> open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))), A!10)),
% 22.74/22.96 inference(symmetry,[status(thm)],[475])).
% 22.74/22.96 tff(477,plain,
% 22.74/22.96 (((~disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10))) | (~in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) | (~open_subset(tptp_fun_E_0(C!12, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10))))) | open_subset(tptp_fun_E_0(C!12, B!11, A!10), A!10)),
% 22.74/22.96 inference(tautology,[status(thm)],[])).
% 22.74/22.96 tff(478,plain,
% 22.74/22.96 (open_subset(tptp_fun_E_0(C!12, B!11, A!10), A!10)),
% 22.74/22.96 inference(unit_resolution,[status(thm)],[477, 449])).
% 22.74/22.96 tff(479,plain,
% 22.74/22.96 (open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))), A!10)),
% 22.74/22.96 inference(modus_ponens,[status(thm)],[478, 476])).
% 22.74/22.96 tff(480,plain,
% 22.74/22.96 ((~(closed_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), A!10) <=> open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))), A!10))) | closed_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), A!10) | (~open_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))), A!10))),
% 22.74/22.96 inference(tautology,[status(thm)],[])).
% 22.74/22.96 tff(481,plain,
% 22.74/22.96 (closed_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), A!10)),
% 22.74/22.96 inference(unit_resolution,[status(thm)],[480, 479, 470])).
% 22.74/22.96 tff(482,plain,
% 22.74/22.96 (subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)) = subset_complement(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10))),
% 22.74/22.96 inference(symmetry,[status(thm)],[459])).
% 22.74/22.96 tff(483,plain,
% 22.74/22.96 (subset(B!11, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))) <=> subset(B!11, subset_complement(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)))),
% 22.74/22.96 inference(monotonicity,[status(thm)],[482])).
% 22.74/22.96 tff(484,plain,
% 22.74/22.96 (subset(B!11, subset_complement(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10))) <=> subset(B!11, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)))),
% 22.74/22.96 inference(symmetry,[status(thm)],[483])).
% 22.74/22.96 tff(485,plain,
% 22.74/22.96 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C)))))) | ((~element(B!11, powerset(the_carrier(A!10)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (disjoint(B!11, C) <=> subset(B!11, subset_complement(the_carrier(A!10), C)))))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C)))))) | (~element(B!11, powerset(the_carrier(A!10)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (disjoint(B!11, C) <=> subset(B!11, subset_complement(the_carrier(A!10), C)))))),
% 22.74/22.96 inference(rewrite,[status(thm)],[])).
% 22.74/22.96 tff(486,plain,
% 22.74/22.96 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C)))))) | ((~element(B!11, powerset(the_carrier(A!10)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (disjoint(B!11, C) <=> subset(B!11, subset_complement(the_carrier(A!10), C)))))),
% 22.74/22.96 inference(quant_inst,[status(thm)],[])).
% 22.74/22.96 tff(487,plain,
% 22.74/22.96 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C)))))) | (~element(B!11, powerset(the_carrier(A!10)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (disjoint(B!11, C) <=> subset(B!11, subset_complement(the_carrier(A!10), C))))),
% 22.74/22.96 inference(modus_ponens,[status(thm)],[486, 485])).
% 22.74/22.96 tff(488,plain,
% 22.74/22.96 (![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (disjoint(B!11, C) <=> subset(B!11, subset_complement(the_carrier(A!10), C))))),
% 22.74/22.96 inference(unit_resolution,[status(thm)],[487, 350, 19])).
% 22.74/22.96 tff(489,plain,
% 22.74/22.96 (((~![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (disjoint(B!11, C) <=> subset(B!11, subset_complement(the_carrier(A!10), C))))) | ((~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))) | (disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10)) <=> subset(B!11, subset_complement(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)))))) <=> ((~![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (disjoint(B!11, C) <=> subset(B!11, subset_complement(the_carrier(A!10), C))))) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))) | (disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10)) <=> subset(B!11, subset_complement(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)))))),
% 22.74/22.96 inference(rewrite,[status(thm)],[])).
% 22.74/22.96 tff(490,plain,
% 22.74/22.96 ((~![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (disjoint(B!11, C) <=> subset(B!11, subset_complement(the_carrier(A!10), C))))) | ((~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))) | (disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10)) <=> subset(B!11, subset_complement(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)))))),
% 22.74/22.96 inference(quant_inst,[status(thm)],[])).
% 22.74/22.96 tff(491,plain,
% 22.74/22.96 ((~![C: $i] : ((~element(C, powerset(the_carrier(A!10)))) | (disjoint(B!11, C) <=> subset(B!11, subset_complement(the_carrier(A!10), C))))) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))) | (disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10)) <=> subset(B!11, subset_complement(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10))))),
% 22.74/22.96 inference(modus_ponens,[status(thm)],[490, 489])).
% 22.74/22.96 tff(492,plain,
% 22.74/22.96 (disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10)) <=> subset(B!11, subset_complement(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)))),
% 22.74/22.96 inference(unit_resolution,[status(thm)],[491, 488, 455])).
% 22.74/22.96 tff(493,plain,
% 22.74/22.96 (((~disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10))) | (~in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) | (~open_subset(tptp_fun_E_0(C!12, B!11, A!10), A!10)) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10))))) | disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10))),
% 22.74/22.96 inference(tautology,[status(thm)],[])).
% 22.74/22.96 tff(494,plain,
% 22.74/22.96 (disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10))),
% 22.74/22.96 inference(unit_resolution,[status(thm)],[493, 449])).
% 22.74/22.96 tff(495,plain,
% 22.74/22.96 ((~(disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10)) <=> subset(B!11, subset_complement(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10))))) | (~disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10))) | subset(B!11, subset_complement(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)))),
% 22.74/22.96 inference(tautology,[status(thm)],[])).
% 22.74/22.96 tff(496,plain,
% 22.74/22.96 ((~(disjoint(B!11, tptp_fun_E_0(C!12, B!11, A!10)) <=> subset(B!11, subset_complement(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10))))) | subset(B!11, subset_complement(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)))),
% 22.74/22.96 inference(unit_resolution,[status(thm)],[495, 494])).
% 22.74/22.96 tff(497,plain,
% 22.74/22.96 (subset(B!11, subset_complement(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)))),
% 22.74/22.96 inference(unit_resolution,[status(thm)],[496, 492])).
% 22.74/22.96 tff(498,plain,
% 22.74/22.96 (subset(B!11, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)))),
% 22.74/22.96 inference(modus_ponens,[status(thm)],[497, 484])).
% 22.74/22.96 tff(499,plain,
% 22.74/22.96 (![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | in(C!12, D) | (~closed_subset(D, A!10)) | (~subset(B!11, D)))),
% 22.74/22.96 inference(unit_resolution,[status(thm)],[433, 446])).
% 22.74/22.96 tff(500,plain,
% 22.74/22.96 (((~![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | in(C!12, D) | (~closed_subset(D, A!10)) | (~subset(B!11, D)))) | ((~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), powerset(the_carrier(A!10)))) | in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))) | (~closed_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), A!10)) | (~subset(B!11, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)))))) <=> ((~![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | in(C!12, D) | (~closed_subset(D, A!10)) | (~subset(B!11, D)))) | (~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), powerset(the_carrier(A!10)))) | in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))) | (~closed_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), A!10)) | (~subset(B!11, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)))))),
% 22.74/22.96 inference(rewrite,[status(thm)],[])).
% 22.74/22.96 tff(501,plain,
% 22.74/22.96 ((~![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | in(C!12, D) | (~closed_subset(D, A!10)) | (~subset(B!11, D)))) | ((~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), powerset(the_carrier(A!10)))) | in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))) | (~closed_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), A!10)) | (~subset(B!11, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)))))),
% 22.74/22.96 inference(quant_inst,[status(thm)],[])).
% 22.74/22.96 tff(502,plain,
% 22.74/22.96 ((~![D: $i] : ((~element(D, powerset(the_carrier(A!10)))) | in(C!12, D) | (~closed_subset(D, A!10)) | (~subset(B!11, D)))) | (~element(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), powerset(the_carrier(A!10)))) | in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))) | (~closed_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), A!10)) | (~subset(B!11, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))))),
% 22.74/22.96 inference(modus_ponens,[status(thm)],[501, 500])).
% 22.74/22.96 tff(503,plain,
% 22.74/22.96 (in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))) | (~closed_subset(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), A!10))),
% 22.74/22.96 inference(unit_resolution,[status(thm)],[502, 499, 465, 498])).
% 22.74/22.96 tff(504,plain,
% 22.74/22.96 (in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)))),
% 22.74/22.96 inference(unit_resolution,[status(thm)],[503, 481])).
% 22.74/22.96 tff(505,plain,
% 22.74/22.96 ((((~in(C!12, the_carrier(A!10))) | in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) <=> in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)))) | (~((~in(C!12, the_carrier(A!10))) | in(C!12, tptp_fun_E_0(C!12, B!11, A!10)))) | (~in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))))),
% 22.74/22.96 inference(tautology,[status(thm)],[])).
% 22.74/22.96 tff(506,plain,
% 22.74/22.96 (((~in(C!12, the_carrier(A!10))) | in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) <=> in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)))),
% 22.74/22.96 inference(unit_resolution,[status(thm)],[505, 504, 453])).
% 22.74/22.96 tff(507,plain,
% 22.74/22.96 (((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((~element(the_carrier(A!10), powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)) = set_difference(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10))) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | (~element(the_carrier(A!10), powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)) = set_difference(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10))) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))))),
% 22.74/22.96 inference(rewrite,[status(thm)],[])).
% 22.74/22.96 tff(508,plain,
% 22.74/22.96 (((subset_difference(the_carrier(A!10), the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)) = set_difference(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10))) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))) | (~element(the_carrier(A!10), powerset(the_carrier(A!10))))) <=> ((~element(the_carrier(A!10), powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)) = set_difference(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10))) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))))),
% 22.74/22.96 inference(rewrite,[status(thm)],[])).
% 22.74/22.96 tff(509,plain,
% 22.74/22.96 (((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((subset_difference(the_carrier(A!10), the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)) = set_difference(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10))) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))) | (~element(the_carrier(A!10), powerset(the_carrier(A!10)))))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((~element(the_carrier(A!10), powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)) = set_difference(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10))) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10))))))),
% 22.74/22.97 inference(monotonicity,[status(thm)],[508])).
% 22.74/22.97 tff(510,plain,
% 22.74/22.97 (((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((subset_difference(the_carrier(A!10), the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)) = set_difference(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10))) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))) | (~element(the_carrier(A!10), powerset(the_carrier(A!10)))))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | (~element(the_carrier(A!10), powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)) = set_difference(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10))) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))))),
% 22.74/22.97 inference(transitivity,[status(thm)],[509, 507])).
% 22.74/22.97 tff(511,plain,
% 22.74/22.97 ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((subset_difference(the_carrier(A!10), the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)) = set_difference(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10))) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10)))) | (~element(the_carrier(A!10), powerset(the_carrier(A!10)))))),
% 22.74/22.97 inference(quant_inst,[status(thm)],[])).
% 22.74/22.97 tff(512,plain,
% 22.74/22.97 ((~![A: $i, B: $i, C: $i] : ((subset_difference(A, B, C) = set_difference(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | (~element(the_carrier(A!10), powerset(the_carrier(A!10)))) | (subset_difference(the_carrier(A!10), the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)) = set_difference(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10))) | (~element(tptp_fun_E_0(C!12, B!11, A!10), powerset(the_carrier(A!10))))),
% 22.74/22.97 inference(modus_ponens,[status(thm)],[511, 510])).
% 22.74/22.97 tff(513,plain,
% 22.74/22.97 (subset_difference(the_carrier(A!10), the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)) = set_difference(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10))),
% 22.74/22.97 inference(unit_resolution,[status(thm)],[512, 220, 207, 455])).
% 22.74/22.97 tff(514,plain,
% 22.74/22.97 (subset_difference(the_carrier(A!10), the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)) = subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))),
% 22.74/22.97 inference(monotonicity,[status(thm)],[190])).
% 22.74/22.97 tff(515,plain,
% 22.74/22.97 (subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)) = subset_difference(the_carrier(A!10), the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10))),
% 22.74/22.97 inference(symmetry,[status(thm)],[514])).
% 22.74/22.97 tff(516,plain,
% 22.74/22.97 (subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)) = set_difference(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10))),
% 22.74/22.97 inference(transitivity,[status(thm)],[515, 513])).
% 22.74/22.97 tff(517,plain,
% 22.74/22.97 ((~((~(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)) = set_difference(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)))) | (~(((~in(C!12, the_carrier(A!10))) | in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) <=> in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))))))) | (~(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)) = set_difference(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)))) | (~(((~in(C!12, the_carrier(A!10))) | in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) <=> in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)))))),
% 22.74/22.97 inference(tautology,[status(thm)],[])).
% 22.74/22.97 tff(518,plain,
% 22.74/22.97 (~((~(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)) = set_difference(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)))) | (~(((~in(C!12, the_carrier(A!10))) | in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) <=> in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))))))),
% 22.74/22.97 inference(unit_resolution,[status(thm)],[517, 516, 506])).
% 22.74/22.97 tff(519,plain,
% 22.74/22.97 (((~((~(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)) = set_difference(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)))) | (~(((~in(C!12, the_carrier(A!10))) | in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) <=> in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))))))) | (~((subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)) = set_difference(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10))) | (((~in(tptp_fun_D_3(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), tptp_fun_E_0(C!12, B!11, A!10), the_carrier(A!10)), the_carrier(A!10))) | in(tptp_fun_D_3(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), tptp_fun_E_0(C!12, B!11, A!10), the_carrier(A!10)), tptp_fun_E_0(C!12, B!11, A!10))) <=> in(tptp_fun_D_3(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), tptp_fun_E_0(C!12, B!11, A!10), the_carrier(A!10)), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))))))) | ((~(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)) = set_difference(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)))) | (~(((~in(C!12, the_carrier(A!10))) | in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) <=> in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))))))),
% 22.74/22.97 inference(tautology,[status(thm)],[])).
% 22.74/22.97 tff(520,plain,
% 22.74/22.97 ((~((~(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)) = set_difference(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)))) | (~(((~in(C!12, the_carrier(A!10))) | in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) <=> in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))))))) | (~((subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)) = set_difference(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10))) | (((~in(tptp_fun_D_3(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), tptp_fun_E_0(C!12, B!11, A!10), the_carrier(A!10)), the_carrier(A!10))) | in(tptp_fun_D_3(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), tptp_fun_E_0(C!12, B!11, A!10), the_carrier(A!10)), tptp_fun_E_0(C!12, B!11, A!10))) <=> in(tptp_fun_D_3(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), tptp_fun_E_0(C!12, B!11, A!10), the_carrier(A!10)), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))))))),
% 22.82/23.02 inference(unit_resolution,[status(thm)],[519, 518])).
% 22.82/23.02 tff(521,plain,
% 22.82/23.02 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_3(C, B, A), A)) | in(tptp_fun_D_3(C, B, A), B)) <=> in(tptp_fun_D_3(C, B, A), C))))))) | (~((~((~(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)) = set_difference(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10)))) | (~(((~in(C!12, the_carrier(A!10))) | in(C!12, tptp_fun_E_0(C!12, B!11, A!10))) <=> in(C!12, subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))))))) | (~((subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)) = set_difference(the_carrier(A!10), tptp_fun_E_0(C!12, B!11, A!10))) | (((~in(tptp_fun_D_3(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), tptp_fun_E_0(C!12, B!11, A!10), the_carrier(A!10)), the_carrier(A!10))) | in(tptp_fun_D_3(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), tptp_fun_E_0(C!12, B!11, A!10), the_carrier(A!10)), tptp_fun_E_0(C!12, B!11, A!10))) <=> in(tptp_fun_D_3(subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10)), tptp_fun_E_0(C!12, B!11, A!10), the_carrier(A!10)), subset_difference(the_carrier(A!10), cast_as_carrier_subset(A!10), tptp_fun_E_0(C!12, B!11, A!10))))))))),
% 22.82/23.02 inference(quant_inst,[status(thm)],[])).
% 22.82/23.02 tff(522,plain,
% 22.82/23.02 ($false),
% 22.82/23.02 inference(unit_resolution,[status(thm)],[521, 120, 520])).
% 22.82/23.02 % SZS output end Proof
% 22.82/23.03 % E exiting
%------------------------------------------------------------------------------