TSTP Solution File: SEU349+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU349+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 07:29:04 EDT 2022
% Result : Theorem 6.20s 4.18s
% Output : Proof 6.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU349+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 12:37:30 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 6.20/4.18 % SZS status Theorem
% 6.20/4.18 % SZS output start Proof
% 6.20/4.18 tff(related_reflexive_type, type, (
% 6.20/4.18 related_reflexive: ( $i * $i * $i ) > $o)).
% 6.20/4.18 tff(cast_to_el_of_LattPOSet_type, type, (
% 6.20/4.18 cast_to_el_of_LattPOSet: ( $i * $i ) > $i)).
% 6.20/4.18 tff(tptp_fun_C_20_type, type, (
% 6.20/4.18 tptp_fun_C_20: $i)).
% 6.20/4.18 tff(tptp_fun_B_18_type, type, (
% 6.20/4.18 tptp_fun_B_18: $i)).
% 6.20/4.18 tff(tptp_fun_D_0_type, type, (
% 6.20/4.18 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 6.20/4.18 tff(tptp_fun_A_19_type, type, (
% 6.20/4.18 tptp_fun_A_19: $i)).
% 6.20/4.18 tff(rel_str_of_type, type, (
% 6.20/4.18 rel_str_of: ( $i * $i ) > $i)).
% 6.20/4.18 tff(k2_lattice3_type, type, (
% 6.20/4.18 k2_lattice3: $i > $i)).
% 6.20/4.18 tff(the_carrier_type, type, (
% 6.20/4.18 the_carrier: $i > $i)).
% 6.20/4.18 tff(poset_of_lattice_type, type, (
% 6.20/4.18 poset_of_lattice: $i > $i)).
% 6.20/4.18 tff(element_type, type, (
% 6.20/4.18 element: ( $i * $i ) > $o)).
% 6.20/4.18 tff(latt_str_type, type, (
% 6.20/4.18 latt_str: $i > $o)).
% 6.20/4.18 tff(relstr_set_smaller_type, type, (
% 6.20/4.18 relstr_set_smaller: ( $i * $i * $i ) > $o)).
% 6.20/4.18 tff(latt_element_smaller_type, type, (
% 6.20/4.18 latt_element_smaller: ( $i * $i * $i ) > $o)).
% 6.20/4.18 tff(lattice_type, type, (
% 6.20/4.18 lattice: $i > $o)).
% 6.20/4.18 tff(empty_carrier_type, type, (
% 6.20/4.18 empty_carrier: $i > $o)).
% 6.20/4.18 tff(in_type, type, (
% 6.20/4.18 in: ( $i * $i ) > $o)).
% 6.20/4.18 tff(below_type, type, (
% 6.20/4.18 below: ( $i * $i * $i ) > $o)).
% 6.20/4.18 tff(tptp_fun_D_1_type, type, (
% 6.20/4.18 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 6.20/4.18 tff(the_InternalRel_type, type, (
% 6.20/4.18 the_InternalRel: $i > $i)).
% 6.20/4.18 tff(relation_of_lattice_type, type, (
% 6.20/4.18 relation_of_lattice: $i > $i)).
% 6.20/4.18 tff(strict_rel_str_type, type, (
% 6.20/4.18 strict_rel_str: $i > $o)).
% 6.20/4.18 tff(rel_str_type, type, (
% 6.20/4.18 rel_str: $i > $o)).
% 6.20/4.18 tff(antisymmetric_relstr_type, type, (
% 6.20/4.18 antisymmetric_relstr: $i > $o)).
% 6.20/4.18 tff(transitive_relstr_type, type, (
% 6.20/4.18 transitive_relstr: $i > $o)).
% 6.20/4.18 tff(reflexive_relstr_type, type, (
% 6.20/4.18 reflexive_relstr: $i > $o)).
% 6.20/4.18 tff(relation_of2_type, type, (
% 6.20/4.18 relation_of2: ( $i * $i * $i ) > $o)).
% 6.20/4.18 tff(relation_of2_as_subset_type, type, (
% 6.20/4.18 relation_of2_as_subset: ( $i * $i * $i ) > $o)).
% 6.20/4.18 tff(v1_partfun1_type, type, (
% 6.20/4.18 v1_partfun1: ( $i * $i * $i ) > $o)).
% 6.20/4.18 tff(transitive_type, type, (
% 6.20/4.18 transitive: $i > $o)).
% 6.20/4.18 tff(antisymmetric_type, type, (
% 6.20/4.18 antisymmetric: $i > $o)).
% 6.20/4.18 tff(reflexive_type, type, (
% 6.20/4.18 reflexive: $i > $o)).
% 6.20/4.18 tff(related_type, type, (
% 6.20/4.18 related: ( $i * $i * $i ) > $o)).
% 6.20/4.18 tff(below_refl_type, type, (
% 6.20/4.18 below_refl: ( $i * $i * $i ) > $o)).
% 6.20/4.18 tff(cast_to_el_of_lattice_type, type, (
% 6.20/4.18 cast_to_el_of_lattice: ( $i * $i ) > $i)).
% 6.20/4.18 tff(join_absorbing_type, type, (
% 6.20/4.18 join_absorbing: $i > $o)).
% 6.20/4.18 tff(meet_absorbing_type, type, (
% 6.20/4.18 meet_absorbing: $i > $o)).
% 6.20/4.18 tff(meet_associative_type, type, (
% 6.20/4.18 meet_associative: $i > $o)).
% 6.20/4.18 tff(meet_commutative_type, type, (
% 6.20/4.18 meet_commutative: $i > $o)).
% 6.20/4.18 tff(join_associative_type, type, (
% 6.20/4.18 join_associative: $i > $o)).
% 6.20/4.18 tff(join_commutative_type, type, (
% 6.20/4.18 join_commutative: $i > $o)).
% 6.20/4.18 tff(1,plain,
% 6.20/4.18 ((((~empty_carrier(B!18)) & lattice(B!18) & latt_str(B!18)) & (~((~element(C!20, the_carrier(B!18))) | (latt_element_smaller(B!18, C!20, A!19) <=> relstr_set_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20)))))) <=> ((~empty_carrier(B!18)) & lattice(B!18) & latt_str(B!18) & (~((~element(C!20, the_carrier(B!18))) | (latt_element_smaller(B!18, C!20, A!19) <=> relstr_set_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20))))))),
% 6.20/4.18 inference(rewrite,[status(thm)],[])).
% 6.20/4.18 tff(2,plain,
% 6.20/4.18 ((~(~((~empty_carrier(B!18)) & lattice(B!18) & latt_str(B!18)))) <=> ((~empty_carrier(B!18)) & lattice(B!18) & latt_str(B!18))),
% 6.20/4.18 inference(rewrite,[status(thm)],[])).
% 6.20/4.18 tff(3,plain,
% 6.20/4.18 (((~(~((~empty_carrier(B!18)) & lattice(B!18) & latt_str(B!18)))) & (~((~element(C!20, the_carrier(B!18))) | (latt_element_smaller(B!18, C!20, A!19) <=> relstr_set_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20)))))) <=> (((~empty_carrier(B!18)) & lattice(B!18) & latt_str(B!18)) & (~((~element(C!20, the_carrier(B!18))) | (latt_element_smaller(B!18, C!20, A!19) <=> relstr_set_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20))))))),
% 6.20/4.18 inference(monotonicity,[status(thm)],[2])).
% 6.20/4.18 tff(4,plain,
% 6.20/4.18 (((~(~((~empty_carrier(B!18)) & lattice(B!18) & latt_str(B!18)))) & (~((~element(C!20, the_carrier(B!18))) | (latt_element_smaller(B!18, C!20, A!19) <=> relstr_set_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20)))))) <=> ((~empty_carrier(B!18)) & lattice(B!18) & latt_str(B!18) & (~((~element(C!20, the_carrier(B!18))) | (latt_element_smaller(B!18, C!20, A!19) <=> relstr_set_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20))))))),
% 6.20/4.18 inference(transitivity,[status(thm)],[3, 1])).
% 6.20/4.18 tff(5,plain,
% 6.20/4.18 ((~![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))))) <=> (~![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C))))))),
% 6.20/4.18 inference(rewrite,[status(thm)],[])).
% 6.20/4.18 tff(6,plain,
% 6.20/4.18 ((~![A: $i, B: $i] : ((((~empty_carrier(B)) & lattice(B)) & latt_str(B)) => ![C: $i] : (element(C, the_carrier(B)) => (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))))) <=> (~![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C))))))),
% 6.20/4.18 inference(rewrite,[status(thm)],[])).
% 6.20/4.18 tff(7,axiom,(~![A: $i, B: $i] : ((((~empty_carrier(B)) & lattice(B)) & latt_str(B)) => ![C: $i] : (element(C, the_carrier(B)) => (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t30_lattice3')).
% 6.20/4.18 tff(8,plain,
% 6.20/4.18 (~![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))))),
% 6.20/4.18 inference(modus_ponens,[status(thm)],[7, 6])).
% 6.20/4.18 tff(9,plain,
% 6.20/4.18 (~![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))))),
% 6.20/4.18 inference(modus_ponens,[status(thm)],[8, 5])).
% 6.20/4.18 tff(10,plain,
% 6.20/4.18 (~![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))))),
% 6.20/4.18 inference(modus_ponens,[status(thm)],[9, 5])).
% 6.20/4.18 tff(11,plain,
% 6.20/4.18 (~![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))))),
% 6.20/4.18 inference(modus_ponens,[status(thm)],[10, 5])).
% 6.20/4.18 tff(12,plain,
% 6.20/4.18 (~![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))))),
% 6.20/4.18 inference(modus_ponens,[status(thm)],[11, 5])).
% 6.20/4.18 tff(13,plain,
% 6.20/4.18 (~![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))))),
% 6.20/4.18 inference(modus_ponens,[status(thm)],[12, 5])).
% 6.20/4.18 tff(14,plain,
% 6.20/4.18 (~![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))))),
% 6.20/4.18 inference(modus_ponens,[status(thm)],[13, 5])).
% 6.20/4.18 tff(15,plain,
% 6.20/4.18 ((~empty_carrier(B!18)) & lattice(B!18) & latt_str(B!18) & (~((~element(C!20, the_carrier(B!18))) | (latt_element_smaller(B!18, C!20, A!19) <=> relstr_set_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20)))))),
% 6.20/4.18 inference(modus_ponens,[status(thm)],[14, 4])).
% 6.20/4.18 tff(16,plain,
% 6.20/4.18 (latt_str(B!18)),
% 6.20/4.18 inference(and_elim,[status(thm)],[15])).
% 6.20/4.18 tff(17,plain,
% 6.20/4.18 (lattice(B!18)),
% 6.20/4.18 inference(and_elim,[status(thm)],[15])).
% 6.20/4.18 tff(18,plain,
% 6.20/4.18 (~empty_carrier(B!18)),
% 6.20/4.18 inference(and_elim,[status(thm)],[15])).
% 6.20/4.18 tff(19,plain,
% 6.20/4.18 (^[A: $i] : rewrite((empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B))))),
% 6.20/4.18 inference(bind,[status(th)],[])).
% 6.20/4.18 tff(20,plain,
% 6.20/4.18 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))),
% 6.20/4.18 inference(quant_intro,[status(thm)],[19])).
% 6.20/4.18 tff(21,plain,
% 6.20/4.18 (^[A: $i] : refl((empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A))))),
% 6.20/4.18 inference(bind,[status(th)],[])).
% 6.20/4.18 tff(22,plain,
% 6.20/4.18 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A)))),
% 6.20/4.18 inference(quant_intro,[status(thm)],[21])).
% 6.20/4.18 tff(23,plain,
% 6.20/4.18 (^[A: $i] : rewrite((empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A))))),
% 6.20/4.18 inference(bind,[status(th)],[])).
% 6.20/4.18 tff(24,plain,
% 6.20/4.18 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A)))),
% 6.20/4.18 inference(quant_intro,[status(thm)],[23])).
% 6.20/4.18 tff(25,plain,
% 6.20/4.18 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A)))),
% 6.20/4.18 inference(transitivity,[status(thm)],[24, 22])).
% 6.20/4.18 tff(26,plain,
% 6.20/4.18 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & lattice(A) & latt_str(A)) <=> (~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))), ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) <=> (~(~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))))), rewrite((~(~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)))), ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))), (((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B))) <=> ((empty_carrier(A) | (~latt_str(A)) | (~lattice(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B))))), rewrite(((empty_carrier(A) | (~latt_str(A)) | (~lattice(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A)))), (((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A)))))),
% 6.20/4.18 inference(bind,[status(th)],[])).
% 6.20/4.18 tff(27,plain,
% 6.20/4.18 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A)))),
% 6.20/4.18 inference(quant_intro,[status(thm)],[26])).
% 6.20/4.18 tff(28,plain,
% 6.20/4.18 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B))) <=> ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))),
% 6.20/4.18 inference(rewrite,[status(thm)],[])).
% 6.20/4.18 tff(29,plain,
% 6.20/4.18 (^[A: $i] : trans(monotonicity(rewrite((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) <=> ((~empty_carrier(A)) & lattice(A) & latt_str(A))), quant_intro(proof_bind(^[B: $i] : rewrite((element(B, the_carrier(A)) => (cast_to_el_of_LattPOSet(A, B) = B)) <=> ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))), (![B: $i] : (element(B, the_carrier(A)) => (cast_to_el_of_LattPOSet(A, B) = B)) <=> ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => (cast_to_el_of_LattPOSet(A, B) = B))) <=> (((~empty_carrier(A)) & lattice(A) & latt_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B))))), rewrite((((~empty_carrier(A)) & lattice(A) & latt_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => (cast_to_el_of_LattPOSet(A, B) = B))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))))),
% 6.20/4.18 inference(bind,[status(th)],[])).
% 6.20/4.18 tff(30,plain,
% 6.20/4.18 (![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => (cast_to_el_of_LattPOSet(A, B) = B))) <=> ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))),
% 6.20/4.18 inference(quant_intro,[status(thm)],[29])).
% 6.20/4.18 tff(31,axiom,(![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => (cast_to_el_of_LattPOSet(A, B) = B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_lattice3')).
% 6.20/4.18 tff(32,plain,
% 6.20/4.18 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))),
% 6.20/4.18 inference(modus_ponens,[status(thm)],[31, 30])).
% 6.20/4.18 tff(33,plain,
% 6.20/4.18 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))),
% 6.20/4.18 inference(modus_ponens,[status(thm)],[32, 28])).
% 6.20/4.18 tff(34,plain,(
% 6.20/4.18 ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))),
% 6.20/4.18 inference(skolemize,[status(sab)],[33])).
% 6.20/4.18 tff(35,plain,
% 6.20/4.18 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A)))),
% 6.20/4.18 inference(modus_ponens,[status(thm)],[34, 27])).
% 6.20/4.18 tff(36,plain,
% 6.20/4.18 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A)))),
% 6.20/4.18 inference(modus_ponens,[status(thm)],[35, 25])).
% 6.20/4.18 tff(37,plain,
% 6.20/4.18 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))),
% 6.20/4.18 inference(modus_ponens,[status(thm)],[36, 20])).
% 6.20/4.18 tff(38,plain,
% 6.20/4.18 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))) | (empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | ![B: $i] : ((~element(B, the_carrier(B!18))) | (cast_to_el_of_LattPOSet(B!18, B) = B)))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | ![B: $i] : ((~element(B, the_carrier(B!18))) | (cast_to_el_of_LattPOSet(B!18, B) = B)))),
% 6.20/4.18 inference(rewrite,[status(thm)],[])).
% 6.20/4.18 tff(39,plain,
% 6.20/4.18 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))) | (empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | ![B: $i] : ((~element(B, the_carrier(B!18))) | (cast_to_el_of_LattPOSet(B!18, B) = B)))),
% 6.20/4.18 inference(quant_inst,[status(thm)],[])).
% 6.20/4.18 tff(40,plain,
% 6.20/4.18 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | ![B: $i] : ((~element(B, the_carrier(B!18))) | (cast_to_el_of_LattPOSet(B!18, B) = B))),
% 6.20/4.18 inference(modus_ponens,[status(thm)],[39, 38])).
% 6.20/4.18 tff(41,plain,
% 6.20/4.18 (![B: $i] : ((~element(B, the_carrier(B!18))) | (cast_to_el_of_LattPOSet(B!18, B) = B))),
% 6.20/4.18 inference(unit_resolution,[status(thm)],[40, 37, 18, 17, 16])).
% 6.20/4.18 tff(42,plain,
% 6.20/4.18 (~((~element(C!20, the_carrier(B!18))) | (latt_element_smaller(B!18, C!20, A!19) <=> relstr_set_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20))))),
% 6.20/4.18 inference(and_elim,[status(thm)],[15])).
% 6.20/4.18 tff(43,plain,
% 6.20/4.18 (element(C!20, the_carrier(B!18))),
% 6.20/4.18 inference(or_elim,[status(thm)],[42])).
% 6.20/4.18 tff(44,plain,
% 6.20/4.18 (((~![B: $i] : ((~element(B, the_carrier(B!18))) | (cast_to_el_of_LattPOSet(B!18, B) = B))) | ((~element(C!20, the_carrier(B!18))) | (cast_to_el_of_LattPOSet(B!18, C!20) = C!20))) <=> ((~![B: $i] : ((~element(B, the_carrier(B!18))) | (cast_to_el_of_LattPOSet(B!18, B) = B))) | (~element(C!20, the_carrier(B!18))) | (cast_to_el_of_LattPOSet(B!18, C!20) = C!20))),
% 6.20/4.18 inference(rewrite,[status(thm)],[])).
% 6.20/4.18 tff(45,plain,
% 6.20/4.18 ((~![B: $i] : ((~element(B, the_carrier(B!18))) | (cast_to_el_of_LattPOSet(B!18, B) = B))) | ((~element(C!20, the_carrier(B!18))) | (cast_to_el_of_LattPOSet(B!18, C!20) = C!20))),
% 6.20/4.18 inference(quant_inst,[status(thm)],[])).
% 6.20/4.18 tff(46,plain,
% 6.20/4.18 ((~![B: $i] : ((~element(B, the_carrier(B!18))) | (cast_to_el_of_LattPOSet(B!18, B) = B))) | (~element(C!20, the_carrier(B!18))) | (cast_to_el_of_LattPOSet(B!18, C!20) = C!20)),
% 6.20/4.18 inference(modus_ponens,[status(thm)],[45, 44])).
% 6.20/4.18 tff(47,plain,
% 6.20/4.18 (cast_to_el_of_LattPOSet(B!18, C!20) = C!20),
% 6.20/4.18 inference(unit_resolution,[status(thm)],[46, 43, 41])).
% 6.20/4.18 tff(48,plain,
% 6.20/4.18 (cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)) = cast_to_el_of_LattPOSet(B!18, C!20)),
% 6.20/4.18 inference(monotonicity,[status(thm)],[47])).
% 6.20/4.18 tff(49,plain,
% 6.20/4.18 (cast_to_el_of_LattPOSet(B!18, C!20) = cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20))),
% 6.20/4.18 inference(symmetry,[status(thm)],[48])).
% 6.20/4.18 tff(50,plain,
% 6.20/4.18 (^[A: $i] : refl(((poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | empty_carrier(A) | (~latt_str(A)) | (~lattice(A))) <=> ((poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))),
% 6.20/4.18 inference(bind,[status(th)],[])).
% 6.20/4.18 tff(51,plain,
% 6.20/4.18 (![A: $i] : ((poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | empty_carrier(A) | (~latt_str(A)) | (~lattice(A))) <=> ![A: $i] : ((poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | empty_carrier(A) | (~latt_str(A)) | (~lattice(A)))),
% 6.20/4.18 inference(quant_intro,[status(thm)],[50])).
% 6.20/4.18 tff(52,plain,
% 6.20/4.18 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & lattice(A) & latt_str(A)) <=> (~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))), ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) <=> (~(~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))))), rewrite((~(~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)))), ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))), (((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A)))) <=> ((empty_carrier(A) | (~latt_str(A)) | (~lattice(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A)))))), rewrite(((empty_carrier(A) | (~latt_str(A)) | (~lattice(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A)))) <=> ((poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | empty_carrier(A) | (~latt_str(A)) | (~lattice(A)))), (((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A)))) <=> ((poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | empty_carrier(A) | (~latt_str(A)) | (~lattice(A)))))),
% 6.20/4.18 inference(bind,[status(th)],[])).
% 6.20/4.18 tff(53,plain,
% 6.20/4.18 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A)))) <=> ![A: $i] : ((poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | empty_carrier(A) | (~latt_str(A)) | (~lattice(A)))),
% 6.20/4.18 inference(quant_intro,[status(thm)],[52])).
% 6.20/4.18 tff(54,plain,
% 6.20/4.18 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A)))) <=> ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))))),
% 6.20/4.18 inference(rewrite,[status(thm)],[])).
% 6.20/4.18 tff(55,plain,
% 6.20/4.18 (^[A: $i] : trans(monotonicity(rewrite((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) <=> ((~empty_carrier(A)) & lattice(A) & latt_str(A))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A)))) <=> (((~empty_carrier(A)) & lattice(A) & latt_str(A)) => (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A)))))), rewrite((((~empty_carrier(A)) & lattice(A) & latt_str(A)) => (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A)))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A)))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))))))),
% 6.20/4.18 inference(bind,[status(th)],[])).
% 6.20/4.18 tff(56,plain,
% 6.20/4.18 (![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A)))) <=> ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))))),
% 6.20/4.18 inference(quant_intro,[status(thm)],[55])).
% 6.20/4.18 tff(57,axiom,(![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_lattice3')).
% 6.20/4.18 tff(58,plain,
% 6.20/4.18 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))))),
% 6.20/4.18 inference(modus_ponens,[status(thm)],[57, 56])).
% 6.20/4.18 tff(59,plain,
% 6.20/4.18 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))))),
% 6.20/4.18 inference(modus_ponens,[status(thm)],[58, 54])).
% 6.20/4.18 tff(60,plain,(
% 6.20/4.18 ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))))),
% 6.20/4.18 inference(skolemize,[status(sab)],[59])).
% 6.20/4.18 tff(61,plain,
% 6.20/4.18 (![A: $i] : ((poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | empty_carrier(A) | (~latt_str(A)) | (~lattice(A)))),
% 6.20/4.18 inference(modus_ponens,[status(thm)],[60, 53])).
% 6.20/4.18 tff(62,plain,
% 6.20/4.18 (![A: $i] : ((poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | empty_carrier(A) | (~latt_str(A)) | (~lattice(A)))),
% 6.20/4.18 inference(modus_ponens,[status(thm)],[61, 51])).
% 6.20/4.18 tff(63,plain,
% 6.20/4.18 (((~![A: $i] : ((poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | empty_carrier(A) | (~latt_str(A)) | (~lattice(A)))) | (empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (poset_of_lattice(B!18) = rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) <=> ((~![A: $i] : ((poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | empty_carrier(A) | (~latt_str(A)) | (~lattice(A)))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (poset_of_lattice(B!18) = rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 6.20/4.18 inference(rewrite,[status(thm)],[])).
% 6.20/4.18 tff(64,plain,
% 6.20/4.18 (((poset_of_lattice(B!18) = rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18))) <=> (empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (poset_of_lattice(B!18) = rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 6.20/4.18 inference(rewrite,[status(thm)],[])).
% 6.20/4.18 tff(65,plain,
% 6.20/4.18 (((~![A: $i] : ((poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | empty_carrier(A) | (~latt_str(A)) | (~lattice(A)))) | ((poset_of_lattice(B!18) = rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)))) <=> ((~![A: $i] : ((poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | empty_carrier(A) | (~latt_str(A)) | (~lattice(A)))) | (empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (poset_of_lattice(B!18) = rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))),
% 6.20/4.18 inference(monotonicity,[status(thm)],[64])).
% 6.20/4.18 tff(66,plain,
% 6.20/4.18 (((~![A: $i] : ((poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | empty_carrier(A) | (~latt_str(A)) | (~lattice(A)))) | ((poset_of_lattice(B!18) = rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)))) <=> ((~![A: $i] : ((poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | empty_carrier(A) | (~latt_str(A)) | (~lattice(A)))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (poset_of_lattice(B!18) = rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 6.20/4.18 inference(transitivity,[status(thm)],[65, 63])).
% 6.20/4.18 tff(67,plain,
% 6.20/4.18 ((~![A: $i] : ((poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | empty_carrier(A) | (~latt_str(A)) | (~lattice(A)))) | ((poset_of_lattice(B!18) = rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)))),
% 6.20/4.18 inference(quant_inst,[status(thm)],[])).
% 6.20/4.18 tff(68,plain,
% 6.20/4.18 ((~![A: $i] : ((poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | empty_carrier(A) | (~latt_str(A)) | (~lattice(A)))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (poset_of_lattice(B!18) = rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))),
% 6.20/4.18 inference(modus_ponens,[status(thm)],[67, 66])).
% 6.20/4.18 tff(69,plain,
% 6.20/4.18 (poset_of_lattice(B!18) = rel_str_of(the_carrier(B!18), k2_lattice3(B!18))),
% 6.20/4.18 inference(unit_resolution,[status(thm)],[68, 62, 18, 17, 16])).
% 6.20/4.18 tff(70,plain,
% 6.20/4.18 (rel_str_of(the_carrier(B!18), k2_lattice3(B!18)) = poset_of_lattice(B!18)),
% 6.20/4.18 inference(symmetry,[status(thm)],[69])).
% 6.20/4.18 tff(71,plain,
% 6.20/4.18 (the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) = the_carrier(poset_of_lattice(B!18))),
% 6.20/4.18 inference(monotonicity,[status(thm)],[70])).
% 6.20/4.18 tff(72,plain,
% 6.20/4.18 (the_carrier(poset_of_lattice(B!18)) = the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))),
% 6.20/4.18 inference(symmetry,[status(thm)],[71])).
% 6.20/4.18 tff(73,plain,
% 6.20/4.18 (rel_str_of(the_carrier(poset_of_lattice(B!18)), the_InternalRel(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) = rel_str_of(the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_InternalRel(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 6.20/4.18 inference(monotonicity,[status(thm)],[72])).
% 6.20/4.18 tff(74,plain,
% 6.20/4.18 (rel_str_of(the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_InternalRel(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) = rel_str_of(the_carrier(poset_of_lattice(B!18)), the_InternalRel(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 6.20/4.18 inference(symmetry,[status(thm)],[73])).
% 6.20/4.18 tff(75,plain,
% 6.20/4.18 (strict_rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) <=> strict_rel_str(poset_of_lattice(B!18))),
% 6.20/4.18 inference(monotonicity,[status(thm)],[70])).
% 6.20/4.18 tff(76,plain,
% 6.20/4.18 (strict_rel_str(poset_of_lattice(B!18)) <=> strict_rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))),
% 6.20/4.18 inference(symmetry,[status(thm)],[75])).
% 6.20/4.18 tff(77,plain,
% 6.20/4.18 (^[A: $i] : refl((empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~((~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A))) | (~rel_str(poset_of_lattice(A)))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~((~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A))) | (~rel_str(poset_of_lattice(A)))))))),
% 6.20/4.18 inference(bind,[status(th)],[])).
% 6.20/4.18 tff(78,plain,
% 6.20/4.18 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~((~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A))) | (~rel_str(poset_of_lattice(A)))))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~((~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A))) | (~rel_str(poset_of_lattice(A))))))),
% 6.20/4.18 inference(quant_intro,[status(thm)],[77])).
% 6.20/4.18 tff(79,plain,
% 6.20/4.18 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & lattice(A) & latt_str(A)) <=> (~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))), ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) <=> (~(~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))))), rewrite((~(~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)))), ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))), rewrite((strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)) & rel_str(poset_of_lattice(A))) <=> (~((~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A))) | (~rel_str(poset_of_lattice(A)))))), (((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)) & rel_str(poset_of_lattice(A)))) <=> ((empty_carrier(A) | (~latt_str(A)) | (~lattice(A))) | (~((~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A))) | (~rel_str(poset_of_lattice(A)))))))), rewrite(((empty_carrier(A) | (~latt_str(A)) | (~lattice(A))) | (~((~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A))) | (~rel_str(poset_of_lattice(A)))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~((~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A))) | (~rel_str(poset_of_lattice(A))))))), (((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)) & rel_str(poset_of_lattice(A)))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~((~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A))) | (~rel_str(poset_of_lattice(A))))))))),
% 6.20/4.19 inference(bind,[status(th)],[])).
% 6.20/4.19 tff(80,plain,
% 6.20/4.19 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)) & rel_str(poset_of_lattice(A)))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~((~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A))) | (~rel_str(poset_of_lattice(A))))))),
% 6.20/4.19 inference(quant_intro,[status(thm)],[79])).
% 6.20/4.19 tff(81,plain,
% 6.20/4.19 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)) & rel_str(poset_of_lattice(A)))) <=> ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)) & rel_str(poset_of_lattice(A))))),
% 6.20/4.19 inference(rewrite,[status(thm)],[])).
% 6.20/4.19 tff(82,plain,
% 6.20/4.19 (^[A: $i] : trans(monotonicity(rewrite((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) <=> ((~empty_carrier(A)) & lattice(A) & latt_str(A))), trans(monotonicity(trans(monotonicity(rewrite(((strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A))) & transitive_relstr(poset_of_lattice(A))) <=> (strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)))), ((((strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A))) & transitive_relstr(poset_of_lattice(A))) & antisymmetric_relstr(poset_of_lattice(A))) <=> ((strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A))) & antisymmetric_relstr(poset_of_lattice(A))))), rewrite(((strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A))) & antisymmetric_relstr(poset_of_lattice(A))) <=> (strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)))), ((((strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A))) & transitive_relstr(poset_of_lattice(A))) & antisymmetric_relstr(poset_of_lattice(A))) <=> (strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A))))), (((((strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A))) & transitive_relstr(poset_of_lattice(A))) & antisymmetric_relstr(poset_of_lattice(A))) & rel_str(poset_of_lattice(A))) <=> ((strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A))) & rel_str(poset_of_lattice(A))))), rewrite(((strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A))) & rel_str(poset_of_lattice(A))) <=> (strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)) & rel_str(poset_of_lattice(A)))), (((((strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A))) & transitive_relstr(poset_of_lattice(A))) & antisymmetric_relstr(poset_of_lattice(A))) & rel_str(poset_of_lattice(A))) <=> (strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)) & rel_str(poset_of_lattice(A))))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ((((strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A))) & transitive_relstr(poset_of_lattice(A))) & antisymmetric_relstr(poset_of_lattice(A))) & rel_str(poset_of_lattice(A)))) <=> (((~empty_carrier(A)) & lattice(A) & latt_str(A)) => (strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)) & rel_str(poset_of_lattice(A)))))), rewrite((((~empty_carrier(A)) & lattice(A) & latt_str(A)) => (strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)) & rel_str(poset_of_lattice(A)))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)) & rel_str(poset_of_lattice(A))))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ((((strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A))) & transitive_relstr(poset_of_lattice(A))) & antisymmetric_relstr(poset_of_lattice(A))) & rel_str(poset_of_lattice(A)))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)) & rel_str(poset_of_lattice(A))))))),
% 6.20/4.19 inference(bind,[status(th)],[])).
% 6.20/4.19 tff(83,plain,
% 6.20/4.19 (![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ((((strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A))) & transitive_relstr(poset_of_lattice(A))) & antisymmetric_relstr(poset_of_lattice(A))) & rel_str(poset_of_lattice(A)))) <=> ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)) & rel_str(poset_of_lattice(A))))),
% 6.20/4.19 inference(quant_intro,[status(thm)],[82])).
% 6.20/4.19 tff(84,axiom,(![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ((((strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A))) & transitive_relstr(poset_of_lattice(A))) & antisymmetric_relstr(poset_of_lattice(A))) & rel_str(poset_of_lattice(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k3_lattice3')).
% 6.20/4.19 tff(85,plain,
% 6.20/4.19 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)) & rel_str(poset_of_lattice(A))))),
% 6.20/4.19 inference(modus_ponens,[status(thm)],[84, 83])).
% 6.20/4.19 tff(86,plain,
% 6.20/4.19 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)) & rel_str(poset_of_lattice(A))))),
% 6.20/4.19 inference(modus_ponens,[status(thm)],[85, 81])).
% 6.20/4.19 tff(87,plain,(
% 6.20/4.19 ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)) & rel_str(poset_of_lattice(A))))),
% 6.20/4.19 inference(skolemize,[status(sab)],[86])).
% 6.20/4.19 tff(88,plain,
% 6.20/4.19 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~((~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A))) | (~rel_str(poset_of_lattice(A))))))),
% 6.20/4.19 inference(modus_ponens,[status(thm)],[87, 80])).
% 6.20/4.19 tff(89,plain,
% 6.20/4.19 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~((~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A))) | (~rel_str(poset_of_lattice(A))))))),
% 6.20/4.19 inference(modus_ponens,[status(thm)],[88, 78])).
% 6.20/4.19 tff(90,plain,
% 6.20/4.19 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~((~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A))) | (~rel_str(poset_of_lattice(A))))))) | (empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (~((~strict_rel_str(poset_of_lattice(B!18))) | (~reflexive_relstr(poset_of_lattice(B!18))) | (~transitive_relstr(poset_of_lattice(B!18))) | (~antisymmetric_relstr(poset_of_lattice(B!18))) | (~rel_str(poset_of_lattice(B!18))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~((~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A))) | (~rel_str(poset_of_lattice(A))))))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (~((~strict_rel_str(poset_of_lattice(B!18))) | (~reflexive_relstr(poset_of_lattice(B!18))) | (~transitive_relstr(poset_of_lattice(B!18))) | (~antisymmetric_relstr(poset_of_lattice(B!18))) | (~rel_str(poset_of_lattice(B!18))))))),
% 6.20/4.19 inference(rewrite,[status(thm)],[])).
% 6.20/4.19 tff(91,plain,
% 6.20/4.19 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~((~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A))) | (~rel_str(poset_of_lattice(A))))))) | (empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (~((~strict_rel_str(poset_of_lattice(B!18))) | (~reflexive_relstr(poset_of_lattice(B!18))) | (~transitive_relstr(poset_of_lattice(B!18))) | (~antisymmetric_relstr(poset_of_lattice(B!18))) | (~rel_str(poset_of_lattice(B!18))))))),
% 6.20/4.19 inference(quant_inst,[status(thm)],[])).
% 6.20/4.19 tff(92,plain,
% 6.20/4.19 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~((~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A))) | (~rel_str(poset_of_lattice(A))))))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (~((~strict_rel_str(poset_of_lattice(B!18))) | (~reflexive_relstr(poset_of_lattice(B!18))) | (~transitive_relstr(poset_of_lattice(B!18))) | (~antisymmetric_relstr(poset_of_lattice(B!18))) | (~rel_str(poset_of_lattice(B!18)))))),
% 6.20/4.19 inference(modus_ponens,[status(thm)],[91, 90])).
% 6.20/4.19 tff(93,plain,
% 6.20/4.19 (~((~strict_rel_str(poset_of_lattice(B!18))) | (~reflexive_relstr(poset_of_lattice(B!18))) | (~transitive_relstr(poset_of_lattice(B!18))) | (~antisymmetric_relstr(poset_of_lattice(B!18))) | (~rel_str(poset_of_lattice(B!18))))),
% 6.20/4.19 inference(unit_resolution,[status(thm)],[92, 89, 18, 17, 16])).
% 6.20/4.19 tff(94,plain,
% 6.20/4.19 (((~strict_rel_str(poset_of_lattice(B!18))) | (~reflexive_relstr(poset_of_lattice(B!18))) | (~transitive_relstr(poset_of_lattice(B!18))) | (~antisymmetric_relstr(poset_of_lattice(B!18))) | (~rel_str(poset_of_lattice(B!18)))) | strict_rel_str(poset_of_lattice(B!18))),
% 6.20/4.19 inference(tautology,[status(thm)],[])).
% 6.20/4.19 tff(95,plain,
% 6.20/4.19 (strict_rel_str(poset_of_lattice(B!18))),
% 6.20/4.19 inference(unit_resolution,[status(thm)],[94, 93])).
% 6.20/4.19 tff(96,plain,
% 6.20/4.19 (strict_rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))),
% 6.20/4.19 inference(modus_ponens,[status(thm)],[95, 76])).
% 6.20/4.19 tff(97,plain,
% 6.20/4.19 (rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) <=> rel_str(poset_of_lattice(B!18))),
% 6.20/4.19 inference(monotonicity,[status(thm)],[70])).
% 6.20/4.19 tff(98,plain,
% 6.20/4.19 (rel_str(poset_of_lattice(B!18)) <=> rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))),
% 6.20/4.19 inference(symmetry,[status(thm)],[97])).
% 6.20/4.19 tff(99,plain,
% 6.20/4.19 (((~strict_rel_str(poset_of_lattice(B!18))) | (~reflexive_relstr(poset_of_lattice(B!18))) | (~transitive_relstr(poset_of_lattice(B!18))) | (~antisymmetric_relstr(poset_of_lattice(B!18))) | (~rel_str(poset_of_lattice(B!18)))) | rel_str(poset_of_lattice(B!18))),
% 6.20/4.19 inference(tautology,[status(thm)],[])).
% 6.20/4.19 tff(100,plain,
% 6.20/4.19 (rel_str(poset_of_lattice(B!18))),
% 6.20/4.19 inference(unit_resolution,[status(thm)],[99, 93])).
% 6.20/4.19 tff(101,plain,
% 6.20/4.19 (rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))),
% 6.20/4.19 inference(modus_ponens,[status(thm)],[100, 98])).
% 6.20/4.19 tff(102,plain,
% 6.20/4.19 (^[A: $i] : refl(((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A))) <=> ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A))))),
% 6.20/4.19 inference(bind,[status(th)],[])).
% 6.20/4.19 tff(103,plain,
% 6.20/4.19 (![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A))) <=> ![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 6.20/4.19 inference(quant_intro,[status(thm)],[102])).
% 6.20/4.19 tff(104,plain,
% 6.20/4.19 (![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A))) <=> ![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 6.20/4.19 inference(rewrite,[status(thm)],[])).
% 6.20/4.19 tff(105,plain,
% 6.20/4.19 (^[A: $i] : trans(monotonicity(rewrite((strict_rel_str(A) => (A = rel_str_of(the_carrier(A), the_InternalRel(A)))) <=> ((~strict_rel_str(A)) | (A = rel_str_of(the_carrier(A), the_InternalRel(A))))), ((rel_str(A) => (strict_rel_str(A) => (A = rel_str_of(the_carrier(A), the_InternalRel(A))))) <=> (rel_str(A) => ((~strict_rel_str(A)) | (A = rel_str_of(the_carrier(A), the_InternalRel(A))))))), rewrite((rel_str(A) => ((~strict_rel_str(A)) | (A = rel_str_of(the_carrier(A), the_InternalRel(A))))) <=> ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))), ((rel_str(A) => (strict_rel_str(A) => (A = rel_str_of(the_carrier(A), the_InternalRel(A))))) <=> ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))))),
% 6.20/4.19 inference(bind,[status(th)],[])).
% 6.20/4.19 tff(106,plain,
% 6.20/4.19 (![A: $i] : (rel_str(A) => (strict_rel_str(A) => (A = rel_str_of(the_carrier(A), the_InternalRel(A))))) <=> ![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 6.20/4.19 inference(quant_intro,[status(thm)],[105])).
% 6.20/4.19 tff(107,axiom,(![A: $i] : (rel_str(A) => (strict_rel_str(A) => (A = rel_str_of(the_carrier(A), the_InternalRel(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','abstractness_v1_orders_2')).
% 6.20/4.19 tff(108,plain,
% 6.20/4.19 (![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 6.20/4.19 inference(modus_ponens,[status(thm)],[107, 106])).
% 6.20/4.19 tff(109,plain,
% 6.20/4.19 (![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 6.20/4.19 inference(modus_ponens,[status(thm)],[108, 104])).
% 6.20/4.19 tff(110,plain,(
% 6.20/4.19 ![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 6.20/4.19 inference(skolemize,[status(sab)],[109])).
% 6.20/4.19 tff(111,plain,
% 6.20/4.19 (![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 6.20/4.19 inference(modus_ponens,[status(thm)],[110, 103])).
% 6.20/4.19 tff(112,plain,
% 6.20/4.19 (((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | ((~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (rel_str_of(the_carrier(B!18), k2_lattice3(B!18)) = rel_str_of(the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_InternalRel(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~strict_rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))) <=> ((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | (~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (rel_str_of(the_carrier(B!18), k2_lattice3(B!18)) = rel_str_of(the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_InternalRel(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~strict_rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))),
% 6.20/4.19 inference(rewrite,[status(thm)],[])).
% 6.20/4.19 tff(113,plain,
% 6.20/4.19 (((rel_str_of(the_carrier(B!18), k2_lattice3(B!18)) = rel_str_of(the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_InternalRel(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~strict_rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) <=> ((~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (rel_str_of(the_carrier(B!18), k2_lattice3(B!18)) = rel_str_of(the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_InternalRel(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~strict_rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))),
% 6.20/4.19 inference(rewrite,[status(thm)],[])).
% 6.20/4.19 tff(114,plain,
% 6.20/4.19 (((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | ((rel_str_of(the_carrier(B!18), k2_lattice3(B!18)) = rel_str_of(the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_InternalRel(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~strict_rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))) <=> ((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | ((~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (rel_str_of(the_carrier(B!18), k2_lattice3(B!18)) = rel_str_of(the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_InternalRel(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~strict_rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))))),
% 6.20/4.19 inference(monotonicity,[status(thm)],[113])).
% 6.20/4.19 tff(115,plain,
% 6.20/4.19 (((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | ((rel_str_of(the_carrier(B!18), k2_lattice3(B!18)) = rel_str_of(the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_InternalRel(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~strict_rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))) <=> ((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | (~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (rel_str_of(the_carrier(B!18), k2_lattice3(B!18)) = rel_str_of(the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_InternalRel(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~strict_rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))),
% 6.20/4.19 inference(transitivity,[status(thm)],[114, 112])).
% 6.20/4.19 tff(116,plain,
% 6.20/4.19 ((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | ((rel_str_of(the_carrier(B!18), k2_lattice3(B!18)) = rel_str_of(the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_InternalRel(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~strict_rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))),
% 6.20/4.19 inference(quant_inst,[status(thm)],[])).
% 6.20/4.19 tff(117,plain,
% 6.20/4.19 ((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | (~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (rel_str_of(the_carrier(B!18), k2_lattice3(B!18)) = rel_str_of(the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_InternalRel(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~strict_rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 6.20/4.19 inference(modus_ponens,[status(thm)],[116, 115])).
% 6.20/4.19 tff(118,plain,
% 6.20/4.19 ((~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (rel_str_of(the_carrier(B!18), k2_lattice3(B!18)) = rel_str_of(the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_InternalRel(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~strict_rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 6.20/4.19 inference(unit_resolution,[status(thm)],[117, 111])).
% 6.20/4.19 tff(119,plain,
% 6.20/4.19 (rel_str_of(the_carrier(B!18), k2_lattice3(B!18)) = rel_str_of(the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_InternalRel(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 6.20/4.19 inference(unit_resolution,[status(thm)],[118, 101, 96])).
% 6.20/4.19 tff(120,plain,
% 6.20/4.19 (^[A: $i] : refl((empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A))) <=> (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A))))),
% 6.20/4.19 inference(bind,[status(th)],[])).
% 6.20/4.19 tff(121,plain,
% 6.20/4.19 (![A: $i] : (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))),
% 6.20/4.19 inference(quant_intro,[status(thm)],[120])).
% 6.20/4.19 tff(122,plain,
% 6.20/4.19 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & lattice(A) & latt_str(A)) <=> (~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))), ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) <=> (~(~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))))), rewrite((~(~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)))), ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))), (((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (k2_lattice3(A) = relation_of_lattice(A))) <=> ((empty_carrier(A) | (~latt_str(A)) | (~lattice(A))) | (k2_lattice3(A) = relation_of_lattice(A))))), rewrite(((empty_carrier(A) | (~latt_str(A)) | (~lattice(A))) | (k2_lattice3(A) = relation_of_lattice(A))) <=> (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))), (((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (k2_lattice3(A) = relation_of_lattice(A))) <=> (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))))),
% 6.20/4.19 inference(bind,[status(th)],[])).
% 6.20/4.19 tff(123,plain,
% 6.20/4.19 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (k2_lattice3(A) = relation_of_lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))),
% 6.20/4.19 inference(quant_intro,[status(thm)],[122])).
% 6.20/4.19 tff(124,plain,
% 6.20/4.19 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (k2_lattice3(A) = relation_of_lattice(A))) <=> ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (k2_lattice3(A) = relation_of_lattice(A)))),
% 6.20/4.19 inference(rewrite,[status(thm)],[])).
% 6.20/4.19 tff(125,plain,
% 6.20/4.19 (^[A: $i] : trans(monotonicity(rewrite((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) <=> ((~empty_carrier(A)) & lattice(A) & latt_str(A))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => (k2_lattice3(A) = relation_of_lattice(A))) <=> (((~empty_carrier(A)) & lattice(A) & latt_str(A)) => (k2_lattice3(A) = relation_of_lattice(A))))), rewrite((((~empty_carrier(A)) & lattice(A) & latt_str(A)) => (k2_lattice3(A) = relation_of_lattice(A))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (k2_lattice3(A) = relation_of_lattice(A)))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => (k2_lattice3(A) = relation_of_lattice(A))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (k2_lattice3(A) = relation_of_lattice(A)))))),
% 6.20/4.19 inference(bind,[status(th)],[])).
% 6.20/4.19 tff(126,plain,
% 6.20/4.19 (![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => (k2_lattice3(A) = relation_of_lattice(A))) <=> ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (k2_lattice3(A) = relation_of_lattice(A)))),
% 6.20/4.19 inference(quant_intro,[status(thm)],[125])).
% 6.20/4.19 tff(127,axiom,(![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => (k2_lattice3(A) = relation_of_lattice(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k2_lattice3')).
% 6.20/4.19 tff(128,plain,
% 6.20/4.19 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (k2_lattice3(A) = relation_of_lattice(A)))),
% 6.20/4.19 inference(modus_ponens,[status(thm)],[127, 126])).
% 6.20/4.19 tff(129,plain,
% 6.20/4.19 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (k2_lattice3(A) = relation_of_lattice(A)))),
% 6.20/4.19 inference(modus_ponens,[status(thm)],[128, 124])).
% 6.20/4.19 tff(130,plain,(
% 6.20/4.19 ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (k2_lattice3(A) = relation_of_lattice(A)))),
% 6.20/4.19 inference(skolemize,[status(sab)],[129])).
% 6.20/4.19 tff(131,plain,
% 6.20/4.19 (![A: $i] : (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))),
% 6.20/4.19 inference(modus_ponens,[status(thm)],[130, 123])).
% 6.20/4.19 tff(132,plain,
% 6.20/4.19 (![A: $i] : (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))),
% 6.20/4.19 inference(modus_ponens,[status(thm)],[131, 121])).
% 6.20/4.19 tff(133,plain,
% 6.20/4.19 (((~![A: $i] : (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))) | (empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (k2_lattice3(B!18) = relation_of_lattice(B!18)))) <=> ((~![A: $i] : (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (k2_lattice3(B!18) = relation_of_lattice(B!18)))),
% 6.20/4.19 inference(rewrite,[status(thm)],[])).
% 6.20/4.19 tff(134,plain,
% 6.20/4.19 ((empty_carrier(B!18) | (k2_lattice3(B!18) = relation_of_lattice(B!18)) | (~latt_str(B!18)) | (~lattice(B!18))) <=> (empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (k2_lattice3(B!18) = relation_of_lattice(B!18)))),
% 6.20/4.19 inference(rewrite,[status(thm)],[])).
% 6.20/4.19 tff(135,plain,
% 6.20/4.19 (((~![A: $i] : (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))) | (empty_carrier(B!18) | (k2_lattice3(B!18) = relation_of_lattice(B!18)) | (~latt_str(B!18)) | (~lattice(B!18)))) <=> ((~![A: $i] : (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))) | (empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (k2_lattice3(B!18) = relation_of_lattice(B!18))))),
% 6.20/4.19 inference(monotonicity,[status(thm)],[134])).
% 6.20/4.19 tff(136,plain,
% 6.20/4.19 (((~![A: $i] : (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))) | (empty_carrier(B!18) | (k2_lattice3(B!18) = relation_of_lattice(B!18)) | (~latt_str(B!18)) | (~lattice(B!18)))) <=> ((~![A: $i] : (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (k2_lattice3(B!18) = relation_of_lattice(B!18)))),
% 6.20/4.19 inference(transitivity,[status(thm)],[135, 133])).
% 6.20/4.19 tff(137,plain,
% 6.20/4.19 ((~![A: $i] : (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))) | (empty_carrier(B!18) | (k2_lattice3(B!18) = relation_of_lattice(B!18)) | (~latt_str(B!18)) | (~lattice(B!18)))),
% 6.20/4.19 inference(quant_inst,[status(thm)],[])).
% 6.20/4.19 tff(138,plain,
% 6.20/4.19 ((~![A: $i] : (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (k2_lattice3(B!18) = relation_of_lattice(B!18))),
% 6.20/4.19 inference(modus_ponens,[status(thm)],[137, 136])).
% 6.20/4.19 tff(139,plain,
% 6.20/4.19 (k2_lattice3(B!18) = relation_of_lattice(B!18)),
% 6.20/4.19 inference(unit_resolution,[status(thm)],[138, 132, 18, 17, 16])).
% 6.20/4.19 tff(140,plain,
% 6.20/4.19 (relation_of_lattice(B!18) = k2_lattice3(B!18)),
% 6.20/4.19 inference(symmetry,[status(thm)],[139])).
% 6.20/4.19 tff(141,plain,
% 6.20/4.19 (rel_str_of(the_carrier(B!18), relation_of_lattice(B!18)) = rel_str_of(the_carrier(B!18), k2_lattice3(B!18))),
% 6.20/4.19 inference(monotonicity,[status(thm)],[140])).
% 6.20/4.19 tff(142,plain,
% 6.20/4.19 (rel_str_of(the_carrier(B!18), relation_of_lattice(B!18)) = rel_str_of(the_carrier(poset_of_lattice(B!18)), the_InternalRel(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 6.20/4.19 inference(transitivity,[status(thm)],[141, 119, 74])).
% 6.20/4.19 tff(143,plain,
% 6.20/4.19 (^[A: $i, B: $i, C: $i] : refl((relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)) <=> (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)))),
% 6.20/4.19 inference(bind,[status(th)],[])).
% 6.20/4.19 tff(144,plain,
% 6.20/4.19 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 6.20/4.19 inference(quant_intro,[status(thm)],[143])).
% 6.20/4.19 tff(145,plain,
% 6.20/4.19 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 6.20/4.19 inference(rewrite,[status(thm)],[])).
% 6.20/4.19 tff(146,axiom,(![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 6.20/4.19 tff(147,plain,
% 6.20/4.19 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 6.20/4.19 inference(modus_ponens,[status(thm)],[146, 145])).
% 6.20/4.19 tff(148,plain,(
% 6.20/4.19 ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 6.20/4.19 inference(skolemize,[status(sab)],[147])).
% 6.20/4.19 tff(149,plain,
% 6.20/4.19 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 6.20/4.19 inference(modus_ponens,[status(thm)],[148, 144])).
% 6.20/4.19 tff(150,plain,
% 6.20/4.19 ((~![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))) | (relation_of2_as_subset(relation_of_lattice(B!18), the_carrier(B!18), the_carrier(B!18)) <=> relation_of2(relation_of_lattice(B!18), the_carrier(B!18), the_carrier(B!18)))),
% 6.20/4.19 inference(quant_inst,[status(thm)],[])).
% 6.20/4.19 tff(151,plain,
% 6.20/4.19 (relation_of2_as_subset(relation_of_lattice(B!18), the_carrier(B!18), the_carrier(B!18)) <=> relation_of2(relation_of_lattice(B!18), the_carrier(B!18), the_carrier(B!18))),
% 6.20/4.19 inference(unit_resolution,[status(thm)],[150, 149])).
% 6.20/4.19 tff(152,plain,
% 6.20/4.19 (relation_of2_as_subset(relation_of_lattice(B!18), the_carrier(B!18), the_carrier(B!18)) <=> relation_of2_as_subset(k2_lattice3(B!18), the_carrier(B!18), the_carrier(B!18))),
% 6.20/4.19 inference(monotonicity,[status(thm)],[140])).
% 6.20/4.19 tff(153,plain,
% 6.20/4.19 (relation_of2_as_subset(k2_lattice3(B!18), the_carrier(B!18), the_carrier(B!18)) <=> relation_of2_as_subset(relation_of_lattice(B!18), the_carrier(B!18), the_carrier(B!18))),
% 6.20/4.19 inference(symmetry,[status(thm)],[152])).
% 6.20/4.19 tff(154,plain,
% 6.20/4.19 (^[A: $i] : refl((empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~((~reflexive(k2_lattice3(A))) | (~antisymmetric(k2_lattice3(A))) | (~transitive(k2_lattice3(A))) | (~v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A))) | (~relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A)))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~((~reflexive(k2_lattice3(A))) | (~antisymmetric(k2_lattice3(A))) | (~transitive(k2_lattice3(A))) | (~v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A))) | (~relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A)))))))),
% 6.20/4.19 inference(bind,[status(th)],[])).
% 6.20/4.19 tff(155,plain,
% 6.20/4.19 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~((~reflexive(k2_lattice3(A))) | (~antisymmetric(k2_lattice3(A))) | (~transitive(k2_lattice3(A))) | (~v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A))) | (~relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A)))))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~((~reflexive(k2_lattice3(A))) | (~antisymmetric(k2_lattice3(A))) | (~transitive(k2_lattice3(A))) | (~v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A))) | (~relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A))))))),
% 6.20/4.19 inference(quant_intro,[status(thm)],[154])).
% 6.20/4.19 tff(156,plain,
% 6.20/4.19 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & lattice(A) & latt_str(A)) <=> (~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))), ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) <=> (~(~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))))), rewrite((~(~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)))), ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))), rewrite((reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A)) & transitive(k2_lattice3(A)) & v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A)) & relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A))) <=> (~((~reflexive(k2_lattice3(A))) | (~antisymmetric(k2_lattice3(A))) | (~transitive(k2_lattice3(A))) | (~v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A))) | (~relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A)))))), (((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A)) & transitive(k2_lattice3(A)) & v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A)) & relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A)))) <=> ((empty_carrier(A) | (~latt_str(A)) | (~lattice(A))) | (~((~reflexive(k2_lattice3(A))) | (~antisymmetric(k2_lattice3(A))) | (~transitive(k2_lattice3(A))) | (~v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A))) | (~relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A)))))))), rewrite(((empty_carrier(A) | (~latt_str(A)) | (~lattice(A))) | (~((~reflexive(k2_lattice3(A))) | (~antisymmetric(k2_lattice3(A))) | (~transitive(k2_lattice3(A))) | (~v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A))) | (~relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A)))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~((~reflexive(k2_lattice3(A))) | (~antisymmetric(k2_lattice3(A))) | (~transitive(k2_lattice3(A))) | (~v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A))) | (~relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A))))))), (((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A)) & transitive(k2_lattice3(A)) & v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A)) & relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A)))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~((~reflexive(k2_lattice3(A))) | (~antisymmetric(k2_lattice3(A))) | (~transitive(k2_lattice3(A))) | (~v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A))) | (~relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A))))))))),
% 6.20/4.19 inference(bind,[status(th)],[])).
% 6.20/4.19 tff(157,plain,
% 6.20/4.19 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A)) & transitive(k2_lattice3(A)) & v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A)) & relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A)))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~((~reflexive(k2_lattice3(A))) | (~antisymmetric(k2_lattice3(A))) | (~transitive(k2_lattice3(A))) | (~v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A))) | (~relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A))))))),
% 6.20/4.19 inference(quant_intro,[status(thm)],[156])).
% 6.20/4.19 tff(158,plain,
% 6.20/4.19 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A)) & transitive(k2_lattice3(A)) & v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A)) & relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A)))) <=> ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A)) & transitive(k2_lattice3(A)) & v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A)) & relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A))))),
% 6.20/4.19 inference(rewrite,[status(thm)],[])).
% 6.20/4.19 tff(159,plain,
% 6.20/4.19 (^[A: $i] : trans(monotonicity(rewrite((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) <=> ((~empty_carrier(A)) & lattice(A) & latt_str(A))), trans(monotonicity(trans(monotonicity(rewrite(((reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A))) & transitive(k2_lattice3(A))) <=> (reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A)) & transitive(k2_lattice3(A)))), ((((reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A))) & transitive(k2_lattice3(A))) & v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A))) <=> ((reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A)) & transitive(k2_lattice3(A))) & v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A))))), rewrite(((reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A)) & transitive(k2_lattice3(A))) & v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A))) <=> (reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A)) & transitive(k2_lattice3(A)) & v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A)))), ((((reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A))) & transitive(k2_lattice3(A))) & v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A))) <=> (reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A)) & transitive(k2_lattice3(A)) & v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A))))), (((((reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A))) & transitive(k2_lattice3(A))) & v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A))) & relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A))) <=> ((reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A)) & transitive(k2_lattice3(A)) & v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A))) & relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A))))), rewrite(((reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A)) & transitive(k2_lattice3(A)) & v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A))) & relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A))) <=> (reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A)) & transitive(k2_lattice3(A)) & v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A)) & relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A)))), (((((reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A))) & transitive(k2_lattice3(A))) & v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A))) & relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A))) <=> (reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A)) & transitive(k2_lattice3(A)) & v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A)) & relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A))))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ((((reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A))) & transitive(k2_lattice3(A))) & v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A))) & relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A)))) <=> (((~empty_carrier(A)) & lattice(A) & latt_str(A)) => (reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A)) & transitive(k2_lattice3(A)) & v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A)) & relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A)))))), rewrite((((~empty_carrier(A)) & lattice(A) & latt_str(A)) => (reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A)) & transitive(k2_lattice3(A)) & v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A)) & relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A)))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A)) & transitive(k2_lattice3(A)) & v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A)) & relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A))))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ((((reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A))) & transitive(k2_lattice3(A))) & v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A))) & relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A)))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A)) & transitive(k2_lattice3(A)) & v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A)) & relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A))))))),
% 6.20/4.19 inference(bind,[status(th)],[])).
% 6.20/4.19 tff(160,plain,
% 6.20/4.19 (![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ((((reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A))) & transitive(k2_lattice3(A))) & v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A))) & relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A)))) <=> ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A)) & transitive(k2_lattice3(A)) & v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A)) & relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A))))),
% 6.20/4.19 inference(quant_intro,[status(thm)],[159])).
% 6.20/4.19 tff(161,axiom,(![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ((((reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A))) & transitive(k2_lattice3(A))) & v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A))) & relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k2_lattice3')).
% 6.20/4.19 tff(162,plain,
% 6.20/4.19 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A)) & transitive(k2_lattice3(A)) & v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A)) & relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A))))),
% 6.20/4.19 inference(modus_ponens,[status(thm)],[161, 160])).
% 6.20/4.19 tff(163,plain,
% 6.20/4.19 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A)) & transitive(k2_lattice3(A)) & v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A)) & relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A))))),
% 6.20/4.19 inference(modus_ponens,[status(thm)],[162, 158])).
% 6.20/4.19 tff(164,plain,(
% 6.20/4.19 ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A)) & transitive(k2_lattice3(A)) & v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A)) & relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A))))),
% 6.20/4.19 inference(skolemize,[status(sab)],[163])).
% 6.20/4.19 tff(165,plain,
% 6.20/4.19 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~((~reflexive(k2_lattice3(A))) | (~antisymmetric(k2_lattice3(A))) | (~transitive(k2_lattice3(A))) | (~v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A))) | (~relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A))))))),
% 6.20/4.19 inference(modus_ponens,[status(thm)],[164, 157])).
% 6.20/4.19 tff(166,plain,
% 6.20/4.19 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~((~reflexive(k2_lattice3(A))) | (~antisymmetric(k2_lattice3(A))) | (~transitive(k2_lattice3(A))) | (~v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A))) | (~relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A))))))),
% 6.20/4.19 inference(modus_ponens,[status(thm)],[165, 155])).
% 6.20/4.19 tff(167,plain,
% 6.20/4.19 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~((~reflexive(k2_lattice3(A))) | (~antisymmetric(k2_lattice3(A))) | (~transitive(k2_lattice3(A))) | (~v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A))) | (~relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A))))))) | (empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (~((~reflexive(k2_lattice3(B!18))) | (~antisymmetric(k2_lattice3(B!18))) | (~transitive(k2_lattice3(B!18))) | (~v1_partfun1(k2_lattice3(B!18), the_carrier(B!18), the_carrier(B!18))) | (~relation_of2_as_subset(k2_lattice3(B!18), the_carrier(B!18), the_carrier(B!18))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~((~reflexive(k2_lattice3(A))) | (~antisymmetric(k2_lattice3(A))) | (~transitive(k2_lattice3(A))) | (~v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A))) | (~relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A))))))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (~((~reflexive(k2_lattice3(B!18))) | (~antisymmetric(k2_lattice3(B!18))) | (~transitive(k2_lattice3(B!18))) | (~v1_partfun1(k2_lattice3(B!18), the_carrier(B!18), the_carrier(B!18))) | (~relation_of2_as_subset(k2_lattice3(B!18), the_carrier(B!18), the_carrier(B!18))))))),
% 6.20/4.19 inference(rewrite,[status(thm)],[])).
% 6.20/4.19 tff(168,plain,
% 6.20/4.19 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~((~reflexive(k2_lattice3(A))) | (~antisymmetric(k2_lattice3(A))) | (~transitive(k2_lattice3(A))) | (~v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A))) | (~relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A))))))) | (empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (~((~reflexive(k2_lattice3(B!18))) | (~antisymmetric(k2_lattice3(B!18))) | (~transitive(k2_lattice3(B!18))) | (~v1_partfun1(k2_lattice3(B!18), the_carrier(B!18), the_carrier(B!18))) | (~relation_of2_as_subset(k2_lattice3(B!18), the_carrier(B!18), the_carrier(B!18))))))),
% 6.20/4.19 inference(quant_inst,[status(thm)],[])).
% 6.20/4.19 tff(169,plain,
% 6.20/4.19 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~((~reflexive(k2_lattice3(A))) | (~antisymmetric(k2_lattice3(A))) | (~transitive(k2_lattice3(A))) | (~v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A))) | (~relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A))))))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (~((~reflexive(k2_lattice3(B!18))) | (~antisymmetric(k2_lattice3(B!18))) | (~transitive(k2_lattice3(B!18))) | (~v1_partfun1(k2_lattice3(B!18), the_carrier(B!18), the_carrier(B!18))) | (~relation_of2_as_subset(k2_lattice3(B!18), the_carrier(B!18), the_carrier(B!18)))))),
% 6.20/4.19 inference(modus_ponens,[status(thm)],[168, 167])).
% 6.20/4.19 tff(170,plain,
% 6.20/4.19 (~((~reflexive(k2_lattice3(B!18))) | (~antisymmetric(k2_lattice3(B!18))) | (~transitive(k2_lattice3(B!18))) | (~v1_partfun1(k2_lattice3(B!18), the_carrier(B!18), the_carrier(B!18))) | (~relation_of2_as_subset(k2_lattice3(B!18), the_carrier(B!18), the_carrier(B!18))))),
% 6.20/4.19 inference(unit_resolution,[status(thm)],[169, 166, 18, 17, 16])).
% 6.20/4.19 tff(171,plain,
% 6.20/4.19 (((~reflexive(k2_lattice3(B!18))) | (~antisymmetric(k2_lattice3(B!18))) | (~transitive(k2_lattice3(B!18))) | (~v1_partfun1(k2_lattice3(B!18), the_carrier(B!18), the_carrier(B!18))) | (~relation_of2_as_subset(k2_lattice3(B!18), the_carrier(B!18), the_carrier(B!18)))) | relation_of2_as_subset(k2_lattice3(B!18), the_carrier(B!18), the_carrier(B!18))),
% 6.20/4.19 inference(tautology,[status(thm)],[])).
% 6.20/4.19 tff(172,plain,
% 6.20/4.19 (relation_of2_as_subset(k2_lattice3(B!18), the_carrier(B!18), the_carrier(B!18))),
% 6.20/4.19 inference(unit_resolution,[status(thm)],[171, 170])).
% 6.20/4.19 tff(173,plain,
% 6.20/4.19 (relation_of2_as_subset(relation_of_lattice(B!18), the_carrier(B!18), the_carrier(B!18))),
% 6.20/4.19 inference(modus_ponens,[status(thm)],[172, 153])).
% 6.20/4.19 tff(174,plain,
% 6.20/4.19 ((~(relation_of2_as_subset(relation_of_lattice(B!18), the_carrier(B!18), the_carrier(B!18)) <=> relation_of2(relation_of_lattice(B!18), the_carrier(B!18), the_carrier(B!18)))) | (~relation_of2_as_subset(relation_of_lattice(B!18), the_carrier(B!18), the_carrier(B!18))) | relation_of2(relation_of_lattice(B!18), the_carrier(B!18), the_carrier(B!18))),
% 6.20/4.19 inference(tautology,[status(thm)],[])).
% 6.20/4.19 tff(175,plain,
% 6.20/4.19 (relation_of2(relation_of_lattice(B!18), the_carrier(B!18), the_carrier(B!18))),
% 6.20/4.19 inference(unit_resolution,[status(thm)],[174, 173, 151])).
% 6.20/4.19 tff(176,plain,
% 6.20/4.19 (^[A: $i, B: $i] : refl(((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D)))))))),
% 6.20/4.19 inference(bind,[status(th)],[])).
% 6.20/4.19 tff(177,plain,
% 6.20/4.19 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 6.20/4.19 inference(quant_intro,[status(thm)],[176])).
% 6.20/4.19 tff(178,plain,
% 6.20/4.19 (^[A: $i, B: $i] : rewrite(((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D)))))))),
% 6.20/4.19 inference(bind,[status(th)],[])).
% 6.20/4.19 tff(179,plain,
% 6.20/4.19 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 6.20/4.19 inference(quant_intro,[status(thm)],[178])).
% 6.20/4.19 tff(180,plain,
% 6.20/4.19 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 6.20/4.19 inference(transitivity,[status(thm)],[179, 177])).
% 6.20/4.19 tff(181,plain,
% 6.20/4.19 (^[A: $i, B: $i] : rewrite(((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D)))) <=> ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D)))))))),
% 6.20/4.19 inference(bind,[status(th)],[])).
% 6.20/4.19 tff(182,plain,
% 6.20/4.19 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D)))) <=> ![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 6.20/4.19 inference(quant_intro,[status(thm)],[181])).
% 6.20/4.19 tff(183,plain,
% 6.20/4.19 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D)))) <=> ![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))),
% 6.20/4.19 inference(rewrite,[status(thm)],[])).
% 6.20/4.19 tff(184,plain,
% 6.20/4.19 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i, D: $i] : rewrite(((rel_str_of(A, B) = rel_str_of(C, D)) => ((A = C) & (B = D))) <=> ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))), (![C: $i, D: $i] : ((rel_str_of(A, B) = rel_str_of(C, D)) => ((A = C) & (B = D))) <=> ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))), ((relation_of2(B, A, A) => ![C: $i, D: $i] : ((rel_str_of(A, B) = rel_str_of(C, D)) => ((A = C) & (B = D)))) <=> (relation_of2(B, A, A) => ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D)))))), rewrite((relation_of2(B, A, A) => ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D)))) <=> ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))), ((relation_of2(B, A, A) => ![C: $i, D: $i] : ((rel_str_of(A, B) = rel_str_of(C, D)) => ((A = C) & (B = D)))) <=> ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))))),
% 6.20/4.19 inference(bind,[status(th)],[])).
% 6.20/4.19 tff(185,plain,
% 6.20/4.19 (![A: $i, B: $i] : (relation_of2(B, A, A) => ![C: $i, D: $i] : ((rel_str_of(A, B) = rel_str_of(C, D)) => ((A = C) & (B = D)))) <=> ![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))),
% 6.20/4.19 inference(quant_intro,[status(thm)],[184])).
% 6.20/4.19 tff(186,axiom,(![A: $i, B: $i] : (relation_of2(B, A, A) => ![C: $i, D: $i] : ((rel_str_of(A, B) = rel_str_of(C, D)) => ((A = C) & (B = D))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','free_g1_orders_2')).
% 6.20/4.19 tff(187,plain,
% 6.20/4.19 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))),
% 6.20/4.19 inference(modus_ponens,[status(thm)],[186, 185])).
% 6.20/4.19 tff(188,plain,
% 6.20/4.19 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))),
% 6.20/4.19 inference(modus_ponens,[status(thm)],[187, 183])).
% 6.20/4.19 tff(189,plain,(
% 6.20/4.19 ![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))),
% 6.20/4.19 inference(skolemize,[status(sab)],[188])).
% 6.20/4.19 tff(190,plain,
% 6.20/4.19 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 6.20/4.19 inference(modus_ponens,[status(thm)],[189, 182])).
% 6.20/4.19 tff(191,plain,
% 6.20/4.19 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 6.20/4.19 inference(modus_ponens,[status(thm)],[190, 180])).
% 6.20/4.19 tff(192,plain,
% 6.20/4.19 (((~![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))) | ((~relation_of2(relation_of_lattice(B!18), the_carrier(B!18), the_carrier(B!18))) | ![C: $i, D: $i] : ((~(rel_str_of(the_carrier(B!18), relation_of_lattice(B!18)) = rel_str_of(C, D))) | (~((~(the_carrier(B!18) = C)) | (~(relation_of_lattice(B!18) = D))))))) <=> ((~![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))) | (~relation_of2(relation_of_lattice(B!18), the_carrier(B!18), the_carrier(B!18))) | ![C: $i, D: $i] : ((~(rel_str_of(the_carrier(B!18), relation_of_lattice(B!18)) = rel_str_of(C, D))) | (~((~(the_carrier(B!18) = C)) | (~(relation_of_lattice(B!18) = D))))))),
% 6.20/4.19 inference(rewrite,[status(thm)],[])).
% 6.20/4.19 tff(193,plain,
% 6.20/4.19 ((~![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))) | ((~relation_of2(relation_of_lattice(B!18), the_carrier(B!18), the_carrier(B!18))) | ![C: $i, D: $i] : ((~(rel_str_of(the_carrier(B!18), relation_of_lattice(B!18)) = rel_str_of(C, D))) | (~((~(the_carrier(B!18) = C)) | (~(relation_of_lattice(B!18) = D))))))),
% 6.20/4.19 inference(quant_inst,[status(thm)],[])).
% 6.20/4.19 tff(194,plain,
% 6.20/4.19 ((~![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))) | (~relation_of2(relation_of_lattice(B!18), the_carrier(B!18), the_carrier(B!18))) | ![C: $i, D: $i] : ((~(rel_str_of(the_carrier(B!18), relation_of_lattice(B!18)) = rel_str_of(C, D))) | (~((~(the_carrier(B!18) = C)) | (~(relation_of_lattice(B!18) = D)))))),
% 6.20/4.19 inference(modus_ponens,[status(thm)],[193, 192])).
% 6.20/4.19 tff(195,plain,
% 6.20/4.19 ((~relation_of2(relation_of_lattice(B!18), the_carrier(B!18), the_carrier(B!18))) | ![C: $i, D: $i] : ((~(rel_str_of(the_carrier(B!18), relation_of_lattice(B!18)) = rel_str_of(C, D))) | (~((~(the_carrier(B!18) = C)) | (~(relation_of_lattice(B!18) = D)))))),
% 6.20/4.19 inference(unit_resolution,[status(thm)],[194, 191])).
% 6.20/4.19 tff(196,plain,
% 6.20/4.19 (![C: $i, D: $i] : ((~(rel_str_of(the_carrier(B!18), relation_of_lattice(B!18)) = rel_str_of(C, D))) | (~((~(the_carrier(B!18) = C)) | (~(relation_of_lattice(B!18) = D)))))),
% 6.20/4.19 inference(unit_resolution,[status(thm)],[195, 175])).
% 6.20/4.19 tff(197,plain,
% 6.20/4.19 (((~![C: $i, D: $i] : ((~(rel_str_of(the_carrier(B!18), relation_of_lattice(B!18)) = rel_str_of(C, D))) | (~((~(the_carrier(B!18) = C)) | (~(relation_of_lattice(B!18) = D)))))) | ((~(rel_str_of(the_carrier(B!18), relation_of_lattice(B!18)) = rel_str_of(the_carrier(poset_of_lattice(B!18)), the_InternalRel(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))) | (~((~(the_carrier(B!18) = the_carrier(poset_of_lattice(B!18)))) | (~(relation_of_lattice(B!18) = the_InternalRel(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))))))) <=> ((~![C: $i, D: $i] : ((~(rel_str_of(the_carrier(B!18), relation_of_lattice(B!18)) = rel_str_of(C, D))) | (~((~(the_carrier(B!18) = C)) | (~(relation_of_lattice(B!18) = D)))))) | (~(rel_str_of(the_carrier(B!18), relation_of_lattice(B!18)) = rel_str_of(the_carrier(poset_of_lattice(B!18)), the_InternalRel(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))) | (~((~(the_carrier(B!18) = the_carrier(poset_of_lattice(B!18)))) | (~(relation_of_lattice(B!18) = the_InternalRel(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))))))),
% 6.20/4.20 inference(rewrite,[status(thm)],[])).
% 6.20/4.20 tff(198,plain,
% 6.20/4.20 ((~![C: $i, D: $i] : ((~(rel_str_of(the_carrier(B!18), relation_of_lattice(B!18)) = rel_str_of(C, D))) | (~((~(the_carrier(B!18) = C)) | (~(relation_of_lattice(B!18) = D)))))) | ((~(rel_str_of(the_carrier(B!18), relation_of_lattice(B!18)) = rel_str_of(the_carrier(poset_of_lattice(B!18)), the_InternalRel(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))) | (~((~(the_carrier(B!18) = the_carrier(poset_of_lattice(B!18)))) | (~(relation_of_lattice(B!18) = the_InternalRel(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))))))),
% 6.20/4.20 inference(quant_inst,[status(thm)],[])).
% 6.20/4.20 tff(199,plain,
% 6.20/4.20 ((~![C: $i, D: $i] : ((~(rel_str_of(the_carrier(B!18), relation_of_lattice(B!18)) = rel_str_of(C, D))) | (~((~(the_carrier(B!18) = C)) | (~(relation_of_lattice(B!18) = D)))))) | (~(rel_str_of(the_carrier(B!18), relation_of_lattice(B!18)) = rel_str_of(the_carrier(poset_of_lattice(B!18)), the_InternalRel(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))) | (~((~(the_carrier(B!18) = the_carrier(poset_of_lattice(B!18)))) | (~(relation_of_lattice(B!18) = the_InternalRel(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))))),
% 6.20/4.20 inference(modus_ponens,[status(thm)],[198, 197])).
% 6.20/4.20 tff(200,plain,
% 6.20/4.20 ((~(rel_str_of(the_carrier(B!18), relation_of_lattice(B!18)) = rel_str_of(the_carrier(poset_of_lattice(B!18)), the_InternalRel(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))) | (~((~(the_carrier(B!18) = the_carrier(poset_of_lattice(B!18)))) | (~(relation_of_lattice(B!18) = the_InternalRel(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))))),
% 6.20/4.20 inference(unit_resolution,[status(thm)],[199, 196])).
% 6.20/4.20 tff(201,plain,
% 6.20/4.20 (~((~(the_carrier(B!18) = the_carrier(poset_of_lattice(B!18)))) | (~(relation_of_lattice(B!18) = the_InternalRel(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))))),
% 6.20/4.20 inference(unit_resolution,[status(thm)],[200, 142])).
% 6.20/4.20 tff(202,plain,
% 6.20/4.20 (((~(the_carrier(B!18) = the_carrier(poset_of_lattice(B!18)))) | (~(relation_of_lattice(B!18) = the_InternalRel(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))) | (the_carrier(B!18) = the_carrier(poset_of_lattice(B!18)))),
% 6.20/4.20 inference(tautology,[status(thm)],[])).
% 6.20/4.20 tff(203,plain,
% 6.20/4.20 (the_carrier(B!18) = the_carrier(poset_of_lattice(B!18))),
% 6.20/4.20 inference(unit_resolution,[status(thm)],[202, 201])).
% 6.20/4.20 tff(204,plain,
% 6.20/4.20 (the_carrier(B!18) = the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))),
% 6.20/4.20 inference(transitivity,[status(thm)],[203, 72])).
% 6.20/4.20 tff(205,plain,
% 6.20/4.20 (element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(B!18)) <=> element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 6.20/4.20 inference(monotonicity,[status(thm)],[204])).
% 6.20/4.20 tff(206,plain,
% 6.20/4.20 (element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(B!18))),
% 6.20/4.20 inference(symmetry,[status(thm)],[205])).
% 6.20/4.20 tff(207,plain,
% 6.20/4.20 (relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20)) <=> relstr_set_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20))),
% 6.20/4.20 inference(monotonicity,[status(thm)],[70])).
% 6.20/4.20 tff(208,plain,
% 6.20/4.20 (relstr_set_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20)) <=> relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20))),
% 6.20/4.20 inference(symmetry,[status(thm)],[207])).
% 6.20/4.20 tff(209,plain,
% 6.20/4.20 ((~relstr_set_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20))) <=> (~relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.20/4.20 inference(monotonicity,[status(thm)],[208])).
% 6.20/4.20 tff(210,assumption,(~relstr_set_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20))), introduced(assumption)).
% 6.20/4.20 tff(211,plain,
% 6.20/4.20 (~relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20))),
% 6.20/4.20 inference(modus_ponens,[status(thm)],[210, 209])).
% 6.20/4.20 tff(212,plain,
% 6.20/4.20 (element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18)))),
% 6.20/4.20 inference(monotonicity,[status(thm)],[71])).
% 6.20/4.20 tff(213,plain,
% 6.20/4.20 (element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18))) <=> element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 6.20/4.20 inference(symmetry,[status(thm)],[212])).
% 6.20/4.20 tff(214,plain,
% 6.20/4.20 (^[A: $i, B: $i] : refl((element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A))) | empty_carrier(A) | (~element(B, the_carrier(A))) | (~lattice(A)) | (~latt_str(A))) <=> (element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A))) | empty_carrier(A) | (~element(B, the_carrier(A))) | (~lattice(A)) | (~latt_str(A))))),
% 6.20/4.20 inference(bind,[status(th)],[])).
% 6.20/4.20 tff(215,plain,
% 6.20/4.20 (![A: $i, B: $i] : (element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A))) | empty_carrier(A) | (~element(B, the_carrier(A))) | (~lattice(A)) | (~latt_str(A))) <=> ![A: $i, B: $i] : (element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A))) | empty_carrier(A) | (~element(B, the_carrier(A))) | (~lattice(A)) | (~latt_str(A)))),
% 6.20/4.20 inference(quant_intro,[status(thm)],[214])).
% 6.20/4.20 tff(216,plain,
% 6.20/4.20 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(A))) <=> (~(empty_carrier(A) | (~element(B, the_carrier(A))) | (~lattice(A)) | (~latt_str(A))))), ((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(A)))) <=> (~(~(empty_carrier(A) | (~element(B, the_carrier(A))) | (~lattice(A)) | (~latt_str(A))))))), rewrite((~(~(empty_carrier(A) | (~element(B, the_carrier(A))) | (~lattice(A)) | (~latt_str(A))))) <=> (empty_carrier(A) | (~element(B, the_carrier(A))) | (~lattice(A)) | (~latt_str(A)))), ((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(A)))) <=> (empty_carrier(A) | (~element(B, the_carrier(A))) | (~lattice(A)) | (~latt_str(A))))), (((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(A)))) | element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A)))) <=> ((empty_carrier(A) | (~element(B, the_carrier(A))) | (~lattice(A)) | (~latt_str(A))) | element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A)))))), rewrite(((empty_carrier(A) | (~element(B, the_carrier(A))) | (~lattice(A)) | (~latt_str(A))) | element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A)))) <=> (element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A))) | empty_carrier(A) | (~element(B, the_carrier(A))) | (~lattice(A)) | (~latt_str(A)))), (((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(A)))) | element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A)))) <=> (element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A))) | empty_carrier(A) | (~element(B, the_carrier(A))) | (~lattice(A)) | (~latt_str(A)))))),
% 6.20/4.20 inference(bind,[status(th)],[])).
% 6.20/4.20 tff(217,plain,
% 6.20/4.20 (![A: $i, B: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(A)))) | element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A)))) <=> ![A: $i, B: $i] : (element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A))) | empty_carrier(A) | (~element(B, the_carrier(A))) | (~lattice(A)) | (~latt_str(A)))),
% 6.20/4.20 inference(quant_intro,[status(thm)],[216])).
% 6.20/4.20 tff(218,plain,
% 6.20/4.20 (![A: $i, B: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(A)))) | element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A)))) <=> ![A: $i, B: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(A)))) | element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A))))),
% 6.20/4.20 inference(rewrite,[status(thm)],[])).
% 6.20/4.20 tff(219,plain,
% 6.20/4.20 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) <=> ((~empty_carrier(A)) & lattice(A) & latt_str(A))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) & element(B, the_carrier(A))) <=> (((~empty_carrier(A)) & lattice(A) & latt_str(A)) & element(B, the_carrier(A))))), rewrite((((~empty_carrier(A)) & lattice(A) & latt_str(A)) & element(B, the_carrier(A))) <=> ((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(A)))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) & element(B, the_carrier(A))) <=> ((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(A))))), ((((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) & element(B, the_carrier(A))) => element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A)))) <=> (((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(A))) => element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A)))))), rewrite((((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(A))) => element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A)))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(A)))) | element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A))))), ((((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) & element(B, the_carrier(A))) => element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A)))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(A)))) | element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A))))))),
% 6.20/4.20 inference(bind,[status(th)],[])).
% 6.20/4.20 tff(220,plain,
% 6.20/4.20 (![A: $i, B: $i] : (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) & element(B, the_carrier(A))) => element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A)))) <=> ![A: $i, B: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(A)))) | element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A))))),
% 6.20/4.20 inference(quant_intro,[status(thm)],[219])).
% 6.20/4.20 tff(221,axiom,(![A: $i, B: $i] : (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) & element(B, the_carrier(A))) => element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k4_lattice3')).
% 6.20/4.20 tff(222,plain,
% 6.20/4.20 (![A: $i, B: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(A)))) | element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A))))),
% 6.20/4.20 inference(modus_ponens,[status(thm)],[221, 220])).
% 6.20/4.20 tff(223,plain,
% 6.20/4.20 (![A: $i, B: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(A)))) | element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A))))),
% 6.20/4.20 inference(modus_ponens,[status(thm)],[222, 218])).
% 6.20/4.20 tff(224,plain,(
% 6.20/4.20 ![A: $i, B: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(A)))) | element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A))))),
% 6.20/4.20 inference(skolemize,[status(sab)],[223])).
% 6.20/4.20 tff(225,plain,
% 6.20/4.20 (![A: $i, B: $i] : (element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A))) | empty_carrier(A) | (~element(B, the_carrier(A))) | (~lattice(A)) | (~latt_str(A)))),
% 6.20/4.20 inference(modus_ponens,[status(thm)],[224, 217])).
% 6.20/4.20 tff(226,plain,
% 6.20/4.20 (![A: $i, B: $i] : (element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A))) | empty_carrier(A) | (~element(B, the_carrier(A))) | (~lattice(A)) | (~latt_str(A)))),
% 6.20/4.20 inference(modus_ponens,[status(thm)],[225, 215])).
% 6.20/4.20 tff(227,plain,
% 6.20/4.20 (((~![A: $i, B: $i] : (element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A))) | empty_carrier(A) | (~element(B, the_carrier(A))) | (~lattice(A)) | (~latt_str(A)))) | (empty_carrier(B!18) | (~element(C!20, the_carrier(B!18))) | (~latt_str(B!18)) | (~lattice(B!18)) | element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18))))) <=> ((~![A: $i, B: $i] : (element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A))) | empty_carrier(A) | (~element(B, the_carrier(A))) | (~lattice(A)) | (~latt_str(A)))) | empty_carrier(B!18) | (~element(C!20, the_carrier(B!18))) | (~latt_str(B!18)) | (~lattice(B!18)) | element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18))))),
% 6.20/4.20 inference(rewrite,[status(thm)],[])).
% 6.20/4.20 tff(228,plain,
% 6.20/4.20 ((element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18))) | empty_carrier(B!18) | (~element(C!20, the_carrier(B!18))) | (~lattice(B!18)) | (~latt_str(B!18))) <=> (empty_carrier(B!18) | (~element(C!20, the_carrier(B!18))) | (~latt_str(B!18)) | (~lattice(B!18)) | element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18))))),
% 6.20/4.20 inference(rewrite,[status(thm)],[])).
% 6.20/4.20 tff(229,plain,
% 6.20/4.20 (((~![A: $i, B: $i] : (element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A))) | empty_carrier(A) | (~element(B, the_carrier(A))) | (~lattice(A)) | (~latt_str(A)))) | (element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18))) | empty_carrier(B!18) | (~element(C!20, the_carrier(B!18))) | (~lattice(B!18)) | (~latt_str(B!18)))) <=> ((~![A: $i, B: $i] : (element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A))) | empty_carrier(A) | (~element(B, the_carrier(A))) | (~lattice(A)) | (~latt_str(A)))) | (empty_carrier(B!18) | (~element(C!20, the_carrier(B!18))) | (~latt_str(B!18)) | (~lattice(B!18)) | element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18)))))),
% 6.20/4.20 inference(monotonicity,[status(thm)],[228])).
% 6.20/4.20 tff(230,plain,
% 6.20/4.20 (((~![A: $i, B: $i] : (element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A))) | empty_carrier(A) | (~element(B, the_carrier(A))) | (~lattice(A)) | (~latt_str(A)))) | (element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18))) | empty_carrier(B!18) | (~element(C!20, the_carrier(B!18))) | (~lattice(B!18)) | (~latt_str(B!18)))) <=> ((~![A: $i, B: $i] : (element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A))) | empty_carrier(A) | (~element(B, the_carrier(A))) | (~lattice(A)) | (~latt_str(A)))) | empty_carrier(B!18) | (~element(C!20, the_carrier(B!18))) | (~latt_str(B!18)) | (~lattice(B!18)) | element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18))))),
% 6.20/4.20 inference(transitivity,[status(thm)],[229, 227])).
% 6.20/4.20 tff(231,plain,
% 6.20/4.20 ((~![A: $i, B: $i] : (element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A))) | empty_carrier(A) | (~element(B, the_carrier(A))) | (~lattice(A)) | (~latt_str(A)))) | (element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18))) | empty_carrier(B!18) | (~element(C!20, the_carrier(B!18))) | (~lattice(B!18)) | (~latt_str(B!18)))),
% 6.20/4.20 inference(quant_inst,[status(thm)],[])).
% 6.20/4.20 tff(232,plain,
% 6.20/4.20 ((~![A: $i, B: $i] : (element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A))) | empty_carrier(A) | (~element(B, the_carrier(A))) | (~lattice(A)) | (~latt_str(A)))) | empty_carrier(B!18) | (~element(C!20, the_carrier(B!18))) | (~latt_str(B!18)) | (~lattice(B!18)) | element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18)))),
% 6.20/4.20 inference(modus_ponens,[status(thm)],[231, 230])).
% 6.20/4.20 tff(233,plain,
% 6.20/4.20 (element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18)))),
% 6.20/4.20 inference(unit_resolution,[status(thm)],[232, 226, 18, 17, 16, 43])).
% 6.20/4.20 tff(234,plain,
% 6.20/4.20 (element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 6.20/4.20 inference(modus_ponens,[status(thm)],[233, 213])).
% 6.20/4.20 tff(235,plain,
% 6.20/4.20 (^[A: $i] : refl(((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B)))))))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B)))))))))))),
% 6.20/4.20 inference(bind,[status(th)],[])).
% 6.20/4.20 tff(236,plain,
% 6.20/4.20 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B)))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B))))))))))),
% 6.20/4.20 inference(quant_intro,[status(thm)],[235])).
% 6.20/4.20 tff(237,plain,
% 6.20/4.20 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B)))))))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B)))))))))))),
% 6.20/4.20 inference(bind,[status(th)],[])).
% 6.20/4.20 tff(238,plain,
% 6.20/4.20 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B)))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B))))))))))),
% 6.20/4.20 inference(quant_intro,[status(thm)],[237])).
% 6.20/4.20 tff(239,plain,
% 6.20/4.20 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B)))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B))))))))))),
% 6.20/4.20 inference(transitivity,[status(thm)],[238, 236])).
% 6.20/4.20 tff(240,plain,
% 6.20/4.20 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B)))) & (relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B)))))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B)))))))))))),
% 6.20/4.20 inference(bind,[status(th)],[])).
% 6.20/4.20 tff(241,plain,
% 6.20/4.20 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B)))) & (relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B)))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B))))))))))),
% 6.20/4.20 inference(quant_intro,[status(thm)],[240])).
% 6.20/4.20 tff(242,plain,
% 6.20/4.20 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B))))))),
% 6.20/4.20 inference(rewrite,[status(thm)],[])).
% 6.20/4.20 tff(243,plain,
% 6.20/4.20 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i, C: $i] : trans(monotonicity(rewrite((relstr_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, D, C)))) <=> (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B))))), ((element(C, the_carrier(A)) => (relstr_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, D, C))))) <=> (element(C, the_carrier(A)) => (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B))))))), rewrite((element(C, the_carrier(A)) => (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B))))) <=> ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B)))))), ((element(C, the_carrier(A)) => (relstr_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, D, C))))) <=> ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B)))))))), (![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, D, C))))) <=> ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B))))))), ((rel_str(A) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, D, C)))))) <=> (rel_str(A) => ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B)))))))), rewrite((rel_str(A) => ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B)))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B))))))), ((rel_str(A) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, D, C)))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B))))))))),
% 6.20/4.20 inference(bind,[status(th)],[])).
% 6.20/4.20 tff(244,plain,
% 6.20/4.20 (![A: $i] : (rel_str(A) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, D, C)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B))))))),
% 6.20/4.20 inference(quant_intro,[status(thm)],[243])).
% 6.20/4.20 tff(245,axiom,(![A: $i] : (rel_str(A) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, D, C))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d9_lattice3')).
% 6.20/4.20 tff(246,plain,
% 6.20/4.20 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B))))))),
% 6.20/4.20 inference(modus_ponens,[status(thm)],[245, 244])).
% 6.20/4.20 tff(247,plain,
% 6.20/4.20 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B))))))),
% 6.20/4.20 inference(modus_ponens,[status(thm)],[246, 242])).
% 6.20/4.20 tff(248,plain,(
% 6.20/4.20 ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B)))) & (relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B))))))))),
% 6.20/4.20 inference(skolemize,[status(sab)],[247])).
% 6.20/4.20 tff(249,plain,
% 6.20/4.20 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B))))))))))),
% 6.20/4.20 inference(modus_ponens,[status(thm)],[248, 241])).
% 6.20/4.20 tff(250,plain,
% 6.20/4.20 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B))))))))))),
% 6.20/4.20 inference(modus_ponens,[status(thm)],[249, 239])).
% 6.20/4.20 tff(251,plain,
% 6.20/4.20 (((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B))))))))))) | ((~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | ![B: $i, C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~((~((~relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, C)))) | (~(relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), B, C) | (~(related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), C) | (~element(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), B))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B))))))))))) | (~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | ![B: $i, C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~((~((~relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, C)))) | (~(relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), B, C) | (~(related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), C) | (~element(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), B))))))))))),
% 6.20/4.20 inference(rewrite,[status(thm)],[])).
% 6.20/4.20 tff(252,plain,
% 6.20/4.20 (((~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | ![B: $i, C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~((~((~relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), B, C)) | ![D: $i] : (related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, C) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(D, B))))) | (~(relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), B, C) | (~(related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), C) | (~element(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), B)))))))))) <=> ((~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | ![B: $i, C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~((~((~relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, C)))) | (~(relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), B, C) | (~(related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), C) | (~element(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), B))))))))))),
% 6.20/4.20 inference(rewrite,[status(thm)],[])).
% 6.20/4.20 tff(253,plain,
% 6.20/4.20 (((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B))))))))))) | ((~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | ![B: $i, C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~((~((~relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), B, C)) | ![D: $i] : (related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, C) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(D, B))))) | (~(relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), B, C) | (~(related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), C) | (~element(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), B))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B))))))))))) | ((~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | ![B: $i, C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~((~((~relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, C)))) | (~(relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), B, C) | (~(related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), C) | (~element(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), B)))))))))))),
% 6.20/4.20 inference(monotonicity,[status(thm)],[252])).
% 6.20/4.20 tff(254,plain,
% 6.20/4.20 (((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B))))))))))) | ((~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | ![B: $i, C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~((~((~relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), B, C)) | ![D: $i] : (related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, C) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(D, B))))) | (~(relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), B, C) | (~(related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), C) | (~element(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), B))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B))))))))))) | (~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | ![B: $i, C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~((~((~relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, C)))) | (~(relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), B, C) | (~(related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), C) | (~element(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), B))))))))))),
% 6.20/4.20 inference(transitivity,[status(thm)],[253, 251])).
% 6.20/4.20 tff(255,plain,
% 6.20/4.20 ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B))))))))))) | ((~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | ![B: $i, C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~((~((~relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), B, C)) | ![D: $i] : (related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, C) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(D, B))))) | (~(relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), B, C) | (~(related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), C) | (~element(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), B))))))))))),
% 6.20/4.20 inference(quant_inst,[status(thm)],[])).
% 6.20/4.20 tff(256,plain,
% 6.20/4.20 ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B))))))))))) | (~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | ![B: $i, C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~((~((~relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, C)))) | (~(relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), B, C) | (~(related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), C) | (~element(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), B)))))))))),
% 6.20/4.20 inference(modus_ponens,[status(thm)],[255, 254])).
% 6.20/4.20 tff(257,plain,
% 6.20/4.20 ((~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | ![B: $i, C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~((~((~relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, C)))) | (~(relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), B, C) | (~(related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), C) | (~element(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), B)))))))))),
% 6.20/4.20 inference(unit_resolution,[status(thm)],[256, 250])).
% 6.20/4.20 tff(258,plain,
% 6.20/4.20 (![B: $i, C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~((~((~relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, C)))) | (~(relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), B, C) | (~(related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), C) | (~element(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), B)))))))))),
% 6.20/4.20 inference(unit_resolution,[status(thm)],[257, 101])).
% 6.20/4.20 tff(259,plain,
% 6.20/4.20 (((~![B: $i, C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~((~((~relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, C)))) | (~(relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), B, C) | (~(related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), C) | (~element(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), B)))))))))) | ((~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~((~((~relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20))) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, cast_to_el_of_LattPOSet(B!18, C!20))))) | (~(relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20)) | (~(related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), A!19)))))))))) <=> ((~![B: $i, C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~((~((~relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, C)))) | (~(relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), B, C) | (~(related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), C) | (~element(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), B)))))))))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~((~((~relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20))) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, cast_to_el_of_LattPOSet(B!18, C!20))))) | (~(relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20)) | (~(related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), A!19)))))))))),
% 6.20/4.21 inference(rewrite,[status(thm)],[])).
% 6.20/4.21 tff(260,plain,
% 6.20/4.21 ((~![B: $i, C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~((~((~relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, C)))) | (~(relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), B, C) | (~(related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), C) | (~element(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), B)))))))))) | ((~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~((~((~relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20))) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, cast_to_el_of_LattPOSet(B!18, C!20))))) | (~(relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20)) | (~(related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), A!19)))))))))),
% 6.20/4.21 inference(quant_inst,[status(thm)],[])).
% 6.20/4.21 tff(261,plain,
% 6.20/4.21 ((~![B: $i, C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~((~((~relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, C)))) | (~(relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), B, C) | (~(related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), C) | (~element(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), B)))))))))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~((~((~relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20))) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, cast_to_el_of_LattPOSet(B!18, C!20))))) | (~(relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20)) | (~(related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), A!19))))))))),
% 6.20/4.21 inference(modus_ponens,[status(thm)],[260, 259])).
% 6.20/4.21 tff(262,plain,
% 6.20/4.21 ((~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~((~((~relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20))) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, cast_to_el_of_LattPOSet(B!18, C!20))))) | (~(relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20)) | (~(related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), A!19))))))))),
% 6.20/4.21 inference(unit_resolution,[status(thm)],[261, 258])).
% 6.20/4.21 tff(263,plain,
% 6.20/4.21 (~((~((~relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20))) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, cast_to_el_of_LattPOSet(B!18, C!20))))) | (~(relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20)) | (~(related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), A!19)))))))),
% 6.20/4.21 inference(unit_resolution,[status(thm)],[262, 234])).
% 6.20/4.21 tff(264,plain,
% 6.20/4.21 (((~((~relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20))) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, cast_to_el_of_LattPOSet(B!18, C!20))))) | (~(relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20)) | (~(related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), A!19))))))) | (relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20)) | (~(related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), A!19)))))),
% 6.20/4.21 inference(tautology,[status(thm)],[])).
% 6.20/4.21 tff(265,plain,
% 6.20/4.21 (relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20)) | (~(related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), A!19))))),
% 6.20/4.21 inference(unit_resolution,[status(thm)],[264, 263])).
% 6.20/4.21 tff(266,plain,
% 6.20/4.21 ((~(relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20)) | (~(related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), A!19)))))) | relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20)) | (~(related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), A!19))))),
% 6.20/4.21 inference(tautology,[status(thm)],[])).
% 6.20/4.21 tff(267,plain,
% 6.20/4.21 (relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20)) | (~(related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), A!19))))),
% 6.20/4.21 inference(unit_resolution,[status(thm)],[266, 265])).
% 6.20/4.21 tff(268,plain,
% 6.20/4.21 (~(related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), A!19)))),
% 6.20/4.21 inference(unit_resolution,[status(thm)],[267, 211])).
% 6.20/4.21 tff(269,plain,
% 6.20/4.21 ((related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), A!19))) | element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 6.20/4.21 inference(tautology,[status(thm)],[])).
% 6.20/4.21 tff(270,plain,
% 6.20/4.21 (element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 6.20/4.21 inference(unit_resolution,[status(thm)],[269, 268])).
% 6.20/4.21 tff(271,plain,
% 6.20/4.21 (element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(B!18))),
% 6.20/4.21 inference(modus_ponens,[status(thm)],[270, 206])).
% 6.20/4.21 tff(272,plain,
% 6.20/4.21 (((~![B: $i] : ((~element(B, the_carrier(B!18))) | (cast_to_el_of_LattPOSet(B!18, B) = B))) | ((~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(B!18))) | (cast_to_el_of_LattPOSet(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) = tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))) <=> ((~![B: $i] : ((~element(B, the_carrier(B!18))) | (cast_to_el_of_LattPOSet(B!18, B) = B))) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(B!18))) | (cast_to_el_of_LattPOSet(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) = tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))),
% 6.20/4.21 inference(rewrite,[status(thm)],[])).
% 6.20/4.21 tff(273,plain,
% 6.20/4.21 ((~![B: $i] : ((~element(B, the_carrier(B!18))) | (cast_to_el_of_LattPOSet(B!18, B) = B))) | ((~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(B!18))) | (cast_to_el_of_LattPOSet(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) = tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))),
% 6.20/4.21 inference(quant_inst,[status(thm)],[])).
% 6.20/4.21 tff(274,plain,
% 6.20/4.21 ((~![B: $i] : ((~element(B, the_carrier(B!18))) | (cast_to_el_of_LattPOSet(B!18, B) = B))) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(B!18))) | (cast_to_el_of_LattPOSet(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) = tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 6.20/4.21 inference(modus_ponens,[status(thm)],[273, 272])).
% 6.20/4.21 tff(275,plain,
% 6.20/4.21 ((~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(B!18))) | (cast_to_el_of_LattPOSet(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) = tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 6.20/4.21 inference(unit_resolution,[status(thm)],[274, 41])).
% 6.20/4.21 tff(276,plain,
% 6.20/4.21 (cast_to_el_of_LattPOSet(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) = tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))),
% 6.20/4.21 inference(unit_resolution,[status(thm)],[275, 271])).
% 6.20/4.21 tff(277,plain,
% 6.20/4.21 (related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20))) <=> related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20))),
% 6.20/4.21 inference(monotonicity,[status(thm)],[69, 276, 48])).
% 6.20/4.21 tff(278,plain,
% 6.20/4.21 (related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.20/4.21 inference(symmetry,[status(thm)],[277])).
% 6.20/4.21 tff(279,plain,
% 6.20/4.21 ((~related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20))) <=> (~related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20))))),
% 6.20/4.21 inference(monotonicity,[status(thm)],[278])).
% 6.20/4.21 tff(280,plain,
% 6.20/4.21 (reflexive_relstr(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) <=> reflexive_relstr(poset_of_lattice(B!18))),
% 6.20/4.21 inference(monotonicity,[status(thm)],[70])).
% 6.20/4.21 tff(281,plain,
% 6.20/4.21 (reflexive_relstr(poset_of_lattice(B!18)) <=> reflexive_relstr(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))),
% 6.20/4.21 inference(symmetry,[status(thm)],[280])).
% 6.20/4.21 tff(282,plain,
% 6.20/4.21 (((~strict_rel_str(poset_of_lattice(B!18))) | (~reflexive_relstr(poset_of_lattice(B!18))) | (~transitive_relstr(poset_of_lattice(B!18))) | (~antisymmetric_relstr(poset_of_lattice(B!18))) | (~rel_str(poset_of_lattice(B!18)))) | reflexive_relstr(poset_of_lattice(B!18))),
% 6.20/4.21 inference(tautology,[status(thm)],[])).
% 6.20/4.21 tff(283,plain,
% 6.20/4.21 (reflexive_relstr(poset_of_lattice(B!18))),
% 6.20/4.21 inference(unit_resolution,[status(thm)],[282, 93])).
% 6.20/4.21 tff(284,plain,
% 6.20/4.21 (reflexive_relstr(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))),
% 6.20/4.21 inference(modus_ponens,[status(thm)],[283, 281])).
% 6.20/4.21 tff(285,plain,
% 6.20/4.21 (empty_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) <=> empty_carrier(poset_of_lattice(B!18))),
% 6.20/4.21 inference(monotonicity,[status(thm)],[70])).
% 6.20/4.21 tff(286,plain,
% 6.20/4.21 (empty_carrier(poset_of_lattice(B!18)) <=> empty_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))),
% 6.20/4.21 inference(symmetry,[status(thm)],[285])).
% 6.20/4.21 tff(287,plain,
% 6.20/4.21 ((~empty_carrier(poset_of_lattice(B!18))) <=> (~empty_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 6.20/4.21 inference(monotonicity,[status(thm)],[286])).
% 6.20/4.21 tff(288,plain,
% 6.20/4.21 (^[A: $i] : refl((empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~(empty_carrier(poset_of_lattice(A)) | (~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A)))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~(empty_carrier(poset_of_lattice(A)) | (~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A)))))))),
% 6.20/4.21 inference(bind,[status(th)],[])).
% 6.20/4.21 tff(289,plain,
% 6.20/4.21 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~(empty_carrier(poset_of_lattice(A)) | (~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A)))))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~(empty_carrier(poset_of_lattice(A)) | (~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A))))))),
% 6.20/4.21 inference(quant_intro,[status(thm)],[288])).
% 6.20/4.21 tff(290,plain,
% 6.20/4.21 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & lattice(A) & latt_str(A)) <=> (~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))), ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) <=> (~(~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))))), rewrite((~(~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)))), ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))), rewrite(((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A))) <=> (~(empty_carrier(poset_of_lattice(A)) | (~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A)))))), (((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)))) <=> ((empty_carrier(A) | (~latt_str(A)) | (~lattice(A))) | (~(empty_carrier(poset_of_lattice(A)) | (~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A)))))))), rewrite(((empty_carrier(A) | (~latt_str(A)) | (~lattice(A))) | (~(empty_carrier(poset_of_lattice(A)) | (~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A)))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~(empty_carrier(poset_of_lattice(A)) | (~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A))))))), (((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~(empty_carrier(poset_of_lattice(A)) | (~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A))))))))),
% 6.20/4.21 inference(bind,[status(th)],[])).
% 6.20/4.21 tff(291,plain,
% 6.20/4.21 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~(empty_carrier(poset_of_lattice(A)) | (~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A))))))),
% 6.20/4.21 inference(quant_intro,[status(thm)],[290])).
% 6.20/4.21 tff(292,plain,
% 6.20/4.21 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)))) <=> ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A))))),
% 6.20/4.21 inference(rewrite,[status(thm)],[])).
% 6.20/4.21 tff(293,plain,
% 6.20/4.21 (^[A: $i] : trans(monotonicity(rewrite((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) <=> ((~empty_carrier(A)) & lattice(A) & latt_str(A))), trans(monotonicity(trans(monotonicity(rewrite((((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A))) & reflexive_relstr(poset_of_lattice(A))) <=> ((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)))), (((((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A))) & reflexive_relstr(poset_of_lattice(A))) & transitive_relstr(poset_of_lattice(A))) <=> (((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A))) & transitive_relstr(poset_of_lattice(A))))), rewrite((((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A))) & transitive_relstr(poset_of_lattice(A))) <=> ((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)))), (((((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A))) & reflexive_relstr(poset_of_lattice(A))) & transitive_relstr(poset_of_lattice(A))) <=> ((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A))))), ((((((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A))) & reflexive_relstr(poset_of_lattice(A))) & transitive_relstr(poset_of_lattice(A))) & antisymmetric_relstr(poset_of_lattice(A))) <=> (((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A))) & antisymmetric_relstr(poset_of_lattice(A))))), rewrite((((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A))) & antisymmetric_relstr(poset_of_lattice(A))) <=> ((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)))), ((((((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A))) & reflexive_relstr(poset_of_lattice(A))) & transitive_relstr(poset_of_lattice(A))) & antisymmetric_relstr(poset_of_lattice(A))) <=> ((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A))))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => (((((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A))) & reflexive_relstr(poset_of_lattice(A))) & transitive_relstr(poset_of_lattice(A))) & antisymmetric_relstr(poset_of_lattice(A)))) <=> (((~empty_carrier(A)) & lattice(A) & latt_str(A)) => ((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)))))), rewrite((((~empty_carrier(A)) & lattice(A) & latt_str(A)) => ((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A))))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => (((((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A))) & reflexive_relstr(poset_of_lattice(A))) & transitive_relstr(poset_of_lattice(A))) & antisymmetric_relstr(poset_of_lattice(A)))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A))))))),
% 6.20/4.21 inference(bind,[status(th)],[])).
% 6.20/4.21 tff(294,plain,
% 6.20/4.21 (![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => (((((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A))) & reflexive_relstr(poset_of_lattice(A))) & transitive_relstr(poset_of_lattice(A))) & antisymmetric_relstr(poset_of_lattice(A)))) <=> ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A))))),
% 6.20/4.21 inference(quant_intro,[status(thm)],[293])).
% 6.20/4.21 tff(295,axiom,(![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => (((((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A))) & reflexive_relstr(poset_of_lattice(A))) & transitive_relstr(poset_of_lattice(A))) & antisymmetric_relstr(poset_of_lattice(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc4_lattice3')).
% 6.20/4.21 tff(296,plain,
% 6.20/4.21 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A))))),
% 6.20/4.21 inference(modus_ponens,[status(thm)],[295, 294])).
% 6.20/4.21 tff(297,plain,
% 6.20/4.21 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A))))),
% 6.20/4.21 inference(modus_ponens,[status(thm)],[296, 292])).
% 6.20/4.21 tff(298,plain,(
% 6.20/4.21 ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A))))),
% 6.20/4.21 inference(skolemize,[status(sab)],[297])).
% 6.20/4.21 tff(299,plain,
% 6.20/4.21 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~(empty_carrier(poset_of_lattice(A)) | (~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A))))))),
% 6.20/4.21 inference(modus_ponens,[status(thm)],[298, 291])).
% 6.20/4.21 tff(300,plain,
% 6.20/4.21 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~(empty_carrier(poset_of_lattice(A)) | (~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A))))))),
% 6.20/4.21 inference(modus_ponens,[status(thm)],[299, 289])).
% 6.20/4.21 tff(301,plain,
% 6.20/4.21 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~(empty_carrier(poset_of_lattice(A)) | (~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A))))))) | (empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (~((~strict_rel_str(poset_of_lattice(B!18))) | (~reflexive_relstr(poset_of_lattice(B!18))) | (~transitive_relstr(poset_of_lattice(B!18))) | (~antisymmetric_relstr(poset_of_lattice(B!18))) | empty_carrier(poset_of_lattice(B!18)))))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~(empty_carrier(poset_of_lattice(A)) | (~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A))))))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (~((~strict_rel_str(poset_of_lattice(B!18))) | (~reflexive_relstr(poset_of_lattice(B!18))) | (~transitive_relstr(poset_of_lattice(B!18))) | (~antisymmetric_relstr(poset_of_lattice(B!18))) | empty_carrier(poset_of_lattice(B!18)))))),
% 6.20/4.21 inference(rewrite,[status(thm)],[])).
% 6.20/4.21 tff(302,plain,
% 6.20/4.21 ((empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (~(empty_carrier(poset_of_lattice(B!18)) | (~strict_rel_str(poset_of_lattice(B!18))) | (~reflexive_relstr(poset_of_lattice(B!18))) | (~transitive_relstr(poset_of_lattice(B!18))) | (~antisymmetric_relstr(poset_of_lattice(B!18)))))) <=> (empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (~((~strict_rel_str(poset_of_lattice(B!18))) | (~reflexive_relstr(poset_of_lattice(B!18))) | (~transitive_relstr(poset_of_lattice(B!18))) | (~antisymmetric_relstr(poset_of_lattice(B!18))) | empty_carrier(poset_of_lattice(B!18)))))),
% 6.20/4.21 inference(rewrite,[status(thm)],[])).
% 6.20/4.21 tff(303,plain,
% 6.20/4.21 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~(empty_carrier(poset_of_lattice(A)) | (~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A))))))) | (empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (~(empty_carrier(poset_of_lattice(B!18)) | (~strict_rel_str(poset_of_lattice(B!18))) | (~reflexive_relstr(poset_of_lattice(B!18))) | (~transitive_relstr(poset_of_lattice(B!18))) | (~antisymmetric_relstr(poset_of_lattice(B!18))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~(empty_carrier(poset_of_lattice(A)) | (~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A))))))) | (empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (~((~strict_rel_str(poset_of_lattice(B!18))) | (~reflexive_relstr(poset_of_lattice(B!18))) | (~transitive_relstr(poset_of_lattice(B!18))) | (~antisymmetric_relstr(poset_of_lattice(B!18))) | empty_carrier(poset_of_lattice(B!18))))))),
% 6.20/4.21 inference(monotonicity,[status(thm)],[302])).
% 6.20/4.21 tff(304,plain,
% 6.20/4.21 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~(empty_carrier(poset_of_lattice(A)) | (~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A))))))) | (empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (~(empty_carrier(poset_of_lattice(B!18)) | (~strict_rel_str(poset_of_lattice(B!18))) | (~reflexive_relstr(poset_of_lattice(B!18))) | (~transitive_relstr(poset_of_lattice(B!18))) | (~antisymmetric_relstr(poset_of_lattice(B!18))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~(empty_carrier(poset_of_lattice(A)) | (~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A))))))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (~((~strict_rel_str(poset_of_lattice(B!18))) | (~reflexive_relstr(poset_of_lattice(B!18))) | (~transitive_relstr(poset_of_lattice(B!18))) | (~antisymmetric_relstr(poset_of_lattice(B!18))) | empty_carrier(poset_of_lattice(B!18)))))),
% 6.20/4.21 inference(transitivity,[status(thm)],[303, 301])).
% 6.20/4.21 tff(305,plain,
% 6.20/4.21 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~(empty_carrier(poset_of_lattice(A)) | (~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A))))))) | (empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (~(empty_carrier(poset_of_lattice(B!18)) | (~strict_rel_str(poset_of_lattice(B!18))) | (~reflexive_relstr(poset_of_lattice(B!18))) | (~transitive_relstr(poset_of_lattice(B!18))) | (~antisymmetric_relstr(poset_of_lattice(B!18))))))),
% 6.20/4.21 inference(quant_inst,[status(thm)],[])).
% 6.20/4.21 tff(306,plain,
% 6.20/4.21 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~(empty_carrier(poset_of_lattice(A)) | (~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A))))))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (~((~strict_rel_str(poset_of_lattice(B!18))) | (~reflexive_relstr(poset_of_lattice(B!18))) | (~transitive_relstr(poset_of_lattice(B!18))) | (~antisymmetric_relstr(poset_of_lattice(B!18))) | empty_carrier(poset_of_lattice(B!18))))),
% 6.20/4.21 inference(modus_ponens,[status(thm)],[305, 304])).
% 6.20/4.21 tff(307,plain,
% 6.20/4.21 (~((~strict_rel_str(poset_of_lattice(B!18))) | (~reflexive_relstr(poset_of_lattice(B!18))) | (~transitive_relstr(poset_of_lattice(B!18))) | (~antisymmetric_relstr(poset_of_lattice(B!18))) | empty_carrier(poset_of_lattice(B!18)))),
% 6.20/4.21 inference(unit_resolution,[status(thm)],[306, 300, 18, 17, 16])).
% 6.20/4.21 tff(308,plain,
% 6.20/4.21 (((~strict_rel_str(poset_of_lattice(B!18))) | (~reflexive_relstr(poset_of_lattice(B!18))) | (~transitive_relstr(poset_of_lattice(B!18))) | (~antisymmetric_relstr(poset_of_lattice(B!18))) | empty_carrier(poset_of_lattice(B!18))) | (~empty_carrier(poset_of_lattice(B!18)))),
% 6.20/4.21 inference(tautology,[status(thm)],[])).
% 6.20/4.21 tff(309,plain,
% 6.20/4.21 (~empty_carrier(poset_of_lattice(B!18))),
% 6.20/4.21 inference(unit_resolution,[status(thm)],[308, 307])).
% 6.20/4.21 tff(310,plain,
% 6.20/4.21 (~empty_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))),
% 6.20/4.21 inference(modus_ponens,[status(thm)],[309, 287])).
% 6.20/4.21 tff(311,plain,
% 6.20/4.21 (^[A: $i, B: $i, C: $i] : refl(((related_reflexive(A, B, C) <=> related(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A))) <=> ((related_reflexive(A, B, C) <=> related(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A))))),
% 6.20/4.21 inference(bind,[status(th)],[])).
% 6.20/4.21 tff(312,plain,
% 6.20/4.21 (![A: $i, B: $i, C: $i] : ((related_reflexive(A, B, C) <=> related(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A))) <=> ![A: $i, B: $i, C: $i] : ((related_reflexive(A, B, C) <=> related(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))),
% 6.20/4.21 inference(quant_intro,[status(thm)],[311])).
% 6.20/4.21 tff(313,plain,
% 6.20/4.21 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & reflexive_relstr(A) & rel_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A))) <=> (~(empty_carrier(A) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A))))), ((~((~empty_carrier(A)) & reflexive_relstr(A) & rel_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) <=> (~(~(empty_carrier(A) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A))))))), rewrite((~(~(empty_carrier(A) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A))))) <=> (empty_carrier(A) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))), ((~((~empty_carrier(A)) & reflexive_relstr(A) & rel_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) <=> (empty_carrier(A) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A))))), (((~((~empty_carrier(A)) & reflexive_relstr(A) & rel_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (related_reflexive(A, B, C) <=> related(A, B, C))) <=> ((empty_carrier(A) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A))) | (related_reflexive(A, B, C) <=> related(A, B, C))))), rewrite(((empty_carrier(A) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A))) | (related_reflexive(A, B, C) <=> related(A, B, C))) <=> ((related_reflexive(A, B, C) <=> related(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))), (((~((~empty_carrier(A)) & reflexive_relstr(A) & rel_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (related_reflexive(A, B, C) <=> related(A, B, C))) <=> ((related_reflexive(A, B, C) <=> related(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))))),
% 6.20/4.21 inference(bind,[status(th)],[])).
% 6.20/4.21 tff(314,plain,
% 6.20/4.21 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & reflexive_relstr(A) & rel_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (related_reflexive(A, B, C) <=> related(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((related_reflexive(A, B, C) <=> related(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))),
% 6.20/4.21 inference(quant_intro,[status(thm)],[313])).
% 6.20/4.21 tff(315,plain,
% 6.20/4.21 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & reflexive_relstr(A) & rel_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (related_reflexive(A, B, C) <=> related(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & reflexive_relstr(A) & rel_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (related_reflexive(A, B, C) <=> related(A, B, C)))),
% 6.20/4.21 inference(rewrite,[status(thm)],[])).
% 6.20/4.21 tff(316,plain,
% 6.20/4.21 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~empty_carrier(A)) & reflexive_relstr(A)) & rel_str(A)) <=> ((~empty_carrier(A)) & reflexive_relstr(A) & rel_str(A))), (((((~empty_carrier(A)) & reflexive_relstr(A)) & rel_str(A)) & element(B, the_carrier(A))) <=> (((~empty_carrier(A)) & reflexive_relstr(A) & rel_str(A)) & element(B, the_carrier(A))))), rewrite((((~empty_carrier(A)) & reflexive_relstr(A) & rel_str(A)) & element(B, the_carrier(A))) <=> ((~empty_carrier(A)) & reflexive_relstr(A) & rel_str(A) & element(B, the_carrier(A)))), (((((~empty_carrier(A)) & reflexive_relstr(A)) & rel_str(A)) & element(B, the_carrier(A))) <=> ((~empty_carrier(A)) & reflexive_relstr(A) & rel_str(A) & element(B, the_carrier(A))))), ((((((~empty_carrier(A)) & reflexive_relstr(A)) & rel_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) <=> (((~empty_carrier(A)) & reflexive_relstr(A) & rel_str(A) & element(B, the_carrier(A))) & element(C, the_carrier(A))))), rewrite((((~empty_carrier(A)) & reflexive_relstr(A) & rel_str(A) & element(B, the_carrier(A))) & element(C, the_carrier(A))) <=> ((~empty_carrier(A)) & reflexive_relstr(A) & rel_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))), ((((((~empty_carrier(A)) & reflexive_relstr(A)) & rel_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) <=> ((~empty_carrier(A)) & reflexive_relstr(A) & rel_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A))))), (((((((~empty_carrier(A)) & reflexive_relstr(A)) & rel_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => (related_reflexive(A, B, C) <=> related(A, B, C))) <=> (((~empty_carrier(A)) & reflexive_relstr(A) & rel_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A))) => (related_reflexive(A, B, C) <=> related(A, B, C))))), rewrite((((~empty_carrier(A)) & reflexive_relstr(A) & rel_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A))) => (related_reflexive(A, B, C) <=> related(A, B, C))) <=> ((~((~empty_carrier(A)) & reflexive_relstr(A) & rel_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (related_reflexive(A, B, C) <=> related(A, B, C)))), (((((((~empty_carrier(A)) & reflexive_relstr(A)) & rel_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => (related_reflexive(A, B, C) <=> related(A, B, C))) <=> ((~((~empty_carrier(A)) & reflexive_relstr(A) & rel_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (related_reflexive(A, B, C) <=> related(A, B, C)))))),
% 6.20/4.21 inference(bind,[status(th)],[])).
% 6.20/4.21 tff(317,plain,
% 6.20/4.21 (![A: $i, B: $i, C: $i] : ((((((~empty_carrier(A)) & reflexive_relstr(A)) & rel_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => (related_reflexive(A, B, C) <=> related(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & reflexive_relstr(A) & rel_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (related_reflexive(A, B, C) <=> related(A, B, C)))),
% 6.20/4.21 inference(quant_intro,[status(thm)],[316])).
% 6.20/4.21 tff(318,axiom,(![A: $i, B: $i, C: $i] : ((((((~empty_carrier(A)) & reflexive_relstr(A)) & rel_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => (related_reflexive(A, B, C) <=> related(A, B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_r3_orders_2')).
% 6.20/4.21 tff(319,plain,
% 6.20/4.21 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & reflexive_relstr(A) & rel_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (related_reflexive(A, B, C) <=> related(A, B, C)))),
% 6.20/4.21 inference(modus_ponens,[status(thm)],[318, 317])).
% 6.20/4.21 tff(320,plain,
% 6.20/4.21 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & reflexive_relstr(A) & rel_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (related_reflexive(A, B, C) <=> related(A, B, C)))),
% 6.20/4.21 inference(modus_ponens,[status(thm)],[319, 315])).
% 6.20/4.21 tff(321,plain,(
% 6.20/4.21 ![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & reflexive_relstr(A) & rel_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (related_reflexive(A, B, C) <=> related(A, B, C)))),
% 6.20/4.21 inference(skolemize,[status(sab)],[320])).
% 6.20/4.21 tff(322,plain,
% 6.20/4.21 (![A: $i, B: $i, C: $i] : ((related_reflexive(A, B, C) <=> related(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))),
% 6.20/4.21 inference(modus_ponens,[status(thm)],[321, 314])).
% 6.20/4.21 tff(323,plain,
% 6.20/4.21 (![A: $i, B: $i, C: $i] : ((related_reflexive(A, B, C) <=> related(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))),
% 6.20/4.21 inference(modus_ponens,[status(thm)],[322, 312])).
% 6.20/4.21 tff(324,plain,
% 6.20/4.21 (((~![A: $i, B: $i, C: $i] : ((related_reflexive(A, B, C) <=> related(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))) | (empty_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) | (~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~reflexive_relstr(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20))))) <=> ((~![A: $i, B: $i, C: $i] : ((related_reflexive(A, B, C) <=> related(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))) | empty_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) | (~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~reflexive_relstr(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20))))),
% 6.20/4.21 inference(rewrite,[status(thm)],[])).
% 6.20/4.21 tff(325,plain,
% 6.20/4.21 (((related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20))) | empty_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~reflexive_relstr(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) <=> (empty_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) | (~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~reflexive_relstr(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20))))),
% 6.20/4.21 inference(rewrite,[status(thm)],[])).
% 6.20/4.21 tff(326,plain,
% 6.20/4.21 (((~![A: $i, B: $i, C: $i] : ((related_reflexive(A, B, C) <=> related(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))) | ((related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20))) | empty_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~reflexive_relstr(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))) <=> ((~![A: $i, B: $i, C: $i] : ((related_reflexive(A, B, C) <=> related(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))) | (empty_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) | (~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~reflexive_relstr(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)))))),
% 6.20/4.22 inference(monotonicity,[status(thm)],[325])).
% 6.20/4.22 tff(327,plain,
% 6.20/4.22 (((~![A: $i, B: $i, C: $i] : ((related_reflexive(A, B, C) <=> related(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))) | ((related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20))) | empty_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~reflexive_relstr(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))) <=> ((~![A: $i, B: $i, C: $i] : ((related_reflexive(A, B, C) <=> related(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))) | empty_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) | (~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~reflexive_relstr(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20))))),
% 6.20/4.22 inference(transitivity,[status(thm)],[326, 324])).
% 6.20/4.22 tff(328,plain,
% 6.20/4.22 ((~![A: $i, B: $i, C: $i] : ((related_reflexive(A, B, C) <=> related(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))) | ((related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20))) | empty_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~reflexive_relstr(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))),
% 6.20/4.22 inference(quant_inst,[status(thm)],[])).
% 6.20/4.22 tff(329,plain,
% 6.20/4.22 ((~![A: $i, B: $i, C: $i] : ((related_reflexive(A, B, C) <=> related(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))) | empty_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) | (~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~reflexive_relstr(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.20/4.22 inference(modus_ponens,[status(thm)],[328, 327])).
% 6.20/4.22 tff(330,plain,
% 6.20/4.22 (related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20))),
% 6.20/4.22 inference(unit_resolution,[status(thm)],[329, 323, 310, 101, 284, 234, 270])).
% 6.20/4.22 tff(331,plain,
% 6.20/4.22 ((related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), A!19))) | (~related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.20/4.22 inference(tautology,[status(thm)],[])).
% 6.20/4.22 tff(332,plain,
% 6.20/4.22 (~related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20))),
% 6.20/4.22 inference(unit_resolution,[status(thm)],[331, 268])).
% 6.20/4.22 tff(333,plain,
% 6.20/4.22 ((~(related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)))) | (~related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20))),
% 6.20/4.22 inference(tautology,[status(thm)],[])).
% 6.20/4.22 tff(334,plain,
% 6.20/4.22 ((~(related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)))) | (~related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.20/4.22 inference(unit_resolution,[status(thm)],[333, 332])).
% 6.20/4.22 tff(335,plain,
% 6.20/4.22 (~related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20))),
% 6.20/4.22 inference(unit_resolution,[status(thm)],[334, 330])).
% 6.20/4.22 tff(336,plain,
% 6.20/4.22 (~related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.20/4.22 inference(modus_ponens,[status(thm)],[335, 279])).
% 6.20/4.22 tff(337,plain,
% 6.20/4.22 (^[A: $i] : rewrite((empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))))))),
% 6.20/4.22 inference(bind,[status(th)],[])).
% 6.20/4.22 tff(338,plain,
% 6.20/4.22 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))),
% 6.20/4.22 inference(quant_intro,[status(thm)],[337])).
% 6.20/4.22 tff(339,plain,
% 6.20/4.22 (^[A: $i] : refl((empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A))))),
% 6.20/4.22 inference(bind,[status(th)],[])).
% 6.20/4.22 tff(340,plain,
% 6.20/4.22 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A)))),
% 6.20/4.22 inference(quant_intro,[status(thm)],[339])).
% 6.20/4.22 tff(341,plain,
% 6.20/4.22 (^[A: $i] : rewrite((empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A))))),
% 6.20/4.22 inference(bind,[status(th)],[])).
% 6.20/4.22 tff(342,plain,
% 6.20/4.22 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A)))),
% 6.20/4.22 inference(quant_intro,[status(thm)],[341])).
% 6.20/4.22 tff(343,plain,
% 6.20/4.22 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A)))),
% 6.20/4.22 inference(transitivity,[status(thm)],[342, 340])).
% 6.20/4.22 tff(344,plain,
% 6.20/4.22 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & lattice(A) & latt_str(A)) <=> (~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))), ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) <=> (~(~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))))), rewrite((~(~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)))), ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))), (((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))))) <=> ((empty_carrier(A) | (~latt_str(A)) | (~lattice(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))))))), rewrite(((empty_carrier(A) | (~latt_str(A)) | (~lattice(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A)))), (((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A)))))),
% 6.20/4.22 inference(bind,[status(th)],[])).
% 6.20/4.22 tff(345,plain,
% 6.20/4.22 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A)))),
% 6.20/4.22 inference(quant_intro,[status(thm)],[344])).
% 6.20/4.22 tff(346,plain,
% 6.20/4.22 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))),
% 6.20/4.22 inference(rewrite,[status(thm)],[])).
% 6.20/4.22 tff(347,plain,
% 6.20/4.22 (^[A: $i] : trans(monotonicity(rewrite((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) <=> ((~empty_carrier(A)) & lattice(A) & latt_str(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((element(C, the_carrier(A)) => (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))) <=> ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))))), (![C: $i] : (element(C, the_carrier(A)) => (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))) <=> ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))))), ((element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) <=> (element(B, the_carrier(A)) => ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))), rewrite((element(B, the_carrier(A)) => ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))))), ((element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))))))), (![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))))) <=> (((~empty_carrier(A)) & lattice(A) & latt_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))))))), rewrite((((~empty_carrier(A)) & lattice(A) & latt_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))))),
% 6.20/4.22 inference(bind,[status(th)],[])).
% 6.20/4.22 tff(348,plain,
% 6.20/4.22 (![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))),
% 6.20/4.22 inference(quant_intro,[status(thm)],[347])).
% 6.20/4.22 tff(349,axiom,(![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t7_lattice3')).
% 6.20/4.22 tff(350,plain,
% 6.20/4.22 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))),
% 6.20/4.22 inference(modus_ponens,[status(thm)],[349, 348])).
% 6.20/4.22 tff(351,plain,
% 6.20/4.22 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))),
% 6.25/4.22 inference(modus_ponens,[status(thm)],[350, 346])).
% 6.25/4.22 tff(352,plain,(
% 6.25/4.22 ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))),
% 6.25/4.22 inference(skolemize,[status(sab)],[351])).
% 6.25/4.22 tff(353,plain,
% 6.25/4.22 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A)))),
% 6.25/4.22 inference(modus_ponens,[status(thm)],[352, 345])).
% 6.25/4.22 tff(354,plain,
% 6.25/4.22 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A)))),
% 6.25/4.22 inference(modus_ponens,[status(thm)],[353, 343])).
% 6.25/4.22 tff(355,plain,
% 6.25/4.22 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))),
% 6.25/4.22 inference(modus_ponens,[status(thm)],[354, 338])).
% 6.25/4.22 tff(356,plain,
% 6.25/4.22 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))) | (empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | ![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, B, C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, B), cast_to_el_of_LattPOSet(B!18, C))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | ![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, B, C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, B), cast_to_el_of_LattPOSet(B!18, C))))))),
% 6.25/4.22 inference(rewrite,[status(thm)],[])).
% 6.25/4.22 tff(357,plain,
% 6.25/4.22 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))) | (empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | ![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, B, C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, B), cast_to_el_of_LattPOSet(B!18, C))))))),
% 6.25/4.22 inference(quant_inst,[status(thm)],[])).
% 6.25/4.22 tff(358,plain,
% 6.25/4.22 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | ![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, B, C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, B), cast_to_el_of_LattPOSet(B!18, C)))))),
% 6.25/4.22 inference(modus_ponens,[status(thm)],[357, 356])).
% 6.25/4.22 tff(359,plain,
% 6.25/4.22 (![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, B, C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, B), cast_to_el_of_LattPOSet(B!18, C)))))),
% 6.25/4.22 inference(unit_resolution,[status(thm)],[358, 18, 17, 16, 355])).
% 6.25/4.22 tff(360,plain,
% 6.25/4.22 (((~![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, B, C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, B), cast_to_el_of_LattPOSet(B!18, C)))))) | ((~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(B!18))) | ![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))), cast_to_el_of_LattPOSet(B!18, C)))))) <=> ((~![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, B, C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, B), cast_to_el_of_LattPOSet(B!18, C)))))) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(B!18))) | ![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))), cast_to_el_of_LattPOSet(B!18, C)))))),
% 6.25/4.22 inference(rewrite,[status(thm)],[])).
% 6.25/4.22 tff(361,plain,
% 6.25/4.22 ((~![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, B, C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, B), cast_to_el_of_LattPOSet(B!18, C)))))) | ((~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(B!18))) | ![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))), cast_to_el_of_LattPOSet(B!18, C)))))),
% 6.25/4.22 inference(quant_inst,[status(thm)],[])).
% 6.25/4.22 tff(362,plain,
% 6.25/4.22 ((~![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, B, C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, B), cast_to_el_of_LattPOSet(B!18, C)))))) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(B!18))) | ![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))), cast_to_el_of_LattPOSet(B!18, C))))),
% 6.25/4.22 inference(modus_ponens,[status(thm)],[361, 360])).
% 6.25/4.22 tff(363,plain,
% 6.25/4.22 ((~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(B!18))) | ![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))), cast_to_el_of_LattPOSet(B!18, C))))),
% 6.25/4.22 inference(unit_resolution,[status(thm)],[362, 359])).
% 6.25/4.22 tff(364,plain,
% 6.25/4.22 (![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))), cast_to_el_of_LattPOSet(B!18, C))))),
% 6.25/4.22 inference(unit_resolution,[status(thm)],[363, 271])).
% 6.25/4.22 tff(365,plain,
% 6.25/4.22 (^[A: $i] : rewrite((empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B))))),
% 6.25/4.22 inference(bind,[status(th)],[])).
% 6.25/4.22 tff(366,plain,
% 6.25/4.22 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)))),
% 6.25/4.22 inference(quant_intro,[status(thm)],[365])).
% 6.25/4.22 tff(367,plain,
% 6.25/4.22 (^[A: $i] : refl((empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A))))),
% 6.25/4.22 inference(bind,[status(th)],[])).
% 6.25/4.22 tff(368,plain,
% 6.25/4.22 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A)))),
% 6.25/4.22 inference(quant_intro,[status(thm)],[367])).
% 6.25/4.22 tff(369,plain,
% 6.25/4.22 (^[A: $i] : rewrite((empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A))))),
% 6.25/4.22 inference(bind,[status(th)],[])).
% 6.25/4.22 tff(370,plain,
% 6.25/4.22 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A)))),
% 6.25/4.22 inference(quant_intro,[status(thm)],[369])).
% 6.25/4.22 tff(371,plain,
% 6.25/4.22 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A)))),
% 6.25/4.22 inference(transitivity,[status(thm)],[370, 368])).
% 6.25/4.22 tff(372,plain,
% 6.25/4.22 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & lattice(A) & latt_str(A)) <=> (~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))), ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) <=> (~(~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))))), rewrite((~(~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)))), ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))), (((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B))) <=> ((empty_carrier(A) | (~latt_str(A)) | (~lattice(A))) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B))))), rewrite(((empty_carrier(A) | (~latt_str(A)) | (~lattice(A))) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A)))), (((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A)))))),
% 6.25/4.22 inference(bind,[status(th)],[])).
% 6.25/4.22 tff(373,plain,
% 6.25/4.22 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A)))),
% 6.25/4.22 inference(quant_intro,[status(thm)],[372])).
% 6.25/4.22 tff(374,plain,
% 6.25/4.22 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B))) <=> ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)))),
% 6.25/4.22 inference(rewrite,[status(thm)],[])).
% 6.25/4.22 tff(375,plain,
% 6.25/4.22 (^[A: $i] : trans(monotonicity(rewrite((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) <=> ((~empty_carrier(A)) & lattice(A) & latt_str(A))), quant_intro(proof_bind(^[B: $i] : rewrite((element(B, the_carrier(poset_of_lattice(A))) => (cast_to_el_of_lattice(A, B) = B)) <=> ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)))), (![B: $i] : (element(B, the_carrier(poset_of_lattice(A))) => (cast_to_el_of_lattice(A, B) = B)) <=> ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(poset_of_lattice(A))) => (cast_to_el_of_lattice(A, B) = B))) <=> (((~empty_carrier(A)) & lattice(A) & latt_str(A)) => ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B))))), rewrite((((~empty_carrier(A)) & lattice(A) & latt_str(A)) => ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(poset_of_lattice(A))) => (cast_to_el_of_lattice(A, B) = B))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)))))),
% 6.25/4.22 inference(bind,[status(th)],[])).
% 6.25/4.22 tff(376,plain,
% 6.25/4.22 (![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(poset_of_lattice(A))) => (cast_to_el_of_lattice(A, B) = B))) <=> ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)))),
% 6.25/4.22 inference(quant_intro,[status(thm)],[375])).
% 6.25/4.22 tff(377,axiom,(![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(poset_of_lattice(A))) => (cast_to_el_of_lattice(A, B) = B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_lattice3')).
% 6.25/4.22 tff(378,plain,
% 6.25/4.22 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)))),
% 6.25/4.22 inference(modus_ponens,[status(thm)],[377, 376])).
% 6.25/4.22 tff(379,plain,
% 6.25/4.22 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)))),
% 6.25/4.22 inference(modus_ponens,[status(thm)],[378, 374])).
% 6.25/4.22 tff(380,plain,(
% 6.25/4.22 ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)))),
% 6.25/4.22 inference(skolemize,[status(sab)],[379])).
% 6.25/4.22 tff(381,plain,
% 6.25/4.22 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A)))),
% 6.25/4.22 inference(modus_ponens,[status(thm)],[380, 373])).
% 6.25/4.22 tff(382,plain,
% 6.25/4.22 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A)))),
% 6.25/4.22 inference(modus_ponens,[status(thm)],[381, 371])).
% 6.25/4.22 tff(383,plain,
% 6.25/4.22 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)))),
% 6.25/4.22 inference(modus_ponens,[status(thm)],[382, 366])).
% 6.25/4.22 tff(384,plain,
% 6.25/4.22 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)))) | (empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(B!18)))) | (cast_to_el_of_lattice(B!18, B) = B)))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(B!18)))) | (cast_to_el_of_lattice(B!18, B) = B)))),
% 6.25/4.22 inference(rewrite,[status(thm)],[])).
% 6.25/4.22 tff(385,plain,
% 6.25/4.22 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)))) | (empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(B!18)))) | (cast_to_el_of_lattice(B!18, B) = B)))),
% 6.25/4.22 inference(quant_inst,[status(thm)],[])).
% 6.25/4.22 tff(386,plain,
% 6.25/4.22 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(B!18)))) | (cast_to_el_of_lattice(B!18, B) = B))),
% 6.25/4.22 inference(modus_ponens,[status(thm)],[385, 384])).
% 6.25/4.22 tff(387,plain,
% 6.25/4.22 (![B: $i] : ((~element(B, the_carrier(poset_of_lattice(B!18)))) | (cast_to_el_of_lattice(B!18, B) = B))),
% 6.25/4.22 inference(unit_resolution,[status(thm)],[386, 383, 18, 17, 16])).
% 6.25/4.22 tff(388,plain,
% 6.25/4.22 (((~![B: $i] : ((~element(B, the_carrier(poset_of_lattice(B!18)))) | (cast_to_el_of_lattice(B!18, B) = B))) | ((~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18)))) | (cast_to_el_of_lattice(B!18, cast_to_el_of_LattPOSet(B!18, C!20)) = cast_to_el_of_LattPOSet(B!18, C!20)))) <=> ((~![B: $i] : ((~element(B, the_carrier(poset_of_lattice(B!18)))) | (cast_to_el_of_lattice(B!18, B) = B))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18)))) | (cast_to_el_of_lattice(B!18, cast_to_el_of_LattPOSet(B!18, C!20)) = cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.25/4.22 inference(rewrite,[status(thm)],[])).
% 6.25/4.22 tff(389,plain,
% 6.25/4.22 ((~![B: $i] : ((~element(B, the_carrier(poset_of_lattice(B!18)))) | (cast_to_el_of_lattice(B!18, B) = B))) | ((~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18)))) | (cast_to_el_of_lattice(B!18, cast_to_el_of_LattPOSet(B!18, C!20)) = cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.25/4.22 inference(quant_inst,[status(thm)],[])).
% 6.25/4.22 tff(390,plain,
% 6.25/4.22 ((~![B: $i] : ((~element(B, the_carrier(poset_of_lattice(B!18)))) | (cast_to_el_of_lattice(B!18, B) = B))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18)))) | (cast_to_el_of_lattice(B!18, cast_to_el_of_LattPOSet(B!18, C!20)) = cast_to_el_of_LattPOSet(B!18, C!20))),
% 6.25/4.22 inference(modus_ponens,[status(thm)],[389, 388])).
% 6.25/4.22 tff(391,plain,
% 6.25/4.22 (cast_to_el_of_lattice(B!18, cast_to_el_of_LattPOSet(B!18, C!20)) = cast_to_el_of_LattPOSet(B!18, C!20)),
% 6.25/4.22 inference(unit_resolution,[status(thm)],[390, 387, 233])).
% 6.25/4.22 tff(392,plain,
% 6.25/4.22 (cast_to_el_of_LattPOSet(B!18, C!20) = cast_to_el_of_lattice(B!18, cast_to_el_of_LattPOSet(B!18, C!20))),
% 6.25/4.22 inference(symmetry,[status(thm)],[391])).
% 6.25/4.22 tff(393,plain,
% 6.25/4.22 (element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18)) <=> element(cast_to_el_of_lattice(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), the_carrier(B!18))),
% 6.25/4.22 inference(monotonicity,[status(thm)],[392])).
% 6.25/4.22 tff(394,plain,
% 6.25/4.22 (element(cast_to_el_of_lattice(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), the_carrier(B!18)) <=> element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))),
% 6.25/4.22 inference(symmetry,[status(thm)],[393])).
% 6.25/4.22 tff(395,plain,
% 6.25/4.22 (^[A: $i, B: $i] : refl((empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A))) <=> (empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A))))),
% 6.25/4.22 inference(bind,[status(th)],[])).
% 6.25/4.22 tff(396,plain,
% 6.25/4.22 (![A: $i, B: $i] : (empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A))) <=> ![A: $i, B: $i] : (empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A)))),
% 6.25/4.22 inference(quant_intro,[status(thm)],[395])).
% 6.25/4.22 tff(397,plain,
% 6.25/4.22 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A)))) <=> (~(empty_carrier(A) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A))))), ((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A))))) <=> (~(~(empty_carrier(A) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A))))))), rewrite((~(~(empty_carrier(A) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A))))) <=> (empty_carrier(A) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A)))), ((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A))))) <=> (empty_carrier(A) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A))))), (((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A))))) | element(cast_to_el_of_lattice(A, B), the_carrier(A))) <=> ((empty_carrier(A) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A))) | element(cast_to_el_of_lattice(A, B), the_carrier(A))))), rewrite(((empty_carrier(A) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A))) | element(cast_to_el_of_lattice(A, B), the_carrier(A))) <=> (empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A)))), (((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A))))) | element(cast_to_el_of_lattice(A, B), the_carrier(A))) <=> (empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A)))))),
% 6.25/4.22 inference(bind,[status(th)],[])).
% 6.25/4.22 tff(398,plain,
% 6.25/4.22 (![A: $i, B: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A))))) | element(cast_to_el_of_lattice(A, B), the_carrier(A))) <=> ![A: $i, B: $i] : (empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A)))),
% 6.25/4.22 inference(quant_intro,[status(thm)],[397])).
% 6.25/4.22 tff(399,plain,
% 6.25/4.22 (![A: $i, B: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A))))) | element(cast_to_el_of_lattice(A, B), the_carrier(A))) <=> ![A: $i, B: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A))))) | element(cast_to_el_of_lattice(A, B), the_carrier(A)))),
% 6.25/4.22 inference(rewrite,[status(thm)],[])).
% 6.25/4.22 tff(400,plain,
% 6.25/4.22 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) <=> ((~empty_carrier(A)) & lattice(A) & latt_str(A))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) & element(B, the_carrier(poset_of_lattice(A)))) <=> (((~empty_carrier(A)) & lattice(A) & latt_str(A)) & element(B, the_carrier(poset_of_lattice(A)))))), rewrite((((~empty_carrier(A)) & lattice(A) & latt_str(A)) & element(B, the_carrier(poset_of_lattice(A)))) <=> ((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A))))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) & element(B, the_carrier(poset_of_lattice(A)))) <=> ((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A)))))), ((((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) & element(B, the_carrier(poset_of_lattice(A)))) => element(cast_to_el_of_lattice(A, B), the_carrier(A))) <=> (((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A)))) => element(cast_to_el_of_lattice(A, B), the_carrier(A))))), rewrite((((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A)))) => element(cast_to_el_of_lattice(A, B), the_carrier(A))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A))))) | element(cast_to_el_of_lattice(A, B), the_carrier(A)))), ((((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) & element(B, the_carrier(poset_of_lattice(A)))) => element(cast_to_el_of_lattice(A, B), the_carrier(A))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A))))) | element(cast_to_el_of_lattice(A, B), the_carrier(A)))))),
% 6.25/4.23 inference(bind,[status(th)],[])).
% 6.25/4.23 tff(401,plain,
% 6.25/4.23 (![A: $i, B: $i] : (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) & element(B, the_carrier(poset_of_lattice(A)))) => element(cast_to_el_of_lattice(A, B), the_carrier(A))) <=> ![A: $i, B: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A))))) | element(cast_to_el_of_lattice(A, B), the_carrier(A)))),
% 6.25/4.23 inference(quant_intro,[status(thm)],[400])).
% 6.25/4.23 tff(402,axiom,(![A: $i, B: $i] : (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) & element(B, the_carrier(poset_of_lattice(A)))) => element(cast_to_el_of_lattice(A, B), the_carrier(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k5_lattice3')).
% 6.25/4.23 tff(403,plain,
% 6.25/4.23 (![A: $i, B: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A))))) | element(cast_to_el_of_lattice(A, B), the_carrier(A)))),
% 6.25/4.23 inference(modus_ponens,[status(thm)],[402, 401])).
% 6.25/4.23 tff(404,plain,
% 6.25/4.23 (![A: $i, B: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A))))) | element(cast_to_el_of_lattice(A, B), the_carrier(A)))),
% 6.25/4.23 inference(modus_ponens,[status(thm)],[403, 399])).
% 6.25/4.23 tff(405,plain,(
% 6.25/4.23 ![A: $i, B: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A))))) | element(cast_to_el_of_lattice(A, B), the_carrier(A)))),
% 6.25/4.23 inference(skolemize,[status(sab)],[404])).
% 6.25/4.23 tff(406,plain,
% 6.25/4.23 (![A: $i, B: $i] : (empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A)))),
% 6.25/4.23 inference(modus_ponens,[status(thm)],[405, 398])).
% 6.25/4.23 tff(407,plain,
% 6.25/4.23 (![A: $i, B: $i] : (empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A)))),
% 6.25/4.23 inference(modus_ponens,[status(thm)],[406, 396])).
% 6.25/4.23 tff(408,plain,
% 6.25/4.23 (((~![A: $i, B: $i] : (empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A)))) | (empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18)))) | element(cast_to_el_of_lattice(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), the_carrier(B!18)))) <=> ((~![A: $i, B: $i] : (empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A)))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18)))) | element(cast_to_el_of_lattice(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), the_carrier(B!18)))),
% 6.25/4.23 inference(rewrite,[status(thm)],[])).
% 6.25/4.23 tff(409,plain,
% 6.25/4.23 ((empty_carrier(B!18) | element(cast_to_el_of_lattice(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), the_carrier(B!18)) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18)))) | (~lattice(B!18)) | (~latt_str(B!18))) <=> (empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18)))) | element(cast_to_el_of_lattice(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), the_carrier(B!18)))),
% 6.25/4.23 inference(rewrite,[status(thm)],[])).
% 6.25/4.23 tff(410,plain,
% 6.25/4.23 (((~![A: $i, B: $i] : (empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A)))) | (empty_carrier(B!18) | element(cast_to_el_of_lattice(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), the_carrier(B!18)) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18)))) | (~lattice(B!18)) | (~latt_str(B!18)))) <=> ((~![A: $i, B: $i] : (empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A)))) | (empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18)))) | element(cast_to_el_of_lattice(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), the_carrier(B!18))))),
% 6.25/4.23 inference(monotonicity,[status(thm)],[409])).
% 6.25/4.23 tff(411,plain,
% 6.25/4.23 (((~![A: $i, B: $i] : (empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A)))) | (empty_carrier(B!18) | element(cast_to_el_of_lattice(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), the_carrier(B!18)) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18)))) | (~lattice(B!18)) | (~latt_str(B!18)))) <=> ((~![A: $i, B: $i] : (empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A)))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18)))) | element(cast_to_el_of_lattice(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), the_carrier(B!18)))),
% 6.25/4.23 inference(transitivity,[status(thm)],[410, 408])).
% 6.25/4.23 tff(412,plain,
% 6.25/4.23 ((~![A: $i, B: $i] : (empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A)))) | (empty_carrier(B!18) | element(cast_to_el_of_lattice(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), the_carrier(B!18)) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18)))) | (~lattice(B!18)) | (~latt_str(B!18)))),
% 6.25/4.23 inference(quant_inst,[status(thm)],[])).
% 6.25/4.23 tff(413,plain,
% 6.25/4.23 ((~![A: $i, B: $i] : (empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A)))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18)))) | element(cast_to_el_of_lattice(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), the_carrier(B!18))),
% 6.25/4.23 inference(modus_ponens,[status(thm)],[412, 411])).
% 6.25/4.23 tff(414,plain,
% 6.25/4.23 (element(cast_to_el_of_lattice(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), the_carrier(B!18))),
% 6.25/4.23 inference(unit_resolution,[status(thm)],[413, 407, 18, 17, 16, 233])).
% 6.25/4.23 tff(415,plain,
% 6.25/4.23 (element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))),
% 6.25/4.23 inference(modus_ponens,[status(thm)],[414, 394])).
% 6.25/4.23 tff(416,plain,
% 6.25/4.23 (((~![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))), cast_to_el_of_LattPOSet(B!18, C))))) | ((~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)))))) <=> ((~![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))), cast_to_el_of_LattPOSet(B!18, C))))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)))))),
% 6.25/4.23 inference(rewrite,[status(thm)],[])).
% 6.25/4.23 tff(417,plain,
% 6.25/4.23 ((~![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))), cast_to_el_of_LattPOSet(B!18, C))))) | ((~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)))))),
% 6.25/4.23 inference(quant_inst,[status(thm)],[])).
% 6.25/4.23 tff(418,plain,
% 6.25/4.23 ((~![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))), cast_to_el_of_LattPOSet(B!18, C))))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20))))),
% 6.25/4.23 inference(modus_ponens,[status(thm)],[417, 416])).
% 6.25/4.23 tff(419,plain,
% 6.25/4.23 (below_refl(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.25/4.23 inference(unit_resolution,[status(thm)],[418, 415, 364])).
% 6.25/4.23 tff(420,plain,
% 6.25/4.23 (^[A: $i] : refl((empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~join_commutative(A)) | (~join_associative(A)) | (~meet_commutative(A)) | (~meet_associative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)))) | (~lattice(A))) <=> (empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~join_commutative(A)) | (~join_associative(A)) | (~meet_commutative(A)) | (~meet_associative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)))) | (~lattice(A))))),
% 6.25/4.23 inference(bind,[status(th)],[])).
% 6.25/4.23 tff(421,plain,
% 6.25/4.23 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~join_commutative(A)) | (~join_associative(A)) | (~meet_commutative(A)) | (~meet_associative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)))) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~join_commutative(A)) | (~join_associative(A)) | (~meet_commutative(A)) | (~meet_associative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)))) | (~lattice(A)))),
% 6.25/4.23 inference(quant_intro,[status(thm)],[420])).
% 6.25/4.23 tff(422,plain,
% 6.25/4.23 (^[A: $i] : trans(monotonicity(rewrite(((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)) <=> (~(empty_carrier(A) | (~join_commutative(A)) | (~join_associative(A)) | (~meet_commutative(A)) | (~meet_associative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A))))), trans(monotonicity(rewrite(((~empty_carrier(A)) & lattice(A)) <=> (~(empty_carrier(A) | (~lattice(A))))), ((~((~empty_carrier(A)) & lattice(A))) <=> (~(~(empty_carrier(A) | (~lattice(A))))))), rewrite((~(~(empty_carrier(A) | (~lattice(A))))) <=> (empty_carrier(A) | (~lattice(A)))), ((~((~empty_carrier(A)) & lattice(A))) <=> (empty_carrier(A) | (~lattice(A))))), ((((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)) | (~((~empty_carrier(A)) & lattice(A))) | (~latt_str(A))) <=> ((~(empty_carrier(A) | (~join_commutative(A)) | (~join_associative(A)) | (~meet_commutative(A)) | (~meet_associative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)))) | (empty_carrier(A) | (~lattice(A))) | (~latt_str(A))))), rewrite(((~(empty_carrier(A) | (~join_commutative(A)) | (~join_associative(A)) | (~meet_commutative(A)) | (~meet_associative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)))) | (empty_carrier(A) | (~lattice(A))) | (~latt_str(A))) <=> (empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~join_commutative(A)) | (~join_associative(A)) | (~meet_commutative(A)) | (~meet_associative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)))) | (~lattice(A)))), ((((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)) | (~((~empty_carrier(A)) & lattice(A))) | (~latt_str(A))) <=> (empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~join_commutative(A)) | (~join_associative(A)) | (~meet_commutative(A)) | (~meet_associative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)))) | (~lattice(A)))))),
% 6.25/4.23 inference(bind,[status(th)],[])).
% 6.25/4.23 tff(423,plain,
% 6.25/4.23 (![A: $i] : (((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)) | (~((~empty_carrier(A)) & lattice(A))) | (~latt_str(A))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~join_commutative(A)) | (~join_associative(A)) | (~meet_commutative(A)) | (~meet_associative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)))) | (~lattice(A)))),
% 6.25/4.23 inference(quant_intro,[status(thm)],[422])).
% 6.25/4.23 tff(424,plain,
% 6.25/4.23 (![A: $i] : (((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)) | (~((~empty_carrier(A)) & lattice(A))) | (~latt_str(A))) <=> ![A: $i] : (((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)) | (~((~empty_carrier(A)) & lattice(A))) | (~latt_str(A)))),
% 6.25/4.23 inference(rewrite,[status(thm)],[])).
% 6.25/4.23 tff(425,plain,
% 6.25/4.23 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~empty_carrier(A)) & join_commutative(A)) & join_associative(A)) <=> ((~empty_carrier(A)) & join_commutative(A) & join_associative(A))), (((((~empty_carrier(A)) & join_commutative(A)) & join_associative(A)) & meet_commutative(A)) <=> (((~empty_carrier(A)) & join_commutative(A) & join_associative(A)) & meet_commutative(A)))), rewrite((((~empty_carrier(A)) & join_commutative(A) & join_associative(A)) & meet_commutative(A)) <=> ((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A))), (((((~empty_carrier(A)) & join_commutative(A)) & join_associative(A)) & meet_commutative(A)) <=> ((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A)))), ((((((~empty_carrier(A)) & join_commutative(A)) & join_associative(A)) & meet_commutative(A)) & meet_associative(A)) <=> (((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A)) & meet_associative(A)))), rewrite((((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A)) & meet_associative(A)) <=> ((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A))), ((((((~empty_carrier(A)) & join_commutative(A)) & join_associative(A)) & meet_commutative(A)) & meet_associative(A)) <=> ((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A)))), (((((((~empty_carrier(A)) & join_commutative(A)) & join_associative(A)) & meet_commutative(A)) & meet_associative(A)) & meet_absorbing(A)) <=> (((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A)) & meet_absorbing(A)))), rewrite((((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A)) & meet_absorbing(A)) <=> ((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A))), (((((((~empty_carrier(A)) & join_commutative(A)) & join_associative(A)) & meet_commutative(A)) & meet_associative(A)) & meet_absorbing(A)) <=> ((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A)))), ((((((((~empty_carrier(A)) & join_commutative(A)) & join_associative(A)) & meet_commutative(A)) & meet_associative(A)) & meet_absorbing(A)) & join_absorbing(A)) <=> (((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A)) & join_absorbing(A)))), rewrite((((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A)) & join_absorbing(A)) <=> ((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A))), ((((((((~empty_carrier(A)) & join_commutative(A)) & join_associative(A)) & meet_commutative(A)) & meet_associative(A)) & meet_absorbing(A)) & join_absorbing(A)) <=> ((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)))), ((((~empty_carrier(A)) & lattice(A)) => (((((((~empty_carrier(A)) & join_commutative(A)) & join_associative(A)) & meet_commutative(A)) & meet_associative(A)) & meet_absorbing(A)) & join_absorbing(A))) <=> (((~empty_carrier(A)) & lattice(A)) => ((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A))))), rewrite((((~empty_carrier(A)) & lattice(A)) => ((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A))) <=> ((~((~empty_carrier(A)) & lattice(A))) | ((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)))), ((((~empty_carrier(A)) & lattice(A)) => (((((((~empty_carrier(A)) & join_commutative(A)) & join_associative(A)) & meet_commutative(A)) & meet_associative(A)) & meet_absorbing(A)) & join_absorbing(A))) <=> ((~((~empty_carrier(A)) & lattice(A))) | ((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A))))), ((latt_str(A) => (((~empty_carrier(A)) & lattice(A)) => (((((((~empty_carrier(A)) & join_commutative(A)) & join_associative(A)) & meet_commutative(A)) & meet_associative(A)) & meet_absorbing(A)) & join_absorbing(A)))) <=> (latt_str(A) => ((~((~empty_carrier(A)) & lattice(A))) | ((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)))))), rewrite((latt_str(A) => ((~((~empty_carrier(A)) & lattice(A))) | ((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)))) <=> (((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)) | (~((~empty_carrier(A)) & lattice(A))) | (~latt_str(A)))), ((latt_str(A) => (((~empty_carrier(A)) & lattice(A)) => (((((((~empty_carrier(A)) & join_commutative(A)) & join_associative(A)) & meet_commutative(A)) & meet_associative(A)) & meet_absorbing(A)) & join_absorbing(A)))) <=> (((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)) | (~((~empty_carrier(A)) & lattice(A))) | (~latt_str(A)))))),
% 6.25/4.23 inference(bind,[status(th)],[])).
% 6.25/4.23 tff(426,plain,
% 6.25/4.23 (![A: $i] : (latt_str(A) => (((~empty_carrier(A)) & lattice(A)) => (((((((~empty_carrier(A)) & join_commutative(A)) & join_associative(A)) & meet_commutative(A)) & meet_associative(A)) & meet_absorbing(A)) & join_absorbing(A)))) <=> ![A: $i] : (((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)) | (~((~empty_carrier(A)) & lattice(A))) | (~latt_str(A)))),
% 6.25/4.23 inference(quant_intro,[status(thm)],[425])).
% 6.25/4.23 tff(427,axiom,(![A: $i] : (latt_str(A) => (((~empty_carrier(A)) & lattice(A)) => (((((((~empty_carrier(A)) & join_commutative(A)) & join_associative(A)) & meet_commutative(A)) & meet_associative(A)) & meet_absorbing(A)) & join_absorbing(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc1_lattices')).
% 6.25/4.23 tff(428,plain,
% 6.25/4.23 (![A: $i] : (((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)) | (~((~empty_carrier(A)) & lattice(A))) | (~latt_str(A)))),
% 6.25/4.23 inference(modus_ponens,[status(thm)],[427, 426])).
% 6.25/4.23 tff(429,plain,
% 6.25/4.23 (![A: $i] : (((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)) | (~((~empty_carrier(A)) & lattice(A))) | (~latt_str(A)))),
% 6.25/4.23 inference(modus_ponens,[status(thm)],[428, 424])).
% 6.25/4.23 tff(430,plain,(
% 6.25/4.23 ![A: $i] : (((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)) | (~((~empty_carrier(A)) & lattice(A))) | (~latt_str(A)))),
% 6.25/4.23 inference(skolemize,[status(sab)],[429])).
% 6.25/4.23 tff(431,plain,
% 6.25/4.23 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~join_commutative(A)) | (~join_associative(A)) | (~meet_commutative(A)) | (~meet_associative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)))) | (~lattice(A)))),
% 6.25/4.23 inference(modus_ponens,[status(thm)],[430, 423])).
% 6.25/4.23 tff(432,plain,
% 6.25/4.23 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~join_commutative(A)) | (~join_associative(A)) | (~meet_commutative(A)) | (~meet_associative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)))) | (~lattice(A)))),
% 6.25/4.23 inference(modus_ponens,[status(thm)],[431, 421])).
% 6.25/4.23 tff(433,plain,
% 6.25/4.23 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~join_commutative(A)) | (~join_associative(A)) | (~meet_commutative(A)) | (~meet_associative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)))) | (~lattice(A)))) | (empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (~(empty_carrier(B!18) | (~join_commutative(B!18)) | (~join_associative(B!18)) | (~meet_commutative(B!18)) | (~meet_associative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)))))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~join_commutative(A)) | (~join_associative(A)) | (~meet_commutative(A)) | (~meet_associative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)))) | (~lattice(A)))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (~(empty_carrier(B!18) | (~join_commutative(B!18)) | (~join_associative(B!18)) | (~meet_commutative(B!18)) | (~meet_associative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)))))),
% 6.25/4.23 inference(rewrite,[status(thm)],[])).
% 6.25/4.23 tff(434,plain,
% 6.25/4.23 ((empty_carrier(B!18) | (~latt_str(B!18)) | (~(empty_carrier(B!18) | (~join_commutative(B!18)) | (~join_associative(B!18)) | (~meet_commutative(B!18)) | (~meet_associative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)))) | (~lattice(B!18))) <=> (empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (~(empty_carrier(B!18) | (~join_commutative(B!18)) | (~join_associative(B!18)) | (~meet_commutative(B!18)) | (~meet_associative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)))))),
% 6.25/4.23 inference(rewrite,[status(thm)],[])).
% 6.25/4.23 tff(435,plain,
% 6.25/4.23 ((~(empty_carrier(B!18) | (~join_commutative(B!18)) | (~join_associative(B!18)) | (~meet_commutative(B!18)) | (~meet_associative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)))) <=> (~(empty_carrier(B!18) | (~join_commutative(B!18)) | (~join_associative(B!18)) | (~meet_commutative(B!18)) | (~meet_associative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18))))),
% 6.25/4.23 inference(rewrite,[status(thm)],[])).
% 6.25/4.23 tff(436,plain,
% 6.25/4.23 ((empty_carrier(B!18) | (~latt_str(B!18)) | (~(empty_carrier(B!18) | (~join_commutative(B!18)) | (~join_associative(B!18)) | (~meet_commutative(B!18)) | (~meet_associative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)))) | (~lattice(B!18))) <=> (empty_carrier(B!18) | (~latt_str(B!18)) | (~(empty_carrier(B!18) | (~join_commutative(B!18)) | (~join_associative(B!18)) | (~meet_commutative(B!18)) | (~meet_associative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)))) | (~lattice(B!18)))),
% 6.25/4.23 inference(monotonicity,[status(thm)],[435])).
% 6.25/4.23 tff(437,plain,
% 6.25/4.23 ((empty_carrier(B!18) | (~latt_str(B!18)) | (~(empty_carrier(B!18) | (~join_commutative(B!18)) | (~join_associative(B!18)) | (~meet_commutative(B!18)) | (~meet_associative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)))) | (~lattice(B!18))) <=> (empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (~(empty_carrier(B!18) | (~join_commutative(B!18)) | (~join_associative(B!18)) | (~meet_commutative(B!18)) | (~meet_associative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)))))),
% 6.25/4.23 inference(transitivity,[status(thm)],[436, 434])).
% 6.25/4.23 tff(438,plain,
% 6.25/4.23 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~join_commutative(A)) | (~join_associative(A)) | (~meet_commutative(A)) | (~meet_associative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)))) | (~lattice(A)))) | (empty_carrier(B!18) | (~latt_str(B!18)) | (~(empty_carrier(B!18) | (~join_commutative(B!18)) | (~join_associative(B!18)) | (~meet_commutative(B!18)) | (~meet_associative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)))) | (~lattice(B!18)))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~join_commutative(A)) | (~join_associative(A)) | (~meet_commutative(A)) | (~meet_associative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)))) | (~lattice(A)))) | (empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (~(empty_carrier(B!18) | (~join_commutative(B!18)) | (~join_associative(B!18)) | (~meet_commutative(B!18)) | (~meet_associative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18))))))),
% 6.25/4.23 inference(monotonicity,[status(thm)],[437])).
% 6.25/4.23 tff(439,plain,
% 6.25/4.23 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~join_commutative(A)) | (~join_associative(A)) | (~meet_commutative(A)) | (~meet_associative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)))) | (~lattice(A)))) | (empty_carrier(B!18) | (~latt_str(B!18)) | (~(empty_carrier(B!18) | (~join_commutative(B!18)) | (~join_associative(B!18)) | (~meet_commutative(B!18)) | (~meet_associative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)))) | (~lattice(B!18)))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~join_commutative(A)) | (~join_associative(A)) | (~meet_commutative(A)) | (~meet_associative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)))) | (~lattice(A)))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (~(empty_carrier(B!18) | (~join_commutative(B!18)) | (~join_associative(B!18)) | (~meet_commutative(B!18)) | (~meet_associative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)))))),
% 6.25/4.23 inference(transitivity,[status(thm)],[438, 433])).
% 6.25/4.23 tff(440,plain,
% 6.25/4.23 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~join_commutative(A)) | (~join_associative(A)) | (~meet_commutative(A)) | (~meet_associative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)))) | (~lattice(A)))) | (empty_carrier(B!18) | (~latt_str(B!18)) | (~(empty_carrier(B!18) | (~join_commutative(B!18)) | (~join_associative(B!18)) | (~meet_commutative(B!18)) | (~meet_associative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)))) | (~lattice(B!18)))),
% 6.25/4.23 inference(quant_inst,[status(thm)],[])).
% 6.25/4.23 tff(441,plain,
% 6.25/4.23 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~join_commutative(A)) | (~join_associative(A)) | (~meet_commutative(A)) | (~meet_associative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)))) | (~lattice(A)))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~lattice(B!18)) | (~(empty_carrier(B!18) | (~join_commutative(B!18)) | (~join_associative(B!18)) | (~meet_commutative(B!18)) | (~meet_associative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18))))),
% 6.25/4.23 inference(modus_ponens,[status(thm)],[440, 439])).
% 6.25/4.23 tff(442,plain,
% 6.25/4.23 (~(empty_carrier(B!18) | (~join_commutative(B!18)) | (~join_associative(B!18)) | (~meet_commutative(B!18)) | (~meet_associative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)))),
% 6.25/4.23 inference(unit_resolution,[status(thm)],[441, 432, 18, 17, 16])).
% 6.25/4.23 tff(443,plain,
% 6.25/4.23 ((empty_carrier(B!18) | (~join_commutative(B!18)) | (~join_associative(B!18)) | (~meet_commutative(B!18)) | (~meet_associative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18))) | join_absorbing(B!18)),
% 6.25/4.23 inference(tautology,[status(thm)],[])).
% 6.25/4.23 tff(444,plain,
% 6.25/4.23 (join_absorbing(B!18)),
% 6.25/4.23 inference(unit_resolution,[status(thm)],[443, 442])).
% 6.25/4.23 tff(445,plain,
% 6.25/4.23 ((empty_carrier(B!18) | (~join_commutative(B!18)) | (~join_associative(B!18)) | (~meet_commutative(B!18)) | (~meet_associative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18))) | meet_absorbing(B!18)),
% 6.25/4.23 inference(tautology,[status(thm)],[])).
% 6.25/4.23 tff(446,plain,
% 6.25/4.23 (meet_absorbing(B!18)),
% 6.25/4.23 inference(unit_resolution,[status(thm)],[445, 442])).
% 6.25/4.23 tff(447,plain,
% 6.25/4.23 ((empty_carrier(B!18) | (~join_commutative(B!18)) | (~join_associative(B!18)) | (~meet_commutative(B!18)) | (~meet_associative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18))) | meet_commutative(B!18)),
% 6.25/4.23 inference(tautology,[status(thm)],[])).
% 6.25/4.23 tff(448,plain,
% 6.25/4.23 (meet_commutative(B!18)),
% 6.25/4.23 inference(unit_resolution,[status(thm)],[447, 442])).
% 6.25/4.23 tff(449,plain,
% 6.25/4.23 (^[A: $i, B: $i, C: $i] : refl(((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A)))) <=> ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A)))))),
% 6.25/4.23 inference(bind,[status(th)],[])).
% 6.25/4.23 tff(450,plain,
% 6.25/4.23 (![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A)))) <=> ![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))),
% 6.25/4.23 inference(quant_intro,[status(thm)],[449])).
% 6.25/4.23 tff(451,plain,
% 6.25/4.23 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A))) <=> (~(empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A)))))), ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) <=> (~(~(empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A)))))))), rewrite((~(~(empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A)))))) <=> (empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))), ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) <=> (empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A)))))), (((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C))) <=> ((empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C))))), rewrite(((empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C))) <=> ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))), (((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C))) <=> ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))))),
% 6.25/4.23 inference(bind,[status(th)],[])).
% 6.25/4.23 tff(452,plain,
% 6.25/4.23 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))),
% 6.25/4.23 inference(quant_intro,[status(thm)],[451])).
% 6.25/4.23 tff(453,plain,
% 6.25/4.23 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C)))),
% 6.25/4.23 inference(rewrite,[status(thm)],[])).
% 6.25/4.23 tff(454,plain,
% 6.25/4.23 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A))), (((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) <=> (((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A)) & join_absorbing(A)))), rewrite((((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A)) & join_absorbing(A)) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A))), (((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A)))), ((((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) & latt_str(A)) <=> (((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A)) & latt_str(A)))), rewrite((((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A)) & latt_str(A)) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A))), ((((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) & latt_str(A)) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A)))), (((((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) & latt_str(A)) & element(B, the_carrier(A))) <=> (((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A)) & element(B, the_carrier(A))))), rewrite((((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A)) & element(B, the_carrier(A))) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)))), (((((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) & latt_str(A)) & element(B, the_carrier(A))) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A))))), ((((((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) & latt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) <=> (((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A))) & element(C, the_carrier(A))))), rewrite((((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A))) & element(C, the_carrier(A))) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))), ((((((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) & latt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A))))), (((((((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) & latt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => (below_refl(A, B, C) <=> below(A, B, C))) <=> (((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A))) => (below_refl(A, B, C) <=> below(A, B, C))))), rewrite((((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A))) => (below_refl(A, B, C) <=> below(A, B, C))) <=> ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C)))), (((((((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) & latt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => (below_refl(A, B, C) <=> below(A, B, C))) <=> ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C)))))),
% 6.25/4.23 inference(bind,[status(th)],[])).
% 6.25/4.23 tff(455,plain,
% 6.25/4.23 (![A: $i, B: $i, C: $i] : ((((((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) & latt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => (below_refl(A, B, C) <=> below(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C)))),
% 6.25/4.23 inference(quant_intro,[status(thm)],[454])).
% 6.25/4.23 tff(456,axiom,(![A: $i, B: $i, C: $i] : ((((((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) & latt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => (below_refl(A, B, C) <=> below(A, B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_r3_lattices')).
% 6.25/4.23 tff(457,plain,
% 6.25/4.23 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C)))),
% 6.25/4.23 inference(modus_ponens,[status(thm)],[456, 455])).
% 6.25/4.23 tff(458,plain,
% 6.25/4.23 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C)))),
% 6.25/4.23 inference(modus_ponens,[status(thm)],[457, 453])).
% 6.25/4.23 tff(459,plain,(
% 6.25/4.23 ![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C)))),
% 6.25/4.23 inference(skolemize,[status(sab)],[458])).
% 6.25/4.23 tff(460,plain,
% 6.25/4.23 (![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))),
% 6.25/4.23 inference(modus_ponens,[status(thm)],[459, 452])).
% 6.25/4.23 tff(461,plain,
% 6.25/4.23 (![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))),
% 6.25/4.23 inference(modus_ponens,[status(thm)],[460, 450])).
% 6.25/4.23 tff(462,plain,
% 6.25/4.23 (((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | (empty_carrier(B!18) | (~latt_str(B!18)) | (~meet_commutative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) <=> below(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20))))) <=> ((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~meet_commutative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) <=> below(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20))))),
% 6.25/4.23 inference(rewrite,[status(thm)],[])).
% 6.25/4.23 tff(463,plain,
% 6.25/4.23 (((below_refl(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) <=> below(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20))) | empty_carrier(B!18) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | (~meet_commutative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)) | (~latt_str(B!18)) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(B!18)))) <=> (empty_carrier(B!18) | (~latt_str(B!18)) | (~meet_commutative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) <=> below(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20))))),
% 6.25/4.23 inference(rewrite,[status(thm)],[])).
% 6.25/4.23 tff(464,plain,
% 6.25/4.23 (((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | ((below_refl(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) <=> below(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20))) | empty_carrier(B!18) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | (~meet_commutative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)) | (~latt_str(B!18)) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(B!18))))) <=> ((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | (empty_carrier(B!18) | (~latt_str(B!18)) | (~meet_commutative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) <=> below(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)))))),
% 6.25/4.23 inference(monotonicity,[status(thm)],[463])).
% 6.25/4.23 tff(465,plain,
% 6.25/4.23 (((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | ((below_refl(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) <=> below(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20))) | empty_carrier(B!18) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | (~meet_commutative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)) | (~latt_str(B!18)) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(B!18))))) <=> ((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~meet_commutative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) <=> below(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20))))),
% 6.25/4.24 inference(transitivity,[status(thm)],[464, 462])).
% 6.25/4.24 tff(466,plain,
% 6.25/4.24 ((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | ((below_refl(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) <=> below(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20))) | empty_carrier(B!18) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | (~meet_commutative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)) | (~latt_str(B!18)) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(B!18))))),
% 6.25/4.24 inference(quant_inst,[status(thm)],[])).
% 6.25/4.24 tff(467,plain,
% 6.25/4.24 ((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~meet_commutative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) <=> below(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.25/4.24 inference(modus_ponens,[status(thm)],[466, 465])).
% 6.25/4.24 tff(468,plain,
% 6.25/4.24 (below_refl(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) <=> below(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20))),
% 6.25/4.24 inference(unit_resolution,[status(thm)],[467, 461, 18, 16, 448, 446, 444, 415, 271])).
% 6.25/4.24 tff(469,plain,
% 6.25/4.24 (latt_element_smaller(B!18, cast_to_el_of_LattPOSet(B!18, C!20), A!19) <=> latt_element_smaller(B!18, C!20, A!19)),
% 6.25/4.24 inference(monotonicity,[status(thm)],[47])).
% 6.25/4.24 tff(470,plain,
% 6.25/4.24 (latt_element_smaller(B!18, C!20, A!19) <=> latt_element_smaller(B!18, cast_to_el_of_LattPOSet(B!18, C!20), A!19)),
% 6.25/4.24 inference(symmetry,[status(thm)],[469])).
% 6.25/4.24 tff(471,plain,
% 6.25/4.24 ((~(latt_element_smaller(B!18, C!20, A!19) <=> relstr_set_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20)))) <=> ((~latt_element_smaller(B!18, C!20, A!19)) <=> relstr_set_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.25/4.24 inference(rewrite,[status(thm)],[])).
% 6.25/4.24 tff(472,plain,
% 6.25/4.24 (~(latt_element_smaller(B!18, C!20, A!19) <=> relstr_set_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.25/4.24 inference(or_elim,[status(thm)],[42])).
% 6.25/4.24 tff(473,plain,
% 6.25/4.24 ((~latt_element_smaller(B!18, C!20, A!19)) <=> relstr_set_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20))),
% 6.25/4.24 inference(modus_ponens,[status(thm)],[472, 471])).
% 6.25/4.24 tff(474,plain,
% 6.25/4.24 (latt_element_smaller(B!18, C!20, A!19) | relstr_set_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20)) | (~((~latt_element_smaller(B!18, C!20, A!19)) <=> relstr_set_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20))))),
% 6.25/4.24 inference(tautology,[status(thm)],[])).
% 6.25/4.24 tff(475,plain,
% 6.25/4.24 (latt_element_smaller(B!18, C!20, A!19) | relstr_set_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20))),
% 6.25/4.24 inference(unit_resolution,[status(thm)],[474, 473])).
% 6.25/4.24 tff(476,plain,
% 6.25/4.24 (latt_element_smaller(B!18, C!20, A!19)),
% 6.25/4.24 inference(unit_resolution,[status(thm)],[475, 210])).
% 6.25/4.24 tff(477,plain,
% 6.25/4.24 (latt_element_smaller(B!18, cast_to_el_of_LattPOSet(B!18, C!20), A!19)),
% 6.25/4.24 inference(modus_ponens,[status(thm)],[476, 470])).
% 6.25/4.24 tff(478,plain,
% 6.25/4.24 (^[A: $i] : refl((empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C)))))))))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C)))))))))))),
% 6.25/4.24 inference(bind,[status(th)],[])).
% 6.25/4.24 tff(479,plain,
% 6.25/4.24 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C)))))))))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))),
% 6.25/4.24 inference(quant_intro,[status(thm)],[478])).
% 6.25/4.24 tff(480,plain,
% 6.25/4.24 (^[A: $i] : rewrite((empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C)))))))))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C)))))))))))),
% 6.25/4.24 inference(bind,[status(th)],[])).
% 6.25/4.24 tff(481,plain,
% 6.25/4.24 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C)))))))))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))),
% 6.25/4.24 inference(quant_intro,[status(thm)],[480])).
% 6.25/4.24 tff(482,plain,
% 6.25/4.24 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C)))))))))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))),
% 6.25/4.24 inference(transitivity,[status(thm)],[481, 479])).
% 6.25/4.24 tff(483,plain,
% 6.25/4.24 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & latt_str(A)) <=> (~(empty_carrier(A) | (~latt_str(A))))), ((~((~empty_carrier(A)) & latt_str(A))) <=> (~(~(empty_carrier(A) | (~latt_str(A))))))), rewrite((~(~(empty_carrier(A) | (~latt_str(A))))) <=> (empty_carrier(A) | (~latt_str(A)))), ((~((~empty_carrier(A)) & latt_str(A))) <=> (empty_carrier(A) | (~latt_str(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~element(B, the_carrier(A))) | ![C: $i] : (((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A))))) & (latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))), (![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A))))) & (latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))), (((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A))))) & (latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C)))))))) <=> ((empty_carrier(A) | (~latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C)))))))))))), rewrite(((empty_carrier(A) | (~latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C)))))))))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))), (((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A))))) & (latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C)))))))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))))),
% 6.25/4.24 inference(bind,[status(th)],[])).
% 6.25/4.24 tff(484,plain,
% 6.25/4.24 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A))))) & (latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C)))))))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))),
% 6.25/4.24 inference(quant_intro,[status(thm)],[483])).
% 6.25/4.24 tff(485,plain,
% 6.25/4.24 (^[A: $i] : rewrite(((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A))))) & (latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))) <=> ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A))))) & (latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C)))))))))),
% 6.25/4.24 inference(bind,[status(th)],[])).
% 6.25/4.24 tff(486,plain,
% 6.25/4.24 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A))))) & (latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A))))) & (latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))),
% 6.25/4.24 inference(quant_intro,[status(thm)],[485])).
% 6.25/4.24 tff(487,plain,
% 6.25/4.24 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A))))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))))),
% 6.25/4.24 inference(rewrite,[status(thm)],[])).
% 6.25/4.24 tff(488,plain,
% 6.25/4.24 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((latt_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, D, B)))) <=> (latt_element_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A))))))), (![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, D, B)))) <=> ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A))))))), ((element(B, the_carrier(A)) => ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, D, B))))) <=> (element(B, the_carrier(A)) => ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))))), rewrite((element(B, the_carrier(A)) => ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A))))))), ((element(B, the_carrier(A)) => ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, D, B))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A))))))))), (![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, D, B))))) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))))), ((((~empty_carrier(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, D, B)))))) <=> (((~empty_carrier(A)) & latt_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A))))))))), rewrite((((~empty_carrier(A)) & latt_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A))))))) <=> ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))))), ((((~empty_carrier(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, D, B)))))) <=> ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))))))),
% 6.25/4.24 inference(bind,[status(th)],[])).
% 6.25/4.24 tff(489,plain,
% 6.25/4.24 (![A: $i] : (((~empty_carrier(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, D, B)))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))))),
% 6.25/4.24 inference(quant_intro,[status(thm)],[488])).
% 6.25/4.24 tff(490,axiom,(![A: $i] : (((~empty_carrier(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, D, B))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d17_lattice3')).
% 6.25/4.24 tff(491,plain,
% 6.25/4.24 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))))),
% 6.25/4.24 inference(modus_ponens,[status(thm)],[490, 489])).
% 6.25/4.24 tff(492,plain,
% 6.25/4.24 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))))),
% 6.25/4.24 inference(modus_ponens,[status(thm)],[491, 487])).
% 6.25/4.24 tff(493,plain,(
% 6.25/4.24 ![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A))))) & (latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))),
% 6.25/4.24 inference(skolemize,[status(sab)],[492])).
% 6.25/4.24 tff(494,plain,
% 6.25/4.24 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A))))) & (latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))),
% 6.25/4.24 inference(modus_ponens,[status(thm)],[493, 486])).
% 6.25/4.24 tff(495,plain,
% 6.25/4.24 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))),
% 6.25/4.24 inference(modus_ponens,[status(thm)],[494, 484])).
% 6.25/4.24 tff(496,plain,
% 6.25/4.24 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))),
% 6.25/4.24 inference(modus_ponens,[status(thm)],[495, 482])).
% 6.25/4.24 tff(497,plain,
% 6.25/4.24 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))) | (empty_carrier(B!18) | (~latt_str(B!18)) | ![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_element_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, D, B)))) | (~(latt_element_smaller(B!18, B, C) | (~(below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(C, B, B!18), C))))))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))) | empty_carrier(B!18) | (~latt_str(B!18)) | ![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_element_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, D, B)))) | (~(latt_element_smaller(B!18, B, C) | (~(below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(C, B, B!18), C))))))))))),
% 6.25/4.24 inference(rewrite,[status(thm)],[])).
% 6.25/4.24 tff(498,plain,
% 6.25/4.24 ((empty_carrier(B!18) | (~latt_str(B!18)) | ![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_element_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | below(B!18, D, B) | (~element(D, the_carrier(B!18)))))) | (~(latt_element_smaller(B!18, B, C) | (~(below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))) <=> (empty_carrier(B!18) | (~latt_str(B!18)) | ![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_element_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, D, B)))) | (~(latt_element_smaller(B!18, B, C) | (~(below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(C, B, B!18), C))))))))))),
% 6.25/4.24 inference(rewrite,[status(thm)],[])).
% 6.25/4.24 tff(499,plain,
% 6.25/4.24 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))) | (empty_carrier(B!18) | (~latt_str(B!18)) | ![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_element_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | below(B!18, D, B) | (~element(D, the_carrier(B!18)))))) | (~(latt_element_smaller(B!18, B, C) | (~(below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(C, B, B!18), C))))))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))) | (empty_carrier(B!18) | (~latt_str(B!18)) | ![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_element_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, D, B)))) | (~(latt_element_smaller(B!18, B, C) | (~(below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))))),
% 6.25/4.24 inference(monotonicity,[status(thm)],[498])).
% 6.25/4.24 tff(500,plain,
% 6.25/4.24 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))) | (empty_carrier(B!18) | (~latt_str(B!18)) | ![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_element_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | below(B!18, D, B) | (~element(D, the_carrier(B!18)))))) | (~(latt_element_smaller(B!18, B, C) | (~(below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(C, B, B!18), C))))))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))) | empty_carrier(B!18) | (~latt_str(B!18)) | ![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_element_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, D, B)))) | (~(latt_element_smaller(B!18, B, C) | (~(below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(C, B, B!18), C))))))))))),
% 6.25/4.24 inference(transitivity,[status(thm)],[499, 497])).
% 6.25/4.24 tff(501,plain,
% 6.25/4.24 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))) | (empty_carrier(B!18) | (~latt_str(B!18)) | ![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_element_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | below(B!18, D, B) | (~element(D, the_carrier(B!18)))))) | (~(latt_element_smaller(B!18, B, C) | (~(below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(C, B, B!18), C))))))))))),
% 6.25/4.24 inference(quant_inst,[status(thm)],[])).
% 6.25/4.24 tff(502,plain,
% 6.25/4.24 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~(below(A, tptp_fun_D_0(C, B, A), B) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))) | empty_carrier(B!18) | (~latt_str(B!18)) | ![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_element_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, D, B)))) | (~(latt_element_smaller(B!18, B, C) | (~(below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))),
% 6.25/4.24 inference(modus_ponens,[status(thm)],[501, 500])).
% 6.25/4.24 tff(503,plain,
% 6.25/4.24 (![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_element_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, D, B)))) | (~(latt_element_smaller(B!18, B, C) | (~(below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))),
% 6.25/4.24 inference(unit_resolution,[status(thm)],[502, 496, 18, 16])).
% 6.25/4.24 tff(504,plain,
% 6.25/4.24 (((~![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_element_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, D, B)))) | (~(latt_element_smaller(B!18, B, C) | (~(below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))) | ((~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | ![C: $i] : (~((~((~latt_element_smaller(B!18, cast_to_el_of_LattPOSet(B!18, C!20), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, D, cast_to_el_of_LattPOSet(B!18, C!20))))) | (~(latt_element_smaller(B!18, cast_to_el_of_LattPOSet(B!18, C!20), C) | (~(below(B!18, tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), cast_to_el_of_LattPOSet(B!18, C!20)) | (~element(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), C)))))))))) <=> ((~![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_element_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, D, B)))) | (~(latt_element_smaller(B!18, B, C) | (~(below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | ![C: $i] : (~((~((~latt_element_smaller(B!18, cast_to_el_of_LattPOSet(B!18, C!20), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, D, cast_to_el_of_LattPOSet(B!18, C!20))))) | (~(latt_element_smaller(B!18, cast_to_el_of_LattPOSet(B!18, C!20), C) | (~(below(B!18, tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), cast_to_el_of_LattPOSet(B!18, C!20)) | (~element(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), C)))))))))),
% 6.25/4.24 inference(rewrite,[status(thm)],[])).
% 6.25/4.24 tff(505,plain,
% 6.25/4.24 ((~![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_element_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, D, B)))) | (~(latt_element_smaller(B!18, B, C) | (~(below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))) | ((~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | ![C: $i] : (~((~((~latt_element_smaller(B!18, cast_to_el_of_LattPOSet(B!18, C!20), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, D, cast_to_el_of_LattPOSet(B!18, C!20))))) | (~(latt_element_smaller(B!18, cast_to_el_of_LattPOSet(B!18, C!20), C) | (~(below(B!18, tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), cast_to_el_of_LattPOSet(B!18, C!20)) | (~element(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), C)))))))))),
% 6.25/4.24 inference(quant_inst,[status(thm)],[])).
% 6.25/4.24 tff(506,plain,
% 6.25/4.24 ((~![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_element_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, D, B)))) | (~(latt_element_smaller(B!18, B, C) | (~(below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | ![C: $i] : (~((~((~latt_element_smaller(B!18, cast_to_el_of_LattPOSet(B!18, C!20), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, D, cast_to_el_of_LattPOSet(B!18, C!20))))) | (~(latt_element_smaller(B!18, cast_to_el_of_LattPOSet(B!18, C!20), C) | (~(below(B!18, tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), cast_to_el_of_LattPOSet(B!18, C!20)) | (~element(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), C))))))))),
% 6.25/4.24 inference(modus_ponens,[status(thm)],[505, 504])).
% 6.25/4.24 tff(507,plain,
% 6.25/4.24 ((~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | ![C: $i] : (~((~((~latt_element_smaller(B!18, cast_to_el_of_LattPOSet(B!18, C!20), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, D, cast_to_el_of_LattPOSet(B!18, C!20))))) | (~(latt_element_smaller(B!18, cast_to_el_of_LattPOSet(B!18, C!20), C) | (~(below(B!18, tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), cast_to_el_of_LattPOSet(B!18, C!20)) | (~element(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), C))))))))),
% 6.25/4.24 inference(unit_resolution,[status(thm)],[506, 503])).
% 6.25/4.24 tff(508,plain,
% 6.25/4.24 (![C: $i] : (~((~((~latt_element_smaller(B!18, cast_to_el_of_LattPOSet(B!18, C!20), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, D, cast_to_el_of_LattPOSet(B!18, C!20))))) | (~(latt_element_smaller(B!18, cast_to_el_of_LattPOSet(B!18, C!20), C) | (~(below(B!18, tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), cast_to_el_of_LattPOSet(B!18, C!20)) | (~element(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), C))))))))),
% 6.25/4.24 inference(unit_resolution,[status(thm)],[507, 415])).
% 6.25/4.24 tff(509,plain,
% 6.25/4.24 ((~![C: $i] : (~((~((~latt_element_smaller(B!18, cast_to_el_of_LattPOSet(B!18, C!20), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, D, cast_to_el_of_LattPOSet(B!18, C!20))))) | (~(latt_element_smaller(B!18, cast_to_el_of_LattPOSet(B!18, C!20), C) | (~(below(B!18, tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), cast_to_el_of_LattPOSet(B!18, C!20)) | (~element(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), C))))))))) | (~((~((~latt_element_smaller(B!18, cast_to_el_of_LattPOSet(B!18, C!20), A!19)) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(B!18))) | below(B!18, D, cast_to_el_of_LattPOSet(B!18, C!20))))) | (~(latt_element_smaller(B!18, cast_to_el_of_LattPOSet(B!18, C!20), A!19) | (~(below(B!18, tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), cast_to_el_of_LattPOSet(B!18, C!20)) | (~element(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), A!19))))))))),
% 6.25/4.24 inference(quant_inst,[status(thm)],[])).
% 6.25/4.24 tff(510,plain,
% 6.25/4.24 (~((~((~latt_element_smaller(B!18, cast_to_el_of_LattPOSet(B!18, C!20), A!19)) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(B!18))) | below(B!18, D, cast_to_el_of_LattPOSet(B!18, C!20))))) | (~(latt_element_smaller(B!18, cast_to_el_of_LattPOSet(B!18, C!20), A!19) | (~(below(B!18, tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), cast_to_el_of_LattPOSet(B!18, C!20)) | (~element(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), A!19)))))))),
% 6.25/4.24 inference(unit_resolution,[status(thm)],[509, 508])).
% 6.25/4.24 tff(511,plain,
% 6.25/4.24 (((~((~latt_element_smaller(B!18, cast_to_el_of_LattPOSet(B!18, C!20), A!19)) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(B!18))) | below(B!18, D, cast_to_el_of_LattPOSet(B!18, C!20))))) | (~(latt_element_smaller(B!18, cast_to_el_of_LattPOSet(B!18, C!20), A!19) | (~(below(B!18, tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), cast_to_el_of_LattPOSet(B!18, C!20)) | (~element(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), A!19))))))) | ((~latt_element_smaller(B!18, cast_to_el_of_LattPOSet(B!18, C!20), A!19)) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(B!18))) | below(B!18, D, cast_to_el_of_LattPOSet(B!18, C!20))))),
% 6.25/4.24 inference(tautology,[status(thm)],[])).
% 6.25/4.24 tff(512,plain,
% 6.25/4.24 ((~latt_element_smaller(B!18, cast_to_el_of_LattPOSet(B!18, C!20), A!19)) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(B!18))) | below(B!18, D, cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.25/4.24 inference(unit_resolution,[status(thm)],[511, 510])).
% 6.25/4.24 tff(513,plain,
% 6.25/4.24 ((~((~latt_element_smaller(B!18, cast_to_el_of_LattPOSet(B!18, C!20), A!19)) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(B!18))) | below(B!18, D, cast_to_el_of_LattPOSet(B!18, C!20))))) | (~latt_element_smaller(B!18, cast_to_el_of_LattPOSet(B!18, C!20), A!19)) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(B!18))) | below(B!18, D, cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.25/4.24 inference(tautology,[status(thm)],[])).
% 6.25/4.24 tff(514,plain,
% 6.25/4.24 ((~latt_element_smaller(B!18, cast_to_el_of_LattPOSet(B!18, C!20), A!19)) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(B!18))) | below(B!18, D, cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.25/4.24 inference(unit_resolution,[status(thm)],[513, 512])).
% 6.25/4.25 tff(515,plain,
% 6.25/4.25 (![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(B!18))) | below(B!18, D, cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.25/4.25 inference(unit_resolution,[status(thm)],[514, 477])).
% 6.25/4.25 tff(516,plain,
% 6.25/4.25 ((related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), A!19))) | in(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), A!19)),
% 6.25/4.25 inference(tautology,[status(thm)],[])).
% 6.25/4.25 tff(517,plain,
% 6.25/4.25 (in(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), A!19)),
% 6.25/4.25 inference(unit_resolution,[status(thm)],[516, 268])).
% 6.25/4.25 tff(518,plain,
% 6.25/4.25 (((~![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(B!18))) | below(B!18, D, cast_to_el_of_LattPOSet(B!18, C!20)))) | ((~in(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), A!19)) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(B!18))) | below(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)))) <=> ((~![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(B!18))) | below(B!18, D, cast_to_el_of_LattPOSet(B!18, C!20)))) | (~in(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), A!19)) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(B!18))) | below(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.25/4.25 inference(rewrite,[status(thm)],[])).
% 6.25/4.25 tff(519,plain,
% 6.25/4.25 ((~![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(B!18))) | below(B!18, D, cast_to_el_of_LattPOSet(B!18, C!20)))) | ((~in(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), A!19)) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(B!18))) | below(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.25/4.25 inference(quant_inst,[status(thm)],[])).
% 6.25/4.25 tff(520,plain,
% 6.25/4.25 ((~![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(B!18))) | below(B!18, D, cast_to_el_of_LattPOSet(B!18, C!20)))) | (~in(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), A!19)) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(B!18))) | below(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20))),
% 6.25/4.25 inference(modus_ponens,[status(thm)],[519, 518])).
% 6.25/4.25 tff(521,plain,
% 6.25/4.25 ((~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(B!18))) | below(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20))),
% 6.25/4.25 inference(unit_resolution,[status(thm)],[520, 517, 515])).
% 6.25/4.25 tff(522,plain,
% 6.25/4.25 (below(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20))),
% 6.25/4.25 inference(unit_resolution,[status(thm)],[521, 271])).
% 6.25/4.25 tff(523,plain,
% 6.25/4.25 ((~(below_refl(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) <=> below(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)))) | below_refl(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) | (~below(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.25/4.25 inference(tautology,[status(thm)],[])).
% 6.25/4.25 tff(524,plain,
% 6.25/4.25 ((~(below_refl(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) <=> below(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)))) | below_refl(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20))),
% 6.25/4.25 inference(unit_resolution,[status(thm)],[523, 522])).
% 6.25/4.25 tff(525,plain,
% 6.25/4.25 (below_refl(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20))),
% 6.25/4.25 inference(unit_resolution,[status(thm)],[524, 468])).
% 6.25/4.25 tff(526,plain,
% 6.25/4.25 ((~(below_refl(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20))))) | (~below_refl(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20))) | related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.25/4.25 inference(tautology,[status(thm)],[])).
% 6.25/4.25 tff(527,plain,
% 6.25/4.25 (related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.25/4.25 inference(unit_resolution,[status(thm)],[526, 525, 419])).
% 6.25/4.25 tff(528,plain,
% 6.25/4.25 ($false),
% 6.25/4.25 inference(unit_resolution,[status(thm)],[527, 336])).
% 6.25/4.25 tff(529,plain,(relstr_set_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20))), inference(lemma,lemma(discharge,[]))).
% 6.25/4.25 tff(530,plain,
% 6.25/4.25 ((~latt_element_smaller(B!18, C!20, A!19)) | (~relstr_set_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20))) | (~((~latt_element_smaller(B!18, C!20, A!19)) <=> relstr_set_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20))))),
% 6.25/4.25 inference(tautology,[status(thm)],[])).
% 6.25/4.25 tff(531,plain,
% 6.25/4.25 ((~latt_element_smaller(B!18, C!20, A!19)) | (~relstr_set_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.25/4.25 inference(unit_resolution,[status(thm)],[530, 473])).
% 6.25/4.25 tff(532,plain,
% 6.25/4.25 (~latt_element_smaller(B!18, C!20, A!19)),
% 6.25/4.25 inference(unit_resolution,[status(thm)],[531, 529])).
% 6.25/4.25 tff(533,plain,
% 6.25/4.25 (((~![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_element_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, D, B)))) | (~(latt_element_smaller(B!18, B, C) | (~(below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))) | ((~element(C!20, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_element_smaller(B!18, C!20, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, D, C!20)))) | (~(latt_element_smaller(B!18, C!20, C) | (~(below(B!18, tptp_fun_D_0(C, C!20, B!18), C!20) | (~element(tptp_fun_D_0(C, C!20, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(C, C!20, B!18), C)))))))))) <=> ((~![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_element_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, D, B)))) | (~(latt_element_smaller(B!18, B, C) | (~(below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))) | (~element(C!20, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_element_smaller(B!18, C!20, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, D, C!20)))) | (~(latt_element_smaller(B!18, C!20, C) | (~(below(B!18, tptp_fun_D_0(C, C!20, B!18), C!20) | (~element(tptp_fun_D_0(C, C!20, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(C, C!20, B!18), C)))))))))),
% 6.25/4.25 inference(rewrite,[status(thm)],[])).
% 6.25/4.25 tff(534,plain,
% 6.25/4.25 ((~![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_element_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, D, B)))) | (~(latt_element_smaller(B!18, B, C) | (~(below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))) | ((~element(C!20, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_element_smaller(B!18, C!20, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, D, C!20)))) | (~(latt_element_smaller(B!18, C!20, C) | (~(below(B!18, tptp_fun_D_0(C, C!20, B!18), C!20) | (~element(tptp_fun_D_0(C, C!20, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(C, C!20, B!18), C)))))))))),
% 6.25/4.25 inference(quant_inst,[status(thm)],[])).
% 6.25/4.25 tff(535,plain,
% 6.25/4.25 ((~![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_element_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, D, B)))) | (~(latt_element_smaller(B!18, B, C) | (~(below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))) | (~element(C!20, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_element_smaller(B!18, C!20, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, D, C!20)))) | (~(latt_element_smaller(B!18, C!20, C) | (~(below(B!18, tptp_fun_D_0(C, C!20, B!18), C!20) | (~element(tptp_fun_D_0(C, C!20, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(C, C!20, B!18), C))))))))),
% 6.25/4.25 inference(modus_ponens,[status(thm)],[534, 533])).
% 6.25/4.25 tff(536,plain,
% 6.25/4.25 (![C: $i] : (~((~((~latt_element_smaller(B!18, C!20, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, D, C!20)))) | (~(latt_element_smaller(B!18, C!20, C) | (~(below(B!18, tptp_fun_D_0(C, C!20, B!18), C!20) | (~element(tptp_fun_D_0(C, C!20, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(C, C!20, B!18), C))))))))),
% 6.25/4.25 inference(unit_resolution,[status(thm)],[535, 43, 503])).
% 6.25/4.25 tff(537,plain,
% 6.25/4.25 ((~![C: $i] : (~((~((~latt_element_smaller(B!18, C!20, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, D, C!20)))) | (~(latt_element_smaller(B!18, C!20, C) | (~(below(B!18, tptp_fun_D_0(C, C!20, B!18), C!20) | (~element(tptp_fun_D_0(C, C!20, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(C, C!20, B!18), C))))))))) | (~((~((~latt_element_smaller(B!18, C!20, A!19)) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(B!18))) | below(B!18, D, C!20)))) | (~(latt_element_smaller(B!18, C!20, A!19) | (~(below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19))))))))),
% 6.25/4.25 inference(quant_inst,[status(thm)],[])).
% 6.25/4.25 tff(538,plain,
% 6.25/4.25 (~((~((~latt_element_smaller(B!18, C!20, A!19)) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(B!18))) | below(B!18, D, C!20)))) | (~(latt_element_smaller(B!18, C!20, A!19) | (~(below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19)))))))),
% 6.28/4.25 inference(unit_resolution,[status(thm)],[537, 536])).
% 6.28/4.25 tff(539,plain,
% 6.28/4.25 (((~((~latt_element_smaller(B!18, C!20, A!19)) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(B!18))) | below(B!18, D, C!20)))) | (~(latt_element_smaller(B!18, C!20, A!19) | (~(below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19))))))) | (latt_element_smaller(B!18, C!20, A!19) | (~(below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19)))))),
% 6.28/4.25 inference(tautology,[status(thm)],[])).
% 6.28/4.25 tff(540,plain,
% 6.28/4.25 (latt_element_smaller(B!18, C!20, A!19) | (~(below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19))))),
% 6.28/4.25 inference(unit_resolution,[status(thm)],[539, 538])).
% 6.28/4.25 tff(541,plain,
% 6.28/4.25 ((~(latt_element_smaller(B!18, C!20, A!19) | (~(below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19)))))) | latt_element_smaller(B!18, C!20, A!19) | (~(below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19))))),
% 6.28/4.25 inference(tautology,[status(thm)],[])).
% 6.28/4.25 tff(542,plain,
% 6.28/4.25 (latt_element_smaller(B!18, C!20, A!19) | (~(below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19))))),
% 6.28/4.25 inference(unit_resolution,[status(thm)],[541, 540])).
% 6.28/4.25 tff(543,plain,
% 6.28/4.25 (~(below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19)))),
% 6.28/4.25 inference(unit_resolution,[status(thm)],[542, 532])).
% 6.28/4.25 tff(544,plain,
% 6.28/4.25 ((below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19))) | element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))),
% 6.28/4.25 inference(tautology,[status(thm)],[])).
% 6.28/4.25 tff(545,plain,
% 6.28/4.25 (element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))),
% 6.28/4.25 inference(unit_resolution,[status(thm)],[544, 543])).
% 6.28/4.25 tff(546,plain,
% 6.28/4.25 (((~![B: $i] : ((~element(B, the_carrier(B!18))) | (cast_to_el_of_LattPOSet(B!18, B) = B))) | ((~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | (cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18)) = tptp_fun_D_0(A!19, C!20, B!18)))) <=> ((~![B: $i] : ((~element(B, the_carrier(B!18))) | (cast_to_el_of_LattPOSet(B!18, B) = B))) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | (cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18)) = tptp_fun_D_0(A!19, C!20, B!18)))),
% 6.28/4.25 inference(rewrite,[status(thm)],[])).
% 6.28/4.25 tff(547,plain,
% 6.28/4.25 ((~![B: $i] : ((~element(B, the_carrier(B!18))) | (cast_to_el_of_LattPOSet(B!18, B) = B))) | ((~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | (cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18)) = tptp_fun_D_0(A!19, C!20, B!18)))),
% 6.28/4.25 inference(quant_inst,[status(thm)],[])).
% 6.28/4.25 tff(548,plain,
% 6.28/4.25 ((~![B: $i] : ((~element(B, the_carrier(B!18))) | (cast_to_el_of_LattPOSet(B!18, B) = B))) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | (cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18)) = tptp_fun_D_0(A!19, C!20, B!18))),
% 6.28/4.25 inference(modus_ponens,[status(thm)],[547, 546])).
% 6.28/4.25 tff(549,plain,
% 6.28/4.25 (cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18)) = tptp_fun_D_0(A!19, C!20, B!18)),
% 6.28/4.25 inference(unit_resolution,[status(thm)],[548, 41, 545])).
% 6.28/4.25 tff(550,plain,
% 6.28/4.25 (tptp_fun_D_0(A!19, C!20, B!18) = cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18))),
% 6.28/4.25 inference(symmetry,[status(thm)],[549])).
% 6.28/4.25 tff(551,plain,
% 6.28/4.25 (related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18)), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.28/4.25 inference(monotonicity,[status(thm)],[70, 550, 49])).
% 6.28/4.25 tff(552,plain,
% 6.28/4.25 (related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18)), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20))) <=> related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20))),
% 6.28/4.25 inference(symmetry,[status(thm)],[551])).
% 6.28/4.25 tff(553,plain,
% 6.28/4.25 ((~related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18)), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)))) <=> (~related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.28/4.25 inference(monotonicity,[status(thm)],[552])).
% 6.28/4.25 tff(554,plain,
% 6.28/4.25 (((~![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, B, C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, B), cast_to_el_of_LattPOSet(B!18, C)))))) | ((~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | ![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_0(A!19, C!20, B!18), C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18)), cast_to_el_of_LattPOSet(B!18, C)))))) <=> ((~![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, B, C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, B), cast_to_el_of_LattPOSet(B!18, C)))))) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | ![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_0(A!19, C!20, B!18), C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18)), cast_to_el_of_LattPOSet(B!18, C)))))),
% 6.28/4.25 inference(rewrite,[status(thm)],[])).
% 6.28/4.25 tff(555,plain,
% 6.28/4.25 ((~![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, B, C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, B), cast_to_el_of_LattPOSet(B!18, C)))))) | ((~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | ![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_0(A!19, C!20, B!18), C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18)), cast_to_el_of_LattPOSet(B!18, C)))))),
% 6.28/4.25 inference(quant_inst,[status(thm)],[])).
% 6.28/4.25 tff(556,plain,
% 6.28/4.25 ((~![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, B, C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, B), cast_to_el_of_LattPOSet(B!18, C)))))) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | ![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_0(A!19, C!20, B!18), C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18)), cast_to_el_of_LattPOSet(B!18, C))))),
% 6.28/4.25 inference(modus_ponens,[status(thm)],[555, 554])).
% 6.28/4.25 tff(557,plain,
% 6.28/4.25 (![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_0(A!19, C!20, B!18), C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18)), cast_to_el_of_LattPOSet(B!18, C))))),
% 6.28/4.25 inference(unit_resolution,[status(thm)],[556, 359, 545])).
% 6.28/4.25 tff(558,plain,
% 6.28/4.25 (((~![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_0(A!19, C!20, B!18), C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18)), cast_to_el_of_LattPOSet(B!18, C))))) | ((~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18)), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)))))) <=> ((~![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_0(A!19, C!20, B!18), C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18)), cast_to_el_of_LattPOSet(B!18, C))))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18)), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)))))),
% 6.28/4.25 inference(rewrite,[status(thm)],[])).
% 6.28/4.25 tff(559,plain,
% 6.28/4.25 ((~![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_0(A!19, C!20, B!18), C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18)), cast_to_el_of_LattPOSet(B!18, C))))) | ((~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18)), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)))))),
% 6.28/4.25 inference(quant_inst,[status(thm)],[])).
% 6.28/4.25 tff(560,plain,
% 6.28/4.25 ((~![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_0(A!19, C!20, B!18), C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18)), cast_to_el_of_LattPOSet(B!18, C))))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18)), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20))))),
% 6.28/4.25 inference(modus_ponens,[status(thm)],[559, 558])).
% 6.28/4.25 tff(561,plain,
% 6.28/4.25 (below_refl(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18)), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.28/4.25 inference(unit_resolution,[status(thm)],[560, 415, 557])).
% 6.28/4.25 tff(562,plain,
% 6.28/4.25 (((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | (empty_carrier(B!18) | (~latt_str(B!18)) | (~meet_commutative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) <=> below(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20))))) <=> ((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~meet_commutative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) <=> below(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20))))),
% 6.28/4.25 inference(rewrite,[status(thm)],[])).
% 6.28/4.25 tff(563,plain,
% 6.28/4.25 (((below_refl(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) <=> below(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20))) | empty_carrier(B!18) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | (~meet_commutative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)) | (~latt_str(B!18)) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18)))) <=> (empty_carrier(B!18) | (~latt_str(B!18)) | (~meet_commutative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) <=> below(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20))))),
% 6.28/4.25 inference(rewrite,[status(thm)],[])).
% 6.28/4.25 tff(564,plain,
% 6.28/4.25 (((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | ((below_refl(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) <=> below(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20))) | empty_carrier(B!18) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | (~meet_commutative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)) | (~latt_str(B!18)) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))))) <=> ((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | (empty_carrier(B!18) | (~latt_str(B!18)) | (~meet_commutative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) <=> below(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)))))),
% 6.28/4.25 inference(monotonicity,[status(thm)],[563])).
% 6.28/4.25 tff(565,plain,
% 6.28/4.25 (((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | ((below_refl(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) <=> below(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20))) | empty_carrier(B!18) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | (~meet_commutative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)) | (~latt_str(B!18)) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))))) <=> ((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~meet_commutative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) <=> below(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20))))),
% 6.28/4.25 inference(transitivity,[status(thm)],[564, 562])).
% 6.28/4.25 tff(566,plain,
% 6.28/4.25 ((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | ((below_refl(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) <=> below(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20))) | empty_carrier(B!18) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | (~meet_commutative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)) | (~latt_str(B!18)) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))))),
% 6.28/4.26 inference(quant_inst,[status(thm)],[])).
% 6.28/4.26 tff(567,plain,
% 6.28/4.26 ((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | empty_carrier(B!18) | (~latt_str(B!18)) | (~meet_commutative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | (below_refl(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) <=> below(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.28/4.26 inference(modus_ponens,[status(thm)],[566, 565])).
% 6.28/4.26 tff(568,plain,
% 6.28/4.26 (below_refl(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) <=> below(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20))),
% 6.28/4.26 inference(unit_resolution,[status(thm)],[567, 461, 18, 16, 448, 446, 444, 415, 545])).
% 6.28/4.26 tff(569,plain,
% 6.28/4.26 (below(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) <=> below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20)),
% 6.28/4.26 inference(monotonicity,[status(thm)],[47])).
% 6.28/4.26 tff(570,plain,
% 6.28/4.26 (below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20) <=> below(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20))),
% 6.28/4.26 inference(symmetry,[status(thm)],[569])).
% 6.28/4.26 tff(571,plain,
% 6.28/4.26 ((~below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20)) <=> (~below(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.28/4.26 inference(monotonicity,[status(thm)],[570])).
% 6.28/4.26 tff(572,plain,
% 6.28/4.26 ((below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19))) | (~below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20))),
% 6.28/4.26 inference(tautology,[status(thm)],[])).
% 6.28/4.26 tff(573,plain,
% 6.28/4.26 (~below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20)),
% 6.28/4.26 inference(unit_resolution,[status(thm)],[572, 543])).
% 6.28/4.26 tff(574,plain,
% 6.28/4.26 (~below(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20))),
% 6.28/4.26 inference(modus_ponens,[status(thm)],[573, 571])).
% 6.28/4.26 tff(575,plain,
% 6.28/4.26 ((~(below_refl(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) <=> below(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)))) | (~below_refl(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20))) | below(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20))),
% 6.28/4.26 inference(tautology,[status(thm)],[])).
% 6.28/4.26 tff(576,plain,
% 6.28/4.26 (~below_refl(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20))),
% 6.28/4.26 inference(unit_resolution,[status(thm)],[575, 574, 568])).
% 6.28/4.26 tff(577,plain,
% 6.28/4.26 ((~(below_refl(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18)), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20))))) | below_refl(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) | (~related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18)), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20))))),
% 6.28/4.26 inference(tautology,[status(thm)],[])).
% 6.28/4.26 tff(578,plain,
% 6.28/4.26 (~related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18)), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.28/4.26 inference(unit_resolution,[status(thm)],[577, 576, 561])).
% 6.28/4.26 tff(579,plain,
% 6.28/4.26 (~related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20))),
% 6.28/4.26 inference(modus_ponens,[status(thm)],[578, 553])).
% 6.28/4.26 tff(580,plain,
% 6.28/4.26 (the_carrier(poset_of_lattice(B!18)) = the_carrier(B!18)),
% 6.28/4.26 inference(symmetry,[status(thm)],[203])).
% 6.28/4.26 tff(581,plain,
% 6.28/4.26 (the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) = the_carrier(B!18)),
% 6.28/4.26 inference(transitivity,[status(thm)],[71, 580])).
% 6.28/4.26 tff(582,plain,
% 6.28/4.26 (element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))),
% 6.28/4.26 inference(monotonicity,[status(thm)],[581])).
% 6.28/4.26 tff(583,plain,
% 6.28/4.26 (element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18)) <=> element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 6.28/4.26 inference(symmetry,[status(thm)],[582])).
% 6.28/4.26 tff(584,plain,
% 6.28/4.26 (element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 6.28/4.26 inference(modus_ponens,[status(thm)],[545, 583])).
% 6.28/4.26 tff(585,plain,
% 6.28/4.26 (((~![A: $i, B: $i, C: $i] : ((related_reflexive(A, B, C) <=> related(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))) | (empty_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) | (~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~reflexive_relstr(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20))))) <=> ((~![A: $i, B: $i, C: $i] : ((related_reflexive(A, B, C) <=> related(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))) | empty_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) | (~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~reflexive_relstr(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20))))),
% 6.28/4.26 inference(rewrite,[status(thm)],[])).
% 6.28/4.26 tff(586,plain,
% 6.28/4.26 (((related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20))) | empty_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~reflexive_relstr(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) <=> (empty_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) | (~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~reflexive_relstr(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20))))),
% 6.28/4.26 inference(rewrite,[status(thm)],[])).
% 6.28/4.26 tff(587,plain,
% 6.28/4.26 (((~![A: $i, B: $i, C: $i] : ((related_reflexive(A, B, C) <=> related(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))) | ((related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20))) | empty_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~reflexive_relstr(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))) <=> ((~![A: $i, B: $i, C: $i] : ((related_reflexive(A, B, C) <=> related(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))) | (empty_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) | (~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~reflexive_relstr(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)))))),
% 6.28/4.26 inference(monotonicity,[status(thm)],[586])).
% 6.28/4.26 tff(588,plain,
% 6.28/4.26 (((~![A: $i, B: $i, C: $i] : ((related_reflexive(A, B, C) <=> related(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))) | ((related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20))) | empty_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~reflexive_relstr(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))) <=> ((~![A: $i, B: $i, C: $i] : ((related_reflexive(A, B, C) <=> related(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))) | empty_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) | (~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~reflexive_relstr(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20))))),
% 6.28/4.26 inference(transitivity,[status(thm)],[587, 585])).
% 6.28/4.26 tff(589,plain,
% 6.28/4.26 ((~![A: $i, B: $i, C: $i] : ((related_reflexive(A, B, C) <=> related(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))) | ((related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20))) | empty_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~reflexive_relstr(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))),
% 6.28/4.26 inference(quant_inst,[status(thm)],[])).
% 6.28/4.26 tff(590,plain,
% 6.28/4.26 ((~![A: $i, B: $i, C: $i] : ((related_reflexive(A, B, C) <=> related(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))) | empty_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) | (~rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~reflexive_relstr(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.28/4.26 inference(modus_ponens,[status(thm)],[589, 588])).
% 6.28/4.26 tff(591,plain,
% 6.28/4.26 (related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20))),
% 6.28/4.26 inference(unit_resolution,[status(thm)],[590, 323, 310, 101, 284, 234, 584])).
% 6.28/4.26 tff(592,plain,
% 6.28/4.26 (relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20))),
% 6.28/4.26 inference(modus_ponens,[status(thm)],[529, 208])).
% 6.28/4.26 tff(593,plain,
% 6.28/4.26 (((~((~relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20))) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, cast_to_el_of_LattPOSet(B!18, C!20))))) | (~(relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20)) | (~(related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), cast_to_el_of_LattPOSet(B!18, C!20)) | (~element(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), A!19))))))) | ((~relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20))) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, cast_to_el_of_LattPOSet(B!18, C!20))))),
% 6.28/4.26 inference(tautology,[status(thm)],[])).
% 6.28/4.26 tff(594,plain,
% 6.28/4.26 ((~relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20))) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.28/4.26 inference(unit_resolution,[status(thm)],[593, 263])).
% 6.28/4.26 tff(595,plain,
% 6.28/4.26 ((~((~relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20))) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, cast_to_el_of_LattPOSet(B!18, C!20))))) | (~relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20))) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.28/4.26 inference(tautology,[status(thm)],[])).
% 6.28/4.26 tff(596,plain,
% 6.28/4.26 ((~relstr_set_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20))) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.28/4.26 inference(unit_resolution,[status(thm)],[595, 594])).
% 6.28/4.26 tff(597,plain,
% 6.28/4.26 (![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.28/4.26 inference(unit_resolution,[status(thm)],[596, 592])).
% 6.28/4.26 tff(598,plain,
% 6.28/4.26 ((below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19))) | in(tptp_fun_D_0(A!19, C!20, B!18), A!19)),
% 6.28/4.26 inference(tautology,[status(thm)],[])).
% 6.28/4.26 tff(599,plain,
% 6.28/4.26 (in(tptp_fun_D_0(A!19, C!20, B!18), A!19)),
% 6.28/4.26 inference(unit_resolution,[status(thm)],[598, 543])).
% 6.28/4.26 tff(600,plain,
% 6.28/4.26 (((~![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, cast_to_el_of_LattPOSet(B!18, C!20)))) | ((~in(tptp_fun_D_0(A!19, C!20, B!18), A!19)) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)))) <=> ((~![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, cast_to_el_of_LattPOSet(B!18, C!20)))) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19)) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.28/4.26 inference(rewrite,[status(thm)],[])).
% 6.28/4.26 tff(601,plain,
% 6.28/4.26 ((~![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, cast_to_el_of_LattPOSet(B!18, C!20)))) | ((~in(tptp_fun_D_0(A!19, C!20, B!18), A!19)) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.28/4.26 inference(quant_inst,[status(thm)],[])).
% 6.28/4.26 tff(602,plain,
% 6.28/4.26 ((~![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), D, cast_to_el_of_LattPOSet(B!18, C!20)))) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19)) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20))),
% 6.28/4.28 inference(modus_ponens,[status(thm)],[601, 600])).
% 6.28/4.28 tff(603,plain,
% 6.28/4.28 ((~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20))),
% 6.28/4.28 inference(unit_resolution,[status(thm)],[602, 599, 597])).
% 6.28/4.28 tff(604,plain,
% 6.28/4.28 (related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20))),
% 6.28/4.28 inference(unit_resolution,[status(thm)],[603, 584])).
% 6.28/4.28 tff(605,plain,
% 6.28/4.28 ((~(related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)))) | related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)) | (~related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20)))),
% 6.28/4.28 inference(tautology,[status(thm)],[])).
% 6.28/4.28 tff(606,plain,
% 6.28/4.28 (related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20))),
% 6.28/4.28 inference(unit_resolution,[status(thm)],[605, 604, 591])).
% 6.28/4.28 tff(607,plain,
% 6.28/4.28 ($false),
% 6.28/4.28 inference(unit_resolution,[status(thm)],[606, 579])).
% 6.28/4.28 % SZS output end Proof
%------------------------------------------------------------------------------