TSTP Solution File: SEU394+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU394+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 07:29:19 EDT 2022
% Result : Theorem 4.06s 2.83s
% Output : Proof 4.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SEU394+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Sep 3 13:12:00 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 4.06/2.83 % SZS status Theorem
% 4.06/2.83 % SZS output start Proof
% 4.06/2.83 tff(filter_of_net_str_type, type, (
% 4.06/2.83 filter_of_net_str: ( $i * $i ) > $i)).
% 4.06/2.83 tff(net_of_bool_filter_type, type, (
% 4.06/2.83 net_of_bool_filter: ( $i * $i * $i ) > $i)).
% 4.06/2.83 tff(tptp_fun_B_37_type, type, (
% 4.06/2.83 tptp_fun_B_37: $i)).
% 4.06/2.83 tff(cast_as_carrier_subset_type, type, (
% 4.06/2.83 cast_as_carrier_subset: $i > $i)).
% 4.06/2.83 tff(tptp_fun_A_36_type, type, (
% 4.06/2.83 tptp_fun_A_36: $i)).
% 4.06/2.83 tff(set_difference_type, type, (
% 4.06/2.83 set_difference: ( $i * $i ) > $i)).
% 4.06/2.83 tff(singleton_type, type, (
% 4.06/2.83 singleton: $i > $i)).
% 4.06/2.83 tff(empty_set_type, type, (
% 4.06/2.83 empty_set: $i)).
% 4.06/2.83 tff(element_type, type, (
% 4.06/2.83 element: ( $i * $i ) > $o)).
% 4.06/2.83 tff(powerset_type, type, (
% 4.06/2.83 powerset: $i > $i)).
% 4.06/2.83 tff(the_carrier_type, type, (
% 4.06/2.83 the_carrier: $i > $i)).
% 4.06/2.83 tff(boole_POSet_type, type, (
% 4.06/2.83 boole_POSet: $i > $i)).
% 4.06/2.83 tff(upper_relstr_subset_type, type, (
% 4.06/2.83 upper_relstr_subset: ( $i * $i ) > $o)).
% 4.06/2.83 tff(filtered_subset_type, type, (
% 4.06/2.83 filtered_subset: ( $i * $i ) > $o)).
% 4.06/2.83 tff(empty_type, type, (
% 4.06/2.83 empty: $i > $o)).
% 4.06/2.83 tff(one_sorted_str_type, type, (
% 4.06/2.83 one_sorted_str: $i > $o)).
% 4.06/2.83 tff(proper_element_type, type, (
% 4.06/2.83 proper_element: ( $i * $i ) > $o)).
% 4.06/2.83 tff(empty_carrier_type, type, (
% 4.06/2.83 empty_carrier: $i > $o)).
% 4.06/2.83 tff(in_type, type, (
% 4.06/2.83 in: ( $i * $i ) > $o)).
% 4.06/2.83 tff(relation_type, type, (
% 4.06/2.83 relation: $i > $o)).
% 4.06/2.83 tff(relation_empty_yielding_type, type, (
% 4.06/2.83 relation_empty_yielding: $i > $o)).
% 4.06/2.83 tff(1,plain,
% 4.06/2.83 ((((~empty_carrier(A!36)) & one_sorted_str(A!36)) & (~((~((~empty(B!37)) & filtered_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36))) & upper_relstr_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36))) & proper_element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36))))) & element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36))))))) | (B!37 = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B!37)))))) <=> ((~empty_carrier(A!36)) & one_sorted_str(A!36) & (~((~((~empty(B!37)) & filtered_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36))) & upper_relstr_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36))) & proper_element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36))))) & element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36))))))) | (B!37 = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B!37))))))),
% 4.06/2.83 inference(rewrite,[status(thm)],[])).
% 4.06/2.83 tff(2,plain,
% 4.06/2.83 ((~(~((~empty_carrier(A!36)) & one_sorted_str(A!36)))) <=> ((~empty_carrier(A!36)) & one_sorted_str(A!36))),
% 4.06/2.83 inference(rewrite,[status(thm)],[])).
% 4.06/2.83 tff(3,plain,
% 4.06/2.83 (((~(~((~empty_carrier(A!36)) & one_sorted_str(A!36)))) & (~((~((~empty(B!37)) & filtered_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36))) & upper_relstr_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36))) & proper_element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36))))) & element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36))))))) | (B!37 = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B!37)))))) <=> (((~empty_carrier(A!36)) & one_sorted_str(A!36)) & (~((~((~empty(B!37)) & filtered_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36))) & upper_relstr_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36))) & proper_element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36))))) & element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36))))))) | (B!37 = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B!37))))))),
% 4.06/2.83 inference(monotonicity,[status(thm)],[2])).
% 4.06/2.83 tff(4,plain,
% 4.06/2.83 (((~(~((~empty_carrier(A!36)) & one_sorted_str(A!36)))) & (~((~((~empty(B!37)) & filtered_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36))) & upper_relstr_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36))) & proper_element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36))))) & element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36))))))) | (B!37 = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B!37)))))) <=> ((~empty_carrier(A!36)) & one_sorted_str(A!36) & (~((~((~empty(B!37)) & filtered_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36))) & upper_relstr_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36))) & proper_element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36))))) & element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36))))))) | (B!37 = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B!37))))))),
% 4.06/2.83 inference(transitivity,[status(thm)],[3, 1])).
% 4.06/2.83 tff(5,plain,
% 4.06/2.83 ((~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & proper_element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))) | (B = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B)))))) <=> (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & proper_element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))) | (B = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))))))),
% 4.06/2.83 inference(rewrite,[status(thm)],[])).
% 4.06/2.83 tff(6,plain,
% 4.06/2.83 ((~![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : ((((((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) & proper_element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))) => (B = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B)))))) <=> (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & proper_element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))) | (B = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))))))),
% 4.06/2.83 inference(rewrite,[status(thm)],[])).
% 4.06/2.83 tff(7,axiom,(~![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : ((((((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) & proper_element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))) => (B = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t15_yellow19')).
% 4.06/2.83 tff(8,plain,
% 4.06/2.83 (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & proper_element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))) | (B = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B)))))),
% 4.06/2.83 inference(modus_ponens,[status(thm)],[7, 6])).
% 4.06/2.83 tff(9,plain,
% 4.06/2.83 (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & proper_element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))) | (B = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B)))))),
% 4.06/2.83 inference(modus_ponens,[status(thm)],[8, 5])).
% 4.06/2.83 tff(10,plain,
% 4.06/2.83 (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & proper_element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))) | (B = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B)))))),
% 4.06/2.83 inference(modus_ponens,[status(thm)],[9, 5])).
% 4.06/2.83 tff(11,plain,
% 4.06/2.83 (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & proper_element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))) | (B = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B)))))),
% 4.06/2.83 inference(modus_ponens,[status(thm)],[10, 5])).
% 4.06/2.83 tff(12,plain,
% 4.06/2.83 (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & proper_element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))) | (B = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B)))))),
% 4.06/2.83 inference(modus_ponens,[status(thm)],[11, 5])).
% 4.06/2.83 tff(13,plain,
% 4.06/2.83 (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & proper_element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))) | (B = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B)))))),
% 4.06/2.83 inference(modus_ponens,[status(thm)],[12, 5])).
% 4.06/2.83 tff(14,plain,
% 4.06/2.83 (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & proper_element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))) | (B = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B)))))),
% 4.06/2.83 inference(modus_ponens,[status(thm)],[13, 5])).
% 4.06/2.83 tff(15,plain,
% 4.06/2.83 ((~empty_carrier(A!36)) & one_sorted_str(A!36) & (~((~((~empty(B!37)) & filtered_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36))) & upper_relstr_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36))) & proper_element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36))))) & element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36))))))) | (B!37 = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B!37)))))),
% 4.06/2.83 inference(modus_ponens,[status(thm)],[14, 4])).
% 4.06/2.83 tff(16,plain,
% 4.06/2.83 (one_sorted_str(A!36)),
% 4.06/2.83 inference(and_elim,[status(thm)],[15])).
% 4.06/2.83 tff(17,plain,
% 4.06/2.83 (~empty_carrier(A!36)),
% 4.06/2.83 inference(and_elim,[status(thm)],[15])).
% 4.06/2.83 tff(18,plain,
% 4.06/2.83 (^[A: $i] : refl((empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))))) <=> (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))))))),
% 4.06/2.83 inference(bind,[status(th)],[])).
% 4.06/2.83 tff(19,plain,
% 4.06/2.83 (![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))))) <=> ![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))))),
% 4.06/2.83 inference(quant_intro,[status(thm)],[18])).
% 4.06/2.83 tff(20,plain,
% 4.06/2.83 (^[A: $i] : rewrite((empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))))) <=> (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))))))),
% 4.06/2.83 inference(bind,[status(th)],[])).
% 4.06/2.83 tff(21,plain,
% 4.06/2.83 (![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))))) <=> ![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))))),
% 4.06/2.83 inference(quant_intro,[status(thm)],[20])).
% 4.06/2.83 tff(22,plain,
% 4.06/2.83 (![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))))) <=> ![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))))),
% 4.06/2.83 inference(transitivity,[status(thm)],[21, 19])).
% 4.06/2.83 tff(23,plain,
% 4.06/2.83 (^[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))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))) <=> (~(empty(B) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))))), ((~((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))) <=> (~(~(empty(B) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))))))), rewrite((~(~(empty(B) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))))) <=> (empty(B) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))))), ((~((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))) <=> (empty(B) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))))), (((~((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B)))) <=> ((empty(B) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B)))))), rewrite(((empty(B) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B)))) <=> (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))))), (((~((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B)))) <=> (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))))))), (![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B)))) <=> ![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))))), (((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))))) <=> ((empty_carrier(A) | (~one_sorted_str(A))) | ![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))))))), rewrite(((empty_carrier(A) | (~one_sorted_str(A))) | ![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))))) <=> (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))))), (((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))))) <=> (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))))))),
% 4.06/2.83 inference(bind,[status(th)],[])).
% 4.06/2.83 tff(24,plain,
% 4.06/2.83 (![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))))) <=> ![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))))),
% 4.06/2.83 inference(quant_intro,[status(thm)],[23])).
% 4.06/2.83 tff(25,plain,
% 4.06/2.83 (![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B)))))),
% 4.06/2.83 inference(rewrite,[status(thm)],[])).
% 4.06/2.83 tff(26,plain,
% 4.06/2.83 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) <=> ((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))))), (((((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))) <=> (((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))))), rewrite((((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))) <=> ((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))), (((((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))) <=> ((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))))), ((((((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))) => (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B)))) <=> (((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))) => (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B)))))), rewrite((((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))) => (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B)))) <=> ((~((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))))), ((((((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))) => (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B)))) <=> ((~((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))))))), (![B: $i] : (((((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))) => (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B)))) <=> ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B)))))), ((((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : (((((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))) => (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))))) <=> (((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))))))), rewrite((((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))))) <=> ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B)))))), ((((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : (((((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))) => (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))))) <=> ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B)))))))),
% 4.06/2.83 inference(bind,[status(th)],[])).
% 4.06/2.83 tff(27,plain,
% 4.06/2.83 (![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : (((((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))) => (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B)))))),
% 4.06/2.84 inference(quant_intro,[status(thm)],[26])).
% 4.06/2.84 tff(28,axiom,(![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : (((((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))) => (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t14_yellow19')).
% 4.06/2.84 tff(29,plain,
% 4.06/2.84 (![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B)))))),
% 4.06/2.84 inference(modus_ponens,[status(thm)],[28, 27])).
% 4.06/2.84 tff(30,plain,
% 4.06/2.84 (![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B)))))),
% 4.06/2.84 inference(modus_ponens,[status(thm)],[29, 25])).
% 4.06/2.84 tff(31,plain,(
% 4.06/2.84 ![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(cast_as_carrier_subset(A))) & upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A))) & element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B)))))),
% 4.06/2.84 inference(skolemize,[status(sab)],[30])).
% 4.06/2.84 tff(32,plain,
% 4.06/2.84 (![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))))),
% 4.06/2.84 inference(modus_ponens,[status(thm)],[31, 24])).
% 4.06/2.84 tff(33,plain,
% 4.06/2.84 (![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))))),
% 4.06/2.84 inference(modus_ponens,[status(thm)],[32, 22])).
% 4.06/2.84 tff(34,plain,
% 4.06/2.84 (((~![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))))) | (empty_carrier(A!36) | (~one_sorted_str(A!36)) | ![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36))))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))))) | empty_carrier(A!36) | (~one_sorted_str(A!36)) | ![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36))))))))),
% 4.06/2.84 inference(rewrite,[status(thm)],[])).
% 4.06/2.84 tff(35,plain,
% 4.06/2.84 ((~![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))))) | (empty_carrier(A!36) | (~one_sorted_str(A!36)) | ![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36))))))))),
% 4.06/2.84 inference(quant_inst,[status(thm)],[])).
% 4.06/2.84 tff(36,plain,
% 4.06/2.84 ((~![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A, net_of_bool_filter(A, cast_as_carrier_subset(A), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))))) | empty_carrier(A!36) | (~one_sorted_str(A!36)) | ![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))))),
% 4.06/2.84 inference(modus_ponens,[status(thm)],[35, 34])).
% 4.06/2.84 tff(37,plain,
% 4.06/2.84 (![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))))),
% 4.06/2.84 inference(unit_resolution,[status(thm)],[36, 33, 17, 16])).
% 4.06/2.84 tff(38,plain,
% 4.06/2.84 (~((~((~empty(B!37)) & filtered_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36))) & upper_relstr_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36))) & proper_element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36))))) & element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36))))))) | (B!37 = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B!37))))),
% 4.06/2.84 inference(and_elim,[status(thm)],[15])).
% 4.06/2.84 tff(39,plain,
% 4.06/2.84 ((~empty(B!37)) & filtered_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36))) & upper_relstr_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36))) & proper_element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36))))) & element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))),
% 4.06/2.84 inference(or_elim,[status(thm)],[38])).
% 4.06/2.84 tff(40,plain,
% 4.06/2.84 (element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))),
% 4.06/2.84 inference(and_elim,[status(thm)],[39])).
% 4.06/2.84 tff(41,plain,
% 4.06/2.84 (upper_relstr_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))),
% 4.06/2.84 inference(and_elim,[status(thm)],[39])).
% 4.06/2.84 tff(42,plain,
% 4.06/2.84 (filtered_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))),
% 4.06/2.84 inference(and_elim,[status(thm)],[39])).
% 4.06/2.84 tff(43,plain,
% 4.06/2.84 (~empty(B!37)),
% 4.06/2.84 inference(and_elim,[status(thm)],[39])).
% 4.06/2.84 tff(44,plain,
% 4.06/2.84 (((~![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))))) | (empty(B!37) | (~element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | (~filtered_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (set_difference(B!37, singleton(empty_set)) = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B!37))))) <=> ((~![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))))) | empty(B!37) | (~element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | (~filtered_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (set_difference(B!37, singleton(empty_set)) = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B!37))))),
% 4.06/2.84 inference(rewrite,[status(thm)],[])).
% 4.06/2.84 tff(45,plain,
% 4.06/2.84 ((empty(B!37) | (set_difference(B!37, singleton(empty_set)) = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B!37))) | (~filtered_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36))))))) <=> (empty(B!37) | (~element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | (~filtered_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (set_difference(B!37, singleton(empty_set)) = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B!37))))),
% 4.06/2.84 inference(rewrite,[status(thm)],[])).
% 4.06/2.84 tff(46,plain,
% 4.06/2.84 (((~![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))))) | (empty(B!37) | (set_difference(B!37, singleton(empty_set)) = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B!37))) | (~filtered_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))))) <=> ((~![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))))) | (empty(B!37) | (~element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | (~filtered_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (set_difference(B!37, singleton(empty_set)) = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B!37)))))),
% 4.06/2.84 inference(monotonicity,[status(thm)],[45])).
% 4.06/2.84 tff(47,plain,
% 4.06/2.84 (((~![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))))) | (empty(B!37) | (set_difference(B!37, singleton(empty_set)) = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B!37))) | (~filtered_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))))) <=> ((~![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))))) | empty(B!37) | (~element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | (~filtered_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (set_difference(B!37, singleton(empty_set)) = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B!37))))),
% 4.06/2.84 inference(transitivity,[status(thm)],[46, 44])).
% 4.06/2.84 tff(48,plain,
% 4.06/2.84 ((~![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))))) | (empty(B!37) | (set_difference(B!37, singleton(empty_set)) = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B!37))) | (~filtered_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))))),
% 4.06/2.84 inference(quant_inst,[status(thm)],[])).
% 4.06/2.84 tff(49,plain,
% 4.06/2.84 ((~![B: $i] : (empty(B) | (set_difference(B, singleton(empty_set)) = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B))) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))))) | empty(B!37) | (~element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | (~filtered_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (set_difference(B!37, singleton(empty_set)) = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B!37)))),
% 4.06/2.84 inference(modus_ponens,[status(thm)],[48, 47])).
% 4.06/2.84 tff(50,plain,
% 4.06/2.84 (set_difference(B!37, singleton(empty_set)) = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B!37))),
% 4.06/2.84 inference(unit_resolution,[status(thm)],[49, 43, 42, 41, 40, 37])).
% 4.06/2.84 tff(51,plain,
% 4.06/2.84 (^[A: $i, B: $i] : refl(((set_difference(A, singleton(B)) = A) <=> (~in(B, A))) <=> ((set_difference(A, singleton(B)) = A) <=> (~in(B, A))))),
% 4.06/2.84 inference(bind,[status(th)],[])).
% 4.06/2.84 tff(52,plain,
% 4.06/2.84 (![A: $i, B: $i] : ((set_difference(A, singleton(B)) = A) <=> (~in(B, A))) <=> ![A: $i, B: $i] : ((set_difference(A, singleton(B)) = A) <=> (~in(B, A)))),
% 4.06/2.84 inference(quant_intro,[status(thm)],[51])).
% 4.06/2.84 tff(53,plain,
% 4.06/2.84 (![A: $i, B: $i] : ((set_difference(A, singleton(B)) = A) <=> (~in(B, A))) <=> ![A: $i, B: $i] : ((set_difference(A, singleton(B)) = A) <=> (~in(B, A)))),
% 4.06/2.84 inference(rewrite,[status(thm)],[])).
% 4.06/2.84 tff(54,axiom,(![A: $i, B: $i] : ((set_difference(A, singleton(B)) = A) <=> (~in(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t65_zfmisc_1')).
% 4.06/2.84 tff(55,plain,
% 4.06/2.84 (![A: $i, B: $i] : ((set_difference(A, singleton(B)) = A) <=> (~in(B, A)))),
% 4.06/2.84 inference(modus_ponens,[status(thm)],[54, 53])).
% 4.06/2.84 tff(56,plain,(
% 4.06/2.84 ![A: $i, B: $i] : ((set_difference(A, singleton(B)) = A) <=> (~in(B, A)))),
% 4.06/2.84 inference(skolemize,[status(sab)],[55])).
% 4.06/2.84 tff(57,plain,
% 4.06/2.84 (![A: $i, B: $i] : ((set_difference(A, singleton(B)) = A) <=> (~in(B, A)))),
% 4.06/2.84 inference(modus_ponens,[status(thm)],[56, 52])).
% 4.06/2.84 tff(58,plain,
% 4.06/2.84 ((~![A: $i, B: $i] : ((set_difference(A, singleton(B)) = A) <=> (~in(B, A)))) | ((set_difference(B!37, singleton(empty_set)) = B!37) <=> (~in(empty_set, B!37)))),
% 4.06/2.84 inference(quant_inst,[status(thm)],[])).
% 4.06/2.84 tff(59,plain,
% 4.06/2.84 ((set_difference(B!37, singleton(empty_set)) = B!37) <=> (~in(empty_set, B!37))),
% 4.06/2.84 inference(unit_resolution,[status(thm)],[58, 57])).
% 4.06/2.84 tff(60,plain,
% 4.06/2.84 (^[A: $i] : refl((empty_carrier(A) | (~empty(cast_as_carrier_subset(A))) | (~one_sorted_str(A))) <=> (empty_carrier(A) | (~empty(cast_as_carrier_subset(A))) | (~one_sorted_str(A))))),
% 4.06/2.84 inference(bind,[status(th)],[])).
% 4.06/2.84 tff(61,plain,
% 4.06/2.84 (![A: $i] : (empty_carrier(A) | (~empty(cast_as_carrier_subset(A))) | (~one_sorted_str(A))) <=> ![A: $i] : (empty_carrier(A) | (~empty(cast_as_carrier_subset(A))) | (~one_sorted_str(A)))),
% 4.06/2.84 inference(quant_intro,[status(thm)],[60])).
% 4.06/2.84 tff(62,plain,
% 4.06/2.84 (^[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(cast_as_carrier_subset(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> ((~empty(cast_as_carrier_subset(A))) | (empty_carrier(A) | (~one_sorted_str(A)))))), rewrite(((~empty(cast_as_carrier_subset(A))) | (empty_carrier(A) | (~one_sorted_str(A)))) <=> (empty_carrier(A) | (~empty(cast_as_carrier_subset(A))) | (~one_sorted_str(A)))), (((~empty(cast_as_carrier_subset(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> (empty_carrier(A) | (~empty(cast_as_carrier_subset(A))) | (~one_sorted_str(A)))))),
% 4.06/2.84 inference(bind,[status(th)],[])).
% 4.06/2.84 tff(63,plain,
% 4.06/2.84 (![A: $i] : ((~empty(cast_as_carrier_subset(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> ![A: $i] : (empty_carrier(A) | (~empty(cast_as_carrier_subset(A))) | (~one_sorted_str(A)))),
% 4.06/2.84 inference(quant_intro,[status(thm)],[62])).
% 4.06/2.84 tff(64,plain,
% 4.06/2.84 (![A: $i] : ((~empty(cast_as_carrier_subset(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> ![A: $i] : ((~empty(cast_as_carrier_subset(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 4.06/2.84 inference(rewrite,[status(thm)],[])).
% 4.06/2.84 tff(65,plain,
% 4.06/2.84 (^[A: $i] : rewrite((((~empty_carrier(A)) & one_sorted_str(A)) => (~empty(cast_as_carrier_subset(A)))) <=> ((~empty(cast_as_carrier_subset(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))))),
% 4.06/2.84 inference(bind,[status(th)],[])).
% 4.06/2.84 tff(66,plain,
% 4.06/2.84 (![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => (~empty(cast_as_carrier_subset(A)))) <=> ![A: $i] : ((~empty(cast_as_carrier_subset(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 4.06/2.84 inference(quant_intro,[status(thm)],[65])).
% 4.06/2.85 tff(67,axiom,(![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => (~empty(cast_as_carrier_subset(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc2_pre_topc')).
% 4.06/2.85 tff(68,plain,
% 4.06/2.85 (![A: $i] : ((~empty(cast_as_carrier_subset(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 4.06/2.85 inference(modus_ponens,[status(thm)],[67, 66])).
% 4.06/2.85 tff(69,plain,
% 4.06/2.85 (![A: $i] : ((~empty(cast_as_carrier_subset(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 4.06/2.85 inference(modus_ponens,[status(thm)],[68, 64])).
% 4.06/2.85 tff(70,plain,(
% 4.06/2.85 ![A: $i] : ((~empty(cast_as_carrier_subset(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 4.06/2.85 inference(skolemize,[status(sab)],[69])).
% 4.06/2.85 tff(71,plain,
% 4.06/2.85 (![A: $i] : (empty_carrier(A) | (~empty(cast_as_carrier_subset(A))) | (~one_sorted_str(A)))),
% 4.06/2.85 inference(modus_ponens,[status(thm)],[70, 63])).
% 4.06/2.85 tff(72,plain,
% 4.06/2.85 (![A: $i] : (empty_carrier(A) | (~empty(cast_as_carrier_subset(A))) | (~one_sorted_str(A)))),
% 4.06/2.85 inference(modus_ponens,[status(thm)],[71, 61])).
% 4.06/2.85 tff(73,plain,
% 4.06/2.85 (((~![A: $i] : (empty_carrier(A) | (~empty(cast_as_carrier_subset(A))) | (~one_sorted_str(A)))) | (empty_carrier(A!36) | (~one_sorted_str(A!36)) | (~empty(cast_as_carrier_subset(A!36))))) <=> ((~![A: $i] : (empty_carrier(A) | (~empty(cast_as_carrier_subset(A))) | (~one_sorted_str(A)))) | empty_carrier(A!36) | (~one_sorted_str(A!36)) | (~empty(cast_as_carrier_subset(A!36))))),
% 4.06/2.85 inference(rewrite,[status(thm)],[])).
% 4.06/2.85 tff(74,plain,
% 4.06/2.85 ((empty_carrier(A!36) | (~empty(cast_as_carrier_subset(A!36))) | (~one_sorted_str(A!36))) <=> (empty_carrier(A!36) | (~one_sorted_str(A!36)) | (~empty(cast_as_carrier_subset(A!36))))),
% 4.06/2.85 inference(rewrite,[status(thm)],[])).
% 4.06/2.85 tff(75,plain,
% 4.06/2.85 (((~![A: $i] : (empty_carrier(A) | (~empty(cast_as_carrier_subset(A))) | (~one_sorted_str(A)))) | (empty_carrier(A!36) | (~empty(cast_as_carrier_subset(A!36))) | (~one_sorted_str(A!36)))) <=> ((~![A: $i] : (empty_carrier(A) | (~empty(cast_as_carrier_subset(A))) | (~one_sorted_str(A)))) | (empty_carrier(A!36) | (~one_sorted_str(A!36)) | (~empty(cast_as_carrier_subset(A!36)))))),
% 4.06/2.85 inference(monotonicity,[status(thm)],[74])).
% 4.06/2.85 tff(76,plain,
% 4.06/2.85 (((~![A: $i] : (empty_carrier(A) | (~empty(cast_as_carrier_subset(A))) | (~one_sorted_str(A)))) | (empty_carrier(A!36) | (~empty(cast_as_carrier_subset(A!36))) | (~one_sorted_str(A!36)))) <=> ((~![A: $i] : (empty_carrier(A) | (~empty(cast_as_carrier_subset(A))) | (~one_sorted_str(A)))) | empty_carrier(A!36) | (~one_sorted_str(A!36)) | (~empty(cast_as_carrier_subset(A!36))))),
% 4.06/2.85 inference(transitivity,[status(thm)],[75, 73])).
% 4.06/2.85 tff(77,plain,
% 4.06/2.85 ((~![A: $i] : (empty_carrier(A) | (~empty(cast_as_carrier_subset(A))) | (~one_sorted_str(A)))) | (empty_carrier(A!36) | (~empty(cast_as_carrier_subset(A!36))) | (~one_sorted_str(A!36)))),
% 4.06/2.85 inference(quant_inst,[status(thm)],[])).
% 4.06/2.85 tff(78,plain,
% 4.06/2.85 ((~![A: $i] : (empty_carrier(A) | (~empty(cast_as_carrier_subset(A))) | (~one_sorted_str(A)))) | empty_carrier(A!36) | (~one_sorted_str(A!36)) | (~empty(cast_as_carrier_subset(A!36)))),
% 4.06/2.85 inference(modus_ponens,[status(thm)],[77, 76])).
% 4.06/2.85 tff(79,plain,
% 4.06/2.85 (~empty(cast_as_carrier_subset(A!36))),
% 4.06/2.85 inference(unit_resolution,[status(thm)],[78, 72, 17, 16])).
% 4.06/2.85 tff(80,plain,
% 4.06/2.85 (^[A: $i] : refl((empty(A) | ![B: $i] : (empty(B) | (~filtered_subset(B, boole_POSet(A))) | (~upper_relstr_subset(B, boole_POSet(A))) | (~element(B, powerset(the_carrier(boole_POSet(A))))) | (~proper_element(B, powerset(the_carrier(boole_POSet(A))))) | ![C: $i] : ((~in(C, B)) | (~empty(C))))) <=> (empty(A) | ![B: $i] : (empty(B) | (~filtered_subset(B, boole_POSet(A))) | (~upper_relstr_subset(B, boole_POSet(A))) | (~element(B, powerset(the_carrier(boole_POSet(A))))) | (~proper_element(B, powerset(the_carrier(boole_POSet(A))))) | ![C: $i] : ((~in(C, B)) | (~empty(C))))))),
% 4.06/2.85 inference(bind,[status(th)],[])).
% 4.06/2.85 tff(81,plain,
% 4.06/2.85 (![A: $i] : (empty(A) | ![B: $i] : (empty(B) | (~filtered_subset(B, boole_POSet(A))) | (~upper_relstr_subset(B, boole_POSet(A))) | (~element(B, powerset(the_carrier(boole_POSet(A))))) | (~proper_element(B, powerset(the_carrier(boole_POSet(A))))) | ![C: $i] : ((~in(C, B)) | (~empty(C))))) <=> ![A: $i] : (empty(A) | ![B: $i] : (empty(B) | (~filtered_subset(B, boole_POSet(A))) | (~upper_relstr_subset(B, boole_POSet(A))) | (~element(B, powerset(the_carrier(boole_POSet(A))))) | (~proper_element(B, powerset(the_carrier(boole_POSet(A))))) | ![C: $i] : ((~in(C, B)) | (~empty(C)))))),
% 4.06/2.85 inference(quant_intro,[status(thm)],[80])).
% 4.06/2.85 tff(82,plain,
% 4.06/2.85 (^[A: $i] : rewrite((empty(A) | ![B: $i] : (empty(B) | (~filtered_subset(B, boole_POSet(A))) | (~upper_relstr_subset(B, boole_POSet(A))) | (~element(B, powerset(the_carrier(boole_POSet(A))))) | (~proper_element(B, powerset(the_carrier(boole_POSet(A))))) | ![C: $i] : ((~in(C, B)) | (~empty(C))))) <=> (empty(A) | ![B: $i] : (empty(B) | (~filtered_subset(B, boole_POSet(A))) | (~upper_relstr_subset(B, boole_POSet(A))) | (~element(B, powerset(the_carrier(boole_POSet(A))))) | (~proper_element(B, powerset(the_carrier(boole_POSet(A))))) | ![C: $i] : ((~in(C, B)) | (~empty(C))))))),
% 4.06/2.85 inference(bind,[status(th)],[])).
% 4.06/2.85 tff(83,plain,
% 4.06/2.85 (![A: $i] : (empty(A) | ![B: $i] : (empty(B) | (~filtered_subset(B, boole_POSet(A))) | (~upper_relstr_subset(B, boole_POSet(A))) | (~element(B, powerset(the_carrier(boole_POSet(A))))) | (~proper_element(B, powerset(the_carrier(boole_POSet(A))))) | ![C: $i] : ((~in(C, B)) | (~empty(C))))) <=> ![A: $i] : (empty(A) | ![B: $i] : (empty(B) | (~filtered_subset(B, boole_POSet(A))) | (~upper_relstr_subset(B, boole_POSet(A))) | (~element(B, powerset(the_carrier(boole_POSet(A))))) | (~proper_element(B, powerset(the_carrier(boole_POSet(A))))) | ![C: $i] : ((~in(C, B)) | (~empty(C)))))),
% 4.06/2.85 inference(quant_intro,[status(thm)],[82])).
% 4.06/2.85 tff(84,plain,
% 4.06/2.85 (![A: $i] : (empty(A) | ![B: $i] : (empty(B) | (~filtered_subset(B, boole_POSet(A))) | (~upper_relstr_subset(B, boole_POSet(A))) | (~element(B, powerset(the_carrier(boole_POSet(A))))) | (~proper_element(B, powerset(the_carrier(boole_POSet(A))))) | ![C: $i] : ((~in(C, B)) | (~empty(C))))) <=> ![A: $i] : (empty(A) | ![B: $i] : (empty(B) | (~filtered_subset(B, boole_POSet(A))) | (~upper_relstr_subset(B, boole_POSet(A))) | (~element(B, powerset(the_carrier(boole_POSet(A))))) | (~proper_element(B, powerset(the_carrier(boole_POSet(A))))) | ![C: $i] : ((~in(C, B)) | (~empty(C)))))),
% 4.06/2.85 inference(transitivity,[status(thm)],[83, 81])).
% 4.06/2.85 tff(85,plain,
% 4.06/2.85 (^[A: $i] : rewrite((empty(A) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A)))))) | ![C: $i] : (~(in(C, B) & empty(C))))) <=> (empty(A) | ![B: $i] : (empty(B) | (~filtered_subset(B, boole_POSet(A))) | (~upper_relstr_subset(B, boole_POSet(A))) | (~element(B, powerset(the_carrier(boole_POSet(A))))) | (~proper_element(B, powerset(the_carrier(boole_POSet(A))))) | ![C: $i] : ((~in(C, B)) | (~empty(C))))))),
% 4.06/2.85 inference(bind,[status(th)],[])).
% 4.06/2.85 tff(86,plain,
% 4.06/2.85 (![A: $i] : (empty(A) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A)))))) | ![C: $i] : (~(in(C, B) & empty(C))))) <=> ![A: $i] : (empty(A) | ![B: $i] : (empty(B) | (~filtered_subset(B, boole_POSet(A))) | (~upper_relstr_subset(B, boole_POSet(A))) | (~element(B, powerset(the_carrier(boole_POSet(A))))) | (~proper_element(B, powerset(the_carrier(boole_POSet(A))))) | ![C: $i] : ((~in(C, B)) | (~empty(C)))))),
% 4.06/2.85 inference(quant_intro,[status(thm)],[85])).
% 4.06/2.85 tff(87,plain,
% 4.06/2.85 (![A: $i] : (empty(A) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A)))))) | ![C: $i] : (~(in(C, B) & empty(C))))) <=> ![A: $i] : (empty(A) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A)))))) | ![C: $i] : (~(in(C, B) & empty(C)))))),
% 4.06/2.85 inference(rewrite,[status(thm)],[])).
% 4.06/2.85 tff(88,plain,
% 4.06/2.85 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~empty(B)) & filtered_subset(B, boole_POSet(A))) & upper_relstr_subset(B, boole_POSet(A))) <=> ((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)))), (((((~empty(B)) & filtered_subset(B, boole_POSet(A))) & upper_relstr_subset(B, boole_POSet(A))) & proper_element(B, powerset(the_carrier(boole_POSet(A))))) <=> (((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A))) & proper_element(B, powerset(the_carrier(boole_POSet(A))))))), rewrite((((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A))) & proper_element(B, powerset(the_carrier(boole_POSet(A))))) <=> ((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))))), (((((~empty(B)) & filtered_subset(B, boole_POSet(A))) & upper_relstr_subset(B, boole_POSet(A))) & proper_element(B, powerset(the_carrier(boole_POSet(A))))) <=> ((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A))))))), ((((((~empty(B)) & filtered_subset(B, boole_POSet(A))) & upper_relstr_subset(B, boole_POSet(A))) & proper_element(B, powerset(the_carrier(boole_POSet(A))))) & element(B, powerset(the_carrier(boole_POSet(A))))) <=> (((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A))))) & element(B, powerset(the_carrier(boole_POSet(A))))))), rewrite((((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A))))) & element(B, powerset(the_carrier(boole_POSet(A))))) <=> ((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A)))))), ((((((~empty(B)) & filtered_subset(B, boole_POSet(A))) & upper_relstr_subset(B, boole_POSet(A))) & proper_element(B, powerset(the_carrier(boole_POSet(A))))) & element(B, powerset(the_carrier(boole_POSet(A))))) <=> ((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A))))))), (((((((~empty(B)) & filtered_subset(B, boole_POSet(A))) & upper_relstr_subset(B, boole_POSet(A))) & proper_element(B, powerset(the_carrier(boole_POSet(A))))) & element(B, powerset(the_carrier(boole_POSet(A))))) => ![C: $i] : (~(in(C, B) & empty(C)))) <=> (((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A))))) => ![C: $i] : (~(in(C, B) & empty(C)))))), rewrite((((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A))))) => ![C: $i] : (~(in(C, B) & empty(C)))) <=> ((~((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A)))))) | ![C: $i] : (~(in(C, B) & empty(C))))), (((((((~empty(B)) & filtered_subset(B, boole_POSet(A))) & upper_relstr_subset(B, boole_POSet(A))) & proper_element(B, powerset(the_carrier(boole_POSet(A))))) & element(B, powerset(the_carrier(boole_POSet(A))))) => ![C: $i] : (~(in(C, B) & empty(C)))) <=> ((~((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A)))))) | ![C: $i] : (~(in(C, B) & empty(C))))))), (![B: $i] : ((((((~empty(B)) & filtered_subset(B, boole_POSet(A))) & upper_relstr_subset(B, boole_POSet(A))) & proper_element(B, powerset(the_carrier(boole_POSet(A))))) & element(B, powerset(the_carrier(boole_POSet(A))))) => ![C: $i] : (~(in(C, B) & empty(C)))) <=> ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A)))))) | ![C: $i] : (~(in(C, B) & empty(C)))))), (((~empty(A)) => ![B: $i] : ((((((~empty(B)) & filtered_subset(B, boole_POSet(A))) & upper_relstr_subset(B, boole_POSet(A))) & proper_element(B, powerset(the_carrier(boole_POSet(A))))) & element(B, powerset(the_carrier(boole_POSet(A))))) => ![C: $i] : (~(in(C, B) & empty(C))))) <=> ((~empty(A)) => ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A)))))) | ![C: $i] : (~(in(C, B) & empty(C))))))), rewrite(((~empty(A)) => ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A)))))) | ![C: $i] : (~(in(C, B) & empty(C))))) <=> (empty(A) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A)))))) | ![C: $i] : (~(in(C, B) & empty(C)))))), (((~empty(A)) => ![B: $i] : ((((((~empty(B)) & filtered_subset(B, boole_POSet(A))) & upper_relstr_subset(B, boole_POSet(A))) & proper_element(B, powerset(the_carrier(boole_POSet(A))))) & element(B, powerset(the_carrier(boole_POSet(A))))) => ![C: $i] : (~(in(C, B) & empty(C))))) <=> (empty(A) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A)))))) | ![C: $i] : (~(in(C, B) & empty(C)))))))),
% 4.06/2.85 inference(bind,[status(th)],[])).
% 4.06/2.85 tff(89,plain,
% 4.06/2.85 (![A: $i] : ((~empty(A)) => ![B: $i] : ((((((~empty(B)) & filtered_subset(B, boole_POSet(A))) & upper_relstr_subset(B, boole_POSet(A))) & proper_element(B, powerset(the_carrier(boole_POSet(A))))) & element(B, powerset(the_carrier(boole_POSet(A))))) => ![C: $i] : (~(in(C, B) & empty(C))))) <=> ![A: $i] : (empty(A) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A)))))) | ![C: $i] : (~(in(C, B) & empty(C)))))),
% 4.06/2.85 inference(quant_intro,[status(thm)],[88])).
% 4.06/2.85 tff(90,axiom,(![A: $i] : ((~empty(A)) => ![B: $i] : ((((((~empty(B)) & filtered_subset(B, boole_POSet(A))) & upper_relstr_subset(B, boole_POSet(A))) & proper_element(B, powerset(the_carrier(boole_POSet(A))))) & element(B, powerset(the_carrier(boole_POSet(A))))) => ![C: $i] : (~(in(C, B) & empty(C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2_yellow19')).
% 4.06/2.85 tff(91,plain,
% 4.06/2.85 (![A: $i] : (empty(A) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A)))))) | ![C: $i] : (~(in(C, B) & empty(C)))))),
% 4.06/2.85 inference(modus_ponens,[status(thm)],[90, 89])).
% 4.06/2.85 tff(92,plain,
% 4.06/2.85 (![A: $i] : (empty(A) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A)))))) | ![C: $i] : (~(in(C, B) & empty(C)))))),
% 4.06/2.85 inference(modus_ponens,[status(thm)],[91, 87])).
% 4.06/2.85 tff(93,plain,(
% 4.06/2.85 ![A: $i] : (empty(A) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A)))))) | ![C: $i] : (~(in(C, B) & empty(C)))))),
% 4.06/2.85 inference(skolemize,[status(sab)],[92])).
% 4.06/2.85 tff(94,plain,
% 4.06/2.85 (![A: $i] : (empty(A) | ![B: $i] : (empty(B) | (~filtered_subset(B, boole_POSet(A))) | (~upper_relstr_subset(B, boole_POSet(A))) | (~element(B, powerset(the_carrier(boole_POSet(A))))) | (~proper_element(B, powerset(the_carrier(boole_POSet(A))))) | ![C: $i] : ((~in(C, B)) | (~empty(C)))))),
% 4.06/2.85 inference(modus_ponens,[status(thm)],[93, 86])).
% 4.06/2.85 tff(95,plain,
% 4.06/2.85 (![A: $i] : (empty(A) | ![B: $i] : (empty(B) | (~filtered_subset(B, boole_POSet(A))) | (~upper_relstr_subset(B, boole_POSet(A))) | (~element(B, powerset(the_carrier(boole_POSet(A))))) | (~proper_element(B, powerset(the_carrier(boole_POSet(A))))) | ![C: $i] : ((~in(C, B)) | (~empty(C)))))),
% 4.06/2.85 inference(modus_ponens,[status(thm)],[94, 84])).
% 4.06/2.85 tff(96,plain,
% 4.06/2.85 (((~![A: $i] : (empty(A) | ![B: $i] : (empty(B) | (~filtered_subset(B, boole_POSet(A))) | (~upper_relstr_subset(B, boole_POSet(A))) | (~element(B, powerset(the_carrier(boole_POSet(A))))) | (~proper_element(B, powerset(the_carrier(boole_POSet(A))))) | ![C: $i] : ((~in(C, B)) | (~empty(C)))))) | (empty(cast_as_carrier_subset(A!36)) | ![B: $i] : (empty(B) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | (~proper_element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | ![C: $i] : ((~in(C, B)) | (~empty(C)))))) <=> ((~![A: $i] : (empty(A) | ![B: $i] : (empty(B) | (~filtered_subset(B, boole_POSet(A))) | (~upper_relstr_subset(B, boole_POSet(A))) | (~element(B, powerset(the_carrier(boole_POSet(A))))) | (~proper_element(B, powerset(the_carrier(boole_POSet(A))))) | ![C: $i] : ((~in(C, B)) | (~empty(C)))))) | empty(cast_as_carrier_subset(A!36)) | ![B: $i] : (empty(B) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | (~proper_element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | ![C: $i] : ((~in(C, B)) | (~empty(C)))))),
% 4.06/2.85 inference(rewrite,[status(thm)],[])).
% 4.06/2.85 tff(97,plain,
% 4.06/2.85 ((~![A: $i] : (empty(A) | ![B: $i] : (empty(B) | (~filtered_subset(B, boole_POSet(A))) | (~upper_relstr_subset(B, boole_POSet(A))) | (~element(B, powerset(the_carrier(boole_POSet(A))))) | (~proper_element(B, powerset(the_carrier(boole_POSet(A))))) | ![C: $i] : ((~in(C, B)) | (~empty(C)))))) | (empty(cast_as_carrier_subset(A!36)) | ![B: $i] : (empty(B) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | (~proper_element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | ![C: $i] : ((~in(C, B)) | (~empty(C)))))),
% 4.06/2.85 inference(quant_inst,[status(thm)],[])).
% 4.06/2.85 tff(98,plain,
% 4.06/2.85 ((~![A: $i] : (empty(A) | ![B: $i] : (empty(B) | (~filtered_subset(B, boole_POSet(A))) | (~upper_relstr_subset(B, boole_POSet(A))) | (~element(B, powerset(the_carrier(boole_POSet(A))))) | (~proper_element(B, powerset(the_carrier(boole_POSet(A))))) | ![C: $i] : ((~in(C, B)) | (~empty(C)))))) | empty(cast_as_carrier_subset(A!36)) | ![B: $i] : (empty(B) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | (~proper_element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | ![C: $i] : ((~in(C, B)) | (~empty(C))))),
% 4.06/2.85 inference(modus_ponens,[status(thm)],[97, 96])).
% 4.06/2.85 tff(99,plain,
% 4.06/2.85 (![B: $i] : (empty(B) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | (~proper_element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | ![C: $i] : ((~in(C, B)) | (~empty(C))))),
% 4.06/2.85 inference(unit_resolution,[status(thm)],[98, 95, 79])).
% 4.06/2.85 tff(100,plain,
% 4.06/2.85 (proper_element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))),
% 4.06/2.85 inference(and_elim,[status(thm)],[39])).
% 4.06/2.85 tff(101,plain,
% 4.06/2.85 (((~![B: $i] : (empty(B) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | (~proper_element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | ![C: $i] : ((~in(C, B)) | (~empty(C))))) | (empty(B!37) | (~filtered_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | (~proper_element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | ![C: $i] : ((~empty(C)) | (~in(C, B!37))))) <=> ((~![B: $i] : (empty(B) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | (~proper_element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | ![C: $i] : ((~in(C, B)) | (~empty(C))))) | empty(B!37) | (~filtered_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | (~proper_element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | ![C: $i] : ((~empty(C)) | (~in(C, B!37))))),
% 4.06/2.85 inference(rewrite,[status(thm)],[])).
% 4.06/2.85 tff(102,plain,
% 4.06/2.85 ((empty(B!37) | (~filtered_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | (~proper_element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | ![C: $i] : ((~in(C, B!37)) | (~empty(C)))) <=> (empty(B!37) | (~filtered_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | (~proper_element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | ![C: $i] : ((~empty(C)) | (~in(C, B!37))))),
% 4.06/2.85 inference(rewrite,[status(thm)],[])).
% 4.06/2.85 tff(103,plain,
% 4.06/2.85 (((~![B: $i] : (empty(B) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | (~proper_element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | ![C: $i] : ((~in(C, B)) | (~empty(C))))) | (empty(B!37) | (~filtered_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | (~proper_element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | ![C: $i] : ((~in(C, B!37)) | (~empty(C))))) <=> ((~![B: $i] : (empty(B) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | (~proper_element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | ![C: $i] : ((~in(C, B)) | (~empty(C))))) | (empty(B!37) | (~filtered_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | (~proper_element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | ![C: $i] : ((~empty(C)) | (~in(C, B!37)))))),
% 4.06/2.86 inference(monotonicity,[status(thm)],[102])).
% 4.06/2.86 tff(104,plain,
% 4.06/2.86 (((~![B: $i] : (empty(B) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | (~proper_element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | ![C: $i] : ((~in(C, B)) | (~empty(C))))) | (empty(B!37) | (~filtered_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | (~proper_element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | ![C: $i] : ((~in(C, B!37)) | (~empty(C))))) <=> ((~![B: $i] : (empty(B) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | (~proper_element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | ![C: $i] : ((~in(C, B)) | (~empty(C))))) | empty(B!37) | (~filtered_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | (~proper_element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | ![C: $i] : ((~empty(C)) | (~in(C, B!37))))),
% 4.06/2.86 inference(transitivity,[status(thm)],[103, 101])).
% 4.06/2.86 tff(105,plain,
% 4.06/2.86 ((~![B: $i] : (empty(B) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | (~proper_element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | ![C: $i] : ((~in(C, B)) | (~empty(C))))) | (empty(B!37) | (~filtered_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | (~proper_element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | ![C: $i] : ((~in(C, B!37)) | (~empty(C))))),
% 4.06/2.86 inference(quant_inst,[status(thm)],[])).
% 4.06/2.86 tff(106,plain,
% 4.06/2.86 ((~![B: $i] : (empty(B) | (~filtered_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | (~proper_element(B, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | ![C: $i] : ((~in(C, B)) | (~empty(C))))) | empty(B!37) | (~filtered_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~upper_relstr_subset(B!37, boole_POSet(cast_as_carrier_subset(A!36)))) | (~element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | (~proper_element(B!37, powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A!36)))))) | ![C: $i] : ((~empty(C)) | (~in(C, B!37)))),
% 4.06/2.86 inference(modus_ponens,[status(thm)],[105, 104])).
% 4.06/2.86 tff(107,plain,
% 4.06/2.86 (![C: $i] : ((~empty(C)) | (~in(C, B!37)))),
% 4.06/2.86 inference(unit_resolution,[status(thm)],[106, 43, 42, 41, 100, 40, 99])).
% 4.06/2.86 tff(108,plain,
% 4.06/2.86 (empty(empty_set) <=> empty(empty_set)),
% 4.06/2.86 inference(rewrite,[status(thm)],[])).
% 4.06/2.86 tff(109,axiom,((empty(empty_set) & relation(empty_set)) & relation_empty_yielding(empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc12_relat_1')).
% 4.19/2.88 tff(110,plain,
% 4.19/2.88 (empty(empty_set) & relation(empty_set)),
% 4.19/2.88 inference(and_elim,[status(thm)],[109])).
% 4.19/2.88 tff(111,plain,
% 4.19/2.88 (empty(empty_set)),
% 4.19/2.88 inference(and_elim,[status(thm)],[110])).
% 4.19/2.88 tff(112,plain,
% 4.19/2.88 (empty(empty_set)),
% 4.19/2.88 inference(modus_ponens,[status(thm)],[111, 108])).
% 4.19/2.88 tff(113,plain,
% 4.19/2.88 (((~![C: $i] : ((~empty(C)) | (~in(C, B!37)))) | ((~empty(empty_set)) | (~in(empty_set, B!37)))) <=> ((~![C: $i] : ((~empty(C)) | (~in(C, B!37)))) | (~empty(empty_set)) | (~in(empty_set, B!37)))),
% 4.19/2.88 inference(rewrite,[status(thm)],[])).
% 4.19/2.88 tff(114,plain,
% 4.19/2.88 ((~![C: $i] : ((~empty(C)) | (~in(C, B!37)))) | ((~empty(empty_set)) | (~in(empty_set, B!37)))),
% 4.19/2.88 inference(quant_inst,[status(thm)],[])).
% 4.19/2.88 tff(115,plain,
% 4.19/2.88 ((~![C: $i] : ((~empty(C)) | (~in(C, B!37)))) | (~empty(empty_set)) | (~in(empty_set, B!37))),
% 4.19/2.88 inference(modus_ponens,[status(thm)],[114, 113])).
% 4.19/2.88 tff(116,plain,
% 4.19/2.88 (~in(empty_set, B!37)),
% 4.19/2.88 inference(unit_resolution,[status(thm)],[115, 112, 107])).
% 4.19/2.88 tff(117,plain,
% 4.19/2.88 ((~((set_difference(B!37, singleton(empty_set)) = B!37) <=> (~in(empty_set, B!37)))) | (set_difference(B!37, singleton(empty_set)) = B!37) | in(empty_set, B!37)),
% 4.19/2.88 inference(tautology,[status(thm)],[])).
% 4.19/2.88 tff(118,plain,
% 4.19/2.88 (set_difference(B!37, singleton(empty_set)) = B!37),
% 4.19/2.88 inference(unit_resolution,[status(thm)],[117, 116, 59])).
% 4.19/2.88 tff(119,plain,
% 4.19/2.88 (B!37 = set_difference(B!37, singleton(empty_set))),
% 4.19/2.88 inference(symmetry,[status(thm)],[118])).
% 4.19/2.88 tff(120,plain,
% 4.19/2.88 (B!37 = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B!37))),
% 4.19/2.88 inference(transitivity,[status(thm)],[119, 50])).
% 4.19/2.88 tff(121,plain,
% 4.19/2.88 (~(B!37 = filter_of_net_str(A!36, net_of_bool_filter(A!36, cast_as_carrier_subset(A!36), B!37)))),
% 4.19/2.88 inference(or_elim,[status(thm)],[38])).
% 4.19/2.88 tff(122,plain,
% 4.19/2.88 ($false),
% 4.19/2.88 inference(unit_resolution,[status(thm)],[121, 120])).
% 4.19/2.88 % SZS output end Proof
%------------------------------------------------------------------------------