TSTP Solution File: SEU322+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU322+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 07:28:54 EDT 2022
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU322+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 12:25:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(in_type, type, (
% 0.13/0.39 in: ( $i * $i ) > $o)).
% 0.13/0.39 tff(subset_complement_type, type, (
% 0.13/0.39 subset_complement: ( $i * $i ) > $i)).
% 0.13/0.39 tff(tptp_fun_B_8_type, type, (
% 0.13/0.39 tptp_fun_B_8: $i)).
% 0.13/0.39 tff(the_carrier_type, type, (
% 0.13/0.39 the_carrier: $i > $i)).
% 0.13/0.39 tff(tptp_fun_A_7_type, type, (
% 0.13/0.39 tptp_fun_A_7: $i)).
% 0.13/0.39 tff(tptp_fun_C_0_type, type, (
% 0.13/0.39 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.13/0.39 tff(interior_type, type, (
% 0.13/0.39 interior: ( $i * $i ) > $i)).
% 0.13/0.39 tff(element_type, type, (
% 0.13/0.39 element: ( $i * $i ) > $o)).
% 0.13/0.39 tff(powerset_type, type, (
% 0.13/0.39 powerset: $i > $i)).
% 0.13/0.39 tff(subset_type, type, (
% 0.13/0.39 subset: ( $i * $i ) > $o)).
% 0.13/0.39 tff(top_str_type, type, (
% 0.13/0.39 top_str: $i > $o)).
% 0.13/0.39 tff(topstr_closure_type, type, (
% 0.13/0.39 topstr_closure: ( $i * $i ) > $i)).
% 0.13/0.39 tff(one_sorted_str_type, type, (
% 0.13/0.39 one_sorted_str: $i > $o)).
% 0.13/0.39 tff(empty_carrier_type, type, (
% 0.13/0.39 empty_carrier: $i > $o)).
% 0.13/0.39 tff(empty_type, type, (
% 0.13/0.39 empty: $i > $o)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 (((~(~top_str(A!7))) & (~((~element(B!8, powerset(the_carrier(A!7)))) | subset(interior(A!7, B!8), B!8)))) <=> (top_str(A!7) & (~((~element(B!8, powerset(the_carrier(A!7)))) | subset(interior(A!7, B!8), B!8))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))) <=> (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 ((~![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => subset(interior(A, B), B)))) <=> (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(4,axiom,(~![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => subset(interior(A, B), B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t44_tops_1')).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (top_str(A!7) & (~((~element(B!8, powerset(the_carrier(A!7)))) | subset(interior(A!7, B!8), B!8)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[11, 1])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (~((~element(B!8, powerset(the_carrier(A!7)))) | subset(interior(A!7, B!8), B!8))),
% 0.13/0.39 inference(and_elim,[status(thm)],[12])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (element(B!8, powerset(the_carrier(A!7)))),
% 0.13/0.39 inference(or_elim,[status(thm)],[13])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (^[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)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (![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))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[15])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (![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))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (^[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)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (![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))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[18])).
% 0.13/0.39 tff(20,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')).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.13/0.39 tff(23,plain,(
% 0.13/0.39 ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 0.13/0.39 inference(skolemize,[status(sab)],[22])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | ((~element(B!8, powerset(the_carrier(A!7)))) | (subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8)) = B!8))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | (~element(B!8, powerset(the_carrier(A!7)))) | (subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8)) = B!8))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | ((~element(B!8, powerset(the_carrier(A!7)))) | (subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8)) = B!8))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | (~element(B!8, powerset(the_carrier(A!7)))) | (subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8)) = B!8)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8)) = B!8),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[27, 24, 14])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 (in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8))) <=> in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8)),
% 0.13/0.39 inference(monotonicity,[status(thm)],[28])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 (in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8) <=> in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8)))),
% 0.13/0.39 inference(symmetry,[status(thm)],[29])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 ((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8)) <=> (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[30])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[32])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[34])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[35, 33])).
% 0.13/0.39 tff(37,plain,
% 0.13/0.39 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[37])).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(40,plain,
% 0.13/0.39 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[40])).
% 0.13/0.39 tff(42,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_tarski')).
% 0.13/0.39 tff(43,plain,
% 0.13/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.13/0.39 tff(44,plain,
% 0.13/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.13/0.39 tff(45,plain,(
% 0.13/0.39 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))),
% 0.13/0.39 inference(skolemize,[status(sab)],[44])).
% 0.13/0.39 tff(46,plain,
% 0.13/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.13/0.39 tff(47,plain,
% 0.13/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[46, 36])).
% 0.13/0.39 tff(48,plain,
% 0.13/0.39 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(interior(A!7, B!8), B!8)) | ![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, B!8)))) | (~(subset(interior(A!7, B!8), B!8) | (~((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8)))))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(49,plain,
% 0.13/0.39 (~((~((~subset(interior(A!7, B!8), B!8)) | ![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, B!8)))) | (~(subset(interior(A!7, B!8), B!8) | (~((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8))))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.13/0.39 tff(50,plain,
% 0.13/0.39 (((~((~subset(interior(A!7, B!8), B!8)) | ![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, B!8)))) | (~(subset(interior(A!7, B!8), B!8) | (~((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8)))))) | (subset(interior(A!7, B!8), B!8) | (~((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8))))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(51,plain,
% 0.13/0.39 (subset(interior(A!7, B!8), B!8) | (~((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8)))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.13/0.39 tff(52,plain,
% 0.13/0.39 (~subset(interior(A!7, B!8), B!8)),
% 0.13/0.39 inference(or_elim,[status(thm)],[13])).
% 0.13/0.39 tff(53,plain,
% 0.13/0.39 ((~(subset(interior(A!7, B!8), B!8) | (~((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8))))) | subset(interior(A!7, B!8), B!8) | (~((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8)))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(54,plain,
% 0.13/0.39 ((~(subset(interior(A!7, B!8), B!8) | (~((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8))))) | (~((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8)))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.13/0.39 tff(55,plain,
% 0.13/0.39 (~((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[54, 51])).
% 0.13/0.39 tff(56,plain,
% 0.13/0.39 (((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8)) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(57,plain,
% 0.13/0.39 (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.13/0.39 tff(58,plain,
% 0.13/0.39 (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[57, 31])).
% 0.13/0.39 tff(59,plain,
% 0.13/0.39 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(subset_complement(the_carrier(A!7), B!8), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | ![C: $i] : ((~in(C, subset_complement(the_carrier(A!7), B!8))) | in(C, topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))))) | (~(subset(subset_complement(the_carrier(A!7), B!8), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))) | (~((~in(tptp_fun_C_0(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), subset_complement(the_carrier(A!7), B!8)), subset_complement(the_carrier(A!7), B!8))) | in(tptp_fun_C_0(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), subset_complement(the_carrier(A!7), B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))))))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(60,plain,
% 0.13/0.39 (~((~((~subset(subset_complement(the_carrier(A!7), B!8), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | ![C: $i] : ((~in(C, subset_complement(the_carrier(A!7), B!8))) | in(C, topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))))) | (~(subset(subset_complement(the_carrier(A!7), B!8), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))) | (~((~in(tptp_fun_C_0(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), subset_complement(the_carrier(A!7), B!8)), subset_complement(the_carrier(A!7), B!8))) | in(tptp_fun_C_0(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), subset_complement(the_carrier(A!7), B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[59, 47])).
% 0.13/0.39 tff(61,plain,
% 0.13/0.39 (((~((~subset(subset_complement(the_carrier(A!7), B!8), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | ![C: $i] : ((~in(C, subset_complement(the_carrier(A!7), B!8))) | in(C, topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))))) | (~(subset(subset_complement(the_carrier(A!7), B!8), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))) | (~((~in(tptp_fun_C_0(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), subset_complement(the_carrier(A!7), B!8)), subset_complement(the_carrier(A!7), B!8))) | in(tptp_fun_C_0(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), subset_complement(the_carrier(A!7), B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))))))) | ((~subset(subset_complement(the_carrier(A!7), B!8), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | ![C: $i] : ((~in(C, subset_complement(the_carrier(A!7), B!8))) | in(C, topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(62,plain,
% 0.13/0.39 ((~subset(subset_complement(the_carrier(A!7), B!8), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | ![C: $i] : ((~in(C, subset_complement(the_carrier(A!7), B!8))) | in(C, topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.13/0.39 tff(63,plain,
% 0.13/0.39 (^[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))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(64,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[63])).
% 0.13/0.39 tff(65,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(66,plain,
% 0.13/0.39 (^[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))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(67,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[66])).
% 0.13/0.39 tff(68,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')).
% 0.13/0.39 tff(69,plain,
% 0.13/0.39 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.13/0.39 tff(70,plain,
% 0.13/0.39 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.13/0.39 tff(71,plain,(
% 0.13/0.39 ![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[70])).
% 0.13/0.39 tff(72,plain,
% 0.13/0.39 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.13/0.39 tff(73,plain,
% 0.13/0.39 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | ((~element(B!8, powerset(the_carrier(A!7)))) | element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7))))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | (~element(B!8, powerset(the_carrier(A!7)))) | element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(74,plain,
% 0.13/0.39 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | ((~element(B!8, powerset(the_carrier(A!7)))) | element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(75,plain,
% 0.13/0.39 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | (~element(B!8, powerset(the_carrier(A!7)))) | element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.13/0.39 tff(76,plain,
% 0.13/0.39 (element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[75, 72, 14])).
% 0.13/0.39 tff(77,plain,
% 0.13/0.39 (^[A: $i] : refl(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B)))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(78,plain,
% 0.13/0.39 (![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))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[77])).
% 0.13/0.39 tff(79,plain,
% 0.13/0.39 (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B)))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(80,plain,
% 0.13/0.39 (![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))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[79])).
% 0.13/0.39 tff(81,plain,
% 0.13/0.39 (![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))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[80, 78])).
% 0.13/0.40 tff(82,plain,
% 0.13/0.40 (![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))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(83,plain,
% 0.13/0.40 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((element(B, powerset(the_carrier(A))) => subset(B, topstr_closure(A, B))) <=> ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))), (![B: $i] : (element(B, powerset(the_carrier(A))) => subset(B, topstr_closure(A, B))) <=> ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))), ((top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => subset(B, topstr_closure(A, B)))) <=> (top_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B)))))), rewrite((top_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B)))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))), ((top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => subset(B, topstr_closure(A, B)))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(84,plain,
% 0.13/0.40 (![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))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[83])).
% 0.13/0.40 tff(85,axiom,(![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => subset(B, topstr_closure(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t48_pre_topc')).
% 0.13/0.40 tff(86,plain,
% 0.13/0.40 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.13/0.40 tff(87,plain,
% 0.13/0.40 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.13/0.40 tff(88,plain,(
% 0.13/0.40 ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[87])).
% 0.13/0.40 tff(89,plain,
% 0.13/0.40 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.13/0.40 tff(90,plain,
% 0.13/0.40 (top_str(A!7)),
% 0.13/0.40 inference(and_elim,[status(thm)],[12])).
% 0.13/0.40 tff(91,plain,
% 0.13/0.40 (((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))) | ((~top_str(A!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | subset(B, topstr_closure(A!7, B))))) <=> ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))) | (~top_str(A!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | subset(B, topstr_closure(A!7, B))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(92,plain,
% 0.13/0.40 ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))) | ((~top_str(A!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | subset(B, topstr_closure(A!7, B))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(93,plain,
% 0.13/0.40 ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))) | (~top_str(A!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | subset(B, topstr_closure(A!7, B)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.13/0.40 tff(94,plain,
% 0.13/0.40 (![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | subset(B, topstr_closure(A!7, B)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[93, 90, 89])).
% 0.13/0.40 tff(95,plain,
% 0.13/0.40 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | subset(B, topstr_closure(A!7, B)))) | ((~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))) | subset(subset_complement(the_carrier(A!7), B!8), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | subset(B, topstr_closure(A!7, B)))) | (~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))) | subset(subset_complement(the_carrier(A!7), B!8), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(96,plain,
% 0.13/0.40 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | subset(B, topstr_closure(A!7, B)))) | ((~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))) | subset(subset_complement(the_carrier(A!7), B!8), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(97,plain,
% 0.13/0.40 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | subset(B, topstr_closure(A!7, B)))) | (~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))) | subset(subset_complement(the_carrier(A!7), B!8), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.13/0.40 tff(98,plain,
% 0.13/0.40 (subset(subset_complement(the_carrier(A!7), B!8), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[97, 94, 76])).
% 0.13/0.40 tff(99,plain,
% 0.13/0.40 ((~((~subset(subset_complement(the_carrier(A!7), B!8), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | ![C: $i] : ((~in(C, subset_complement(the_carrier(A!7), B!8))) | in(C, topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))))) | (~subset(subset_complement(the_carrier(A!7), B!8), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | ![C: $i] : ((~in(C, subset_complement(the_carrier(A!7), B!8))) | in(C, topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(100,plain,
% 0.13/0.40 ((~((~subset(subset_complement(the_carrier(A!7), B!8), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | ![C: $i] : ((~in(C, subset_complement(the_carrier(A!7), B!8))) | in(C, topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))))) | ![C: $i] : ((~in(C, subset_complement(the_carrier(A!7), B!8))) | in(C, topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.13/0.40 tff(101,plain,
% 0.13/0.40 (![C: $i] : ((~in(C, subset_complement(the_carrier(A!7), B!8))) | in(C, topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[100, 62])).
% 0.13/0.40 tff(102,plain,
% 0.13/0.40 (^[A: $i] : refl(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B)))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B)))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(103,plain,
% 0.13/0.40 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B)))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[102])).
% 0.13/0.40 tff(104,plain,
% 0.13/0.40 (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B)))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B)))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(105,plain,
% 0.13/0.40 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B)))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[104])).
% 0.13/0.40 tff(106,plain,
% 0.13/0.40 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B)))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[105, 103])).
% 0.13/0.40 tff(107,plain,
% 0.13/0.40 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B)))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(108,plain,
% 0.13/0.40 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((element(B, powerset(the_carrier(A))) => (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))) <=> ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))), (![B: $i] : (element(B, powerset(the_carrier(A))) => (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))) <=> ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))), ((top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B)))))) <=> (top_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B)))))))), rewrite((top_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B)))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))), ((top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B)))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(109,plain,
% 0.13/0.40 (![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B)))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[108])).
% 0.13/0.40 tff(110,axiom,(![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_tops_1')).
% 0.13/0.40 tff(111,plain,
% 0.13/0.40 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.13/0.40 tff(112,plain,
% 0.13/0.40 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.13/0.40 tff(113,plain,(
% 0.13/0.40 ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[112])).
% 0.13/0.40 tff(114,plain,
% 0.13/0.40 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[113, 106])).
% 0.13/0.40 tff(115,plain,
% 0.13/0.40 (((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))) | ((~top_str(A!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | (interior(A!7, B) = subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B))))))) <=> ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))) | (~top_str(A!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | (interior(A!7, B) = subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B))))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(116,plain,
% 0.13/0.40 ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))) | ((~top_str(A!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | (interior(A!7, B) = subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B))))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(117,plain,
% 0.13/0.40 ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))) | (~top_str(A!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | (interior(A!7, B) = subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.13/0.40 tff(118,plain,
% 0.13/0.40 (![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | (interior(A!7, B) = subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B)))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[117, 114, 90])).
% 0.13/0.40 tff(119,plain,
% 0.13/0.40 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | (interior(A!7, B) = subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B)))))) | ((~element(B!8, powerset(the_carrier(A!7)))) | (interior(A!7, B!8) = subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | (interior(A!7, B) = subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B)))))) | (~element(B!8, powerset(the_carrier(A!7)))) | (interior(A!7, B!8) = subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(120,plain,
% 0.13/0.40 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | (interior(A!7, B) = subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B)))))) | ((~element(B!8, powerset(the_carrier(A!7)))) | (interior(A!7, B!8) = subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(121,plain,
% 0.13/0.40 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | (interior(A!7, B) = subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B)))))) | (~element(B!8, powerset(the_carrier(A!7)))) | (interior(A!7, B!8) = subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.13/0.40 tff(122,plain,
% 0.13/0.40 (interior(A!7, B!8) = subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[121, 14, 118])).
% 0.13/0.40 tff(123,plain,
% 0.13/0.40 (subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))) = interior(A!7, B!8)),
% 0.13/0.40 inference(symmetry,[status(thm)],[122])).
% 0.13/0.40 tff(124,plain,
% 0.13/0.40 (in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) <=> in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[123])).
% 0.13/0.40 tff(125,plain,
% 0.13/0.40 (in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8)) <=> in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))),
% 0.13/0.40 inference(symmetry,[status(thm)],[124])).
% 0.13/0.40 tff(126,plain,
% 0.13/0.40 (((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8)) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(127,plain,
% 0.13/0.40 (in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[126, 55])).
% 0.13/0.40 tff(128,plain,
% 0.13/0.40 (in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[127, 125])).
% 0.13/0.40 tff(129,plain,
% 0.13/0.40 (^[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))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(130,plain,
% 0.13/0.40 (![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)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[129])).
% 0.13/0.40 tff(131,plain,
% 0.13/0.40 (^[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)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(132,plain,
% 0.13/0.40 (![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)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[131])).
% 0.13/0.40 tff(133,plain,
% 0.13/0.40 (![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))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(134,plain,
% 0.13/0.40 (^[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)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(135,plain,
% 0.13/0.40 (![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))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[134])).
% 0.13/0.40 tff(136,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')).
% 0.13/0.40 tff(137,plain,
% 0.13/0.40 (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.13/0.40 tff(138,plain,
% 0.13/0.40 (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.13/0.40 tff(139,plain,(
% 0.13/0.40 ![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[138])).
% 0.13/0.40 tff(140,plain,
% 0.13/0.40 (![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[139, 132])).
% 0.13/0.40 tff(141,plain,
% 0.13/0.40 (![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[140, 130])).
% 0.13/0.40 tff(142,plain,
% 0.13/0.40 (((~![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!7)) | element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7))) | (~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))))) <=> ((~![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!7)) | element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7))) | (~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(143,plain,
% 0.13/0.40 ((element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7))) | (~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))) | (~top_str(A!7))) <=> ((~top_str(A!7)) | element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7))) | (~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(144,plain,
% 0.13/0.40 (((~![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!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7))) | (~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))) | (~top_str(A!7)))) <=> ((~![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!7)) | element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7))) | (~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7))))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[143])).
% 0.13/0.40 tff(145,plain,
% 0.13/0.40 (((~![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!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7))) | (~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))) | (~top_str(A!7)))) <=> ((~![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!7)) | element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7))) | (~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[144, 142])).
% 0.13/0.40 tff(146,plain,
% 0.13/0.40 ((~![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!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7))) | (~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))) | (~top_str(A!7)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(147,plain,
% 0.13/0.40 ((~![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!7)) | element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7))) | (~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.13/0.40 tff(148,plain,
% 0.13/0.40 (element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[147, 141, 90, 76])).
% 0.13/0.40 tff(149,plain,
% 0.13/0.40 (^[A: $i, B: $i, C: $i] : refl(((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C)))) <=> ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(150,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C)))) <=> ![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[149])).
% 0.13/0.40 tff(151,plain,
% 0.13/0.40 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((in(B, subset_complement(A, C)) & in(B, C)) <=> (~((~in(B, C)) | (~in(B, subset_complement(A, C)))))), ((~(in(B, subset_complement(A, C)) & in(B, C))) <=> (~(~((~in(B, C)) | (~in(B, subset_complement(A, C)))))))), rewrite((~(~((~in(B, C)) | (~in(B, subset_complement(A, C)))))) <=> ((~in(B, C)) | (~in(B, subset_complement(A, C))))), ((~(in(B, subset_complement(A, C)) & in(B, C))) <=> ((~in(B, C)) | (~in(B, subset_complement(A, C)))))), (((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C)))) <=> ((~element(C, powerset(A))) | ((~in(B, C)) | (~in(B, subset_complement(A, C))))))), rewrite(((~element(C, powerset(A))) | ((~in(B, C)) | (~in(B, subset_complement(A, C))))) <=> ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))), (((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C)))) <=> ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(152,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : ((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[151])).
% 0.13/0.40 tff(153,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : ((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(154,plain,
% 0.13/0.40 (^[A: $i, B: $i, C: $i] : rewrite((element(C, powerset(A)) => (~(in(B, subset_complement(A, C)) & in(B, C)))) <=> ((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(155,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : (element(C, powerset(A)) => (~(in(B, subset_complement(A, C)) & in(B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[154])).
% 0.13/0.40 tff(156,axiom,(![A: $i, B: $i, C: $i] : (element(C, powerset(A)) => (~(in(B, subset_complement(A, C)) & in(B, C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t54_subset_1')).
% 0.13/0.40 tff(157,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : ((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.13/0.40 tff(158,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : ((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[157, 153])).
% 0.13/0.40 tff(159,plain,(
% 0.13/0.40 ![A: $i, B: $i, C: $i] : ((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[158])).
% 0.13/0.40 tff(160,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[159, 152])).
% 0.13/0.40 tff(161,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[160, 150])).
% 0.13/0.40 tff(162,plain,
% 0.13/0.40 (((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))) | ((~element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))) | (~element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(163,plain,
% 0.13/0.40 (((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | (~element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))))) <=> ((~element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(164,plain,
% 0.13/0.40 (((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))) | ((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | (~element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))) | ((~element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[163])).
% 0.13/0.41 tff(165,plain,
% 0.13/0.41 (((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))) | ((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | (~element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))) | (~element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[164, 162])).
% 0.13/0.41 tff(166,plain,
% 0.13/0.41 ((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))) | ((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | (~element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(167,plain,
% 0.13/0.41 ((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))) | (~element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.13/0.41 tff(168,plain,
% 0.13/0.41 ((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[167, 161, 148])).
% 0.13/0.41 tff(169,plain,
% 0.13/0.41 (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[168, 128])).
% 0.13/0.41 tff(170,plain,
% 0.13/0.41 (((~![C: $i] : ((~in(C, subset_complement(the_carrier(A!7), B!8))) | in(C, topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))) | ((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))) <=> ((~![C: $i] : ((~in(C, subset_complement(the_carrier(A!7), B!8))) | in(C, topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(171,plain,
% 0.21/0.41 ((~![C: $i] : ((~in(C, subset_complement(the_carrier(A!7), B!8))) | in(C, topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))) | ((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(172,plain,
% 0.21/0.41 ((~![C: $i] : ((~in(C, subset_complement(the_carrier(A!7), B!8))) | in(C, topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.21/0.41 tff(173,plain,
% 0.21/0.41 (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), B!8))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[172, 169, 101])).
% 0.21/0.41 tff(174,plain,
% 0.21/0.41 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(interior(A!7, B!8), the_carrier(A!7))) | ![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, the_carrier(A!7))))) | (~(subset(interior(A!7, B!8), the_carrier(A!7)) | (~((~in(tptp_fun_C_0(the_carrier(A!7), interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(the_carrier(A!7), interior(A!7, B!8)), the_carrier(A!7))))))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(175,plain,
% 0.21/0.41 (~((~((~subset(interior(A!7, B!8), the_carrier(A!7))) | ![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, the_carrier(A!7))))) | (~(subset(interior(A!7, B!8), the_carrier(A!7)) | (~((~in(tptp_fun_C_0(the_carrier(A!7), interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(the_carrier(A!7), interior(A!7, B!8)), the_carrier(A!7)))))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[174, 47])).
% 0.21/0.41 tff(176,plain,
% 0.21/0.41 (((~((~subset(interior(A!7, B!8), the_carrier(A!7))) | ![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, the_carrier(A!7))))) | (~(subset(interior(A!7, B!8), the_carrier(A!7)) | (~((~in(tptp_fun_C_0(the_carrier(A!7), interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(the_carrier(A!7), interior(A!7, B!8)), the_carrier(A!7))))))) | ((~subset(interior(A!7, B!8), the_carrier(A!7))) | ![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, the_carrier(A!7))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(177,plain,
% 0.21/0.41 ((~subset(interior(A!7, B!8), the_carrier(A!7))) | ![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, the_carrier(A!7)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[176, 175])).
% 0.21/0.41 tff(178,plain,
% 0.21/0.41 (^[A: $i, B: $i] : refl((element(A, powerset(B)) <=> subset(A, B)) <=> (element(A, powerset(B)) <=> subset(A, B)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(179,plain,
% 0.21/0.41 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[178])).
% 0.21/0.41 tff(180,plain,
% 0.21/0.41 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(181,axiom,(![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3_subset')).
% 0.21/0.41 tff(182,plain,
% 0.21/0.41 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.21/0.41 tff(183,plain,(
% 0.21/0.41 ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.21/0.41 inference(skolemize,[status(sab)],[182])).
% 0.21/0.41 tff(184,plain,
% 0.21/0.41 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[183, 179])).
% 0.21/0.41 tff(185,plain,
% 0.21/0.41 ((~![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))) | (element(interior(A!7, B!8), powerset(the_carrier(A!7))) <=> subset(interior(A!7, B!8), the_carrier(A!7)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(186,plain,
% 0.21/0.41 (element(interior(A!7, B!8), powerset(the_carrier(A!7))) <=> subset(interior(A!7, B!8), the_carrier(A!7))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[185, 184])).
% 0.21/0.41 tff(187,plain,
% 0.21/0.41 (^[A: $i, B: $i] : refl((element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A))) <=> (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(188,plain,
% 0.21/0.41 (![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A))) <=> ![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[187])).
% 0.21/0.41 tff(189,plain,
% 0.21/0.41 (^[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(interior(A, B), powerset(the_carrier(A)))) <=> (((~top_str(A)) | (~element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A)))))), rewrite((((~top_str(A)) | (~element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A)))) <=> (element(interior(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(interior(A, B), powerset(the_carrier(A)))) <=> (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(190,plain,
% 0.21/0.41 (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A)))) <=> ![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[189])).
% 0.21/0.41 tff(191,plain,
% 0.21/0.41 (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A)))) <=> ![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(192,plain,
% 0.21/0.41 (^[A: $i, B: $i] : rewrite(((top_str(A) & element(B, powerset(the_carrier(A)))) => element(interior(A, B), powerset(the_carrier(A)))) <=> ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(193,plain,
% 0.21/0.41 (![A: $i, B: $i] : ((top_str(A) & element(B, powerset(the_carrier(A)))) => element(interior(A, B), powerset(the_carrier(A)))) <=> ![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[192])).
% 0.21/0.41 tff(194,axiom,(![A: $i, B: $i] : ((top_str(A) & element(B, powerset(the_carrier(A)))) => element(interior(A, B), powerset(the_carrier(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k1_tops_1')).
% 0.21/0.41 tff(195,plain,
% 0.21/0.41 (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.21/0.41 tff(196,plain,
% 0.21/0.41 (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[195, 191])).
% 0.21/0.41 tff(197,plain,(
% 0.21/0.41 ![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[196])).
% 0.21/0.41 tff(198,plain,
% 0.21/0.41 (![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[197, 190])).
% 0.21/0.41 tff(199,plain,
% 0.21/0.41 (![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[198, 188])).
% 0.21/0.41 tff(200,plain,
% 0.21/0.41 (((~![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | ((~top_str(A!7)) | (~element(B!8, powerset(the_carrier(A!7)))) | element(interior(A!7, B!8), powerset(the_carrier(A!7))))) <=> ((~![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (~top_str(A!7)) | (~element(B!8, powerset(the_carrier(A!7)))) | element(interior(A!7, B!8), powerset(the_carrier(A!7))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(201,plain,
% 0.21/0.41 ((element(interior(A!7, B!8), powerset(the_carrier(A!7))) | (~element(B!8, powerset(the_carrier(A!7)))) | (~top_str(A!7))) <=> ((~top_str(A!7)) | (~element(B!8, powerset(the_carrier(A!7)))) | element(interior(A!7, B!8), powerset(the_carrier(A!7))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(202,plain,
% 0.21/0.41 (((~![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (element(interior(A!7, B!8), powerset(the_carrier(A!7))) | (~element(B!8, powerset(the_carrier(A!7)))) | (~top_str(A!7)))) <=> ((~![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | ((~top_str(A!7)) | (~element(B!8, powerset(the_carrier(A!7)))) | element(interior(A!7, B!8), powerset(the_carrier(A!7)))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[201])).
% 0.21/0.41 tff(203,plain,
% 0.21/0.41 (((~![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (element(interior(A!7, B!8), powerset(the_carrier(A!7))) | (~element(B!8, powerset(the_carrier(A!7)))) | (~top_str(A!7)))) <=> ((~![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (~top_str(A!7)) | (~element(B!8, powerset(the_carrier(A!7)))) | element(interior(A!7, B!8), powerset(the_carrier(A!7))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[202, 200])).
% 0.21/0.41 tff(204,plain,
% 0.21/0.41 ((~![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (element(interior(A!7, B!8), powerset(the_carrier(A!7))) | (~element(B!8, powerset(the_carrier(A!7)))) | (~top_str(A!7)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(205,plain,
% 0.21/0.41 ((~![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (~top_str(A!7)) | (~element(B!8, powerset(the_carrier(A!7)))) | element(interior(A!7, B!8), powerset(the_carrier(A!7)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.21/0.41 tff(206,plain,
% 0.21/0.41 (element(interior(A!7, B!8), powerset(the_carrier(A!7)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[205, 199, 90, 14])).
% 0.21/0.41 tff(207,plain,
% 0.21/0.41 ((~(element(interior(A!7, B!8), powerset(the_carrier(A!7))) <=> subset(interior(A!7, B!8), the_carrier(A!7)))) | (~element(interior(A!7, B!8), powerset(the_carrier(A!7)))) | subset(interior(A!7, B!8), the_carrier(A!7))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(208,plain,
% 0.21/0.41 ((~(element(interior(A!7, B!8), powerset(the_carrier(A!7))) <=> subset(interior(A!7, B!8), the_carrier(A!7)))) | subset(interior(A!7, B!8), the_carrier(A!7))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[207, 206])).
% 0.21/0.41 tff(209,plain,
% 0.21/0.41 (subset(interior(A!7, B!8), the_carrier(A!7))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[208, 186])).
% 0.21/0.41 tff(210,plain,
% 0.21/0.41 ((~((~subset(interior(A!7, B!8), the_carrier(A!7))) | ![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, the_carrier(A!7))))) | (~subset(interior(A!7, B!8), the_carrier(A!7))) | ![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, the_carrier(A!7)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(211,plain,
% 0.21/0.41 ((~((~subset(interior(A!7, B!8), the_carrier(A!7))) | ![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, the_carrier(A!7))))) | ![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, the_carrier(A!7)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[210, 209])).
% 0.21/0.41 tff(212,plain,
% 0.21/0.41 (![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, the_carrier(A!7)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[211, 177])).
% 0.21/0.41 tff(213,plain,
% 0.21/0.41 (((~![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, the_carrier(A!7)))) | ((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7)))) <=> ((~![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, the_carrier(A!7)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(214,plain,
% 0.21/0.41 ((~![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, the_carrier(A!7)))) | ((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(215,plain,
% 0.21/0.41 ((~![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, the_carrier(A!7)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.21/0.41 tff(216,plain,
% 0.21/0.41 (in(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[215, 127, 212])).
% 0.21/0.41 tff(217,plain,
% 0.21/0.41 (^[A: $i, B: $i] : refl(((~in(A, B)) | element(A, B)) <=> ((~in(A, B)) | element(A, B)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(218,plain,
% 0.21/0.41 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[217])).
% 0.21/0.41 tff(219,plain,
% 0.21/0.41 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(220,plain,
% 0.21/0.41 (^[A: $i, B: $i] : rewrite((in(A, B) => element(A, B)) <=> ((~in(A, B)) | element(A, B)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(221,plain,
% 0.21/0.41 (![A: $i, B: $i] : (in(A, B) => element(A, B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[220])).
% 0.21/0.41 tff(222,axiom,(![A: $i, B: $i] : (in(A, B) => element(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_subset')).
% 0.21/0.41 tff(223,plain,
% 0.21/0.41 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.21/0.41 tff(224,plain,
% 0.21/0.41 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[223, 219])).
% 0.21/0.41 tff(225,plain,(
% 0.21/0.41 ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.21/0.41 inference(skolemize,[status(sab)],[224])).
% 0.21/0.41 tff(226,plain,
% 0.21/0.41 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[225, 218])).
% 0.21/0.41 tff(227,plain,
% 0.21/0.41 (((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | ((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7))) | element(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7)))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7))) | element(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(228,plain,
% 0.21/0.41 ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | ((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7))) | element(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(229,plain,
% 0.21/0.41 ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7))) | element(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.21/0.41 tff(230,plain,
% 0.21/0.41 (element(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[229, 226, 216])).
% 0.21/0.41 tff(231,plain,
% 0.21/0.41 (^[A: $i] : refl((one_sorted_str(A) | (~top_str(A))) <=> (one_sorted_str(A) | (~top_str(A))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(232,plain,
% 0.21/0.41 (![A: $i] : (one_sorted_str(A) | (~top_str(A))) <=> ![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[231])).
% 0.21/0.41 tff(233,plain,
% 0.21/0.41 (![A: $i] : (one_sorted_str(A) | (~top_str(A))) <=> ![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(234,plain,
% 0.21/0.41 (^[A: $i] : rewrite((top_str(A) => one_sorted_str(A)) <=> (one_sorted_str(A) | (~top_str(A))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(235,plain,
% 0.21/0.41 (![A: $i] : (top_str(A) => one_sorted_str(A)) <=> ![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[234])).
% 0.21/0.41 tff(236,axiom,(![A: $i] : (top_str(A) => one_sorted_str(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l1_pre_topc')).
% 0.21/0.41 tff(237,plain,
% 0.21/0.41 (![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.21/0.41 tff(238,plain,
% 0.21/0.41 (![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[237, 233])).
% 0.21/0.41 tff(239,plain,(
% 0.21/0.41 ![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[238])).
% 0.21/0.41 tff(240,plain,
% 0.21/0.41 (![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[239, 232])).
% 0.21/0.41 tff(241,plain,
% 0.21/0.41 (((~![A: $i] : (one_sorted_str(A) | (~top_str(A)))) | (one_sorted_str(A!7) | (~top_str(A!7)))) <=> ((~![A: $i] : (one_sorted_str(A) | (~top_str(A)))) | one_sorted_str(A!7) | (~top_str(A!7)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(242,plain,
% 0.21/0.41 ((~![A: $i] : (one_sorted_str(A) | (~top_str(A)))) | (one_sorted_str(A!7) | (~top_str(A!7)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(243,plain,
% 0.21/0.41 ((~![A: $i] : (one_sorted_str(A) | (~top_str(A)))) | one_sorted_str(A!7) | (~top_str(A!7))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.21/0.41 tff(244,plain,
% 0.21/0.41 (one_sorted_str(A!7)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[243, 240, 90])).
% 0.21/0.41 tff(245,plain,
% 0.21/0.41 (^[A: $i] : refl(((~one_sorted_str(A)) | (empty_carrier(A) <=> empty(the_carrier(A)))) <=> ((~one_sorted_str(A)) | (empty_carrier(A) <=> empty(the_carrier(A)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(246,plain,
% 0.21/0.41 (![A: $i] : ((~one_sorted_str(A)) | (empty_carrier(A) <=> empty(the_carrier(A)))) <=> ![A: $i] : ((~one_sorted_str(A)) | (empty_carrier(A) <=> empty(the_carrier(A))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[245])).
% 0.21/0.41 tff(247,plain,
% 0.21/0.41 (![A: $i] : ((~one_sorted_str(A)) | (empty_carrier(A) <=> empty(the_carrier(A)))) <=> ![A: $i] : ((~one_sorted_str(A)) | (empty_carrier(A) <=> empty(the_carrier(A))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(248,plain,
% 0.21/0.41 (^[A: $i] : rewrite((one_sorted_str(A) => (empty_carrier(A) <=> empty(the_carrier(A)))) <=> ((~one_sorted_str(A)) | (empty_carrier(A) <=> empty(the_carrier(A)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(249,plain,
% 0.21/0.41 (![A: $i] : (one_sorted_str(A) => (empty_carrier(A) <=> empty(the_carrier(A)))) <=> ![A: $i] : ((~one_sorted_str(A)) | (empty_carrier(A) <=> empty(the_carrier(A))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[248])).
% 0.21/0.41 tff(250,axiom,(![A: $i] : (one_sorted_str(A) => (empty_carrier(A) <=> empty(the_carrier(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_struct_0')).
% 0.21/0.41 tff(251,plain,
% 0.21/0.41 (![A: $i] : ((~one_sorted_str(A)) | (empty_carrier(A) <=> empty(the_carrier(A))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.21/0.41 tff(252,plain,
% 0.21/0.41 (![A: $i] : ((~one_sorted_str(A)) | (empty_carrier(A) <=> empty(the_carrier(A))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[251, 247])).
% 0.21/0.41 tff(253,plain,(
% 0.21/0.41 ![A: $i] : ((~one_sorted_str(A)) | (empty_carrier(A) <=> empty(the_carrier(A))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[252])).
% 0.21/0.41 tff(254,plain,
% 0.21/0.41 (![A: $i] : ((~one_sorted_str(A)) | (empty_carrier(A) <=> empty(the_carrier(A))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[253, 246])).
% 0.21/0.41 tff(255,plain,
% 0.21/0.41 (((~![A: $i] : ((~one_sorted_str(A)) | (empty_carrier(A) <=> empty(the_carrier(A))))) | ((~one_sorted_str(A!7)) | (empty_carrier(A!7) <=> empty(the_carrier(A!7))))) <=> ((~![A: $i] : ((~one_sorted_str(A)) | (empty_carrier(A) <=> empty(the_carrier(A))))) | (~one_sorted_str(A!7)) | (empty_carrier(A!7) <=> empty(the_carrier(A!7))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(256,plain,
% 0.21/0.41 ((~![A: $i] : ((~one_sorted_str(A)) | (empty_carrier(A) <=> empty(the_carrier(A))))) | ((~one_sorted_str(A!7)) | (empty_carrier(A!7) <=> empty(the_carrier(A!7))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(257,plain,
% 0.21/0.41 ((~![A: $i] : ((~one_sorted_str(A)) | (empty_carrier(A) <=> empty(the_carrier(A))))) | (~one_sorted_str(A!7)) | (empty_carrier(A!7) <=> empty(the_carrier(A!7)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.21/0.41 tff(258,plain,
% 0.21/0.41 ((~one_sorted_str(A!7)) | (empty_carrier(A!7) <=> empty(the_carrier(A!7)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[257, 254])).
% 0.21/0.41 tff(259,plain,
% 0.21/0.41 (empty_carrier(A!7) <=> empty(the_carrier(A!7))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[258, 244])).
% 0.21/0.41 tff(260,plain,
% 0.21/0.41 (^[A: $i, B: $i, C: $i] : refl(((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(261,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[260])).
% 0.21/0.41 tff(262,plain,
% 0.21/0.41 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(A, B) & element(B, powerset(C)) & empty(C)) <=> (~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))), ((~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> (~(~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))))), rewrite((~(~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))), ((~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(263,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[262])).
% 0.21/0.41 tff(264,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(265,plain,
% 0.21/0.41 (^[A: $i, B: $i, C: $i] : rewrite((~((in(A, B) & element(B, powerset(C))) & empty(C))) <=> (~(in(A, B) & element(B, powerset(C)) & empty(C))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(266,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : (~((in(A, B) & element(B, powerset(C))) & empty(C))) <=> ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[265])).
% 0.21/0.41 tff(267,axiom,(![A: $i, B: $i, C: $i] : (~((in(A, B) & element(B, powerset(C))) & empty(C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t5_subset')).
% 0.21/0.41 tff(268,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.21/0.41 tff(269,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[268, 264])).
% 0.21/0.41 tff(270,plain,(
% 0.21/0.41 ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[269])).
% 0.21/0.41 tff(271,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[270, 263])).
% 0.21/0.41 tff(272,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[271, 261])).
% 0.21/0.41 tff(273,plain,
% 0.21/0.41 (((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(the_carrier(A!7))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | (~element(interior(A!7, B!8), powerset(the_carrier(A!7)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~empty(the_carrier(A!7))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | (~element(interior(A!7, B!8), powerset(the_carrier(A!7)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(274,plain,
% 0.21/0.41 ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(the_carrier(A!7))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | (~element(interior(A!7, B!8), powerset(the_carrier(A!7)))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(275,plain,
% 0.21/0.41 ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~empty(the_carrier(A!7))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | (~element(interior(A!7, B!8), powerset(the_carrier(A!7))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.21/0.41 tff(276,plain,
% 0.21/0.41 (~empty(the_carrier(A!7))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[275, 272, 127, 206])).
% 0.21/0.41 tff(277,plain,
% 0.21/0.41 ((~(empty_carrier(A!7) <=> empty(the_carrier(A!7)))) | (~empty_carrier(A!7)) | empty(the_carrier(A!7))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(278,plain,
% 0.21/0.41 (~empty_carrier(A!7)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[277, 276, 259])).
% 0.21/0.41 tff(279,plain,
% 0.21/0.41 (^[A: $i] : refl((empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B)))))) <=> (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B)))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(280,plain,
% 0.21/0.41 (![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B)))))) <=> ![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[279])).
% 0.21/0.41 tff(281,plain,
% 0.21/0.41 (^[A: $i] : rewrite((empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B)))))) <=> (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B)))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(282,plain,
% 0.21/0.41 (![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B)))))) <=> ![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[281])).
% 0.21/0.41 tff(283,plain,
% 0.21/0.41 (![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B)))))) <=> ![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[282, 280])).
% 0.21/0.42 tff(284,plain,
% 0.21/0.42 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & one_sorted_str(A)) <=> (~(empty_carrier(A) | (~one_sorted_str(A))))), ((~((~empty_carrier(A)) & one_sorted_str(A))) <=> (~(~(empty_carrier(A) | (~one_sorted_str(A))))))), rewrite((~(~(empty_carrier(A) | (~one_sorted_str(A))))) <=> (empty_carrier(A) | (~one_sorted_str(A)))), ((~((~empty_carrier(A)) & one_sorted_str(A))) <=> (empty_carrier(A) | (~one_sorted_str(A))))), (((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B)))))) <=> ((empty_carrier(A) | (~one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B)))))))), rewrite(((empty_carrier(A) | (~one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B)))))) <=> (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))))), (((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B)))))) <=> (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(285,plain,
% 0.21/0.42 (![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B)))))) <=> ![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[284])).
% 0.21/0.42 tff(286,plain,
% 0.21/0.42 (![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B)))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(287,plain,
% 0.21/0.42 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((element(C, the_carrier(A)) => (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B)))) <=> ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B)))))), (![C: $i] : (element(C, the_carrier(A)) => (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B)))) <=> ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B)))))), ((element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))) <=> (element(B, powerset(the_carrier(A))) => ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))))), rewrite((element(B, powerset(the_carrier(A))) => ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))) <=> ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B)))))), ((element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))) <=> ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B)))))))), (![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))) <=> ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))))), ((((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B)))))) <=> (((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B)))))))), rewrite((((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B)))))) <=> ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))))), ((((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B)))))) <=> ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(288,plain,
% 0.21/0.42 (![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B)))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[287])).
% 0.21/0.42 tff(289,axiom,(![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l40_tops_1')).
% 0.21/0.42 tff(290,plain,
% 0.21/0.42 (![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.21/0.42 tff(291,plain,
% 0.21/0.42 (![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[290, 286])).
% 0.21/0.42 tff(292,plain,(
% 0.21/0.42 ![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[291])).
% 0.21/0.42 tff(293,plain,
% 0.21/0.42 (![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[292, 285])).
% 0.21/0.42 tff(294,plain,
% 0.21/0.42 (![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[293, 283])).
% 0.21/0.42 tff(295,plain,
% 0.21/0.42 (((~![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))))) | (empty_carrier(A!7) | (~one_sorted_str(A!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (in(C, subset_complement(the_carrier(A!7), B)) <=> (~in(C, B))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))))) | empty_carrier(A!7) | (~one_sorted_str(A!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (in(C, subset_complement(the_carrier(A!7), B)) <=> (~in(C, B))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(296,plain,
% 0.21/0.42 ((~![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))))) | (empty_carrier(A!7) | (~one_sorted_str(A!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (in(C, subset_complement(the_carrier(A!7), B)) <=> (~in(C, B))))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(297,plain,
% 0.21/0.42 ((~![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))))) | empty_carrier(A!7) | (~one_sorted_str(A!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (in(C, subset_complement(the_carrier(A!7), B)) <=> (~in(C, B)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[296, 295])).
% 0.21/0.42 tff(298,plain,
% 0.21/0.42 (empty_carrier(A!7) | (~one_sorted_str(A!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (in(C, subset_complement(the_carrier(A!7), B)) <=> (~in(C, B)))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[297, 294])).
% 0.21/0.42 tff(299,plain,
% 0.21/0.42 (![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (in(C, subset_complement(the_carrier(A!7), B)) <=> (~in(C, B)))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[298, 278, 244])).
% 0.21/0.42 tff(300,plain,
% 0.21/0.42 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (in(C, subset_complement(the_carrier(A!7), B)) <=> (~in(C, B)))))) | ((~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (in(C, subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8))) <=> (~in(C, subset_complement(the_carrier(A!7), B!8))))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (in(C, subset_complement(the_carrier(A!7), B)) <=> (~in(C, B)))))) | (~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (in(C, subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8))) <=> (~in(C, subset_complement(the_carrier(A!7), B!8))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(301,plain,
% 0.21/0.42 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (in(C, subset_complement(the_carrier(A!7), B)) <=> (~in(C, B)))))) | ((~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (in(C, subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8))) <=> (~in(C, subset_complement(the_carrier(A!7), B!8))))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(302,plain,
% 0.21/0.42 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (in(C, subset_complement(the_carrier(A!7), B)) <=> (~in(C, B)))))) | (~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (in(C, subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8))) <=> (~in(C, subset_complement(the_carrier(A!7), B!8)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.21/0.42 tff(303,plain,
% 0.21/0.42 (![C: $i] : ((~element(C, the_carrier(A!7))) | (in(C, subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8))) <=> (~in(C, subset_complement(the_carrier(A!7), B!8)))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[302, 299, 76])).
% 0.21/0.42 tff(304,plain,
% 0.21/0.42 (((~![C: $i] : ((~element(C, the_carrier(A!7))) | (in(C, subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8))) <=> (~in(C, subset_complement(the_carrier(A!7), B!8)))))) | ((~element(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7))) | (in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8))) <=> (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), B!8)))))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!7))) | (in(C, subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8))) <=> (~in(C, subset_complement(the_carrier(A!7), B!8)))))) | (~element(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7))) | (in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8))) <=> (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), B!8)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(305,plain,
% 0.21/0.42 ((~![C: $i] : ((~element(C, the_carrier(A!7))) | (in(C, subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8))) <=> (~in(C, subset_complement(the_carrier(A!7), B!8)))))) | ((~element(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7))) | (in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8))) <=> (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), B!8)))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(306,plain,
% 0.21/0.42 ((~![C: $i] : ((~element(C, the_carrier(A!7))) | (in(C, subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8))) <=> (~in(C, subset_complement(the_carrier(A!7), B!8)))))) | (~element(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7))) | (in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8))) <=> (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), B!8))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[305, 304])).
% 0.21/0.42 tff(307,plain,
% 0.21/0.42 ((~element(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7))) | (in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8))) <=> (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), B!8))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[306, 303])).
% 0.21/0.42 tff(308,plain,
% 0.21/0.42 (in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8))) <=> (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), B!8)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[307, 230])).
% 0.21/0.42 tff(309,plain,
% 0.21/0.42 ((~(in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8))) <=> (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), B!8))))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), B!8))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(310,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[309, 308, 173, 58])).
% 0.21/0.42 % SZS output end Proof
%------------------------------------------------------------------------------