%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU349+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:40 AM UTC 2025
% Result : Theorem 4.41s 4.59s
% Output : Proof 4.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU349+1 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:50:39 EDT 2025
% 0.12/0.33 % CPUTime :
% 4.41/4.59 % SZS status Theorem
% 4.41/4.59 % SZS output start Proof
% 4.41/4.59 tff(related_reflexive_type, type, (
% 4.41/4.59 related_reflexive: ( $i * $i * $i ) > $o)).
% 4.41/4.59 tff(cast_to_el_of_LattPOSet_type, type, (
% 4.41/4.59 cast_to_el_of_LattPOSet: ( $i * $i ) > $i)).
% 4.41/4.59 tff(tptp_fun_C_20_type, type, (
% 4.41/4.59 tptp_fun_C_20: $i)).
% 4.41/4.59 tff(tptp_fun_B_18_type, type, (
% 4.41/4.59 tptp_fun_B_18: $i)).
% 4.41/4.59 tff(tptp_fun_D_0_type, type, (
% 4.41/4.59 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 4.41/4.59 tff(tptp_fun_A_19_type, type, (
% 4.41/4.59 tptp_fun_A_19: $i)).
% 4.41/4.59 tff(rel_str_of_type, type, (
% 4.41/4.59 rel_str_of: ( $i * $i ) > $i)).
% 4.41/4.59 tff(k2_lattice3_type, type, (
% 4.41/4.59 k2_lattice3: $i > $i)).
% 4.41/4.59 tff(the_carrier_type, type, (
% 4.41/4.59 the_carrier: $i > $i)).
% 4.41/4.59 tff(poset_of_lattice_type, type, (
% 4.41/4.59 poset_of_lattice: $i > $i)).
% 4.41/4.59 tff(element_type, type, (
% 4.41/4.59 element: ( $i * $i ) > $o)).
% 4.41/4.59 tff(latt_str_type, type, (
% 4.41/4.59 latt_str: $i > $o)).
% 4.41/4.59 tff(relstr_set_smaller_type, type, (
% 4.41/4.59 relstr_set_smaller: ( $i * $i * $i ) > $o)).
% 4.41/4.59 tff(latt_element_smaller_type, type, (
% 4.41/4.59 latt_element_smaller: ( $i * $i * $i ) > $o)).
% 4.41/4.59 tff(lattice_type, type, (
% 4.41/4.59 lattice: $i > $o)).
% 4.41/4.59 tff(empty_carrier_type, type, (
% 4.41/4.59 empty_carrier: $i > $o)).
% 4.41/4.59 tff(in_type, type, (
% 4.41/4.59 in: ( $i * $i ) > $o)).
% 4.41/4.59 tff(below_type, type, (
% 4.41/4.59 below: ( $i * $i * $i ) > $o)).
% 4.41/4.59 tff(tptp_fun_D_1_type, type, (
% 4.41/4.59 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 4.41/4.59 tff(the_InternalRel_type, type, (
% 4.41/4.59 the_InternalRel: $i > $i)).
% 4.41/4.59 tff(relation_of_lattice_type, type, (
% 4.41/4.59 relation_of_lattice: $i > $i)).
% 4.41/4.59 tff(strict_rel_str_type, type, (
% 4.41/4.59 strict_rel_str: $i > $o)).
% 4.41/4.59 tff(rel_str_type, type, (
% 4.41/4.59 rel_str: $i > $o)).
% 4.41/4.59 tff(antisymmetric_relstr_type, type, (
% 4.41/4.59 antisymmetric_relstr: $i > $o)).
% 4.41/4.59 tff(transitive_relstr_type, type, (
% 4.41/4.59 transitive_relstr: $i > $o)).
% 4.41/4.59 tff(reflexive_relstr_type, type, (
% 4.41/4.59 reflexive_relstr: $i > $o)).
% 4.41/4.59 tff(relation_of2_type, type, (
% 4.41/4.59 relation_of2: ( $i * $i * $i ) > $o)).
% 4.41/4.59 tff(relation_of2_as_subset_type, type, (
% 4.41/4.59 relation_of2_as_subset: ( $i * $i * $i ) > $o)).
% 4.41/4.59 tff(v1_partfun1_type, type, (
% 4.41/4.59 v1_partfun1: ( $i * $i * $i ) > $o)).
% 4.41/4.59 tff(transitive_type, type, (
% 4.41/4.59 transitive: $i > $o)).
% 4.41/4.59 tff(antisymmetric_type, type, (
% 4.41/4.59 antisymmetric: $i > $o)).
% 4.41/4.59 tff(reflexive_type, type, (
% 4.41/4.59 reflexive: $i > $o)).
% 4.41/4.59 tff(related_type, type, (
% 4.41/4.59 related: ( $i * $i * $i ) > $o)).
% 4.41/4.59 tff(below_refl_type, type, (
% 4.41/4.59 below_refl: ( $i * $i * $i ) > $o)).
% 4.41/4.59 tff(cast_to_el_of_lattice_type, type, (
% 4.41/4.59 cast_to_el_of_lattice: ( $i * $i ) > $i)).
% 4.41/4.59 tff(join_absorbing_type, type, (
% 4.41/4.59 join_absorbing: $i > $o)).
% 4.41/4.59 tff(meet_absorbing_type, type, (
% 4.41/4.59 meet_absorbing: $i > $o)).
% 4.41/4.59 tff(meet_associative_type, type, (
% 4.41/4.59 meet_associative: $i > $o)).
% 4.41/4.59 tff(meet_commutative_type, type, (
% 4.41/4.59 meet_commutative: $i > $o)).
% 4.41/4.59 tff(join_associative_type, type, (
% 4.41/4.59 join_associative: $i > $o)).
% 4.41/4.59 tff(join_commutative_type, type, (
% 4.41/4.59 join_commutative: $i > $o)).
% 4.41/4.59 tff(1,plain,
% 4.41/4.59 ((((~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))))))),
% 4.41/4.59 inference(rewrite,[status(thm)],[])).
% 4.41/4.59 tff(2,plain,
% 4.41/4.59 ((~![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))))))),
% 4.41/4.59 inference(rewrite,[status(thm)],[])).
% 4.41/4.59 tff(3,plain,
% 4.41/4.59 ((~![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))))))),
% 4.41/4.59 inference(rewrite,[status(thm)],[])).
% 4.41/4.59 tff(4,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/sandbox2/benchmark/theBenchmark.p','t30_lattice3')).
% 4.41/4.59 tff(5,plain,
% 4.41/4.59 (~![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)))))),
% 4.41/4.59 inference(modus_ponens,[status(thm)],[4, 3])).
% 4.41/4.59 tff(6,plain,
% 4.41/4.59 (~![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)))))),
% 4.41/4.59 inference(modus_ponens,[status(thm)],[5, 2])).
% 4.41/4.59 tff(7,plain,
% 4.41/4.59 (~![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)))))),
% 4.41/4.59 inference(modus_ponens,[status(thm)],[6, 2])).
% 4.41/4.59 tff(8,plain,
% 4.41/4.59 (~![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)))))),
% 4.41/4.59 inference(modus_ponens,[status(thm)],[7, 2])).
% 4.41/4.59 tff(9,plain,
% 4.41/4.59 ((~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)))))),
% 4.41/4.59 inference(modus_ponens,[status(thm)],[8, 1])).
% 4.41/4.59 tff(10,plain,
% 4.41/4.59 (latt_str(B!18)),
% 4.41/4.59 inference(and_elim,[status(thm)],[9])).
% 4.41/4.59 tff(11,plain,
% 4.41/4.59 (lattice(B!18)),
% 4.41/4.59 inference(and_elim,[status(thm)],[9])).
% 4.41/4.59 tff(12,plain,
% 4.41/4.59 (~empty_carrier(B!18)),
% 4.41/4.59 inference(and_elim,[status(thm)],[9])).
% 4.41/4.59 tff(13,plain,
% 4.41/4.59 (^[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))))),
% 4.41/4.59 inference(bind,[status(th)],[])).
% 4.41/4.59 tff(14,plain,
% 4.41/4.59 (![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)))),
% 4.41/4.59 inference(quant_intro,[status(thm)],[13])).
% 4.41/4.59 tff(15,plain,
% 4.41/4.59 (^[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))))),
% 4.41/4.59 inference(bind,[status(th)],[])).
% 4.41/4.59 tff(16,plain,
% 4.41/4.59 (![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)))),
% 4.41/4.59 inference(quant_intro,[status(thm)],[15])).
% 4.41/4.59 tff(17,plain,
% 4.41/4.59 (^[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))))),
% 4.41/4.59 inference(bind,[status(th)],[])).
% 4.41/4.59 tff(18,plain,
% 4.41/4.59 (![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)))),
% 4.41/4.59 inference(quant_intro,[status(thm)],[17])).
% 4.41/4.59 tff(19,plain,
% 4.41/4.59 (![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)))),
% 4.41/4.59 inference(transitivity,[status(thm)],[18, 16])).
% 4.41/4.59 tff(20,plain,
% 4.41/4.59 (^[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)))))),
% 4.41/4.59 inference(bind,[status(th)],[])).
% 4.41/4.59 tff(21,plain,
% 4.41/4.59 (![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)))),
% 4.41/4.59 inference(quant_intro,[status(thm)],[20])).
% 4.41/4.59 tff(22,plain,
% 4.41/4.59 (![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)))),
% 4.41/4.59 inference(rewrite,[status(thm)],[])).
% 4.41/4.59 tff(23,plain,
% 4.41/4.59 (^[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)))))),
% 4.41/4.60 inference(bind,[status(th)],[])).
% 4.41/4.60 tff(24,plain,
% 4.41/4.60 (![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)))),
% 4.41/4.60 inference(quant_intro,[status(thm)],[23])).
% 4.41/4.60 tff(25,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/sandbox2/benchmark/theBenchmark.p','d3_lattice3')).
% 4.41/4.60 tff(26,plain,
% 4.41/4.60 (![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)))),
% 4.41/4.60 inference(modus_ponens,[status(thm)],[25, 24])).
% 4.41/4.60 tff(27,plain,
% 4.41/4.60 (![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)))),
% 4.41/4.60 inference(modus_ponens,[status(thm)],[26, 22])).
% 4.41/4.60 tff(28,plain,(
% 4.41/4.60 ![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)))),
% 4.41/4.60 inference(skolemize,[status(sab)],[27])).
% 4.41/4.60 tff(29,plain,
% 4.41/4.60 (![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)))),
% 4.41/4.60 inference(modus_ponens,[status(thm)],[28, 21])).
% 4.41/4.60 tff(30,plain,
% 4.41/4.60 (![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)))),
% 4.41/4.60 inference(modus_ponens,[status(thm)],[29, 19])).
% 4.41/4.60 tff(31,plain,
% 4.41/4.60 (![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)))),
% 4.41/4.60 inference(modus_ponens,[status(thm)],[30, 14])).
% 4.41/4.60 tff(32,plain,
% 4.41/4.60 (((~![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)))),
% 4.41/4.60 inference(rewrite,[status(thm)],[])).
% 4.41/4.60 tff(33,plain,
% 4.41/4.60 ((~![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)))),
% 4.41/4.60 inference(quant_inst,[status(thm)],[])).
% 4.41/4.60 tff(34,plain,
% 4.41/4.60 ((~![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))),
% 4.41/4.60 inference(modus_ponens,[status(thm)],[33, 32])).
% 4.41/4.60 tff(35,plain,
% 4.41/4.60 (![B: $i] : ((~element(B, the_carrier(B!18))) | (cast_to_el_of_LattPOSet(B!18, B) = B))),
% 4.41/4.60 inference(unit_resolution,[status(thm)],[34, 31, 12, 11, 10])).
% 4.41/4.60 tff(36,plain,
% 4.41/4.60 (~((~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))))),
% 4.41/4.60 inference(and_elim,[status(thm)],[9])).
% 4.41/4.60 tff(37,plain,
% 4.41/4.60 (element(C!20, the_carrier(B!18))),
% 4.41/4.60 inference(or_elim,[status(thm)],[36])).
% 4.41/4.60 tff(38,plain,
% 4.41/4.60 (((~![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))),
% 4.41/4.60 inference(rewrite,[status(thm)],[])).
% 4.41/4.60 tff(39,plain,
% 4.41/4.60 ((~![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))),
% 4.41/4.60 inference(quant_inst,[status(thm)],[])).
% 4.41/4.60 tff(40,plain,
% 4.41/4.60 ((~![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)),
% 4.41/4.60 inference(modus_ponens,[status(thm)],[39, 38])).
% 4.41/4.60 tff(41,plain,
% 4.41/4.60 (cast_to_el_of_LattPOSet(B!18, C!20) = C!20),
% 4.41/4.60 inference(unit_resolution,[status(thm)],[40, 37, 35])).
% 4.41/4.60 tff(42,plain,
% 4.41/4.60 (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)),
% 4.41/4.60 inference(monotonicity,[status(thm)],[41])).
% 4.41/4.60 tff(43,plain,
% 4.41/4.60 (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))),
% 4.41/4.60 inference(symmetry,[status(thm)],[42])).
% 4.41/4.60 tff(44,plain,
% 4.41/4.60 (^[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))))),
% 4.41/4.60 inference(bind,[status(th)],[])).
% 4.41/4.60 tff(45,plain,
% 4.41/4.60 (![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)))),
% 4.41/4.60 inference(quant_intro,[status(thm)],[44])).
% 4.41/4.60 tff(46,plain,
% 4.41/4.60 (^[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)))))),
% 4.41/4.60 inference(bind,[status(th)],[])).
% 4.41/4.60 tff(47,plain,
% 4.41/4.60 (![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)))),
% 4.41/4.60 inference(quant_intro,[status(thm)],[46])).
% 4.41/4.60 tff(48,plain,
% 4.41/4.60 (![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))))),
% 4.41/4.60 inference(rewrite,[status(thm)],[])).
% 4.41/4.60 tff(49,plain,
% 4.41/4.60 (^[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))))))),
% 4.41/4.60 inference(bind,[status(th)],[])).
% 4.41/4.60 tff(50,plain,
% 4.41/4.60 (![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))))),
% 4.41/4.60 inference(quant_intro,[status(thm)],[49])).
% 4.41/4.60 tff(51,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/sandbox2/benchmark/theBenchmark.p','d2_lattice3')).
% 4.41/4.60 tff(52,plain,
% 4.41/4.60 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))))),
% 4.41/4.60 inference(modus_ponens,[status(thm)],[51, 50])).
% 4.41/4.60 tff(53,plain,
% 4.41/4.60 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))))),
% 4.41/4.60 inference(modus_ponens,[status(thm)],[52, 48])).
% 4.41/4.60 tff(54,plain,(
% 4.41/4.60 ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))))),
% 4.41/4.60 inference(skolemize,[status(sab)],[53])).
% 4.41/4.60 tff(55,plain,
% 4.41/4.60 (![A: $i] : ((poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | empty_carrier(A) | (~latt_str(A)) | (~lattice(A)))),
% 4.41/4.60 inference(modus_ponens,[status(thm)],[54, 47])).
% 4.41/4.60 tff(56,plain,
% 4.41/4.60 (![A: $i] : ((poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | empty_carrier(A) | (~latt_str(A)) | (~lattice(A)))),
% 4.41/4.60 inference(modus_ponens,[status(thm)],[55, 45])).
% 4.41/4.60 tff(57,plain,
% 4.41/4.60 (((~![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) | (~lattice(B!18)) | (~latt_str(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) | (~lattice(B!18)) | (~latt_str(B!18)) | (poset_of_lattice(B!18) = rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 4.41/4.60 inference(rewrite,[status(thm)],[])).
% 4.41/4.60 tff(58,plain,
% 4.41/4.60 (((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) | (~lattice(B!18)) | (~latt_str(B!18)) | (poset_of_lattice(B!18) = rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 4.41/4.60 inference(rewrite,[status(thm)],[])).
% 4.41/4.60 tff(59,plain,
% 4.41/4.60 (((~![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) | (~lattice(B!18)) | (~latt_str(B!18)) | (poset_of_lattice(B!18) = rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))),
% 4.41/4.60 inference(monotonicity,[status(thm)],[58])).
% 4.41/4.60 tff(60,plain,
% 4.41/4.60 (((~![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) | (~lattice(B!18)) | (~latt_str(B!18)) | (poset_of_lattice(B!18) = rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 4.41/4.60 inference(transitivity,[status(thm)],[59, 57])).
% 4.41/4.60 tff(61,plain,
% 4.41/4.60 ((~![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)))),
% 4.41/4.60 inference(quant_inst,[status(thm)],[])).
% 4.41/4.60 tff(62,plain,
% 4.41/4.60 ((~![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) | (~lattice(B!18)) | (~latt_str(B!18)) | (poset_of_lattice(B!18) = rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))),
% 4.41/4.60 inference(modus_ponens,[status(thm)],[61, 60])).
% 4.41/4.60 tff(63,plain,
% 4.41/4.60 (poset_of_lattice(B!18) = rel_str_of(the_carrier(B!18), k2_lattice3(B!18))),
% 4.41/4.60 inference(unit_resolution,[status(thm)],[62, 56, 12, 11, 10])).
% 4.41/4.60 tff(64,plain,
% 4.41/4.60 (rel_str_of(the_carrier(B!18), k2_lattice3(B!18)) = poset_of_lattice(B!18)),
% 4.41/4.60 inference(symmetry,[status(thm)],[63])).
% 4.41/4.60 tff(65,plain,
% 4.41/4.60 (the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) = the_carrier(poset_of_lattice(B!18))),
% 4.41/4.60 inference(monotonicity,[status(thm)],[64])).
% 4.41/4.60 tff(66,plain,
% 4.41/4.60 (the_carrier(poset_of_lattice(B!18)) = the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))),
% 4.41/4.60 inference(symmetry,[status(thm)],[65])).
% 4.41/4.60 tff(67,plain,
% 4.41/4.60 (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))))),
% 4.41/4.60 inference(monotonicity,[status(thm)],[66])).
% 4.41/4.60 tff(68,plain,
% 4.41/4.60 (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))))),
% 4.41/4.60 inference(symmetry,[status(thm)],[67])).
% 4.41/4.60 tff(69,plain,
% 4.41/4.60 (strict_rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) <=> strict_rel_str(poset_of_lattice(B!18))),
% 4.41/4.60 inference(monotonicity,[status(thm)],[64])).
% 4.41/4.60 tff(70,plain,
% 4.41/4.60 (strict_rel_str(poset_of_lattice(B!18)) <=> strict_rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))),
% 4.41/4.60 inference(symmetry,[status(thm)],[69])).
% 4.41/4.60 tff(71,plain,
% 4.41/4.60 (^[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)))))))),
% 4.41/4.60 inference(bind,[status(th)],[])).
% 4.41/4.60 tff(72,plain,
% 4.41/4.60 (![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))))))),
% 4.41/4.60 inference(quant_intro,[status(thm)],[71])).
% 4.41/4.60 tff(73,plain,
% 4.41/4.60 (^[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))))))))),
% 4.41/4.60 inference(bind,[status(th)],[])).
% 4.41/4.60 tff(74,plain,
% 4.41/4.60 (![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))))))),
% 4.41/4.60 inference(quant_intro,[status(thm)],[73])).
% 4.41/4.60 tff(75,plain,
% 4.41/4.60 (![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))))),
% 4.41/4.60 inference(rewrite,[status(thm)],[])).
% 4.41/4.60 tff(76,plain,
% 4.41/4.60 (^[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))))))),
% 4.41/4.60 inference(bind,[status(th)],[])).
% 4.41/4.60 tff(77,plain,
% 4.41/4.60 (![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))))),
% 4.41/4.60 inference(quant_intro,[status(thm)],[76])).
% 4.41/4.60 tff(78,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/sandbox2/benchmark/theBenchmark.p','dt_k3_lattice3')).
% 4.41/4.60 tff(79,plain,
% 4.41/4.60 (![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))))),
% 4.41/4.60 inference(modus_ponens,[status(thm)],[78, 77])).
% 4.41/4.60 tff(80,plain,
% 4.41/4.60 (![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))))),
% 4.41/4.60 inference(modus_ponens,[status(thm)],[79, 75])).
% 4.41/4.60 tff(81,plain,(
% 4.41/4.60 ![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))))),
% 4.41/4.60 inference(skolemize,[status(sab)],[80])).
% 4.41/4.60 tff(82,plain,
% 4.41/4.60 (![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))))))),
% 4.41/4.60 inference(modus_ponens,[status(thm)],[81, 74])).
% 4.41/4.60 tff(83,plain,
% 4.41/4.60 (![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))))))),
% 4.41/4.60 inference(modus_ponens,[status(thm)],[82, 72])).
% 4.41/4.60 tff(84,plain,
% 4.41/4.60 (((~![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))))))),
% 4.41/4.60 inference(rewrite,[status(thm)],[])).
% 4.41/4.60 tff(85,plain,
% 4.41/4.60 ((~![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))))))),
% 4.43/4.60 inference(quant_inst,[status(thm)],[])).
% 4.43/4.60 tff(86,plain,
% 4.43/4.60 ((~![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)))))),
% 4.43/4.60 inference(modus_ponens,[status(thm)],[85, 84])).
% 4.43/4.60 tff(87,plain,
% 4.43/4.60 (~((~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))))),
% 4.43/4.60 inference(unit_resolution,[status(thm)],[86, 83, 12, 11, 10])).
% 4.43/4.60 tff(88,plain,
% 4.43/4.60 (((~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))),
% 4.43/4.60 inference(tautology,[status(thm)],[])).
% 4.43/4.60 tff(89,plain,
% 4.43/4.60 (strict_rel_str(poset_of_lattice(B!18))),
% 4.43/4.60 inference(unit_resolution,[status(thm)],[88, 87])).
% 4.43/4.60 tff(90,plain,
% 4.43/4.60 (strict_rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))),
% 4.43/4.60 inference(modus_ponens,[status(thm)],[89, 70])).
% 4.43/4.60 tff(91,plain,
% 4.43/4.60 (rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) <=> rel_str(poset_of_lattice(B!18))),
% 4.43/4.60 inference(monotonicity,[status(thm)],[64])).
% 4.43/4.60 tff(92,plain,
% 4.43/4.60 (rel_str(poset_of_lattice(B!18)) <=> rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))),
% 4.43/4.60 inference(symmetry,[status(thm)],[91])).
% 4.43/4.60 tff(93,plain,
% 4.43/4.60 (((~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))),
% 4.43/4.60 inference(tautology,[status(thm)],[])).
% 4.43/4.60 tff(94,plain,
% 4.43/4.60 (rel_str(poset_of_lattice(B!18))),
% 4.43/4.60 inference(unit_resolution,[status(thm)],[93, 87])).
% 4.43/4.60 tff(95,plain,
% 4.43/4.60 (rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))),
% 4.43/4.60 inference(modus_ponens,[status(thm)],[94, 92])).
% 4.43/4.60 tff(96,plain,
% 4.43/4.60 (^[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))))),
% 4.43/4.60 inference(bind,[status(th)],[])).
% 4.43/4.60 tff(97,plain,
% 4.43/4.60 (![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)))),
% 4.43/4.60 inference(quant_intro,[status(thm)],[96])).
% 4.43/4.60 tff(98,plain,
% 4.43/4.60 (![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)))),
% 4.43/4.60 inference(rewrite,[status(thm)],[])).
% 4.43/4.60 tff(99,plain,
% 4.43/4.60 (^[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)))))),
% 4.43/4.60 inference(bind,[status(th)],[])).
% 4.43/4.60 tff(100,plain,
% 4.43/4.60 (![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)))),
% 4.43/4.60 inference(quant_intro,[status(thm)],[99])).
% 4.43/4.60 tff(101,axiom,(![A: $i] : (rel_str(A) => (strict_rel_str(A) => (A = rel_str_of(the_carrier(A), the_InternalRel(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','abstractness_v1_orders_2')).
% 4.43/4.60 tff(102,plain,
% 4.43/4.60 (![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 4.43/4.60 inference(modus_ponens,[status(thm)],[101, 100])).
% 4.43/4.60 tff(103,plain,
% 4.43/4.60 (![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 4.43/4.60 inference(modus_ponens,[status(thm)],[102, 98])).
% 4.43/4.60 tff(104,plain,(
% 4.43/4.60 ![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 4.43/4.60 inference(skolemize,[status(sab)],[103])).
% 4.43/4.60 tff(105,plain,
% 4.43/4.60 (![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 4.43/4.60 inference(modus_ponens,[status(thm)],[104, 97])).
% 4.43/4.60 tff(106,plain,
% 4.43/4.60 (((~![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)))))),
% 4.43/4.60 inference(rewrite,[status(thm)],[])).
% 4.43/4.60 tff(107,plain,
% 4.43/4.60 (((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)))))),
% 4.43/4.60 inference(rewrite,[status(thm)],[])).
% 4.43/4.60 tff(108,plain,
% 4.43/4.60 (((~![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))))))),
% 4.43/4.60 inference(monotonicity,[status(thm)],[107])).
% 4.43/4.60 tff(109,plain,
% 4.43/4.60 (((~![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)))))),
% 4.43/4.60 inference(transitivity,[status(thm)],[108, 106])).
% 4.43/4.60 tff(110,plain,
% 4.43/4.60 ((~![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)))))),
% 4.43/4.60 inference(quant_inst,[status(thm)],[])).
% 4.43/4.60 tff(111,plain,
% 4.43/4.60 ((~![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))))),
% 4.43/4.60 inference(modus_ponens,[status(thm)],[110, 109])).
% 4.43/4.60 tff(112,plain,
% 4.43/4.60 ((~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))))),
% 4.43/4.60 inference(unit_resolution,[status(thm)],[111, 105])).
% 4.43/4.60 tff(113,plain,
% 4.43/4.60 (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))))),
% 4.43/4.60 inference(unit_resolution,[status(thm)],[112, 95, 90])).
% 4.43/4.60 tff(114,plain,
% 4.43/4.60 (^[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))))),
% 4.43/4.60 inference(bind,[status(th)],[])).
% 4.43/4.60 tff(115,plain,
% 4.43/4.60 (![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)))),
% 4.43/4.60 inference(quant_intro,[status(thm)],[114])).
% 4.43/4.60 tff(116,plain,
% 4.43/4.60 (^[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)))))),
% 4.43/4.60 inference(bind,[status(th)],[])).
% 4.43/4.60 tff(117,plain,
% 4.43/4.60 (![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)))),
% 4.43/4.60 inference(quant_intro,[status(thm)],[116])).
% 4.43/4.60 tff(118,plain,
% 4.43/4.60 (![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)))),
% 4.43/4.60 inference(rewrite,[status(thm)],[])).
% 4.43/4.60 tff(119,plain,
% 4.43/4.60 (^[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)))))),
% 4.43/4.60 inference(bind,[status(th)],[])).
% 4.43/4.60 tff(120,plain,
% 4.43/4.60 (![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)))),
% 4.43/4.60 inference(quant_intro,[status(thm)],[119])).
% 4.43/4.60 tff(121,axiom,(![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => (k2_lattice3(A) = relation_of_lattice(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k2_lattice3')).
% 4.43/4.60 tff(122,plain,
% 4.43/4.60 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (k2_lattice3(A) = relation_of_lattice(A)))),
% 4.43/4.60 inference(modus_ponens,[status(thm)],[121, 120])).
% 4.43/4.60 tff(123,plain,
% 4.43/4.60 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (k2_lattice3(A) = relation_of_lattice(A)))),
% 4.43/4.60 inference(modus_ponens,[status(thm)],[122, 118])).
% 4.43/4.60 tff(124,plain,(
% 4.43/4.60 ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (k2_lattice3(A) = relation_of_lattice(A)))),
% 4.43/4.60 inference(skolemize,[status(sab)],[123])).
% 4.43/4.60 tff(125,plain,
% 4.43/4.60 (![A: $i] : (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))),
% 4.43/4.60 inference(modus_ponens,[status(thm)],[124, 117])).
% 4.43/4.60 tff(126,plain,
% 4.43/4.60 (![A: $i] : (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))),
% 4.43/4.60 inference(modus_ponens,[status(thm)],[125, 115])).
% 4.43/4.60 tff(127,plain,
% 4.43/4.60 (((~![A: $i] : (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))) | (empty_carrier(B!18) | (~lattice(B!18)) | (~latt_str(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) | (~lattice(B!18)) | (~latt_str(B!18)) | (k2_lattice3(B!18) = relation_of_lattice(B!18)))),
% 4.43/4.60 inference(rewrite,[status(thm)],[])).
% 4.43/4.60 tff(128,plain,
% 4.43/4.60 ((empty_carrier(B!18) | (k2_lattice3(B!18) = relation_of_lattice(B!18)) | (~latt_str(B!18)) | (~lattice(B!18))) <=> (empty_carrier(B!18) | (~lattice(B!18)) | (~latt_str(B!18)) | (k2_lattice3(B!18) = relation_of_lattice(B!18)))),
% 4.43/4.60 inference(rewrite,[status(thm)],[])).
% 4.43/4.60 tff(129,plain,
% 4.43/4.60 (((~![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) | (~lattice(B!18)) | (~latt_str(B!18)) | (k2_lattice3(B!18) = relation_of_lattice(B!18))))),
% 4.43/4.60 inference(monotonicity,[status(thm)],[128])).
% 4.43/4.60 tff(130,plain,
% 4.43/4.60 (((~![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) | (~lattice(B!18)) | (~latt_str(B!18)) | (k2_lattice3(B!18) = relation_of_lattice(B!18)))),
% 4.43/4.60 inference(transitivity,[status(thm)],[129, 127])).
% 4.43/4.60 tff(131,plain,
% 4.43/4.60 ((~![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)))),
% 4.43/4.60 inference(quant_inst,[status(thm)],[])).
% 4.43/4.60 tff(132,plain,
% 4.43/4.60 ((~![A: $i] : (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))) | empty_carrier(B!18) | (~lattice(B!18)) | (~latt_str(B!18)) | (k2_lattice3(B!18) = relation_of_lattice(B!18))),
% 4.43/4.60 inference(modus_ponens,[status(thm)],[131, 130])).
% 4.43/4.60 tff(133,plain,
% 4.43/4.60 (k2_lattice3(B!18) = relation_of_lattice(B!18)),
% 4.43/4.60 inference(unit_resolution,[status(thm)],[132, 126, 12, 11, 10])).
% 4.43/4.60 tff(134,plain,
% 4.43/4.60 (relation_of_lattice(B!18) = k2_lattice3(B!18)),
% 4.43/4.60 inference(symmetry,[status(thm)],[133])).
% 4.43/4.60 tff(135,plain,
% 4.43/4.60 (rel_str_of(the_carrier(B!18), relation_of_lattice(B!18)) = rel_str_of(the_carrier(B!18), k2_lattice3(B!18))),
% 4.43/4.60 inference(monotonicity,[status(thm)],[134])).
% 4.43/4.60 tff(136,plain,
% 4.43/4.60 (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))))),
% 4.43/4.60 inference(transitivity,[status(thm)],[135, 113, 68])).
% 4.43/4.60 tff(137,plain,
% 4.43/4.60 (^[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)))),
% 4.43/4.60 inference(bind,[status(th)],[])).
% 4.43/4.60 tff(138,plain,
% 4.43/4.60 (![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))),
% 4.43/4.60 inference(quant_intro,[status(thm)],[137])).
% 4.43/4.60 tff(139,plain,
% 4.43/4.60 (![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))),
% 4.43/4.60 inference(rewrite,[status(thm)],[])).
% 4.43/4.60 tff(140,axiom,(![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 4.43/4.60 tff(141,plain,
% 4.43/4.60 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 4.43/4.60 inference(modus_ponens,[status(thm)],[140, 139])).
% 4.43/4.60 tff(142,plain,(
% 4.43/4.60 ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 4.43/4.60 inference(skolemize,[status(sab)],[141])).
% 4.43/4.60 tff(143,plain,
% 4.43/4.60 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 4.43/4.60 inference(modus_ponens,[status(thm)],[142, 138])).
% 4.43/4.60 tff(144,plain,
% 4.43/4.60 ((~![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)))),
% 4.43/4.60 inference(quant_inst,[status(thm)],[])).
% 4.43/4.60 tff(145,plain,
% 4.43/4.60 (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))),
% 4.43/4.60 inference(unit_resolution,[status(thm)],[144, 143])).
% 4.43/4.60 tff(146,plain,
% 4.43/4.60 (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))),
% 4.43/4.60 inference(monotonicity,[status(thm)],[134])).
% 4.43/4.60 tff(147,plain,
% 4.43/4.60 (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))),
% 4.43/4.60 inference(symmetry,[status(thm)],[146])).
% 4.43/4.60 tff(148,plain,
% 4.43/4.60 (^[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)))))))),
% 4.43/4.60 inference(bind,[status(th)],[])).
% 4.43/4.60 tff(149,plain,
% 4.43/4.60 (![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))))))),
% 4.43/4.60 inference(quant_intro,[status(thm)],[148])).
% 4.43/4.60 tff(150,plain,
% 4.43/4.60 (^[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))))))))),
% 4.43/4.60 inference(bind,[status(th)],[])).
% 4.43/4.60 tff(151,plain,
% 4.43/4.60 (![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))))))),
% 4.43/4.60 inference(quant_intro,[status(thm)],[150])).
% 4.43/4.60 tff(152,plain,
% 4.43/4.60 (![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))))),
% 4.43/4.60 inference(rewrite,[status(thm)],[])).
% 4.43/4.60 tff(153,plain,
% 4.43/4.60 (^[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))))))),
% 4.43/4.61 inference(bind,[status(th)],[])).
% 4.43/4.61 tff(154,plain,
% 4.43/4.61 (![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))))),
% 4.43/4.61 inference(quant_intro,[status(thm)],[153])).
% 4.43/4.61 tff(155,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/sandbox2/benchmark/theBenchmark.p','dt_k2_lattice3')).
% 4.43/4.61 tff(156,plain,
% 4.43/4.61 (![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))))),
% 4.43/4.61 inference(modus_ponens,[status(thm)],[155, 154])).
% 4.43/4.61 tff(157,plain,
% 4.43/4.61 (![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))))),
% 4.43/4.61 inference(modus_ponens,[status(thm)],[156, 152])).
% 4.43/4.61 tff(158,plain,(
% 4.43/4.61 ![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))))),
% 4.43/4.61 inference(skolemize,[status(sab)],[157])).
% 4.43/4.61 tff(159,plain,
% 4.43/4.61 (![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))))))),
% 4.43/4.61 inference(modus_ponens,[status(thm)],[158, 151])).
% 4.43/4.61 tff(160,plain,
% 4.43/4.61 (![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))))))),
% 4.43/4.61 inference(modus_ponens,[status(thm)],[159, 149])).
% 4.43/4.61 tff(161,plain,
% 4.43/4.61 (((~![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))))))),
% 4.43/4.61 inference(rewrite,[status(thm)],[])).
% 4.43/4.61 tff(162,plain,
% 4.43/4.61 ((~![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))))))),
% 4.43/4.61 inference(quant_inst,[status(thm)],[])).
% 4.43/4.61 tff(163,plain,
% 4.43/4.61 ((~![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)))))),
% 4.43/4.61 inference(modus_ponens,[status(thm)],[162, 161])).
% 4.43/4.61 tff(164,plain,
% 4.43/4.61 (~((~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))))),
% 4.43/4.61 inference(unit_resolution,[status(thm)],[163, 160, 12, 11, 10])).
% 4.43/4.61 tff(165,plain,
% 4.43/4.61 (((~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))),
% 4.43/4.61 inference(tautology,[status(thm)],[])).
% 4.43/4.61 tff(166,plain,
% 4.43/4.61 (relation_of2_as_subset(k2_lattice3(B!18), the_carrier(B!18), the_carrier(B!18))),
% 4.43/4.61 inference(unit_resolution,[status(thm)],[165, 164])).
% 4.43/4.61 tff(167,plain,
% 4.43/4.61 (relation_of2_as_subset(relation_of_lattice(B!18), the_carrier(B!18), the_carrier(B!18))),
% 4.43/4.61 inference(modus_ponens,[status(thm)],[166, 147])).
% 4.43/4.61 tff(168,plain,
% 4.43/4.61 ((~(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))),
% 4.43/4.61 inference(tautology,[status(thm)],[])).
% 4.43/4.61 tff(169,plain,
% 4.43/4.61 (relation_of2(relation_of_lattice(B!18), the_carrier(B!18), the_carrier(B!18))),
% 4.43/4.61 inference(unit_resolution,[status(thm)],[168, 167, 145])).
% 4.43/4.61 tff(170,plain,
% 4.43/4.61 (^[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)))))))),
% 4.43/4.61 inference(bind,[status(th)],[])).
% 4.43/4.61 tff(171,plain,
% 4.43/4.61 (![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))))))),
% 4.43/4.61 inference(quant_intro,[status(thm)],[170])).
% 4.43/4.61 tff(172,plain,
% 4.43/4.61 (^[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)))))))),
% 4.43/4.61 inference(bind,[status(th)],[])).
% 4.43/4.61 tff(173,plain,
% 4.43/4.61 (![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))))))),
% 4.43/4.61 inference(quant_intro,[status(thm)],[172])).
% 4.43/4.61 tff(174,plain,
% 4.43/4.61 (![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))))))),
% 4.43/4.61 inference(transitivity,[status(thm)],[173, 171])).
% 4.43/4.61 tff(175,plain,
% 4.43/4.61 (^[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)))))))),
% 4.43/4.61 inference(bind,[status(th)],[])).
% 4.43/4.61 tff(176,plain,
% 4.43/4.61 (![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))))))),
% 4.43/4.61 inference(quant_intro,[status(thm)],[175])).
% 4.43/4.61 tff(177,plain,
% 4.43/4.61 (![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))))),
% 4.43/4.61 inference(rewrite,[status(thm)],[])).
% 4.43/4.61 tff(178,plain,
% 4.43/4.61 (^[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))))))),
% 4.43/4.61 inference(bind,[status(th)],[])).
% 4.43/4.61 tff(179,plain,
% 4.43/4.61 (![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))))),
% 4.43/4.61 inference(quant_intro,[status(thm)],[178])).
% 4.43/4.61 tff(180,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/sandbox2/benchmark/theBenchmark.p','free_g1_orders_2')).
% 4.43/4.61 tff(181,plain,
% 4.43/4.61 (![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))))),
% 4.43/4.61 inference(modus_ponens,[status(thm)],[180, 179])).
% 4.43/4.61 tff(182,plain,
% 4.43/4.61 (![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))))),
% 4.43/4.61 inference(modus_ponens,[status(thm)],[181, 177])).
% 4.43/4.61 tff(183,plain,(
% 4.43/4.61 ![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))))),
% 4.43/4.61 inference(skolemize,[status(sab)],[182])).
% 4.43/4.61 tff(184,plain,
% 4.43/4.61 (![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))))))),
% 4.43/4.61 inference(modus_ponens,[status(thm)],[183, 176])).
% 4.43/4.61 tff(185,plain,
% 4.43/4.61 (![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))))))),
% 4.43/4.61 inference(modus_ponens,[status(thm)],[184, 174])).
% 4.43/4.61 tff(186,plain,
% 4.43/4.61 (((~![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))))))),
% 4.43/4.61 inference(rewrite,[status(thm)],[])).
% 4.43/4.61 tff(187,plain,
% 4.43/4.61 ((~![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))))))),
% 4.43/4.61 inference(quant_inst,[status(thm)],[])).
% 4.43/4.61 tff(188,plain,
% 4.43/4.61 ((~![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)))))),
% 4.43/4.61 inference(modus_ponens,[status(thm)],[187, 186])).
% 4.43/4.61 tff(189,plain,
% 4.43/4.61 ((~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)))))),
% 4.43/4.61 inference(unit_resolution,[status(thm)],[188, 185])).
% 4.43/4.61 tff(190,plain,
% 4.43/4.61 (![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)))))),
% 4.43/4.61 inference(unit_resolution,[status(thm)],[189, 169])).
% 4.43/4.61 tff(191,plain,
% 4.43/4.61 (((~![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))))))))),
% 4.43/4.61 inference(rewrite,[status(thm)],[])).
% 4.43/4.61 tff(192,plain,
% 4.43/4.61 ((~![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))))))))),
% 4.43/4.61 inference(quant_inst,[status(thm)],[])).
% 4.43/4.61 tff(193,plain,
% 4.43/4.61 ((~![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)))))))),
% 4.43/4.61 inference(modus_ponens,[status(thm)],[192, 191])).
% 4.43/4.61 tff(194,plain,
% 4.43/4.61 ((~(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)))))))),
% 4.43/4.61 inference(unit_resolution,[status(thm)],[193, 190])).
% 4.43/4.61 tff(195,plain,
% 4.43/4.61 (~((~(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))))))),
% 4.43/4.61 inference(unit_resolution,[status(thm)],[194, 136])).
% 4.43/4.61 tff(196,plain,
% 4.43/4.61 (((~(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)))),
% 4.43/4.61 inference(tautology,[status(thm)],[])).
% 4.43/4.61 tff(197,plain,
% 4.43/4.61 (the_carrier(B!18) = the_carrier(poset_of_lattice(B!18))),
% 4.43/4.61 inference(unit_resolution,[status(thm)],[196, 195])).
% 4.43/4.61 tff(198,plain,
% 4.43/4.61 (the_carrier(B!18) = the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))),
% 4.43/4.61 inference(transitivity,[status(thm)],[197, 66])).
% 4.43/4.61 tff(199,plain,
% 4.43/4.61 (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))))),
% 4.43/4.61 inference(monotonicity,[status(thm)],[198])).
% 4.43/4.61 tff(200,plain,
% 4.43/4.61 (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))),
% 4.43/4.61 inference(symmetry,[status(thm)],[199])).
% 4.43/4.61 tff(201,plain,
% 4.43/4.61 (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))),
% 4.43/4.61 inference(monotonicity,[status(thm)],[64])).
% 4.43/4.61 tff(202,plain,
% 4.43/4.61 (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))),
% 4.43/4.61 inference(symmetry,[status(thm)],[201])).
% 4.43/4.61 tff(203,plain,
% 4.43/4.61 ((~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)))),
% 4.43/4.61 inference(monotonicity,[status(thm)],[202])).
% 4.43/4.61 tff(204,assumption,(~relstr_set_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20))), introduced(assumption)).
% 4.43/4.61 tff(205,plain,
% 4.43/4.61 (~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))),
% 4.43/4.61 inference(modus_ponens,[status(thm)],[204, 203])).
% 4.43/4.61 tff(206,plain,
% 4.43/4.61 (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)))),
% 4.43/4.61 inference(monotonicity,[status(thm)],[65])).
% 4.43/4.61 tff(207,plain,
% 4.43/4.61 (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))))),
% 4.43/4.61 inference(symmetry,[status(thm)],[206])).
% 4.43/4.61 tff(208,plain,
% 4.43/4.61 (^[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))))),
% 4.43/4.61 inference(bind,[status(th)],[])).
% 4.43/4.61 tff(209,plain,
% 4.43/4.61 (![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)))),
% 4.43/4.61 inference(quant_intro,[status(thm)],[208])).
% 4.43/4.61 tff(210,plain,
% 4.43/4.61 (^[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)))))),
% 4.43/4.61 inference(bind,[status(th)],[])).
% 4.43/4.61 tff(211,plain,
% 4.43/4.61 (![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)))),
% 4.43/4.61 inference(quant_intro,[status(thm)],[210])).
% 4.43/4.61 tff(212,plain,
% 4.43/4.61 (![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))))),
% 4.43/4.61 inference(rewrite,[status(thm)],[])).
% 4.43/4.61 tff(213,plain,
% 4.43/4.61 (^[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))))))),
% 4.43/4.61 inference(bind,[status(th)],[])).
% 4.43/4.61 tff(214,plain,
% 4.43/4.61 (![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))))),
% 4.43/4.61 inference(quant_intro,[status(thm)],[213])).
% 4.43/4.61 tff(215,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/sandbox2/benchmark/theBenchmark.p','dt_k4_lattice3')).
% 4.43/4.61 tff(216,plain,
% 4.43/4.61 (![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))))),
% 4.43/4.61 inference(modus_ponens,[status(thm)],[215, 214])).
% 4.43/4.61 tff(217,plain,
% 4.43/4.61 (![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))))),
% 4.43/4.61 inference(modus_ponens,[status(thm)],[216, 212])).
% 4.43/4.61 tff(218,plain,(
% 4.43/4.61 ![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))))),
% 4.43/4.61 inference(skolemize,[status(sab)],[217])).
% 4.43/4.61 tff(219,plain,
% 4.43/4.61 (![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)))),
% 4.43/4.61 inference(modus_ponens,[status(thm)],[218, 211])).
% 4.43/4.61 tff(220,plain,
% 4.43/4.61 (![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)))),
% 4.43/4.61 inference(modus_ponens,[status(thm)],[219, 209])).
% 4.43/4.61 tff(221,plain,
% 4.43/4.61 (((~![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))) | (~lattice(B!18)) | (~latt_str(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))) | (~lattice(B!18)) | (~latt_str(B!18)) | element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18))))),
% 4.43/4.61 inference(rewrite,[status(thm)],[])).
% 4.43/4.61 tff(222,plain,
% 4.43/4.61 ((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))) | (~lattice(B!18)) | (~latt_str(B!18)) | element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18))))),
% 4.43/4.61 inference(rewrite,[status(thm)],[])).
% 4.43/4.61 tff(223,plain,
% 4.43/4.61 (((~![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))) | (~lattice(B!18)) | (~latt_str(B!18)) | element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18)))))),
% 4.43/4.61 inference(monotonicity,[status(thm)],[222])).
% 4.43/4.61 tff(224,plain,
% 4.43/4.61 (((~![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))) | (~lattice(B!18)) | (~latt_str(B!18)) | element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18))))),
% 4.43/4.61 inference(transitivity,[status(thm)],[223, 221])).
% 4.43/4.61 tff(225,plain,
% 4.43/4.61 ((~![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)))),
% 4.43/4.61 inference(quant_inst,[status(thm)],[])).
% 4.43/4.61 tff(226,plain,
% 4.43/4.61 ((~![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))) | (~lattice(B!18)) | (~latt_str(B!18)) | element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18)))),
% 4.43/4.61 inference(modus_ponens,[status(thm)],[225, 224])).
% 4.43/4.61 tff(227,plain,
% 4.43/4.61 (element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18)))),
% 4.43/4.61 inference(unit_resolution,[status(thm)],[226, 220, 12, 11, 10, 37])).
% 4.43/4.61 tff(228,plain,
% 4.43/4.61 (element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 4.43/4.61 inference(modus_ponens,[status(thm)],[227, 207])).
% 4.43/4.61 tff(229,plain,
% 4.43/4.61 (^[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)))))))))))),
% 4.43/4.61 inference(bind,[status(th)],[])).
% 4.43/4.61 tff(230,plain,
% 4.43/4.61 (![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))))))))))),
% 4.43/4.61 inference(quant_intro,[status(thm)],[229])).
% 4.43/4.61 tff(231,plain,
% 4.43/4.61 (^[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)))))))))))),
% 4.43/4.61 inference(bind,[status(th)],[])).
% 4.43/4.61 tff(232,plain,
% 4.43/4.61 (![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))))))))))),
% 4.43/4.61 inference(quant_intro,[status(thm)],[231])).
% 4.43/4.61 tff(233,plain,
% 4.43/4.61 (![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))))))))))),
% 4.43/4.61 inference(transitivity,[status(thm)],[232, 230])).
% 4.43/4.61 tff(234,plain,
% 4.43/4.61 (^[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)))))))))))),
% 4.43/4.61 inference(bind,[status(th)],[])).
% 4.43/4.61 tff(235,plain,
% 4.43/4.61 (![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))))))))))),
% 4.43/4.61 inference(quant_intro,[status(thm)],[234])).
% 4.43/4.61 tff(236,plain,
% 4.43/4.61 (![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))))))),
% 4.43/4.61 inference(rewrite,[status(thm)],[])).
% 4.43/4.61 tff(237,plain,
% 4.43/4.61 (^[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))))))))),
% 4.43/4.61 inference(bind,[status(th)],[])).
% 4.43/4.61 tff(238,plain,
% 4.43/4.61 (![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))))))),
% 4.43/4.61 inference(quant_intro,[status(thm)],[237])).
% 4.43/4.61 tff(239,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/sandbox2/benchmark/theBenchmark.p','d9_lattice3')).
% 4.43/4.61 tff(240,plain,
% 4.43/4.61 (![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))))))),
% 4.43/4.61 inference(modus_ponens,[status(thm)],[239, 238])).
% 4.43/4.61 tff(241,plain,
% 4.43/4.61 (![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))))))),
% 4.43/4.61 inference(modus_ponens,[status(thm)],[240, 236])).
% 4.43/4.61 tff(242,plain,(
% 4.43/4.61 ![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))))))))),
% 4.43/4.62 inference(skolemize,[status(sab)],[241])).
% 4.43/4.62 tff(243,plain,
% 4.43/4.62 (![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))))))))))),
% 4.43/4.62 inference(modus_ponens,[status(thm)],[242, 235])).
% 4.43/4.62 tff(244,plain,
% 4.43/4.62 (![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))))))))))),
% 4.43/4.62 inference(modus_ponens,[status(thm)],[243, 233])).
% 4.43/4.62 tff(245,plain,
% 4.43/4.62 (((~![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) | (~((~in(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), B)) | (~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))))) | 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)))))))))) <=> ((~![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) | (~((~in(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), B)) | (~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))))) | 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)))))))))),
% 4.43/4.62 inference(rewrite,[status(thm)],[])).
% 4.43/4.62 tff(246,plain,
% 4.43/4.62 (((~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) | (~((~in(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), B)) | (~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))))) | 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)))))))))),
% 4.43/4.62 inference(rewrite,[status(thm)],[])).
% 4.43/4.62 tff(247,plain,
% 4.43/4.62 (((~![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) | (~((~in(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), B)) | (~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))))) | 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))))))))))),
% 4.43/4.62 inference(monotonicity,[status(thm)],[246])).
% 4.43/4.62 tff(248,plain,
% 4.43/4.62 (((~![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) | (~((~in(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), B)) | (~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))))) | 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)))))))))),
% 4.43/4.62 inference(transitivity,[status(thm)],[247, 245])).
% 4.43/4.62 tff(249,plain,
% 4.43/4.62 ((~![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))))))))))),
% 4.43/4.62 inference(quant_inst,[status(thm)],[])).
% 4.43/4.62 tff(250,plain,
% 4.43/4.62 ((~![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) | (~((~in(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), B)) | (~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))))) | 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))))))))),
% 4.43/4.62 inference(modus_ponens,[status(thm)],[249, 248])).
% 4.43/4.62 tff(251,plain,
% 4.43/4.62 ((~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) | (~((~in(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), B)) | (~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))))) | 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))))))))),
% 4.43/4.62 inference(unit_resolution,[status(thm)],[250, 244])).
% 4.43/4.62 tff(252,plain,
% 4.43/4.62 (![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) | (~((~in(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), B)) | (~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))))) | 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))))))))),
% 4.43/4.62 inference(unit_resolution,[status(thm)],[251, 95])).
% 4.43/4.62 tff(253,plain,
% 4.43/4.62 (((~![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) | (~((~in(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), B)) | (~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))))) | 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(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) | (~((~in(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), B)) | (~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))))) | 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(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)))))))))),
% 4.43/4.62 inference(rewrite,[status(thm)],[])).
% 4.43/4.62 tff(254,plain,
% 4.43/4.62 (((~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)) | (~((~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))))) | 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(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)))))))))),
% 4.43/4.62 inference(rewrite,[status(thm)],[])).
% 4.43/4.62 tff(255,plain,
% 4.43/4.62 (((~![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) | (~((~in(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), B)) | (~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))))) | 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(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)) | (~((~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))))) | 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)))))))))) <=> ((~![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) | (~((~in(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), B)) | (~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))))) | 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(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))))))))))),
% 4.43/4.62 inference(monotonicity,[status(thm)],[254])).
% 4.43/4.62 tff(256,plain,
% 4.43/4.62 (((~![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) | (~((~in(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), B)) | (~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))))) | 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(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)) | (~((~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))))) | 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)))))))))) <=> ((~![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) | (~((~in(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), B)) | (~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))))) | 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(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)))))))))),
% 4.43/4.62 inference(transitivity,[status(thm)],[255, 253])).
% 4.43/4.62 tff(257,plain,
% 4.43/4.62 ((~![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) | (~((~in(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), B)) | (~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))))) | 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(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)) | (~((~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))))) | 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)))))))))),
% 4.43/4.62 inference(quant_inst,[status(thm)],[])).
% 4.43/4.62 tff(258,plain,
% 4.43/4.62 ((~![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) | (~((~in(tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))), B)) | (~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))))) | 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(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))))))))),
% 4.43/4.63 inference(modus_ponens,[status(thm)],[257, 256])).
% 4.43/4.63 tff(259,plain,
% 4.43/4.63 ((~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))))))))),
% 4.43/4.63 inference(unit_resolution,[status(thm)],[258, 252])).
% 4.43/4.63 tff(260,plain,
% 4.43/4.63 (~((~((~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)))))))),
% 4.43/4.63 inference(unit_resolution,[status(thm)],[259, 228])).
% 4.43/4.63 tff(261,plain,
% 4.43/4.63 (((~((~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)))))),
% 4.43/4.63 inference(tautology,[status(thm)],[])).
% 4.43/4.63 tff(262,plain,
% 4.43/4.63 (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))))),
% 4.43/4.63 inference(unit_resolution,[status(thm)],[261, 260])).
% 4.43/4.63 tff(263,plain,
% 4.43/4.63 ((~(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))))),
% 4.43/4.63 inference(tautology,[status(thm)],[])).
% 4.43/4.63 tff(264,plain,
% 4.43/4.63 (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))))),
% 4.43/4.63 inference(unit_resolution,[status(thm)],[263, 262])).
% 4.43/4.63 tff(265,plain,
% 4.43/4.63 (~(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)))),
% 4.43/4.63 inference(unit_resolution,[status(thm)],[264, 205])).
% 4.43/4.63 tff(266,plain,
% 4.43/4.63 ((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))))),
% 4.43/4.63 inference(tautology,[status(thm)],[])).
% 4.43/4.63 tff(267,plain,
% 4.43/4.63 (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))))),
% 4.43/4.63 inference(unit_resolution,[status(thm)],[266, 265])).
% 4.43/4.63 tff(268,plain,
% 4.43/4.63 (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))),
% 4.43/4.63 inference(modus_ponens,[status(thm)],[267, 200])).
% 4.43/4.63 tff(269,plain,
% 4.43/4.63 (((~![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)))))),
% 4.43/4.63 inference(rewrite,[status(thm)],[])).
% 4.43/4.63 tff(270,plain,
% 4.43/4.63 ((~![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)))))),
% 4.43/4.63 inference(quant_inst,[status(thm)],[])).
% 4.43/4.63 tff(271,plain,
% 4.43/4.63 ((~![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))))),
% 4.43/4.63 inference(modus_ponens,[status(thm)],[270, 269])).
% 4.43/4.63 tff(272,plain,
% 4.43/4.63 ((~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))))),
% 4.43/4.63 inference(unit_resolution,[status(thm)],[271, 35])).
% 4.43/4.63 tff(273,plain,
% 4.43/4.63 (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)))),
% 4.43/4.63 inference(unit_resolution,[status(thm)],[272, 268])).
% 4.43/4.63 tff(274,plain,
% 4.43/4.63 (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))),
% 4.43/4.63 inference(monotonicity,[status(thm)],[63, 273, 42])).
% 4.43/4.63 tff(275,plain,
% 4.43/4.63 (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)))),
% 4.43/4.63 inference(symmetry,[status(thm)],[274])).
% 4.43/4.63 tff(276,plain,
% 4.43/4.63 ((~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))))),
% 4.43/4.63 inference(monotonicity,[status(thm)],[275])).
% 4.43/4.63 tff(277,plain,
% 4.43/4.63 (reflexive_relstr(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) <=> reflexive_relstr(poset_of_lattice(B!18))),
% 4.43/4.63 inference(monotonicity,[status(thm)],[64])).
% 4.43/4.63 tff(278,plain,
% 4.43/4.63 (reflexive_relstr(poset_of_lattice(B!18)) <=> reflexive_relstr(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))),
% 4.43/4.63 inference(symmetry,[status(thm)],[277])).
% 4.43/4.63 tff(279,plain,
% 4.43/4.63 (((~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))),
% 4.43/4.63 inference(tautology,[status(thm)],[])).
% 4.43/4.63 tff(280,plain,
% 4.43/4.63 (reflexive_relstr(poset_of_lattice(B!18))),
% 4.43/4.63 inference(unit_resolution,[status(thm)],[279, 87])).
% 4.43/4.63 tff(281,plain,
% 4.43/4.63 (reflexive_relstr(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))),
% 4.43/4.63 inference(modus_ponens,[status(thm)],[280, 278])).
% 4.43/4.63 tff(282,plain,
% 4.43/4.63 (empty_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) <=> empty_carrier(poset_of_lattice(B!18))),
% 4.43/4.63 inference(monotonicity,[status(thm)],[64])).
% 4.43/4.63 tff(283,plain,
% 4.43/4.63 (empty_carrier(poset_of_lattice(B!18)) <=> empty_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))),
% 4.43/4.63 inference(symmetry,[status(thm)],[282])).
% 4.43/4.63 tff(284,plain,
% 4.43/4.63 ((~empty_carrier(poset_of_lattice(B!18))) <=> (~empty_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 4.43/4.63 inference(monotonicity,[status(thm)],[283])).
% 4.43/4.63 tff(285,plain,
% 4.43/4.63 (^[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)))))))),
% 4.43/4.63 inference(bind,[status(th)],[])).
% 4.43/4.63 tff(286,plain,
% 4.43/4.63 (![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))))))),
% 4.43/4.63 inference(quant_intro,[status(thm)],[285])).
% 4.43/4.63 tff(287,plain,
% 4.43/4.63 (^[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))))))))),
% 4.43/4.63 inference(bind,[status(th)],[])).
% 4.43/4.63 tff(288,plain,
% 4.43/4.63 (![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))))))),
% 4.43/4.63 inference(quant_intro,[status(thm)],[287])).
% 4.43/4.63 tff(289,plain,
% 4.43/4.63 (![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))))),
% 4.43/4.63 inference(rewrite,[status(thm)],[])).
% 4.43/4.63 tff(290,plain,
% 4.43/4.63 (^[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))))))),
% 4.43/4.63 inference(bind,[status(th)],[])).
% 4.43/4.63 tff(291,plain,
% 4.43/4.63 (![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))))),
% 4.43/4.63 inference(quant_intro,[status(thm)],[290])).
% 4.43/4.63 tff(292,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/sandbox2/benchmark/theBenchmark.p','fc4_lattice3')).
% 4.43/4.63 tff(293,plain,
% 4.43/4.63 (![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))))),
% 4.43/4.63 inference(modus_ponens,[status(thm)],[292, 291])).
% 4.43/4.63 tff(294,plain,
% 4.43/4.63 (![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))))),
% 4.43/4.63 inference(modus_ponens,[status(thm)],[293, 289])).
% 4.43/4.63 tff(295,plain,(
% 4.43/4.63 ![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))))),
% 4.43/4.63 inference(skolemize,[status(sab)],[294])).
% 4.43/4.63 tff(296,plain,
% 4.43/4.63 (![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))))))),
% 4.43/4.63 inference(modus_ponens,[status(thm)],[295, 288])).
% 4.43/4.63 tff(297,plain,
% 4.43/4.63 (![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))))))),
% 4.43/4.63 inference(modus_ponens,[status(thm)],[296, 286])).
% 4.43/4.63 tff(298,plain,
% 4.43/4.63 (((~![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)))))),
% 4.43/4.63 inference(rewrite,[status(thm)],[])).
% 4.43/4.63 tff(299,plain,
% 4.43/4.63 ((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)))))),
% 4.43/4.63 inference(rewrite,[status(thm)],[])).
% 4.43/4.63 tff(300,plain,
% 4.43/4.63 (((~![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))))))),
% 4.43/4.63 inference(monotonicity,[status(thm)],[299])).
% 4.43/4.63 tff(301,plain,
% 4.43/4.63 (((~![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)))))),
% 4.43/4.63 inference(transitivity,[status(thm)],[300, 298])).
% 4.43/4.63 tff(302,plain,
% 4.43/4.63 ((~![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))))))),
% 4.43/4.63 inference(quant_inst,[status(thm)],[])).
% 4.43/4.63 tff(303,plain,
% 4.43/4.63 ((~![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))))),
% 4.43/4.63 inference(modus_ponens,[status(thm)],[302, 301])).
% 4.43/4.63 tff(304,plain,
% 4.43/4.63 (~((~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)))),
% 4.43/4.63 inference(unit_resolution,[status(thm)],[303, 297, 12, 11, 10])).
% 4.43/4.63 tff(305,plain,
% 4.43/4.63 (((~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)))),
% 4.43/4.63 inference(tautology,[status(thm)],[])).
% 4.43/4.63 tff(306,plain,
% 4.43/4.63 (~empty_carrier(poset_of_lattice(B!18))),
% 4.43/4.63 inference(unit_resolution,[status(thm)],[305, 304])).
% 4.43/4.63 tff(307,plain,
% 4.43/4.63 (~empty_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))),
% 4.43/4.63 inference(modus_ponens,[status(thm)],[306, 284])).
% 4.43/4.63 tff(308,plain,
% 4.43/4.63 (^[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))))),
% 4.43/4.63 inference(bind,[status(th)],[])).
% 4.43/4.63 tff(309,plain,
% 4.43/4.63 (![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)))),
% 4.43/4.63 inference(quant_intro,[status(thm)],[308])).
% 4.43/4.63 tff(310,plain,
% 4.43/4.63 (^[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)))))),
% 4.43/4.63 inference(bind,[status(th)],[])).
% 4.43/4.63 tff(311,plain,
% 4.43/4.63 (![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)))),
% 4.43/4.63 inference(quant_intro,[status(thm)],[310])).
% 4.43/4.63 tff(312,plain,
% 4.43/4.63 (![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)))),
% 4.43/4.63 inference(rewrite,[status(thm)],[])).
% 4.43/4.63 tff(313,plain,
% 4.43/4.63 (^[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)))))),
% 4.43/4.63 inference(bind,[status(th)],[])).
% 4.43/4.63 tff(314,plain,
% 4.43/4.63 (![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)))),
% 4.43/4.63 inference(quant_intro,[status(thm)],[313])).
% 4.43/4.63 tff(315,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/sandbox2/benchmark/theBenchmark.p','redefinition_r3_orders_2')).
% 4.43/4.63 tff(316,plain,
% 4.43/4.63 (![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)))),
% 4.43/4.63 inference(modus_ponens,[status(thm)],[315, 314])).
% 4.43/4.63 tff(317,plain,
% 4.43/4.63 (![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)))),
% 4.43/4.63 inference(modus_ponens,[status(thm)],[316, 312])).
% 4.43/4.63 tff(318,plain,(
% 4.43/4.63 ![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)))),
% 4.43/4.63 inference(skolemize,[status(sab)],[317])).
% 4.43/4.63 tff(319,plain,
% 4.43/4.63 (![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)))),
% 4.43/4.63 inference(modus_ponens,[status(thm)],[318, 311])).
% 4.43/4.63 tff(320,plain,
% 4.43/4.63 (![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)))),
% 4.43/4.63 inference(modus_ponens,[status(thm)],[319, 309])).
% 4.43/4.63 tff(321,plain,
% 4.43/4.63 (((~![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(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(cast_to_el_of_LattPOSet(B!18, C!20), 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(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(cast_to_el_of_LattPOSet(B!18, C!20), 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))))),
% 4.43/4.63 inference(rewrite,[status(thm)],[])).
% 4.43/4.63 tff(322,plain,
% 4.43/4.63 (((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(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(cast_to_el_of_LattPOSet(B!18, C!20), 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))))),
% 4.46/4.63 inference(rewrite,[status(thm)],[])).
% 4.46/4.63 tff(323,plain,
% 4.46/4.63 (((~![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(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(cast_to_el_of_LattPOSet(B!18, C!20), 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)))))),
% 4.46/4.63 inference(monotonicity,[status(thm)],[322])).
% 4.46/4.63 tff(324,plain,
% 4.46/4.63 (((~![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(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(cast_to_el_of_LattPOSet(B!18, C!20), 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))))),
% 4.46/4.64 inference(transitivity,[status(thm)],[323, 321])).
% 4.46/4.64 tff(325,plain,
% 4.46/4.64 ((~![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)))))),
% 4.46/4.64 inference(quant_inst,[status(thm)],[])).
% 4.46/4.64 tff(326,plain,
% 4.46/4.64 ((~![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(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(cast_to_el_of_LattPOSet(B!18, C!20), 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)))),
% 4.46/4.64 inference(modus_ponens,[status(thm)],[325, 324])).
% 4.46/4.64 tff(327,plain,
% 4.46/4.64 (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))),
% 4.46/4.64 inference(unit_resolution,[status(thm)],[326, 320, 307, 95, 281, 228, 267])).
% 4.46/4.64 tff(328,plain,
% 4.46/4.64 ((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)))),
% 4.46/4.64 inference(tautology,[status(thm)],[])).
% 4.46/4.64 tff(329,plain,
% 4.46/4.64 (~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))),
% 4.46/4.64 inference(unit_resolution,[status(thm)],[328, 265])).
% 4.46/4.64 tff(330,plain,
% 4.46/4.64 ((~(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))),
% 4.46/4.64 inference(tautology,[status(thm)],[])).
% 4.46/4.64 tff(331,plain,
% 4.46/4.64 ((~(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)))),
% 4.46/4.64 inference(unit_resolution,[status(thm)],[330, 329])).
% 4.46/4.64 tff(332,plain,
% 4.46/4.64 (~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))),
% 4.46/4.64 inference(unit_resolution,[status(thm)],[331, 327])).
% 4.46/4.64 tff(333,plain,
% 4.46/4.64 (~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)))),
% 4.46/4.64 inference(modus_ponens,[status(thm)],[332, 276])).
% 4.46/4.64 tff(334,plain,
% 4.46/4.64 (^[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)))))))),
% 4.46/4.64 inference(bind,[status(th)],[])).
% 4.46/4.64 tff(335,plain,
% 4.46/4.64 (![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))))))),
% 4.46/4.64 inference(quant_intro,[status(thm)],[334])).
% 4.46/4.64 tff(336,plain,
% 4.46/4.64 (^[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))))),
% 4.46/4.64 inference(bind,[status(th)],[])).
% 4.46/4.64 tff(337,plain,
% 4.46/4.64 (![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)))),
% 4.46/4.64 inference(quant_intro,[status(thm)],[336])).
% 4.46/4.64 tff(338,plain,
% 4.46/4.64 (^[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))))),
% 4.46/4.64 inference(bind,[status(th)],[])).
% 4.46/4.64 tff(339,plain,
% 4.46/4.64 (![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)))),
% 4.46/4.64 inference(quant_intro,[status(thm)],[338])).
% 4.46/4.64 tff(340,plain,
% 4.46/4.64 (![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)))),
% 4.46/4.64 inference(transitivity,[status(thm)],[339, 337])).
% 4.46/4.64 tff(341,plain,
% 4.46/4.64 (^[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)))))),
% 4.46/4.64 inference(bind,[status(th)],[])).
% 4.46/4.64 tff(342,plain,
% 4.46/4.64 (![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)))),
% 4.46/4.64 inference(quant_intro,[status(thm)],[341])).
% 4.46/4.64 tff(343,plain,
% 4.46/4.64 (![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))))))),
% 4.46/4.64 inference(rewrite,[status(thm)],[])).
% 4.46/4.64 tff(344,plain,
% 4.46/4.64 (^[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))))))))),
% 4.46/4.64 inference(bind,[status(th)],[])).
% 4.46/4.64 tff(345,plain,
% 4.46/4.64 (![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))))))),
% 4.46/4.64 inference(quant_intro,[status(thm)],[344])).
% 4.46/4.64 tff(346,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/sandbox2/benchmark/theBenchmark.p','t7_lattice3')).
% 4.46/4.64 tff(347,plain,
% 4.46/4.64 (![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))))))),
% 4.46/4.64 inference(modus_ponens,[status(thm)],[346, 345])).
% 4.46/4.64 tff(348,plain,
% 4.46/4.64 (![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))))))),
% 4.46/4.64 inference(modus_ponens,[status(thm)],[347, 343])).
% 4.46/4.64 tff(349,plain,(
% 4.46/4.64 ![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))))))),
% 4.46/4.64 inference(skolemize,[status(sab)],[348])).
% 4.46/4.64 tff(350,plain,
% 4.46/4.64 (![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)))),
% 4.46/4.64 inference(modus_ponens,[status(thm)],[349, 342])).
% 4.46/4.64 tff(351,plain,
% 4.46/4.64 (![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)))),
% 4.46/4.64 inference(modus_ponens,[status(thm)],[350, 340])).
% 4.46/4.64 tff(352,plain,
% 4.46/4.64 (![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))))))),
% 4.46/4.64 inference(modus_ponens,[status(thm)],[351, 335])).
% 4.46/4.64 tff(353,plain,
% 4.46/4.64 (((~![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))))))),
% 4.46/4.64 inference(rewrite,[status(thm)],[])).
% 4.46/4.64 tff(354,plain,
% 4.46/4.64 ((~![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))))))),
% 4.46/4.64 inference(quant_inst,[status(thm)],[])).
% 4.46/4.64 tff(355,plain,
% 4.46/4.64 ((~![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)))))),
% 4.46/4.64 inference(modus_ponens,[status(thm)],[354, 353])).
% 4.46/4.64 tff(356,plain,
% 4.46/4.64 (![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)))))),
% 4.46/4.64 inference(unit_resolution,[status(thm)],[355, 12, 11, 10, 352])).
% 4.46/4.64 tff(357,plain,
% 4.46/4.64 (((~![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)))))),
% 4.46/4.64 inference(rewrite,[status(thm)],[])).
% 4.46/4.64 tff(358,plain,
% 4.46/4.64 ((~![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)))))),
% 4.46/4.64 inference(quant_inst,[status(thm)],[])).
% 4.46/4.64 tff(359,plain,
% 4.46/4.64 ((~![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))))),
% 4.46/4.64 inference(modus_ponens,[status(thm)],[358, 357])).
% 4.46/4.64 tff(360,plain,
% 4.46/4.64 ((~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))))),
% 4.46/4.64 inference(unit_resolution,[status(thm)],[359, 356])).
% 4.46/4.64 tff(361,plain,
% 4.46/4.64 (![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))))),
% 4.46/4.64 inference(unit_resolution,[status(thm)],[360, 268])).
% 4.46/4.64 tff(362,plain,
% 4.46/4.64 (^[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))))),
% 4.46/4.64 inference(bind,[status(th)],[])).
% 4.46/4.64 tff(363,plain,
% 4.46/4.64 (![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)))),
% 4.46/4.64 inference(quant_intro,[status(thm)],[362])).
% 4.46/4.64 tff(364,plain,
% 4.46/4.64 (^[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))))),
% 4.46/4.64 inference(bind,[status(th)],[])).
% 4.46/4.64 tff(365,plain,
% 4.46/4.64 (![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)))),
% 4.46/4.64 inference(quant_intro,[status(thm)],[364])).
% 4.46/4.64 tff(366,plain,
% 4.46/4.64 (^[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))))),
% 4.46/4.64 inference(bind,[status(th)],[])).
% 4.46/4.64 tff(367,plain,
% 4.46/4.64 (![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)))),
% 4.46/4.64 inference(quant_intro,[status(thm)],[366])).
% 4.46/4.64 tff(368,plain,
% 4.46/4.64 (![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)))),
% 4.46/4.64 inference(transitivity,[status(thm)],[367, 365])).
% 4.46/4.64 tff(369,plain,
% 4.46/4.64 (^[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)))))),
% 4.46/4.64 inference(bind,[status(th)],[])).
% 4.46/4.64 tff(370,plain,
% 4.46/4.64 (![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)))),
% 4.46/4.64 inference(quant_intro,[status(thm)],[369])).
% 4.46/4.64 tff(371,plain,
% 4.46/4.64 (![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)))),
% 4.46/4.64 inference(rewrite,[status(thm)],[])).
% 4.46/4.64 tff(372,plain,
% 4.46/4.64 (^[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)))))),
% 4.46/4.64 inference(bind,[status(th)],[])).
% 4.46/4.64 tff(373,plain,
% 4.46/4.64 (![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)))),
% 4.46/4.64 inference(quant_intro,[status(thm)],[372])).
% 4.46/4.64 tff(374,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/sandbox2/benchmark/theBenchmark.p','d4_lattice3')).
% 4.46/4.64 tff(375,plain,
% 4.46/4.64 (![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)))),
% 4.46/4.64 inference(modus_ponens,[status(thm)],[374, 373])).
% 4.46/4.64 tff(376,plain,
% 4.46/4.64 (![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)))),
% 4.46/4.64 inference(modus_ponens,[status(thm)],[375, 371])).
% 4.46/4.64 tff(377,plain,(
% 4.46/4.64 ![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)))),
% 4.46/4.64 inference(skolemize,[status(sab)],[376])).
% 4.46/4.64 tff(378,plain,
% 4.46/4.64 (![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)))),
% 4.46/4.64 inference(modus_ponens,[status(thm)],[377, 370])).
% 4.46/4.64 tff(379,plain,
% 4.46/4.64 (![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)))),
% 4.46/4.64 inference(modus_ponens,[status(thm)],[378, 368])).
% 4.46/4.64 tff(380,plain,
% 4.46/4.64 (![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)))),
% 4.46/4.64 inference(modus_ponens,[status(thm)],[379, 363])).
% 4.46/4.64 tff(381,plain,
% 4.46/4.64 (((~![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)))),
% 4.46/4.64 inference(rewrite,[status(thm)],[])).
% 4.46/4.64 tff(382,plain,
% 4.46/4.64 ((~![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)))),
% 4.46/4.64 inference(quant_inst,[status(thm)],[])).
% 4.46/4.64 tff(383,plain,
% 4.46/4.64 ((~![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))),
% 4.46/4.64 inference(modus_ponens,[status(thm)],[382, 381])).
% 4.46/4.64 tff(384,plain,
% 4.46/4.64 (![B: $i] : ((~element(B, the_carrier(poset_of_lattice(B!18)))) | (cast_to_el_of_lattice(B!18, B) = B))),
% 4.46/4.64 inference(unit_resolution,[status(thm)],[383, 380, 12, 11, 10])).
% 4.46/4.64 tff(385,plain,
% 4.46/4.64 (((~![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)))),
% 4.46/4.64 inference(rewrite,[status(thm)],[])).
% 4.46/4.64 tff(386,plain,
% 4.46/4.64 ((~![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)))),
% 4.46/4.64 inference(quant_inst,[status(thm)],[])).
% 4.46/4.64 tff(387,plain,
% 4.46/4.64 ((~![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))),
% 4.46/4.64 inference(modus_ponens,[status(thm)],[386, 385])).
% 4.46/4.64 tff(388,plain,
% 4.46/4.64 (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)),
% 4.46/4.64 inference(unit_resolution,[status(thm)],[387, 384, 227])).
% 4.46/4.64 tff(389,plain,
% 4.46/4.64 (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))),
% 4.46/4.64 inference(symmetry,[status(thm)],[388])).
% 4.46/4.64 tff(390,plain,
% 4.46/4.64 (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))),
% 4.46/4.64 inference(monotonicity,[status(thm)],[389])).
% 4.46/4.64 tff(391,plain,
% 4.46/4.64 (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))),
% 4.46/4.64 inference(symmetry,[status(thm)],[390])).
% 4.46/4.64 tff(392,plain,
% 4.46/4.64 (^[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))))),
% 4.46/4.64 inference(bind,[status(th)],[])).
% 4.46/4.64 tff(393,plain,
% 4.46/4.64 (![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)))),
% 4.46/4.64 inference(quant_intro,[status(thm)],[392])).
% 4.46/4.64 tff(394,plain,
% 4.46/4.64 (^[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)))))),
% 4.46/4.65 inference(bind,[status(th)],[])).
% 4.46/4.65 tff(395,plain,
% 4.46/4.65 (![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)))),
% 4.46/4.65 inference(quant_intro,[status(thm)],[394])).
% 4.46/4.65 tff(396,plain,
% 4.46/4.65 (![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)))),
% 4.46/4.65 inference(rewrite,[status(thm)],[])).
% 4.46/4.65 tff(397,plain,
% 4.46/4.65 (^[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)))))),
% 4.46/4.65 inference(bind,[status(th)],[])).
% 4.46/4.65 tff(398,plain,
% 4.46/4.65 (![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)))),
% 4.46/4.65 inference(quant_intro,[status(thm)],[397])).
% 4.46/4.65 tff(399,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/sandbox2/benchmark/theBenchmark.p','dt_k5_lattice3')).
% 4.46/4.65 tff(400,plain,
% 4.46/4.65 (![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)))),
% 4.46/4.65 inference(modus_ponens,[status(thm)],[399, 398])).
% 4.46/4.65 tff(401,plain,
% 4.46/4.65 (![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)))),
% 4.46/4.65 inference(modus_ponens,[status(thm)],[400, 396])).
% 4.46/4.65 tff(402,plain,(
% 4.46/4.65 ![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)))),
% 4.46/4.65 inference(skolemize,[status(sab)],[401])).
% 4.46/4.65 tff(403,plain,
% 4.46/4.65 (![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)))),
% 4.46/4.65 inference(modus_ponens,[status(thm)],[402, 395])).
% 4.46/4.65 tff(404,plain,
% 4.46/4.65 (![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)))),
% 4.46/4.65 inference(modus_ponens,[status(thm)],[403, 393])).
% 4.46/4.65 tff(405,plain,
% 4.46/4.65 (((~![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) | (~lattice(B!18)) | (~latt_str(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) | (~lattice(B!18)) | (~latt_str(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)))),
% 4.46/4.65 inference(rewrite,[status(thm)],[])).
% 4.46/4.65 tff(406,plain,
% 4.46/4.65 ((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) | (~lattice(B!18)) | (~latt_str(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)))),
% 4.46/4.65 inference(rewrite,[status(thm)],[])).
% 4.46/4.65 tff(407,plain,
% 4.46/4.65 (((~![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) | (~lattice(B!18)) | (~latt_str(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))))),
% 4.46/4.65 inference(monotonicity,[status(thm)],[406])).
% 4.46/4.65 tff(408,plain,
% 4.46/4.65 (((~![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) | (~lattice(B!18)) | (~latt_str(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)))),
% 4.46/4.65 inference(transitivity,[status(thm)],[407, 405])).
% 4.46/4.65 tff(409,plain,
% 4.46/4.65 ((~![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)))),
% 4.46/4.65 inference(quant_inst,[status(thm)],[])).
% 4.46/4.65 tff(410,plain,
% 4.46/4.65 ((~![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) | (~lattice(B!18)) | (~latt_str(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))),
% 4.46/4.65 inference(modus_ponens,[status(thm)],[409, 408])).
% 4.46/4.65 tff(411,plain,
% 4.46/4.65 (element(cast_to_el_of_lattice(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), the_carrier(B!18))),
% 4.46/4.65 inference(unit_resolution,[status(thm)],[410, 404, 12, 11, 10, 227])).
% 4.46/4.65 tff(412,plain,
% 4.46/4.65 (element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))),
% 4.46/4.65 inference(modus_ponens,[status(thm)],[411, 391])).
% 4.46/4.65 tff(413,plain,
% 4.46/4.65 (((~![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)))))),
% 4.46/4.65 inference(rewrite,[status(thm)],[])).
% 4.46/4.65 tff(414,plain,
% 4.46/4.65 ((~![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)))))),
% 4.46/4.65 inference(quant_inst,[status(thm)],[])).
% 4.46/4.65 tff(415,plain,
% 4.46/4.65 ((~![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))))),
% 4.46/4.65 inference(modus_ponens,[status(thm)],[414, 413])).
% 4.46/4.65 tff(416,plain,
% 4.46/4.65 (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)))),
% 4.46/4.65 inference(unit_resolution,[status(thm)],[415, 412, 361])).
% 4.46/4.65 tff(417,plain,
% 4.46/4.65 (^[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))))),
% 4.46/4.65 inference(bind,[status(th)],[])).
% 4.46/4.65 tff(418,plain,
% 4.46/4.65 (![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)))),
% 4.46/4.65 inference(quant_intro,[status(thm)],[417])).
% 4.46/4.65 tff(419,plain,
% 4.46/4.65 (^[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)))))),
% 4.46/4.65 inference(bind,[status(th)],[])).
% 4.46/4.65 tff(420,plain,
% 4.46/4.65 (![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)))),
% 4.46/4.65 inference(quant_intro,[status(thm)],[419])).
% 4.46/4.65 tff(421,plain,
% 4.46/4.65 (![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)))),
% 4.46/4.65 inference(rewrite,[status(thm)],[])).
% 4.46/4.65 tff(422,plain,
% 4.46/4.65 (^[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)))))),
% 4.46/4.65 inference(bind,[status(th)],[])).
% 4.46/4.65 tff(423,plain,
% 4.46/4.65 (![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)))),
% 4.46/4.65 inference(quant_intro,[status(thm)],[422])).
% 4.46/4.65 tff(424,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/sandbox2/benchmark/theBenchmark.p','cc1_lattices')).
% 4.46/4.65 tff(425,plain,
% 4.46/4.65 (![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)))),
% 4.46/4.65 inference(modus_ponens,[status(thm)],[424, 423])).
% 4.46/4.65 tff(426,plain,
% 4.46/4.65 (![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)))),
% 4.46/4.65 inference(modus_ponens,[status(thm)],[425, 421])).
% 4.46/4.65 tff(427,plain,(
% 4.46/4.65 ![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)))),
% 4.46/4.65 inference(skolemize,[status(sab)],[426])).
% 4.46/4.65 tff(428,plain,
% 4.46/4.65 (![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)))),
% 4.46/4.65 inference(modus_ponens,[status(thm)],[427, 420])).
% 4.46/4.65 tff(429,plain,
% 4.46/4.65 (![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)))),
% 4.46/4.65 inference(modus_ponens,[status(thm)],[428, 418])).
% 4.46/4.65 tff(430,plain,
% 4.46/4.65 (((~![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) | (~lattice(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)))))) <=> ((~![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) | (~lattice(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)))))),
% 4.46/4.65 inference(rewrite,[status(thm)],[])).
% 4.46/4.65 tff(431,plain,
% 4.46/4.65 ((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) | (~lattice(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)))))),
% 4.46/4.65 inference(rewrite,[status(thm)],[])).
% 4.46/4.65 tff(432,plain,
% 4.46/4.65 ((~(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))))),
% 4.46/4.65 inference(rewrite,[status(thm)],[])).
% 4.46/4.65 tff(433,plain,
% 4.46/4.65 ((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)))),
% 4.46/4.65 inference(monotonicity,[status(thm)],[432])).
% 4.46/4.65 tff(434,plain,
% 4.46/4.65 ((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) | (~lattice(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)))))),
% 4.46/4.65 inference(transitivity,[status(thm)],[433, 431])).
% 4.46/4.65 tff(435,plain,
% 4.46/4.65 (((~![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) | (~lattice(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))))))),
% 4.46/4.65 inference(monotonicity,[status(thm)],[434])).
% 4.46/4.65 tff(436,plain,
% 4.46/4.65 (((~![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) | (~lattice(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)))))),
% 4.46/4.65 inference(transitivity,[status(thm)],[435, 430])).
% 4.46/4.65 tff(437,plain,
% 4.46/4.65 ((~![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)))),
% 4.46/4.65 inference(quant_inst,[status(thm)],[])).
% 4.46/4.65 tff(438,plain,
% 4.46/4.65 ((~![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) | (~lattice(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))))),
% 4.46/4.65 inference(modus_ponens,[status(thm)],[437, 436])).
% 4.46/4.65 tff(439,plain,
% 4.46/4.65 (~(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)))),
% 4.46/4.65 inference(unit_resolution,[status(thm)],[438, 429, 12, 11, 10])).
% 4.46/4.65 tff(440,plain,
% 4.46/4.65 ((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)),
% 4.46/4.65 inference(tautology,[status(thm)],[])).
% 4.46/4.65 tff(441,plain,
% 4.46/4.65 (join_absorbing(B!18)),
% 4.46/4.65 inference(unit_resolution,[status(thm)],[440, 439])).
% 4.46/4.65 tff(442,plain,
% 4.46/4.65 ((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)),
% 4.46/4.65 inference(tautology,[status(thm)],[])).
% 4.46/4.65 tff(443,plain,
% 4.46/4.65 (meet_absorbing(B!18)),
% 4.46/4.65 inference(unit_resolution,[status(thm)],[442, 439])).
% 4.46/4.65 tff(444,plain,
% 4.46/4.65 ((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)),
% 4.46/4.65 inference(tautology,[status(thm)],[])).
% 4.46/4.65 tff(445,plain,
% 4.46/4.65 (meet_commutative(B!18)),
% 4.46/4.65 inference(unit_resolution,[status(thm)],[444, 439])).
% 4.46/4.65 tff(446,plain,
% 4.46/4.65 (^[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)))))),
% 4.46/4.65 inference(bind,[status(th)],[])).
% 4.46/4.65 tff(447,plain,
% 4.46/4.65 (![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))))),
% 4.46/4.65 inference(quant_intro,[status(thm)],[446])).
% 4.46/4.65 tff(448,plain,
% 4.46/4.65 (^[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))))))),
% 4.46/4.65 inference(bind,[status(th)],[])).
% 4.46/4.65 tff(449,plain,
% 4.46/4.65 (![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))))),
% 4.46/4.65 inference(quant_intro,[status(thm)],[448])).
% 4.46/4.65 tff(450,plain,
% 4.46/4.65 (![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)))),
% 4.46/4.65 inference(rewrite,[status(thm)],[])).
% 4.46/4.65 tff(451,plain,
% 4.46/4.65 (^[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)))))),
% 4.46/4.65 inference(bind,[status(th)],[])).
% 4.46/4.65 tff(452,plain,
% 4.46/4.65 (![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)))),
% 4.46/4.65 inference(quant_intro,[status(thm)],[451])).
% 4.46/4.65 tff(453,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/sandbox2/benchmark/theBenchmark.p','redefinition_r3_lattices')).
% 4.46/4.65 tff(454,plain,
% 4.46/4.65 (![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)))),
% 4.46/4.65 inference(modus_ponens,[status(thm)],[453, 452])).
% 4.46/4.65 tff(455,plain,
% 4.46/4.65 (![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)))),
% 4.46/4.65 inference(modus_ponens,[status(thm)],[454, 450])).
% 4.46/4.65 tff(456,plain,(
% 4.46/4.65 ![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)))),
% 4.46/4.65 inference(skolemize,[status(sab)],[455])).
% 4.46/4.65 tff(457,plain,
% 4.46/4.65 (![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))))),
% 4.46/4.65 inference(modus_ponens,[status(thm)],[456, 449])).
% 4.46/4.65 tff(458,plain,
% 4.46/4.65 (![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))))),
% 4.46/4.65 inference(modus_ponens,[status(thm)],[457, 447])).
% 4.46/4.65 tff(459,plain,
% 4.46/4.65 (((~![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))))),
% 4.46/4.65 inference(rewrite,[status(thm)],[])).
% 4.46/4.65 tff(460,plain,
% 4.46/4.65 (((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))))),
% 4.46/4.66 inference(rewrite,[status(thm)],[])).
% 4.46/4.66 tff(461,plain,
% 4.46/4.66 (((~![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)))))),
% 4.46/4.66 inference(monotonicity,[status(thm)],[460])).
% 4.46/4.66 tff(462,plain,
% 4.46/4.66 (((~![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))))),
% 4.46/4.66 inference(transitivity,[status(thm)],[461, 459])).
% 4.46/4.66 tff(463,plain,
% 4.46/4.66 ((~![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))))),
% 4.46/4.66 inference(quant_inst,[status(thm)],[])).
% 4.46/4.66 tff(464,plain,
% 4.46/4.66 ((~![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)))),
% 4.46/4.66 inference(modus_ponens,[status(thm)],[463, 462])).
% 4.46/4.66 tff(465,plain,
% 4.46/4.66 (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))),
% 4.46/4.66 inference(unit_resolution,[status(thm)],[464, 458, 12, 10, 445, 443, 441, 412, 268])).
% 4.46/4.66 tff(466,plain,
% 4.46/4.66 (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)),
% 4.46/4.66 inference(monotonicity,[status(thm)],[41])).
% 4.46/4.66 tff(467,plain,
% 4.46/4.66 (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)),
% 4.46/4.66 inference(symmetry,[status(thm)],[466])).
% 4.46/4.66 tff(468,plain,
% 4.46/4.66 (~(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)))),
% 4.46/4.66 inference(or_elim,[status(thm)],[36])).
% 4.46/4.66 tff(469,plain,
% 4.46/4.66 ((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))),
% 4.46/4.66 inference(tautology,[status(thm)],[])).
% 4.46/4.66 tff(470,plain,
% 4.46/4.66 (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))),
% 4.46/4.66 inference(unit_resolution,[status(thm)],[469, 468])).
% 4.46/4.66 tff(471,plain,
% 4.46/4.66 (latt_element_smaller(B!18, C!20, A!19)),
% 4.46/4.66 inference(unit_resolution,[status(thm)],[470, 204])).
% 4.46/4.66 tff(472,plain,
% 4.46/4.66 (latt_element_smaller(B!18, cast_to_el_of_LattPOSet(B!18, C!20), A!19)),
% 4.46/4.66 inference(modus_ponens,[status(thm)],[471, 467])).
% 4.46/4.66 tff(473,plain,
% 4.46/4.66 (^[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) | (~((~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) | (~((~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))))))))))))),
% 4.46/4.66 inference(bind,[status(th)],[])).
% 4.46/4.66 tff(474,plain,
% 4.46/4.66 (![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) | (~((~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)))))))))))),
% 4.46/4.66 inference(quant_intro,[status(thm)],[473])).
% 4.46/4.66 tff(475,plain,
% 4.46/4.66 (^[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) | (~((~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))))))))))))),
% 4.46/4.66 inference(bind,[status(th)],[])).
% 4.46/4.66 tff(476,plain,
% 4.46/4.66 (![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) | (~((~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)))))))))))),
% 4.46/4.66 inference(quant_intro,[status(thm)],[475])).
% 4.46/4.66 tff(477,plain,
% 4.46/4.66 (![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) | (~((~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)))))))))))),
% 4.46/4.66 inference(transitivity,[status(thm)],[476, 474])).
% 4.46/4.66 tff(478,plain,
% 4.46/4.66 (^[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) | (~((~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)))))))) <=> ((~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)))))))))))), (![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)))))))) <=> ![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) | (~((~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) | (~((~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))))))))))))), 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) | (~((~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) | (~((~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) | (~((~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)))))))))))))),
% 4.46/4.66 inference(bind,[status(th)],[])).
% 4.46/4.66 tff(479,plain,
% 4.46/4.66 (![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) | (~((~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)))))))))))),
% 4.46/4.66 inference(quant_intro,[status(thm)],[478])).
% 4.46/4.66 tff(480,plain,
% 4.46/4.66 (![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)))))))),
% 4.46/4.66 inference(rewrite,[status(thm)],[])).
% 4.46/4.66 tff(481,plain,
% 4.46/4.66 (^[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)))))))))),
% 4.46/4.66 inference(bind,[status(th)],[])).
% 4.46/4.66 tff(482,plain,
% 4.46/4.66 (![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)))))))),
% 4.46/4.66 inference(quant_intro,[status(thm)],[481])).
% 4.46/4.66 tff(483,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/sandbox2/benchmark/theBenchmark.p','d17_lattice3')).
% 4.46/4.66 tff(484,plain,
% 4.46/4.66 (![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)))))))),
% 4.46/4.66 inference(modus_ponens,[status(thm)],[483, 482])).
% 4.46/4.66 tff(485,plain,
% 4.46/4.66 (![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)))))))),
% 4.46/4.66 inference(modus_ponens,[status(thm)],[484, 480])).
% 4.46/4.66 tff(486,plain,(
% 4.46/4.66 ![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)))))))))),
% 4.46/4.66 inference(skolemize,[status(sab)],[485])).
% 4.46/4.66 tff(487,plain,
% 4.46/4.66 (![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)))))))))))),
% 4.46/4.66 inference(modus_ponens,[status(thm)],[486, 479])).
% 4.46/4.66 tff(488,plain,
% 4.46/4.66 (![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)))))))))))),
% 4.46/4.66 inference(modus_ponens,[status(thm)],[487, 477])).
% 4.46/4.66 tff(489,plain,
% 4.46/4.66 (((~![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)))))))))))) | (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) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~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) | (~((~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(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) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~in(tptp_fun_D_0(C, B, B!18), C))))))))))),
% 4.46/4.66 inference(rewrite,[status(thm)],[])).
% 4.46/4.66 tff(490,plain,
% 4.46/4.66 ((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) | (~((~in(tptp_fun_D_0(C, B, B!18), 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))))))))))) <=> (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) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~in(tptp_fun_D_0(C, B, B!18), C))))))))))),
% 4.46/4.66 inference(rewrite,[status(thm)],[])).
% 4.46/4.66 tff(491,plain,
% 4.46/4.66 (((~![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)))))))))))) | (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) | (~((~in(tptp_fun_D_0(C, B, B!18), 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)))))))))))) <=> ((~![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)))))))))))) | (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) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))))),
% 4.46/4.66 inference(monotonicity,[status(thm)],[490])).
% 4.46/4.66 tff(492,plain,
% 4.46/4.66 (((~![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)))))))))))) | (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) | (~((~in(tptp_fun_D_0(C, B, B!18), 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)))))))))))) <=> ((~![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)))))))))))) | 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) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~in(tptp_fun_D_0(C, B, B!18), C))))))))))),
% 4.46/4.66 inference(transitivity,[status(thm)],[491, 489])).
% 4.46/4.66 tff(493,plain,
% 4.46/4.66 ((~![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)))))))))))) | (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) | (~((~in(tptp_fun_D_0(C, B, B!18), 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)))))))))))),
% 4.46/4.66 inference(quant_inst,[status(thm)],[])).
% 4.46/4.66 tff(494,plain,
% 4.46/4.66 ((~![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)))))))))))) | 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) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))),
% 4.46/4.66 inference(modus_ponens,[status(thm)],[493, 492])).
% 4.46/4.66 tff(495,plain,
% 4.46/4.66 (![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) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))),
% 4.46/4.66 inference(unit_resolution,[status(thm)],[494, 488, 12, 10])).
% 4.46/4.66 tff(496,plain,
% 4.46/4.66 (((~![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) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~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) | (~((~in(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), 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))))))))))) <=> ((~![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) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~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) | (~((~in(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), 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))))))))))),
% 4.46/4.66 inference(rewrite,[status(thm)],[])).
% 4.46/4.66 tff(497,plain,
% 4.46/4.66 (((~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) | (~((~element(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18))) | 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)) | (~in(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), 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) | (~((~in(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), 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))))))))))),
% 4.46/4.66 inference(rewrite,[status(thm)],[])).
% 4.46/4.66 tff(498,plain,
% 4.46/4.66 (((~![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) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~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) | (~((~element(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18))) | 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)) | (~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) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~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) | (~((~in(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), 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)))))))))))),
% 4.46/4.67 inference(monotonicity,[status(thm)],[497])).
% 4.46/4.67 tff(499,plain,
% 4.46/4.67 (((~![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) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~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) | (~((~element(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18))) | 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)) | (~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) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~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) | (~((~in(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), 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))))))))))),
% 4.46/4.67 inference(transitivity,[status(thm)],[498, 496])).
% 4.46/4.67 tff(500,plain,
% 4.46/4.67 ((~![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) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~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) | (~((~element(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18))) | 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)) | (~in(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), C)))))))))),
% 4.46/4.67 inference(quant_inst,[status(thm)],[])).
% 4.46/4.67 tff(501,plain,
% 4.46/4.67 ((~![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) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~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) | (~((~in(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), 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)))))))))),
% 4.46/4.67 inference(modus_ponens,[status(thm)],[500, 499])).
% 4.46/4.67 tff(502,plain,
% 4.46/4.67 ((~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) | (~((~in(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), 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)))))))))),
% 4.46/4.67 inference(unit_resolution,[status(thm)],[501, 495])).
% 4.46/4.67 tff(503,plain,
% 4.46/4.67 (![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) | (~((~in(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), 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)))))))))),
% 4.46/4.67 inference(unit_resolution,[status(thm)],[502, 412])).
% 4.46/4.67 tff(504,plain,
% 4.46/4.67 (((~![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) | (~((~in(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), 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)))))))))) | (~((~((~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) | (~((~element(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18))) | 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)) | (~in(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), A!19))))))))) <=> ((~![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) | (~((~in(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), 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)))))))))) | (~((~((~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) | (~((~element(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18))) | 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)) | (~in(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), A!19)))))))))),
% 4.46/4.67 inference(rewrite,[status(thm)],[])).
% 4.46/4.67 tff(505,plain,
% 4.46/4.67 ((~((~((~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) | (~((~in(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), 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))))))))) <=> (~((~((~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) | (~((~element(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18))) | 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)) | (~in(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), A!19))))))))),
% 4.46/4.67 inference(rewrite,[status(thm)],[])).
% 4.46/4.67 tff(506,plain,
% 4.46/4.67 (((~![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) | (~((~in(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), 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)))))))))) | (~((~((~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) | (~((~in(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), 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)))))))))) <=> ((~![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) | (~((~in(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), 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)))))))))) | (~((~((~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) | (~((~element(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18))) | 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)) | (~in(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), A!19)))))))))),
% 4.46/4.67 inference(monotonicity,[status(thm)],[505])).
% 4.46/4.67 tff(507,plain,
% 4.46/4.67 (((~![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) | (~((~in(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), 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)))))))))) | (~((~((~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) | (~((~in(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), 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)))))))))) <=> ((~![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) | (~((~in(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), 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)))))))))) | (~((~((~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) | (~((~element(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18))) | 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)) | (~in(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), A!19)))))))))),
% 4.46/4.67 inference(transitivity,[status(thm)],[506, 504])).
% 4.46/4.67 tff(508,plain,
% 4.46/4.67 ((~![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) | (~((~in(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), 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)))))))))) | (~((~((~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) | (~((~in(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), 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)))))))))),
% 4.46/4.67 inference(quant_inst,[status(thm)],[])).
% 4.46/4.67 tff(509,plain,
% 4.46/4.67 ((~![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) | (~((~in(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), 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)))))))))) | (~((~((~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) | (~((~element(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18))) | 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)) | (~in(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), A!19))))))))),
% 4.46/4.67 inference(modus_ponens,[status(thm)],[508, 507])).
% 4.46/4.67 tff(510,plain,
% 4.46/4.67 (~((~((~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) | (~((~element(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18))) | 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)) | (~in(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), A!19)))))))),
% 4.46/4.67 inference(unit_resolution,[status(thm)],[509, 503])).
% 4.46/4.67 tff(511,plain,
% 4.46/4.67 (((~((~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) | (~((~element(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18))) | 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)) | (~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))))),
% 4.46/4.67 inference(tautology,[status(thm)],[])).
% 4.46/4.67 tff(512,plain,
% 4.46/4.67 ((~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)))),
% 4.46/4.67 inference(unit_resolution,[status(thm)],[511, 510])).
% 4.46/4.67 tff(513,plain,
% 4.46/4.67 ((~((~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)))),
% 4.46/4.67 inference(tautology,[status(thm)],[])).
% 4.46/4.67 tff(514,plain,
% 4.46/4.67 ((~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)))),
% 4.46/4.67 inference(unit_resolution,[status(thm)],[513, 512])).
% 4.46/4.67 tff(515,plain,
% 4.46/4.67 (![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)))),
% 4.46/4.67 inference(unit_resolution,[status(thm)],[514, 472])).
% 4.46/4.67 tff(516,plain,
% 4.46/4.67 ((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)),
% 4.46/4.67 inference(tautology,[status(thm)],[])).
% 4.46/4.67 tff(517,plain,
% 4.46/4.67 (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)),
% 4.46/4.67 inference(unit_resolution,[status(thm)],[516, 265])).
% 4.46/4.67 tff(518,plain,
% 4.46/4.67 (((~![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)))),
% 4.46/4.67 inference(rewrite,[status(thm)],[])).
% 4.46/4.67 tff(519,plain,
% 4.46/4.67 ((~![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)))),
% 4.46/4.67 inference(quant_inst,[status(thm)],[])).
% 4.46/4.67 tff(520,plain,
% 4.46/4.67 ((~![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))),
% 4.46/4.67 inference(modus_ponens,[status(thm)],[519, 518])).
% 4.46/4.67 tff(521,plain,
% 4.46/4.67 ((~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))),
% 4.46/4.67 inference(unit_resolution,[status(thm)],[520, 517, 515])).
% 4.46/4.67 tff(522,plain,
% 4.46/4.67 (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))),
% 4.46/4.67 inference(unit_resolution,[status(thm)],[521, 268])).
% 4.46/4.67 tff(523,plain,
% 4.46/4.67 ((~(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)))),
% 4.46/4.67 inference(tautology,[status(thm)],[])).
% 4.46/4.67 tff(524,plain,
% 4.46/4.67 ((~(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))),
% 4.46/4.67 inference(unit_resolution,[status(thm)],[523, 522])).
% 4.46/4.67 tff(525,plain,
% 4.46/4.67 (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))),
% 4.46/4.67 inference(unit_resolution,[status(thm)],[524, 465])).
% 4.46/4.67 tff(526,plain,
% 4.46/4.67 ((~(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)))),
% 4.46/4.67 inference(tautology,[status(thm)],[])).
% 4.46/4.67 tff(527,plain,
% 4.46/4.67 (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)))),
% 4.46/4.67 inference(unit_resolution,[status(thm)],[526, 525, 416])).
% 4.46/4.67 tff(528,plain,
% 4.46/4.67 ($false),
% 4.46/4.67 inference(unit_resolution,[status(thm)],[527, 333])).
% 4.46/4.67 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,[]))).
% 4.46/4.67 tff(530,plain,
% 4.46/4.67 ((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)))),
% 4.46/4.67 inference(tautology,[status(thm)],[])).
% 4.46/4.67 tff(531,plain,
% 4.46/4.67 ((~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)))),
% 4.46/4.67 inference(unit_resolution,[status(thm)],[530, 468])).
% 4.46/4.67 tff(532,plain,
% 4.46/4.67 (~latt_element_smaller(B!18, C!20, A!19)),
% 4.46/4.67 inference(unit_resolution,[status(thm)],[531, 529])).
% 4.46/4.67 tff(533,plain,
% 4.46/4.67 (((~![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) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~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) | (~((~in(tptp_fun_D_0(C, C!20, B!18), 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))))))))))) <=> ((~![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) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~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) | (~((~in(tptp_fun_D_0(C, C!20, B!18), 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))))))))))),
% 4.46/4.68 inference(rewrite,[status(thm)],[])).
% 4.46/4.68 tff(534,plain,
% 4.46/4.68 (((~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) | (~((~element(tptp_fun_D_0(C, C!20, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(C, C!20, B!18), C!20) | (~in(tptp_fun_D_0(C, C!20, 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) | (~((~in(tptp_fun_D_0(C, C!20, B!18), 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))))))))))),
% 4.46/4.68 inference(rewrite,[status(thm)],[])).
% 4.46/4.68 tff(535,plain,
% 4.46/4.68 (((~![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) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~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) | (~((~element(tptp_fun_D_0(C, C!20, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(C, C!20, B!18), C!20) | (~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) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~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) | (~((~in(tptp_fun_D_0(C, C!20, B!18), 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)))))))))))),
% 4.46/4.68 inference(monotonicity,[status(thm)],[534])).
% 4.46/4.68 tff(536,plain,
% 4.46/4.68 (((~![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) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~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) | (~((~element(tptp_fun_D_0(C, C!20, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(C, C!20, B!18), C!20) | (~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) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~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) | (~((~in(tptp_fun_D_0(C, C!20, B!18), 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))))))))))),
% 4.46/4.68 inference(transitivity,[status(thm)],[535, 533])).
% 4.46/4.68 tff(537,plain,
% 4.46/4.68 ((~![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) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~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) | (~((~element(tptp_fun_D_0(C, C!20, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(C, C!20, B!18), C!20) | (~in(tptp_fun_D_0(C, C!20, B!18), C)))))))))),
% 4.46/4.68 inference(quant_inst,[status(thm)],[])).
% 4.46/4.68 tff(538,plain,
% 4.46/4.68 ((~![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) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(C, B, B!18), B) | (~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) | (~((~in(tptp_fun_D_0(C, C!20, B!18), 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)))))))))),
% 4.46/4.68 inference(modus_ponens,[status(thm)],[537, 536])).
% 4.46/4.68 tff(539,plain,
% 4.46/4.68 (![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) | (~((~in(tptp_fun_D_0(C, C!20, B!18), 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)))))))))),
% 4.46/4.68 inference(unit_resolution,[status(thm)],[538, 37, 495])).
% 4.46/4.68 tff(540,plain,
% 4.46/4.68 (((~![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) | (~((~in(tptp_fun_D_0(C, C!20, B!18), 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)))))))))) | (~((~((~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) | (~((~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19))))))))) <=> ((~![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) | (~((~in(tptp_fun_D_0(C, C!20, B!18), 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)))))))))) | (~((~((~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) | (~((~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19)))))))))),
% 4.46/4.68 inference(rewrite,[status(thm)],[])).
% 4.46/4.68 tff(541,plain,
% 4.46/4.68 ((~((~((~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) | (~((~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) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))))))))) <=> (~((~((~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) | (~((~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19))))))))),
% 4.46/4.68 inference(rewrite,[status(thm)],[])).
% 4.46/4.68 tff(542,plain,
% 4.46/4.68 (((~![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) | (~((~in(tptp_fun_D_0(C, C!20, B!18), 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)))))))))) | (~((~((~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) | (~((~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) | (~element(tptp_fun_D_0(A!19, C!20, B!18), 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) | (~((~in(tptp_fun_D_0(C, C!20, B!18), 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)))))))))) | (~((~((~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) | (~((~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19)))))))))),
% 4.46/4.68 inference(monotonicity,[status(thm)],[541])).
% 4.46/4.68 tff(543,plain,
% 4.46/4.68 (((~![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) | (~((~in(tptp_fun_D_0(C, C!20, B!18), 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)))))))))) | (~((~((~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) | (~((~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) | (~element(tptp_fun_D_0(A!19, C!20, B!18), 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) | (~((~in(tptp_fun_D_0(C, C!20, B!18), 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)))))))))) | (~((~((~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) | (~((~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19)))))))))),
% 4.46/4.68 inference(transitivity,[status(thm)],[542, 540])).
% 4.46/4.68 tff(544,plain,
% 4.46/4.68 ((~![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) | (~((~in(tptp_fun_D_0(C, C!20, B!18), 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)))))))))) | (~((~((~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) | (~((~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) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18)))))))))),
% 4.46/4.68 inference(quant_inst,[status(thm)],[])).
% 4.46/4.68 tff(545,plain,
% 4.46/4.68 ((~![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) | (~((~in(tptp_fun_D_0(C, C!20, B!18), 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)))))))))) | (~((~((~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) | (~((~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19))))))))),
% 4.46/4.68 inference(modus_ponens,[status(thm)],[544, 543])).
% 4.46/4.68 tff(546,plain,
% 4.46/4.68 (~((~((~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) | (~((~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19)))))))),
% 4.46/4.68 inference(unit_resolution,[status(thm)],[545, 539])).
% 4.46/4.68 tff(547,plain,
% 4.46/4.68 (((~((~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) | (~((~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19))))))) | (latt_element_smaller(B!18, C!20, A!19) | (~((~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19)))))),
% 4.46/4.68 inference(tautology,[status(thm)],[])).
% 4.46/4.68 tff(548,plain,
% 4.46/4.68 (latt_element_smaller(B!18, C!20, A!19) | (~((~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19))))),
% 4.46/4.68 inference(unit_resolution,[status(thm)],[547, 546])).
% 4.46/4.68 tff(549,plain,
% 4.46/4.68 ((~(latt_element_smaller(B!18, C!20, A!19) | (~((~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19)))))) | latt_element_smaller(B!18, C!20, A!19) | (~((~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19))))),
% 4.46/4.68 inference(tautology,[status(thm)],[])).
% 4.46/4.68 tff(550,plain,
% 4.46/4.68 (latt_element_smaller(B!18, C!20, A!19) | (~((~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19))))),
% 4.46/4.68 inference(unit_resolution,[status(thm)],[549, 548])).
% 4.46/4.68 tff(551,plain,
% 4.46/4.68 (~((~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19)))),
% 4.46/4.68 inference(unit_resolution,[status(thm)],[550, 532])).
% 4.46/4.68 tff(552,plain,
% 4.46/4.68 (((~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(A!19, C!20, 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(B!18))),
% 4.46/4.68 inference(tautology,[status(thm)],[])).
% 4.46/4.68 tff(553,plain,
% 4.46/4.68 (element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))),
% 4.46/4.68 inference(unit_resolution,[status(thm)],[552, 551])).
% 4.46/4.68 tff(554,plain,
% 4.46/4.68 (((~![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)))),
% 4.46/4.68 inference(rewrite,[status(thm)],[])).
% 4.46/4.68 tff(555,plain,
% 4.46/4.68 ((~![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)))),
% 4.46/4.68 inference(quant_inst,[status(thm)],[])).
% 4.46/4.68 tff(556,plain,
% 4.46/4.68 ((~![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))),
% 4.46/4.68 inference(modus_ponens,[status(thm)],[555, 554])).
% 4.46/4.68 tff(557,plain,
% 4.46/4.68 (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)),
% 4.46/4.68 inference(unit_resolution,[status(thm)],[556, 35, 553])).
% 4.46/4.68 tff(558,plain,
% 4.46/4.68 (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))),
% 4.46/4.68 inference(symmetry,[status(thm)],[557])).
% 4.46/4.68 tff(559,plain,
% 4.46/4.68 (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)))),
% 4.46/4.68 inference(monotonicity,[status(thm)],[64, 558, 43])).
% 4.46/4.68 tff(560,plain,
% 4.46/4.68 (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))),
% 4.46/4.68 inference(symmetry,[status(thm)],[559])).
% 4.46/4.68 tff(561,plain,
% 4.46/4.68 ((~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)))),
% 4.46/4.68 inference(monotonicity,[status(thm)],[560])).
% 4.46/4.68 tff(562,plain,
% 4.46/4.68 (((~![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)))))),
% 4.46/4.68 inference(rewrite,[status(thm)],[])).
% 4.46/4.68 tff(563,plain,
% 4.46/4.68 ((~![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)))))),
% 4.46/4.68 inference(quant_inst,[status(thm)],[])).
% 4.46/4.68 tff(564,plain,
% 4.46/4.68 ((~![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))))),
% 4.46/4.68 inference(modus_ponens,[status(thm)],[563, 562])).
% 4.46/4.68 tff(565,plain,
% 4.46/4.68 (![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))))),
% 4.46/4.68 inference(unit_resolution,[status(thm)],[564, 356, 553])).
% 4.46/4.68 tff(566,plain,
% 4.46/4.68 (((~![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)))))),
% 4.46/4.68 inference(rewrite,[status(thm)],[])).
% 4.46/4.68 tff(567,plain,
% 4.46/4.68 ((~![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)))))),
% 4.46/4.68 inference(quant_inst,[status(thm)],[])).
% 4.46/4.68 tff(568,plain,
% 4.46/4.68 ((~![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))))),
% 4.46/4.68 inference(modus_ponens,[status(thm)],[567, 566])).
% 4.46/4.68 tff(569,plain,
% 4.46/4.68 (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)))),
% 4.46/4.69 inference(unit_resolution,[status(thm)],[568, 412, 565])).
% 4.46/4.69 tff(570,plain,
% 4.46/4.69 (((~![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))))),
% 4.46/4.69 inference(rewrite,[status(thm)],[])).
% 4.46/4.69 tff(571,plain,
% 4.46/4.69 (((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))))),
% 4.46/4.69 inference(rewrite,[status(thm)],[])).
% 4.46/4.69 tff(572,plain,
% 4.46/4.69 (((~![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)))))),
% 4.46/4.69 inference(monotonicity,[status(thm)],[571])).
% 4.46/4.69 tff(573,plain,
% 4.46/4.69 (((~![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))))),
% 4.46/4.69 inference(transitivity,[status(thm)],[572, 570])).
% 4.46/4.69 tff(574,plain,
% 4.46/4.69 ((~![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))))),
% 4.46/4.69 inference(quant_inst,[status(thm)],[])).
% 4.46/4.69 tff(575,plain,
% 4.46/4.69 ((~![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)))),
% 4.46/4.69 inference(modus_ponens,[status(thm)],[574, 573])).
% 4.46/4.69 tff(576,plain,
% 4.46/4.69 (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))),
% 4.46/4.69 inference(unit_resolution,[status(thm)],[575, 458, 12, 10, 445, 443, 441, 412, 553])).
% 4.46/4.69 tff(577,plain,
% 4.46/4.69 (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)),
% 4.46/4.69 inference(monotonicity,[status(thm)],[41])).
% 4.46/4.69 tff(578,plain,
% 4.46/4.69 (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))),
% 4.46/4.69 inference(symmetry,[status(thm)],[577])).
% 4.46/4.69 tff(579,plain,
% 4.46/4.69 ((~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)))),
% 4.46/4.69 inference(monotonicity,[status(thm)],[578])).
% 4.46/4.69 tff(580,plain,
% 4.46/4.69 (((~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20) | (~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))),
% 4.46/4.69 inference(tautology,[status(thm)],[])).
% 4.46/4.69 tff(581,plain,
% 4.46/4.69 (~below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20)),
% 4.46/4.69 inference(unit_resolution,[status(thm)],[580, 551])).
% 4.46/4.69 tff(582,plain,
% 4.46/4.69 (~below(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20))),
% 4.46/4.69 inference(modus_ponens,[status(thm)],[581, 579])).
% 4.46/4.69 tff(583,plain,
% 4.46/4.69 ((~(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))),
% 4.46/4.69 inference(tautology,[status(thm)],[])).
% 4.46/4.69 tff(584,plain,
% 4.46/4.69 (~below_refl(B!18, tptp_fun_D_0(A!19, C!20, B!18), cast_to_el_of_LattPOSet(B!18, C!20))),
% 4.46/4.69 inference(unit_resolution,[status(thm)],[583, 582, 576])).
% 4.46/4.69 tff(585,plain,
% 4.46/4.69 ((~(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))))),
% 4.46/4.69 inference(tautology,[status(thm)],[])).
% 4.46/4.69 tff(586,plain,
% 4.46/4.69 (~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)))),
% 4.46/4.69 inference(unit_resolution,[status(thm)],[585, 584, 569])).
% 4.46/4.69 tff(587,plain,
% 4.46/4.69 (~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))),
% 4.46/4.69 inference(modus_ponens,[status(thm)],[586, 561])).
% 4.46/4.69 tff(588,plain,
% 4.46/4.69 (the_carrier(poset_of_lattice(B!18)) = the_carrier(B!18)),
% 4.46/4.69 inference(symmetry,[status(thm)],[197])).
% 4.46/4.69 tff(589,plain,
% 4.46/4.69 (the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) = the_carrier(B!18)),
% 4.46/4.69 inference(transitivity,[status(thm)],[65, 588])).
% 4.46/4.69 tff(590,plain,
% 4.46/4.69 (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))),
% 4.46/4.69 inference(monotonicity,[status(thm)],[589])).
% 4.46/4.69 tff(591,plain,
% 4.46/4.69 (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))))),
% 4.46/4.69 inference(symmetry,[status(thm)],[590])).
% 4.46/4.69 tff(592,plain,
% 4.46/4.69 (element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 4.46/4.69 inference(modus_ponens,[status(thm)],[553, 591])).
% 4.46/4.69 tff(593,plain,
% 4.46/4.69 (((~![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))))),
% 4.46/4.69 inference(rewrite,[status(thm)],[])).
% 4.46/4.69 tff(594,plain,
% 4.46/4.69 (((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))))),
% 4.46/4.69 inference(rewrite,[status(thm)],[])).
% 4.46/4.69 tff(595,plain,
% 4.46/4.69 (((~![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)))))),
% 4.46/4.69 inference(monotonicity,[status(thm)],[594])).
% 4.46/4.69 tff(596,plain,
% 4.46/4.69 (((~![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))))),
% 4.46/4.69 inference(transitivity,[status(thm)],[595, 593])).
% 4.46/4.69 tff(597,plain,
% 4.46/4.69 ((~![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)))))),
% 4.46/4.69 inference(quant_inst,[status(thm)],[])).
% 4.46/4.69 tff(598,plain,
% 4.46/4.69 ((~![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)))),
% 4.46/4.69 inference(modus_ponens,[status(thm)],[597, 596])).
% 4.46/4.69 tff(599,plain,
% 4.46/4.69 (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))),
% 4.46/4.69 inference(unit_resolution,[status(thm)],[598, 320, 307, 95, 281, 228, 592])).
% 4.46/4.69 tff(600,plain,
% 4.46/4.69 (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))),
% 4.46/4.69 inference(modus_ponens,[status(thm)],[529, 202])).
% 4.46/4.69 tff(601,plain,
% 4.46/4.69 (((~((~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))))),
% 4.46/4.69 inference(tautology,[status(thm)],[])).
% 4.46/4.69 tff(602,plain,
% 4.46/4.69 ((~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)))),
% 4.46/4.69 inference(unit_resolution,[status(thm)],[601, 260])).
% 4.46/4.69 tff(603,plain,
% 4.46/4.69 ((~((~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)))),
% 4.46/4.69 inference(tautology,[status(thm)],[])).
% 4.46/4.69 tff(604,plain,
% 4.46/4.69 ((~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)))),
% 4.46/4.69 inference(unit_resolution,[status(thm)],[603, 602])).
% 4.46/4.69 tff(605,plain,
% 4.46/4.69 (![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)))),
% 4.46/4.69 inference(unit_resolution,[status(thm)],[604, 600])).
% 4.46/4.69 tff(606,plain,
% 4.46/4.69 (((~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | below(B!18, tptp_fun_D_0(A!19, C!20, B!18), C!20) | (~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)),
% 4.46/4.69 inference(tautology,[status(thm)],[])).
% 4.46/4.69 tff(607,plain,
% 4.46/4.69 (in(tptp_fun_D_0(A!19, C!20, B!18), A!19)),
% 4.46/4.69 inference(unit_resolution,[status(thm)],[606, 551])).
% 4.46/4.69 tff(608,plain,
% 4.46/4.69 (((~![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)))),
% 4.46/4.70 inference(rewrite,[status(thm)],[])).
% 4.46/4.70 tff(609,plain,
% 4.46/4.70 ((~![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)))),
% 4.46/4.70 inference(quant_inst,[status(thm)],[])).
% 4.46/4.70 tff(610,plain,
% 4.46/4.70 ((~![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))),
% 4.46/4.70 inference(modus_ponens,[status(thm)],[609, 608])).
% 4.46/4.70 tff(611,plain,
% 4.46/4.70 ((~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))),
% 4.46/4.70 inference(unit_resolution,[status(thm)],[610, 607, 605])).
% 4.46/4.70 tff(612,plain,
% 4.46/4.70 (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))),
% 4.46/4.70 inference(unit_resolution,[status(thm)],[611, 592])).
% 4.46/4.70 tff(613,plain,
% 4.46/4.70 ((~(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)))),
% 4.46/4.70 inference(tautology,[status(thm)],[])).
% 4.46/4.70 tff(614,plain,
% 4.46/4.70 (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))),
% 4.46/4.70 inference(unit_resolution,[status(thm)],[613, 612, 599])).
% 4.46/4.70 tff(615,plain,
% 4.46/4.70 ($false),
% 4.46/4.70 inference(unit_resolution,[status(thm)],[614, 587])).
% 4.46/4.70 % SZS output end Proof
% 4.46/4.73 % E exiting
%------------------------------------------------------------------------------