TSTP Solution File: SEU317+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU317+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 : Tue Sep 20 07:28:52 EDT 2022
% Result : Theorem 0.18s 0.42s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU317+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sat Sep 3 12:01:15 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 0.18/0.42 % SZS status Theorem
% 0.18/0.42 % SZS output start Proof
% 0.18/0.42 tff(in_type, type, (
% 0.18/0.42 in: ( $i * $i ) > $o)).
% 0.18/0.42 tff(tptp_fun_D_7_type, type, (
% 0.18/0.42 tptp_fun_D_7: ( $i * $i * $i ) > $i)).
% 0.18/0.42 tff(tptp_fun_A_8_type, type, (
% 0.18/0.42 tptp_fun_A_8: $i)).
% 0.18/0.42 tff(tptp_fun_B_9_type, type, (
% 0.18/0.42 tptp_fun_B_9: $i)).
% 0.18/0.42 tff(tptp_fun_C_0_type, type, (
% 0.18/0.42 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.18/0.42 tff(topstr_closure_type, type, (
% 0.18/0.42 topstr_closure: ( $i * $i ) > $i)).
% 0.18/0.42 tff(subset_type, type, (
% 0.18/0.42 subset: ( $i * $i ) > $o)).
% 0.18/0.42 tff(closed_subset_type, type, (
% 0.18/0.42 closed_subset: ( $i * $i ) > $o)).
% 0.18/0.42 tff(element_type, type, (
% 0.18/0.42 element: ( $i * $i ) > $o)).
% 0.18/0.42 tff(powerset_type, type, (
% 0.18/0.42 powerset: $i > $i)).
% 0.18/0.42 tff(the_carrier_type, type, (
% 0.18/0.42 the_carrier: $i > $i)).
% 0.18/0.42 tff(top_str_type, type, (
% 0.18/0.42 top_str: $i > $o)).
% 0.18/0.42 tff(1,plain,
% 0.18/0.42 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(2,plain,
% 0.18/0.42 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.42 tff(3,plain,
% 0.18/0.42 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(4,plain,
% 0.18/0.42 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[3])).
% 0.18/0.42 tff(5,plain,
% 0.18/0.42 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.18/0.42 inference(transitivity,[status(thm)],[4, 2])).
% 0.18/0.42 tff(6,plain,
% 0.18/0.42 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(7,plain,
% 0.18/0.42 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[6])).
% 0.18/0.42 tff(8,plain,
% 0.18/0.42 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(9,plain,
% 0.18/0.42 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(10,plain,
% 0.18/0.42 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[9])).
% 0.18/0.42 tff(11,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_tarski')).
% 0.18/0.42 tff(12,plain,
% 0.18/0.42 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.18/0.42 tff(13,plain,
% 0.18/0.42 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.18/0.42 tff(14,plain,(
% 0.18/0.42 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))),
% 0.18/0.42 inference(skolemize,[status(sab)],[13])).
% 0.18/0.42 tff(15,plain,
% 0.18/0.42 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.18/0.42 tff(16,plain,
% 0.18/0.42 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.18/0.42 tff(17,plain,
% 0.18/0.42 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | ![C: $i] : ((~in(C, B!9)) | in(C, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))) | (~(subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)) | (~((~in(tptp_fun_C_0(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), B!9), B!9)) | in(tptp_fun_C_0(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(18,plain,
% 0.18/0.42 (~((~((~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | ![C: $i] : ((~in(C, B!9)) | in(C, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))) | (~(subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)) | (~((~in(tptp_fun_C_0(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), B!9), B!9)) | in(tptp_fun_C_0(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.18/0.42 tff(19,plain,
% 0.18/0.42 (((~((~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | ![C: $i] : ((~in(C, B!9)) | in(C, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))) | (~(subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)) | (~((~in(tptp_fun_C_0(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), B!9), B!9)) | in(tptp_fun_C_0(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))))) | ((~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | ![C: $i] : ((~in(C, B!9)) | in(C, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(20,plain,
% 0.18/0.42 ((~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | ![C: $i] : ((~in(C, B!9)) | in(C, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.18/0.42 tff(21,plain,
% 0.18/0.42 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(B!9, the_carrier(A!8))) | ![C: $i] : ((~in(C, B!9)) | in(C, the_carrier(A!8))))) | (~(subset(B!9, the_carrier(A!8)) | (~((~in(tptp_fun_C_0(the_carrier(A!8), B!9), B!9)) | in(tptp_fun_C_0(the_carrier(A!8), B!9), the_carrier(A!8))))))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(22,plain,
% 0.18/0.42 (~((~((~subset(B!9, the_carrier(A!8))) | ![C: $i] : ((~in(C, B!9)) | in(C, the_carrier(A!8))))) | (~(subset(B!9, the_carrier(A!8)) | (~((~in(tptp_fun_C_0(the_carrier(A!8), B!9), B!9)) | in(tptp_fun_C_0(the_carrier(A!8), B!9), the_carrier(A!8)))))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[21, 16])).
% 0.18/0.42 tff(23,plain,
% 0.18/0.42 (((~((~subset(B!9, the_carrier(A!8))) | ![C: $i] : ((~in(C, B!9)) | in(C, the_carrier(A!8))))) | (~(subset(B!9, the_carrier(A!8)) | (~((~in(tptp_fun_C_0(the_carrier(A!8), B!9), B!9)) | in(tptp_fun_C_0(the_carrier(A!8), B!9), the_carrier(A!8))))))) | ((~subset(B!9, the_carrier(A!8))) | ![C: $i] : ((~in(C, B!9)) | in(C, the_carrier(A!8))))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(24,plain,
% 0.18/0.42 ((~subset(B!9, the_carrier(A!8))) | ![C: $i] : ((~in(C, B!9)) | in(C, the_carrier(A!8)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.18/0.42 tff(25,plain,
% 0.18/0.42 (^[A: $i, B: $i] : refl((element(A, powerset(B)) <=> subset(A, B)) <=> (element(A, powerset(B)) <=> subset(A, B)))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(26,plain,
% 0.18/0.42 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[25])).
% 0.18/0.42 tff(27,plain,
% 0.18/0.42 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(28,axiom,(![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t3_subset')).
% 0.18/0.42 tff(29,plain,
% 0.18/0.42 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.18/0.42 tff(30,plain,(
% 0.18/0.42 ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.18/0.42 inference(skolemize,[status(sab)],[29])).
% 0.18/0.42 tff(31,plain,
% 0.18/0.42 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.18/0.42 tff(32,plain,
% 0.18/0.42 ((~![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))) | (element(B!9, powerset(the_carrier(A!8))) <=> subset(B!9, the_carrier(A!8)))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(33,plain,
% 0.18/0.42 (element(B!9, powerset(the_carrier(A!8))) <=> subset(B!9, the_carrier(A!8))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.18/0.42 tff(34,plain,
% 0.18/0.42 (((~(~top_str(A!8))) & (~((~element(B!9, powerset(the_carrier(A!8)))) | subset(B!9, topstr_closure(A!8, B!9))))) <=> (top_str(A!8) & (~((~element(B!9, powerset(the_carrier(A!8)))) | subset(B!9, topstr_closure(A!8, B!9)))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(35,plain,
% 0.18/0.42 ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))) <=> (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B)))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(36,plain,
% 0.18/0.42 ((~![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => subset(B, topstr_closure(A, B))))) <=> (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B)))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(37,axiom,(~![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => subset(B, topstr_closure(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t48_pre_topc')).
% 0.18/0.43 tff(38,plain,
% 0.18/0.43 (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.18/0.43 tff(39,plain,
% 0.18/0.43 (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[38, 35])).
% 0.18/0.43 tff(40,plain,
% 0.18/0.43 (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.18/0.43 tff(41,plain,
% 0.18/0.43 (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[40, 35])).
% 0.18/0.43 tff(42,plain,
% 0.18/0.43 (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[41, 35])).
% 0.18/0.43 tff(43,plain,
% 0.18/0.43 (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.18/0.43 tff(44,plain,
% 0.18/0.43 (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[43, 35])).
% 0.18/0.43 tff(45,plain,
% 0.18/0.43 (top_str(A!8) & (~((~element(B!9, powerset(the_carrier(A!8)))) | subset(B!9, topstr_closure(A!8, B!9))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[44, 34])).
% 0.18/0.43 tff(46,plain,
% 0.18/0.43 (~((~element(B!9, powerset(the_carrier(A!8)))) | subset(B!9, topstr_closure(A!8, B!9)))),
% 0.18/0.43 inference(and_elim,[status(thm)],[45])).
% 0.18/0.43 tff(47,plain,
% 0.18/0.43 (element(B!9, powerset(the_carrier(A!8)))),
% 0.18/0.43 inference(or_elim,[status(thm)],[46])).
% 0.18/0.43 tff(48,plain,
% 0.18/0.43 ((~(element(B!9, powerset(the_carrier(A!8))) <=> subset(B!9, the_carrier(A!8)))) | (~element(B!9, powerset(the_carrier(A!8)))) | subset(B!9, the_carrier(A!8))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(49,plain,
% 0.18/0.43 ((~(element(B!9, powerset(the_carrier(A!8))) <=> subset(B!9, the_carrier(A!8)))) | subset(B!9, the_carrier(A!8))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.18/0.43 tff(50,plain,
% 0.18/0.43 (subset(B!9, the_carrier(A!8))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[49, 33])).
% 0.18/0.43 tff(51,plain,
% 0.18/0.43 ((~((~subset(B!9, the_carrier(A!8))) | ![C: $i] : ((~in(C, B!9)) | in(C, the_carrier(A!8))))) | (~subset(B!9, the_carrier(A!8))) | ![C: $i] : ((~in(C, B!9)) | in(C, the_carrier(A!8)))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(52,plain,
% 0.18/0.43 ((~((~subset(B!9, the_carrier(A!8))) | ![C: $i] : ((~in(C, B!9)) | in(C, the_carrier(A!8))))) | ![C: $i] : ((~in(C, B!9)) | in(C, the_carrier(A!8)))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.18/0.43 tff(53,plain,
% 0.18/0.43 (![C: $i] : ((~in(C, B!9)) | in(C, the_carrier(A!8)))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[52, 24])).
% 0.18/0.43 tff(54,plain,
% 0.18/0.43 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(B!9, topstr_closure(A!8, B!9))) | ![C: $i] : ((~in(C, B!9)) | in(C, topstr_closure(A!8, B!9))))) | (~(subset(B!9, topstr_closure(A!8, B!9)) | (~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))))))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(55,plain,
% 0.18/0.43 (~((~((~subset(B!9, topstr_closure(A!8, B!9))) | ![C: $i] : ((~in(C, B!9)) | in(C, topstr_closure(A!8, B!9))))) | (~(subset(B!9, topstr_closure(A!8, B!9)) | (~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)))))))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[54, 16])).
% 0.18/0.43 tff(56,plain,
% 0.18/0.43 (((~((~subset(B!9, topstr_closure(A!8, B!9))) | ![C: $i] : ((~in(C, B!9)) | in(C, topstr_closure(A!8, B!9))))) | (~(subset(B!9, topstr_closure(A!8, B!9)) | (~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))))))) | (subset(B!9, topstr_closure(A!8, B!9)) | (~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)))))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(57,plain,
% 0.18/0.43 (subset(B!9, topstr_closure(A!8, B!9)) | (~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.18/0.43 tff(58,plain,
% 0.18/0.43 (~subset(B!9, topstr_closure(A!8, B!9))),
% 0.18/0.43 inference(or_elim,[status(thm)],[46])).
% 0.18/0.43 tff(59,plain,
% 0.18/0.43 ((~(subset(B!9, topstr_closure(A!8, B!9)) | (~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)))))) | subset(B!9, topstr_closure(A!8, B!9)) | (~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(60,plain,
% 0.18/0.43 ((~(subset(B!9, topstr_closure(A!8, B!9)) | (~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)))))) | (~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.18/0.43 tff(61,plain,
% 0.18/0.43 (~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[60, 57])).
% 0.18/0.43 tff(62,plain,
% 0.18/0.43 (((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(63,plain,
% 0.18/0.43 (in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.18/0.43 tff(64,plain,
% 0.18/0.43 (((~![C: $i] : ((~in(C, B!9)) | in(C, the_carrier(A!8)))) | ((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), the_carrier(A!8)))) <=> ((~![C: $i] : ((~in(C, B!9)) | in(C, the_carrier(A!8)))) | (~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), the_carrier(A!8)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(65,plain,
% 0.18/0.43 ((~![C: $i] : ((~in(C, B!9)) | in(C, the_carrier(A!8)))) | ((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), the_carrier(A!8)))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(66,plain,
% 0.18/0.43 ((~![C: $i] : ((~in(C, B!9)) | in(C, the_carrier(A!8)))) | (~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), the_carrier(A!8))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.18/0.43 tff(67,plain,
% 0.18/0.43 (in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), the_carrier(A!8))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[66, 63, 53])).
% 0.18/0.43 tff(68,plain,
% 0.18/0.43 (top_str(A!8)),
% 0.18/0.43 inference(and_elim,[status(thm)],[45])).
% 0.18/0.43 tff(69,plain,
% 0.18/0.43 (^[A: $i] : refl(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A)))))))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A)))))))))))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(70,plain,
% 0.18/0.43 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A)))))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A))))))))))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[69])).
% 0.18/0.43 tff(71,plain,
% 0.18/0.43 (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A)))))))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A)))))))))))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(72,plain,
% 0.18/0.43 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A)))))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A))))))))))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[71])).
% 0.18/0.43 tff(73,plain,
% 0.18/0.43 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A)))))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A))))))))))))),
% 0.18/0.43 inference(transitivity,[status(thm)],[72, 70])).
% 0.18/0.43 tff(74,plain,
% 0.18/0.43 (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))) & (in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~(closed_subset(tptp_fun_D_7(C, B, A), A) & subset(B, tptp_fun_D_7(C, B, A)))) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A))))))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A)))))))))))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(75,plain,
% 0.18/0.43 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))) & (in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~(closed_subset(tptp_fun_D_7(C, B, A), A) & subset(B, tptp_fun_D_7(C, B, A)))) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A))))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A))))))))))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[74])).
% 0.18/0.43 tff(76,plain,
% 0.18/0.43 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(77,plain,
% 0.18/0.43 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((in(C, topstr_closure(A, B)) <=> ![D: $i] : (element(D, powerset(the_carrier(A))) => ((closed_subset(D, A) & subset(B, D)) => in(C, D)))) <=> (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A))))))), ((in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (element(D, powerset(the_carrier(A))) => ((closed_subset(D, A) & subset(B, D)) => in(C, D))))) <=> (in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A))))))))), rewrite((in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A))))))) <=> ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))))), ((in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (element(D, powerset(the_carrier(A))) => ((closed_subset(D, A) & subset(B, D)) => in(C, D))))) <=> ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))))))), (![C: $i] : (in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (element(D, powerset(the_carrier(A))) => ((closed_subset(D, A) & subset(B, D)) => in(C, D))))) <=> ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A))))))))), ((element(B, powerset(the_carrier(A))) => ![C: $i] : (in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (element(D, powerset(the_carrier(A))) => ((closed_subset(D, A) & subset(B, D)) => in(C, D)))))) <=> (element(B, powerset(the_carrier(A))) => ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))))))), rewrite((element(B, powerset(the_carrier(A))) => ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))))) <=> ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A))))))))), ((element(B, powerset(the_carrier(A))) => ![C: $i] : (in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (element(D, powerset(the_carrier(A))) => ((closed_subset(D, A) & subset(B, D)) => in(C, D)))))) <=> ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A))))))))))), (![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (element(D, powerset(the_carrier(A))) => ((closed_subset(D, A) & subset(B, D)) => in(C, D)))))) <=> ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))))))), ((top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (element(D, powerset(the_carrier(A))) => ((closed_subset(D, A) & subset(B, D)) => in(C, D))))))) <=> (top_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A))))))))))), rewrite((top_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A))))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))))))), ((top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (element(D, powerset(the_carrier(A))) => ((closed_subset(D, A) & subset(B, D)) => in(C, D))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))))))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(78,plain,
% 0.18/0.44 (![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (element(D, powerset(the_carrier(A))) => ((closed_subset(D, A) & subset(B, D)) => in(C, D))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))))))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[77])).
% 0.18/0.44 tff(79,axiom,(![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (element(D, powerset(the_carrier(A))) => ((closed_subset(D, A) & subset(B, D)) => in(C, D)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t45_pre_topc')).
% 0.18/0.44 tff(80,plain,
% 0.18/0.44 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.18/0.44 tff(81,plain,
% 0.18/0.44 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.18/0.44 tff(82,plain,(
% 0.18/0.44 ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))) & (in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~(closed_subset(tptp_fun_D_7(C, B, A), A) & subset(B, tptp_fun_D_7(C, B, A)))) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))))))))))),
% 0.18/0.44 inference(skolemize,[status(sab)],[81])).
% 0.18/0.44 tff(83,plain,
% 0.18/0.44 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A))))))))))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.18/0.44 tff(84,plain,
% 0.18/0.44 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A))))))))))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[83, 73])).
% 0.18/0.44 tff(85,plain,
% 0.18/0.44 (((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A))))))))))))) | ((~top_str(A!8)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B)) | (~(in(C, tptp_fun_D_7(C, B, A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~subset(B, tptp_fun_D_7(C, B, A!8))))))))))))) <=> ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A))))))))))))) | (~top_str(A!8)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B)) | (~(in(C, tptp_fun_D_7(C, B, A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~subset(B, tptp_fun_D_7(C, B, A!8))))))))))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(86,plain,
% 0.18/0.44 (((~top_str(A!8)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A!8, B)) | (~(in(C, tptp_fun_D_7(C, B, A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~subset(B, tptp_fun_D_7(C, B, A!8)))))))))))) <=> ((~top_str(A!8)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B)) | (~(in(C, tptp_fun_D_7(C, B, A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~subset(B, tptp_fun_D_7(C, B, A!8))))))))))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(87,plain,
% 0.18/0.44 (((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A))))))))))))) | ((~top_str(A!8)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A!8, B)) | (~(in(C, tptp_fun_D_7(C, B, A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~subset(B, tptp_fun_D_7(C, B, A!8))))))))))))) <=> ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A))))))))))))) | ((~top_str(A!8)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B)) | (~(in(C, tptp_fun_D_7(C, B, A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~subset(B, tptp_fun_D_7(C, B, A!8)))))))))))))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[86])).
% 0.18/0.44 tff(88,plain,
% 0.18/0.44 (((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A))))))))))))) | ((~top_str(A!8)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A!8, B)) | (~(in(C, tptp_fun_D_7(C, B, A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~subset(B, tptp_fun_D_7(C, B, A!8))))))))))))) <=> ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A))))))))))))) | (~top_str(A!8)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B)) | (~(in(C, tptp_fun_D_7(C, B, A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~subset(B, tptp_fun_D_7(C, B, A!8))))))))))))),
% 0.18/0.44 inference(transitivity,[status(thm)],[87, 85])).
% 0.18/0.44 tff(89,plain,
% 0.18/0.44 ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A))))))))))))) | ((~top_str(A!8)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A!8, B)) | (~(in(C, tptp_fun_D_7(C, B, A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~subset(B, tptp_fun_D_7(C, B, A!8))))))))))))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(90,plain,
% 0.18/0.44 ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_7(C, B, A)) | (~element(tptp_fun_D_7(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_7(C, B, A), A)) | (~subset(B, tptp_fun_D_7(C, B, A))))))))))))) | (~top_str(A!8)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B)) | (~(in(C, tptp_fun_D_7(C, B, A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~subset(B, tptp_fun_D_7(C, B, A!8)))))))))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.18/0.44 tff(91,plain,
% 0.18/0.44 (![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B)) | (~(in(C, tptp_fun_D_7(C, B, A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~subset(B, tptp_fun_D_7(C, B, A!8)))))))))))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[90, 84, 68])).
% 0.18/0.44 tff(92,plain,
% 0.18/0.44 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B)) | (~(in(C, tptp_fun_D_7(C, B, A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~subset(B, tptp_fun_D_7(C, B, A!8)))))))))))) | ((~element(B!9, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8)))))))))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B)) | (~(in(C, tptp_fun_D_7(C, B, A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~subset(B, tptp_fun_D_7(C, B, A!8)))))))))))) | (~element(B!9, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8)))))))))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(93,plain,
% 0.18/0.44 (((~element(B!9, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B!9, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8))))))))))) <=> ((~element(B!9, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8)))))))))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(94,plain,
% 0.18/0.45 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B)) | (~(in(C, tptp_fun_D_7(C, B, A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~subset(B, tptp_fun_D_7(C, B, A!8)))))))))))) | ((~element(B!9, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B!9, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8)))))))))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B)) | (~(in(C, tptp_fun_D_7(C, B, A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~subset(B, tptp_fun_D_7(C, B, A!8)))))))))))) | ((~element(B!9, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8))))))))))))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[93])).
% 0.18/0.45 tff(95,plain,
% 0.18/0.45 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B)) | (~(in(C, tptp_fun_D_7(C, B, A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~subset(B, tptp_fun_D_7(C, B, A!8)))))))))))) | ((~element(B!9, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B!9, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8)))))))))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B)) | (~(in(C, tptp_fun_D_7(C, B, A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~subset(B, tptp_fun_D_7(C, B, A!8)))))))))))) | (~element(B!9, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8)))))))))))),
% 0.18/0.45 inference(transitivity,[status(thm)],[94, 92])).
% 0.18/0.45 tff(96,plain,
% 0.18/0.45 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B)) | (~(in(C, tptp_fun_D_7(C, B, A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~subset(B, tptp_fun_D_7(C, B, A!8)))))))))))) | ((~element(B!9, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B!9, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8)))))))))))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(97,plain,
% 0.18/0.45 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~subset(B, D)) | (~closed_subset(D, A!8))))) | (~(in(C, topstr_closure(A!8, B)) | (~(in(C, tptp_fun_D_7(C, B, A!8)) | (~element(tptp_fun_D_7(C, B, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B, A!8), A!8)) | (~subset(B, tptp_fun_D_7(C, B, A!8)))))))))))) | (~element(B!9, powerset(the_carrier(A!8)))) | ![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8))))))))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.18/0.45 tff(98,plain,
% 0.18/0.45 (![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8))))))))))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[97, 47, 91])).
% 0.18/0.45 tff(99,plain,
% 0.18/0.45 (((~![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8))))))))))) | ((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), the_carrier(A!8))) | (~((~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), D)))) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))))))))) <=> ((~![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8))))))))))) | (~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), the_carrier(A!8))) | (~((~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), D)))) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))))))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(100,plain,
% 0.18/0.45 (((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), the_carrier(A!8))) | (~((~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))) | ![D: $i] : (in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))))))))) <=> ((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), the_carrier(A!8))) | (~((~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), D)))) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))))))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(101,plain,
% 0.18/0.45 (((~![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8))))))))))) | ((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), the_carrier(A!8))) | (~((~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))) | ![D: $i] : (in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))))))))) <=> ((~![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8))))))))))) | ((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), the_carrier(A!8))) | (~((~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), D)))) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))))))))))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[100])).
% 0.18/0.45 tff(102,plain,
% 0.18/0.45 (((~![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8))))))))))) | ((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), the_carrier(A!8))) | (~((~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))) | ![D: $i] : (in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))))))))) <=> ((~![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8))))))))))) | (~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), the_carrier(A!8))) | (~((~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), D)))) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))))))))),
% 0.18/0.46 inference(transitivity,[status(thm)],[101, 99])).
% 0.18/0.46 tff(103,plain,
% 0.18/0.46 ((~![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8))))))))))) | ((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), the_carrier(A!8))) | (~((~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))) | ![D: $i] : (in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))))))))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(104,plain,
% 0.18/0.46 ((~![C: $i] : ((~in(C, the_carrier(A!8))) | (~((~((~in(C, topstr_closure(A!8, B!9))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D))))) | (~(in(C, topstr_closure(A!8, B!9)) | (~(in(C, tptp_fun_D_7(C, B!9, A!8)) | (~element(tptp_fun_D_7(C, B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(C, B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(C, B!9, A!8))))))))))) | (~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), the_carrier(A!8))) | (~((~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), D)))) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))))))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.18/0.46 tff(105,plain,
% 0.18/0.46 (~((~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), D)))) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))))))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[104, 98, 67])).
% 0.18/0.46 tff(106,plain,
% 0.18/0.46 (((~((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!8)))) | (~closed_subset(D, A!8)) | (~subset(B!9, D)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), D)))) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))))))) | (in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(107,plain,
% 0.18/0.46 (in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.18/0.46 tff(108,plain,
% 0.18/0.46 (((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))) | (~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(109,plain,
% 0.18/0.46 (~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[108, 61])).
% 0.18/0.46 tff(110,plain,
% 0.18/0.46 ((~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))))) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(111,plain,
% 0.18/0.46 ((~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), topstr_closure(A!8, B!9)) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))))) | (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.18/0.46 tff(112,plain,
% 0.18/0.46 (~(in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[111, 107])).
% 0.18/0.46 tff(113,plain,
% 0.18/0.46 ((in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))) | subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(114,plain,
% 0.18/0.46 (subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.18/0.46 tff(115,plain,
% 0.18/0.46 ((~((~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | ![C: $i] : ((~in(C, B!9)) | in(C, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))) | (~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | ![C: $i] : ((~in(C, B!9)) | in(C, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(116,plain,
% 0.18/0.46 ((~((~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))) | ![C: $i] : ((~in(C, B!9)) | in(C, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))))) | ![C: $i] : ((~in(C, B!9)) | in(C, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.18/0.46 tff(117,plain,
% 0.18/0.46 (![C: $i] : ((~in(C, B!9)) | in(C, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[116, 20])).
% 0.18/0.46 tff(118,plain,
% 0.18/0.46 ((in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)) | (~element(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), powerset(the_carrier(A!8)))) | (~closed_subset(tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8), A!8)) | (~subset(B!9, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))) | (~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(119,plain,
% 0.18/0.46 (~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[118, 112])).
% 0.18/0.46 tff(120,plain,
% 0.18/0.46 (((~![C: $i] : ((~in(C, B!9)) | in(C, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))) | ((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))) <=> ((~![C: $i] : ((~in(C, B!9)) | in(C, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))) | (~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(121,plain,
% 0.18/0.46 ((~![C: $i] : ((~in(C, B!9)) | in(C, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))) | ((~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(122,plain,
% 0.18/0.46 ((~![C: $i] : ((~in(C, B!9)) | in(C, tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8)))) | (~in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9)) | in(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), tptp_fun_D_7(tptp_fun_C_0(topstr_closure(A!8, B!9), B!9), B!9, A!8))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.18/0.46 tff(123,plain,
% 0.18/0.46 ($false),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[122, 63, 119, 117])).
% 0.18/0.46 % SZS output end Proof
%------------------------------------------------------------------------------