%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU347+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 4.32s 4.57s
% Output : Proof 4.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU347+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 06:51:57 EDT 2025
% 0.11/0.33 % CPUTime :
% 4.32/4.57 % SZS status Theorem
% 4.32/4.57 % SZS output start Proof
% 4.32/4.57 tff(related_reflexive_type, type, (
% 4.32/4.57 related_reflexive: ( $i * $i * $i ) > $o)).
% 4.32/4.57 tff(tptp_fun_D_0_type, type, (
% 4.32/4.57 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 4.32/4.57 tff(tptp_fun_B_18_type, type, (
% 4.32/4.57 tptp_fun_B_18: $i)).
% 4.32/4.57 tff(tptp_fun_C_20_type, type, (
% 4.32/4.57 tptp_fun_C_20: $i)).
% 4.32/4.57 tff(tptp_fun_A_19_type, type, (
% 4.32/4.57 tptp_fun_A_19: $i)).
% 4.32/4.57 tff(cast_to_el_of_LattPOSet_type, type, (
% 4.32/4.57 cast_to_el_of_LattPOSet: ( $i * $i ) > $i)).
% 4.32/4.57 tff(rel_str_of_type, type, (
% 4.32/4.57 rel_str_of: ( $i * $i ) > $i)).
% 4.32/4.57 tff(k2_lattice3_type, type, (
% 4.32/4.57 k2_lattice3: $i > $i)).
% 4.32/4.57 tff(the_carrier_type, type, (
% 4.32/4.57 the_carrier: $i > $i)).
% 4.32/4.57 tff(poset_of_lattice_type, type, (
% 4.32/4.57 poset_of_lattice: $i > $i)).
% 4.32/4.57 tff(element_type, type, (
% 4.32/4.57 element: ( $i * $i ) > $o)).
% 4.32/4.57 tff(in_type, type, (
% 4.32/4.57 in: ( $i * $i ) > $o)).
% 4.32/4.57 tff(below_type, type, (
% 4.32/4.57 below: ( $i * $i * $i ) > $o)).
% 4.32/4.57 tff(latt_set_smaller_type, type, (
% 4.32/4.57 latt_set_smaller: ( $i * $i * $i ) > $o)).
% 4.32/4.57 tff(relstr_element_smaller_type, type, (
% 4.32/4.57 relstr_element_smaller: ( $i * $i * $i ) > $o)).
% 4.32/4.57 tff(tptp_fun_D_1_type, type, (
% 4.32/4.57 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 4.32/4.57 tff(below_refl_type, type, (
% 4.32/4.57 below_refl: ( $i * $i * $i ) > $o)).
% 4.32/4.57 tff(latt_str_type, type, (
% 4.32/4.57 latt_str: $i > $o)).
% 4.32/4.57 tff(lattice_type, type, (
% 4.32/4.57 lattice: $i > $o)).
% 4.32/4.57 tff(empty_carrier_type, type, (
% 4.32/4.57 empty_carrier: $i > $o)).
% 4.32/4.57 tff(the_InternalRel_type, type, (
% 4.32/4.57 the_InternalRel: $i > $i)).
% 4.32/4.57 tff(relation_of_lattice_type, type, (
% 4.32/4.57 relation_of_lattice: $i > $i)).
% 4.32/4.57 tff(strict_rel_str_type, type, (
% 4.32/4.57 strict_rel_str: $i > $o)).
% 4.32/4.57 tff(rel_str_type, type, (
% 4.32/4.57 rel_str: $i > $o)).
% 4.32/4.57 tff(antisymmetric_relstr_type, type, (
% 4.32/4.57 antisymmetric_relstr: $i > $o)).
% 4.32/4.57 tff(transitive_relstr_type, type, (
% 4.32/4.57 transitive_relstr: $i > $o)).
% 4.32/4.57 tff(reflexive_relstr_type, type, (
% 4.32/4.57 reflexive_relstr: $i > $o)).
% 4.32/4.57 tff(relation_of2_type, type, (
% 4.32/4.57 relation_of2: ( $i * $i * $i ) > $o)).
% 4.32/4.57 tff(relation_of2_as_subset_type, type, (
% 4.32/4.57 relation_of2_as_subset: ( $i * $i * $i ) > $o)).
% 4.32/4.57 tff(v1_partfun1_type, type, (
% 4.32/4.57 v1_partfun1: ( $i * $i * $i ) > $o)).
% 4.32/4.57 tff(transitive_type, type, (
% 4.32/4.57 transitive: $i > $o)).
% 4.32/4.57 tff(antisymmetric_type, type, (
% 4.32/4.57 antisymmetric: $i > $o)).
% 4.32/4.57 tff(reflexive_type, type, (
% 4.32/4.57 reflexive: $i > $o)).
% 4.32/4.57 tff(related_type, type, (
% 4.32/4.57 related: ( $i * $i * $i ) > $o)).
% 4.32/4.57 tff(cast_to_el_of_lattice_type, type, (
% 4.32/4.57 cast_to_el_of_lattice: ( $i * $i ) > $i)).
% 4.32/4.57 tff(join_absorbing_type, type, (
% 4.32/4.57 join_absorbing: $i > $o)).
% 4.32/4.57 tff(meet_absorbing_type, type, (
% 4.32/4.57 meet_absorbing: $i > $o)).
% 4.32/4.57 tff(meet_associative_type, type, (
% 4.32/4.57 meet_associative: $i > $o)).
% 4.32/4.57 tff(meet_commutative_type, type, (
% 4.32/4.57 meet_commutative: $i > $o)).
% 4.32/4.57 tff(join_associative_type, type, (
% 4.32/4.57 join_associative: $i > $o)).
% 4.32/4.57 tff(join_commutative_type, type, (
% 4.32/4.57 join_commutative: $i > $o)).
% 4.32/4.57 tff(1,plain,
% 4.32/4.57 ((((~empty_carrier(B!18)) & lattice(B!18) & latt_str(B!18)) & (~((~element(C!20, the_carrier(B!18))) | (latt_set_smaller(B!18, C!20, A!19) <=> relstr_element_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_set_smaller(B!18, C!20, A!19) <=> relstr_element_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20))))))),
% 4.32/4.57 inference(rewrite,[status(thm)],[])).
% 4.32/4.57 tff(2,plain,
% 4.32/4.57 ((~![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_set_smaller(B, C, A) <=> relstr_element_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_set_smaller(B, C, A) <=> relstr_element_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C))))))),
% 4.32/4.57 inference(rewrite,[status(thm)],[])).
% 4.32/4.57 tff(3,plain,
% 4.32/4.57 ((~![A: $i, B: $i] : ((((~empty_carrier(B)) & lattice(B)) & latt_str(B)) => ![C: $i] : (element(C, the_carrier(B)) => (latt_set_smaller(B, C, A) <=> relstr_element_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_set_smaller(B, C, A) <=> relstr_element_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C))))))),
% 4.32/4.57 inference(rewrite,[status(thm)],[])).
% 4.32/4.57 tff(4,axiom,(~![A: $i, B: $i] : ((((~empty_carrier(B)) & lattice(B)) & latt_str(B)) => ![C: $i] : (element(C, the_carrier(B)) => (latt_set_smaller(B, C, A) <=> relstr_element_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t28_lattice3')).
% 4.32/4.57 tff(5,plain,
% 4.32/4.57 (~![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_set_smaller(B, C, A) <=> relstr_element_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))))),
% 4.32/4.57 inference(modus_ponens,[status(thm)],[4, 3])).
% 4.32/4.57 tff(6,plain,
% 4.32/4.57 (~![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_set_smaller(B, C, A) <=> relstr_element_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))))),
% 4.32/4.57 inference(modus_ponens,[status(thm)],[5, 2])).
% 4.32/4.57 tff(7,plain,
% 4.32/4.57 (~![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_set_smaller(B, C, A) <=> relstr_element_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))))),
% 4.32/4.57 inference(modus_ponens,[status(thm)],[6, 2])).
% 4.32/4.57 tff(8,plain,
% 4.32/4.57 (~![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_set_smaller(B, C, A) <=> relstr_element_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))))),
% 4.32/4.57 inference(modus_ponens,[status(thm)],[7, 2])).
% 4.32/4.57 tff(9,plain,
% 4.32/4.57 ((~empty_carrier(B!18)) & lattice(B!18) & latt_str(B!18) & (~((~element(C!20, the_carrier(B!18))) | (latt_set_smaller(B!18, C!20, A!19) <=> relstr_element_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20)))))),
% 4.32/4.57 inference(modus_ponens,[status(thm)],[8, 1])).
% 4.32/4.57 tff(10,plain,
% 4.32/4.57 (latt_str(B!18)),
% 4.32/4.57 inference(and_elim,[status(thm)],[9])).
% 4.32/4.57 tff(11,plain,
% 4.32/4.57 (lattice(B!18)),
% 4.32/4.57 inference(and_elim,[status(thm)],[9])).
% 4.32/4.57 tff(12,plain,
% 4.32/4.57 (~empty_carrier(B!18)),
% 4.32/4.57 inference(and_elim,[status(thm)],[9])).
% 4.32/4.57 tff(13,plain,
% 4.32/4.57 (^[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))))),
% 4.32/4.57 inference(bind,[status(th)],[])).
% 4.32/4.57 tff(14,plain,
% 4.32/4.57 (![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)))),
% 4.32/4.57 inference(quant_intro,[status(thm)],[13])).
% 4.32/4.57 tff(15,plain,
% 4.32/4.57 (^[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)))))),
% 4.32/4.57 inference(bind,[status(th)],[])).
% 4.32/4.57 tff(16,plain,
% 4.32/4.57 (![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)))),
% 4.32/4.57 inference(quant_intro,[status(thm)],[15])).
% 4.32/4.57 tff(17,plain,
% 4.32/4.57 (![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))))),
% 4.32/4.57 inference(rewrite,[status(thm)],[])).
% 4.32/4.57 tff(18,plain,
% 4.32/4.57 (^[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))))))),
% 4.32/4.57 inference(bind,[status(th)],[])).
% 4.32/4.57 tff(19,plain,
% 4.32/4.57 (![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))))),
% 4.32/4.57 inference(quant_intro,[status(thm)],[18])).
% 4.32/4.57 tff(20,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')).
% 4.32/4.57 tff(21,plain,
% 4.32/4.57 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))))),
% 4.32/4.57 inference(modus_ponens,[status(thm)],[20, 19])).
% 4.32/4.57 tff(22,plain,
% 4.32/4.57 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))))),
% 4.32/4.57 inference(modus_ponens,[status(thm)],[21, 17])).
% 4.32/4.57 tff(23,plain,(
% 4.32/4.57 ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))))),
% 4.32/4.57 inference(skolemize,[status(sab)],[22])).
% 4.32/4.57 tff(24,plain,
% 4.32/4.57 (![A: $i] : ((poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | empty_carrier(A) | (~latt_str(A)) | (~lattice(A)))),
% 4.32/4.57 inference(modus_ponens,[status(thm)],[23, 16])).
% 4.32/4.57 tff(25,plain,
% 4.32/4.57 (![A: $i] : ((poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | empty_carrier(A) | (~latt_str(A)) | (~lattice(A)))),
% 4.32/4.57 inference(modus_ponens,[status(thm)],[24, 14])).
% 4.32/4.57 tff(26,plain,
% 4.32/4.57 (((~![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))))),
% 4.32/4.57 inference(rewrite,[status(thm)],[])).
% 4.32/4.57 tff(27,plain,
% 4.32/4.57 (((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))))),
% 4.32/4.57 inference(rewrite,[status(thm)],[])).
% 4.32/4.57 tff(28,plain,
% 4.32/4.57 (((~![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)))))),
% 4.32/4.57 inference(monotonicity,[status(thm)],[27])).
% 4.32/4.57 tff(29,plain,
% 4.32/4.57 (((~![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))))),
% 4.32/4.57 inference(transitivity,[status(thm)],[28, 26])).
% 4.32/4.57 tff(30,plain,
% 4.32/4.57 ((~![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)))),
% 4.32/4.57 inference(quant_inst,[status(thm)],[])).
% 4.32/4.57 tff(31,plain,
% 4.32/4.57 ((~![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)))),
% 4.32/4.57 inference(modus_ponens,[status(thm)],[30, 29])).
% 4.32/4.57 tff(32,plain,
% 4.32/4.57 (poset_of_lattice(B!18) = rel_str_of(the_carrier(B!18), k2_lattice3(B!18))),
% 4.32/4.57 inference(unit_resolution,[status(thm)],[31, 25, 12, 11, 10])).
% 4.32/4.57 tff(33,plain,
% 4.32/4.57 (rel_str_of(the_carrier(B!18), k2_lattice3(B!18)) = poset_of_lattice(B!18)),
% 4.32/4.57 inference(symmetry,[status(thm)],[32])).
% 4.32/4.57 tff(34,plain,
% 4.32/4.57 (the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) = the_carrier(poset_of_lattice(B!18))),
% 4.32/4.57 inference(monotonicity,[status(thm)],[33])).
% 4.32/4.57 tff(35,plain,
% 4.32/4.57 (the_carrier(poset_of_lattice(B!18)) = the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))),
% 4.32/4.57 inference(symmetry,[status(thm)],[34])).
% 4.32/4.57 tff(36,plain,
% 4.32/4.57 (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))))),
% 4.32/4.57 inference(monotonicity,[status(thm)],[35])).
% 4.32/4.57 tff(37,plain,
% 4.32/4.57 (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))))),
% 4.32/4.57 inference(symmetry,[status(thm)],[36])).
% 4.32/4.57 tff(38,plain,
% 4.32/4.57 (strict_rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) <=> strict_rel_str(poset_of_lattice(B!18))),
% 4.32/4.57 inference(monotonicity,[status(thm)],[33])).
% 4.32/4.57 tff(39,plain,
% 4.32/4.57 (strict_rel_str(poset_of_lattice(B!18)) <=> strict_rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))),
% 4.32/4.57 inference(symmetry,[status(thm)],[38])).
% 4.32/4.57 tff(40,plain,
% 4.32/4.57 (^[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)))))))),
% 4.32/4.57 inference(bind,[status(th)],[])).
% 4.32/4.57 tff(41,plain,
% 4.32/4.57 (![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))))))),
% 4.32/4.57 inference(quant_intro,[status(thm)],[40])).
% 4.32/4.57 tff(42,plain,
% 4.32/4.57 (^[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))))))))),
% 4.32/4.57 inference(bind,[status(th)],[])).
% 4.32/4.57 tff(43,plain,
% 4.32/4.57 (![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))))))),
% 4.32/4.57 inference(quant_intro,[status(thm)],[42])).
% 4.32/4.57 tff(44,plain,
% 4.32/4.57 (![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))))),
% 4.32/4.57 inference(rewrite,[status(thm)],[])).
% 4.32/4.57 tff(45,plain,
% 4.32/4.57 (^[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))))))),
% 4.32/4.57 inference(bind,[status(th)],[])).
% 4.32/4.57 tff(46,plain,
% 4.32/4.57 (![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))))),
% 4.32/4.57 inference(quant_intro,[status(thm)],[45])).
% 4.32/4.57 tff(47,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')).
% 4.32/4.57 tff(48,plain,
% 4.32/4.57 (![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))))),
% 4.32/4.57 inference(modus_ponens,[status(thm)],[47, 46])).
% 4.32/4.57 tff(49,plain,
% 4.32/4.57 (![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))))),
% 4.32/4.57 inference(modus_ponens,[status(thm)],[48, 44])).
% 4.32/4.57 tff(50,plain,(
% 4.32/4.57 ![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))))),
% 4.32/4.57 inference(skolemize,[status(sab)],[49])).
% 4.32/4.57 tff(51,plain,
% 4.32/4.57 (![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))))))),
% 4.32/4.57 inference(modus_ponens,[status(thm)],[50, 43])).
% 4.32/4.57 tff(52,plain,
% 4.32/4.57 (![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))))))),
% 4.32/4.57 inference(modus_ponens,[status(thm)],[51, 41])).
% 4.32/4.57 tff(53,plain,
% 4.32/4.57 (((~![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))))))),
% 4.32/4.57 inference(rewrite,[status(thm)],[])).
% 4.32/4.57 tff(54,plain,
% 4.32/4.57 ((~![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))))))),
% 4.32/4.57 inference(quant_inst,[status(thm)],[])).
% 4.32/4.57 tff(55,plain,
% 4.32/4.57 ((~![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)))))),
% 4.32/4.57 inference(modus_ponens,[status(thm)],[54, 53])).
% 4.32/4.57 tff(56,plain,
% 4.32/4.57 (~((~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))))),
% 4.32/4.57 inference(unit_resolution,[status(thm)],[55, 52, 12, 11, 10])).
% 4.32/4.57 tff(57,plain,
% 4.32/4.57 (((~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))),
% 4.32/4.57 inference(tautology,[status(thm)],[])).
% 4.32/4.57 tff(58,plain,
% 4.32/4.57 (strict_rel_str(poset_of_lattice(B!18))),
% 4.32/4.57 inference(unit_resolution,[status(thm)],[57, 56])).
% 4.32/4.57 tff(59,plain,
% 4.32/4.57 (strict_rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))),
% 4.32/4.57 inference(modus_ponens,[status(thm)],[58, 39])).
% 4.32/4.57 tff(60,plain,
% 4.32/4.57 (rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) <=> rel_str(poset_of_lattice(B!18))),
% 4.32/4.57 inference(monotonicity,[status(thm)],[33])).
% 4.32/4.57 tff(61,plain,
% 4.32/4.57 (rel_str(poset_of_lattice(B!18)) <=> rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))),
% 4.32/4.57 inference(symmetry,[status(thm)],[60])).
% 4.32/4.57 tff(62,plain,
% 4.32/4.57 (((~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))),
% 4.32/4.57 inference(tautology,[status(thm)],[])).
% 4.32/4.57 tff(63,plain,
% 4.32/4.57 (rel_str(poset_of_lattice(B!18))),
% 4.32/4.57 inference(unit_resolution,[status(thm)],[62, 56])).
% 4.32/4.57 tff(64,plain,
% 4.32/4.57 (rel_str(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))),
% 4.32/4.57 inference(modus_ponens,[status(thm)],[63, 61])).
% 4.32/4.57 tff(65,plain,
% 4.32/4.57 (^[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))))),
% 4.32/4.57 inference(bind,[status(th)],[])).
% 4.32/4.57 tff(66,plain,
% 4.32/4.57 (![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)))),
% 4.32/4.57 inference(quant_intro,[status(thm)],[65])).
% 4.32/4.57 tff(67,plain,
% 4.32/4.57 (![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)))),
% 4.32/4.57 inference(rewrite,[status(thm)],[])).
% 4.32/4.57 tff(68,plain,
% 4.32/4.57 (^[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)))))),
% 4.32/4.57 inference(bind,[status(th)],[])).
% 4.32/4.57 tff(69,plain,
% 4.32/4.57 (![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)))),
% 4.32/4.57 inference(quant_intro,[status(thm)],[68])).
% 4.32/4.57 tff(70,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')).
% 4.32/4.57 tff(71,plain,
% 4.32/4.57 (![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 4.32/4.57 inference(modus_ponens,[status(thm)],[70, 69])).
% 4.32/4.57 tff(72,plain,
% 4.32/4.57 (![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 4.32/4.57 inference(modus_ponens,[status(thm)],[71, 67])).
% 4.32/4.57 tff(73,plain,(
% 4.32/4.57 ![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 4.32/4.57 inference(skolemize,[status(sab)],[72])).
% 4.32/4.57 tff(74,plain,
% 4.32/4.57 (![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 4.32/4.57 inference(modus_ponens,[status(thm)],[73, 66])).
% 4.32/4.57 tff(75,plain,
% 4.32/4.57 (((~![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)))))),
% 4.32/4.57 inference(rewrite,[status(thm)],[])).
% 4.32/4.57 tff(76,plain,
% 4.32/4.57 (((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)))))),
% 4.32/4.57 inference(rewrite,[status(thm)],[])).
% 4.32/4.57 tff(77,plain,
% 4.32/4.57 (((~![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))))))),
% 4.32/4.57 inference(monotonicity,[status(thm)],[76])).
% 4.32/4.57 tff(78,plain,
% 4.32/4.57 (((~![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)))))),
% 4.32/4.57 inference(transitivity,[status(thm)],[77, 75])).
% 4.32/4.57 tff(79,plain,
% 4.32/4.57 ((~![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)))))),
% 4.32/4.57 inference(quant_inst,[status(thm)],[])).
% 4.32/4.57 tff(80,plain,
% 4.32/4.57 ((~![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))))),
% 4.32/4.57 inference(modus_ponens,[status(thm)],[79, 78])).
% 4.32/4.57 tff(81,plain,
% 4.32/4.57 ((~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))))),
% 4.32/4.57 inference(unit_resolution,[status(thm)],[80, 74])).
% 4.32/4.57 tff(82,plain,
% 4.32/4.57 (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))))),
% 4.32/4.57 inference(unit_resolution,[status(thm)],[81, 64, 59])).
% 4.32/4.57 tff(83,plain,
% 4.32/4.57 (^[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))))),
% 4.32/4.57 inference(bind,[status(th)],[])).
% 4.32/4.57 tff(84,plain,
% 4.32/4.57 (![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)))),
% 4.32/4.58 inference(quant_intro,[status(thm)],[83])).
% 4.32/4.58 tff(85,plain,
% 4.32/4.58 (^[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)))))),
% 4.32/4.58 inference(bind,[status(th)],[])).
% 4.32/4.58 tff(86,plain,
% 4.32/4.58 (![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)))),
% 4.32/4.58 inference(quant_intro,[status(thm)],[85])).
% 4.32/4.58 tff(87,plain,
% 4.32/4.58 (![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)))),
% 4.32/4.58 inference(rewrite,[status(thm)],[])).
% 4.32/4.58 tff(88,plain,
% 4.32/4.58 (^[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)))))),
% 4.32/4.58 inference(bind,[status(th)],[])).
% 4.32/4.58 tff(89,plain,
% 4.32/4.58 (![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)))),
% 4.32/4.58 inference(quant_intro,[status(thm)],[88])).
% 4.32/4.58 tff(90,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')).
% 4.32/4.58 tff(91,plain,
% 4.32/4.58 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (k2_lattice3(A) = relation_of_lattice(A)))),
% 4.32/4.58 inference(modus_ponens,[status(thm)],[90, 89])).
% 4.32/4.58 tff(92,plain,
% 4.32/4.58 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (k2_lattice3(A) = relation_of_lattice(A)))),
% 4.32/4.58 inference(modus_ponens,[status(thm)],[91, 87])).
% 4.32/4.58 tff(93,plain,(
% 4.32/4.58 ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (k2_lattice3(A) = relation_of_lattice(A)))),
% 4.32/4.58 inference(skolemize,[status(sab)],[92])).
% 4.32/4.58 tff(94,plain,
% 4.32/4.58 (![A: $i] : (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))),
% 4.32/4.58 inference(modus_ponens,[status(thm)],[93, 86])).
% 4.32/4.58 tff(95,plain,
% 4.32/4.58 (![A: $i] : (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))),
% 4.32/4.58 inference(modus_ponens,[status(thm)],[94, 84])).
% 4.32/4.58 tff(96,plain,
% 4.32/4.58 (((~![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)))),
% 4.32/4.58 inference(rewrite,[status(thm)],[])).
% 4.32/4.58 tff(97,plain,
% 4.32/4.58 ((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)))),
% 4.32/4.58 inference(rewrite,[status(thm)],[])).
% 4.32/4.58 tff(98,plain,
% 4.32/4.58 (((~![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))))),
% 4.32/4.58 inference(monotonicity,[status(thm)],[97])).
% 4.32/4.58 tff(99,plain,
% 4.32/4.58 (((~![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)))),
% 4.32/4.58 inference(transitivity,[status(thm)],[98, 96])).
% 4.32/4.58 tff(100,plain,
% 4.32/4.58 ((~![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)))),
% 4.32/4.58 inference(quant_inst,[status(thm)],[])).
% 4.32/4.58 tff(101,plain,
% 4.32/4.58 ((~![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))),
% 4.32/4.58 inference(modus_ponens,[status(thm)],[100, 99])).
% 4.32/4.58 tff(102,plain,
% 4.32/4.58 (k2_lattice3(B!18) = relation_of_lattice(B!18)),
% 4.32/4.58 inference(unit_resolution,[status(thm)],[101, 95, 12, 11, 10])).
% 4.32/4.58 tff(103,plain,
% 4.32/4.58 (relation_of_lattice(B!18) = k2_lattice3(B!18)),
% 4.32/4.58 inference(symmetry,[status(thm)],[102])).
% 4.32/4.58 tff(104,plain,
% 4.32/4.58 (rel_str_of(the_carrier(B!18), relation_of_lattice(B!18)) = rel_str_of(the_carrier(B!18), k2_lattice3(B!18))),
% 4.32/4.58 inference(monotonicity,[status(thm)],[103])).
% 4.32/4.58 tff(105,plain,
% 4.32/4.58 (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))))),
% 4.32/4.58 inference(transitivity,[status(thm)],[104, 82, 37])).
% 4.32/4.58 tff(106,plain,
% 4.32/4.58 (^[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)))),
% 4.32/4.58 inference(bind,[status(th)],[])).
% 4.32/4.58 tff(107,plain,
% 4.32/4.58 (![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))),
% 4.32/4.58 inference(quant_intro,[status(thm)],[106])).
% 4.32/4.58 tff(108,plain,
% 4.32/4.58 (![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))),
% 4.32/4.58 inference(rewrite,[status(thm)],[])).
% 4.32/4.58 tff(109,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')).
% 4.32/4.58 tff(110,plain,
% 4.32/4.58 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 4.32/4.58 inference(modus_ponens,[status(thm)],[109, 108])).
% 4.32/4.58 tff(111,plain,(
% 4.32/4.58 ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 4.32/4.58 inference(skolemize,[status(sab)],[110])).
% 4.32/4.58 tff(112,plain,
% 4.32/4.58 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 4.32/4.58 inference(modus_ponens,[status(thm)],[111, 107])).
% 4.32/4.58 tff(113,plain,
% 4.32/4.58 ((~![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)))),
% 4.32/4.58 inference(quant_inst,[status(thm)],[])).
% 4.32/4.58 tff(114,plain,
% 4.32/4.58 (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))),
% 4.32/4.58 inference(unit_resolution,[status(thm)],[113, 112])).
% 4.32/4.58 tff(115,plain,
% 4.32/4.58 (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))),
% 4.32/4.58 inference(monotonicity,[status(thm)],[103])).
% 4.32/4.58 tff(116,plain,
% 4.32/4.58 (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))),
% 4.32/4.58 inference(symmetry,[status(thm)],[115])).
% 4.32/4.58 tff(117,plain,
% 4.32/4.58 (^[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)))))))),
% 4.32/4.58 inference(bind,[status(th)],[])).
% 4.32/4.58 tff(118,plain,
% 4.32/4.58 (![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))))))),
% 4.32/4.58 inference(quant_intro,[status(thm)],[117])).
% 4.32/4.58 tff(119,plain,
% 4.32/4.58 (^[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))))))))),
% 4.32/4.58 inference(bind,[status(th)],[])).
% 4.32/4.58 tff(120,plain,
% 4.32/4.58 (![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))))))),
% 4.32/4.58 inference(quant_intro,[status(thm)],[119])).
% 4.32/4.58 tff(121,plain,
% 4.32/4.58 (![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))))),
% 4.32/4.58 inference(rewrite,[status(thm)],[])).
% 4.32/4.58 tff(122,plain,
% 4.32/4.58 (^[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))))))),
% 4.32/4.58 inference(bind,[status(th)],[])).
% 4.32/4.58 tff(123,plain,
% 4.32/4.58 (![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))))),
% 4.32/4.58 inference(quant_intro,[status(thm)],[122])).
% 4.32/4.58 tff(124,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')).
% 4.32/4.58 tff(125,plain,
% 4.32/4.58 (![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))))),
% 4.32/4.58 inference(modus_ponens,[status(thm)],[124, 123])).
% 4.32/4.58 tff(126,plain,
% 4.32/4.58 (![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))))),
% 4.32/4.58 inference(modus_ponens,[status(thm)],[125, 121])).
% 4.32/4.58 tff(127,plain,(
% 4.32/4.58 ![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))))),
% 4.32/4.58 inference(skolemize,[status(sab)],[126])).
% 4.32/4.58 tff(128,plain,
% 4.32/4.58 (![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))))))),
% 4.32/4.58 inference(modus_ponens,[status(thm)],[127, 120])).
% 4.32/4.58 tff(129,plain,
% 4.32/4.58 (![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))))))),
% 4.32/4.58 inference(modus_ponens,[status(thm)],[128, 118])).
% 4.32/4.58 tff(130,plain,
% 4.32/4.58 (((~![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))))))),
% 4.32/4.58 inference(rewrite,[status(thm)],[])).
% 4.32/4.58 tff(131,plain,
% 4.32/4.58 ((~![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))))))),
% 4.32/4.58 inference(quant_inst,[status(thm)],[])).
% 4.32/4.58 tff(132,plain,
% 4.32/4.58 ((~![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)))))),
% 4.32/4.58 inference(modus_ponens,[status(thm)],[131, 130])).
% 4.32/4.58 tff(133,plain,
% 4.32/4.58 (~((~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))))),
% 4.32/4.58 inference(unit_resolution,[status(thm)],[132, 129, 12, 11, 10])).
% 4.32/4.58 tff(134,plain,
% 4.32/4.58 (((~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))),
% 4.32/4.58 inference(tautology,[status(thm)],[])).
% 4.32/4.58 tff(135,plain,
% 4.32/4.58 (relation_of2_as_subset(k2_lattice3(B!18), the_carrier(B!18), the_carrier(B!18))),
% 4.32/4.58 inference(unit_resolution,[status(thm)],[134, 133])).
% 4.32/4.58 tff(136,plain,
% 4.32/4.58 (relation_of2_as_subset(relation_of_lattice(B!18), the_carrier(B!18), the_carrier(B!18))),
% 4.32/4.58 inference(modus_ponens,[status(thm)],[135, 116])).
% 4.32/4.58 tff(137,plain,
% 4.32/4.58 ((~(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))),
% 4.32/4.58 inference(tautology,[status(thm)],[])).
% 4.32/4.58 tff(138,plain,
% 4.32/4.58 (relation_of2(relation_of_lattice(B!18), the_carrier(B!18), the_carrier(B!18))),
% 4.32/4.58 inference(unit_resolution,[status(thm)],[137, 136, 114])).
% 4.32/4.58 tff(139,plain,
% 4.32/4.58 (^[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)))))))),
% 4.32/4.58 inference(bind,[status(th)],[])).
% 4.32/4.58 tff(140,plain,
% 4.32/4.58 (![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))))))),
% 4.32/4.58 inference(quant_intro,[status(thm)],[139])).
% 4.32/4.58 tff(141,plain,
% 4.32/4.58 (^[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)))))))),
% 4.32/4.58 inference(bind,[status(th)],[])).
% 4.32/4.58 tff(142,plain,
% 4.32/4.58 (![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))))))),
% 4.32/4.58 inference(quant_intro,[status(thm)],[141])).
% 4.32/4.58 tff(143,plain,
% 4.32/4.58 (![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))))))),
% 4.44/4.58 inference(transitivity,[status(thm)],[142, 140])).
% 4.44/4.58 tff(144,plain,
% 4.44/4.58 (^[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)))))))),
% 4.44/4.58 inference(bind,[status(th)],[])).
% 4.44/4.58 tff(145,plain,
% 4.44/4.58 (![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))))))),
% 4.44/4.58 inference(quant_intro,[status(thm)],[144])).
% 4.44/4.58 tff(146,plain,
% 4.44/4.58 (![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))))),
% 4.44/4.58 inference(rewrite,[status(thm)],[])).
% 4.44/4.58 tff(147,plain,
% 4.44/4.58 (^[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))))))),
% 4.44/4.58 inference(bind,[status(th)],[])).
% 4.44/4.58 tff(148,plain,
% 4.44/4.58 (![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))))),
% 4.44/4.58 inference(quant_intro,[status(thm)],[147])).
% 4.44/4.58 tff(149,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')).
% 4.44/4.58 tff(150,plain,
% 4.44/4.58 (![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))))),
% 4.44/4.58 inference(modus_ponens,[status(thm)],[149, 148])).
% 4.44/4.58 tff(151,plain,
% 4.44/4.58 (![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))))),
% 4.44/4.58 inference(modus_ponens,[status(thm)],[150, 146])).
% 4.44/4.58 tff(152,plain,(
% 4.44/4.58 ![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))))),
% 4.44/4.58 inference(skolemize,[status(sab)],[151])).
% 4.44/4.58 tff(153,plain,
% 4.44/4.58 (![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))))))),
% 4.44/4.58 inference(modus_ponens,[status(thm)],[152, 145])).
% 4.44/4.58 tff(154,plain,
% 4.44/4.58 (![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))))))),
% 4.44/4.58 inference(modus_ponens,[status(thm)],[153, 143])).
% 4.44/4.58 tff(155,plain,
% 4.44/4.58 (((~![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))))))),
% 4.44/4.58 inference(rewrite,[status(thm)],[])).
% 4.44/4.58 tff(156,plain,
% 4.44/4.58 ((~![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))))))),
% 4.44/4.58 inference(quant_inst,[status(thm)],[])).
% 4.44/4.58 tff(157,plain,
% 4.44/4.58 ((~![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)))))),
% 4.44/4.58 inference(modus_ponens,[status(thm)],[156, 155])).
% 4.44/4.58 tff(158,plain,
% 4.44/4.58 ((~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)))))),
% 4.44/4.58 inference(unit_resolution,[status(thm)],[157, 154])).
% 4.44/4.58 tff(159,plain,
% 4.44/4.58 (![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)))))),
% 4.44/4.58 inference(unit_resolution,[status(thm)],[158, 138])).
% 4.44/4.58 tff(160,plain,
% 4.44/4.58 (((~![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))))))))),
% 4.44/4.58 inference(rewrite,[status(thm)],[])).
% 4.44/4.58 tff(161,plain,
% 4.44/4.58 ((~![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))))))))),
% 4.44/4.58 inference(quant_inst,[status(thm)],[])).
% 4.44/4.58 tff(162,plain,
% 4.44/4.58 ((~![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)))))))),
% 4.44/4.58 inference(modus_ponens,[status(thm)],[161, 160])).
% 4.44/4.58 tff(163,plain,
% 4.44/4.58 ((~(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)))))))),
% 4.44/4.58 inference(unit_resolution,[status(thm)],[162, 159])).
% 4.44/4.58 tff(164,plain,
% 4.44/4.58 (~((~(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))))))),
% 4.44/4.58 inference(unit_resolution,[status(thm)],[163, 105])).
% 4.44/4.58 tff(165,plain,
% 4.44/4.58 (((~(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)))),
% 4.44/4.58 inference(tautology,[status(thm)],[])).
% 4.44/4.58 tff(166,plain,
% 4.44/4.58 (the_carrier(B!18) = the_carrier(poset_of_lattice(B!18))),
% 4.44/4.58 inference(unit_resolution,[status(thm)],[165, 164])).
% 4.44/4.58 tff(167,plain,
% 4.44/4.58 (the_carrier(B!18) = the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))),
% 4.44/4.58 inference(transitivity,[status(thm)],[166, 35])).
% 4.44/4.58 tff(168,plain,
% 4.44/4.58 (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))))),
% 4.44/4.58 inference(monotonicity,[status(thm)],[167])).
% 4.44/4.58 tff(169,plain,
% 4.44/4.58 (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))),
% 4.44/4.58 inference(symmetry,[status(thm)],[168])).
% 4.44/4.58 tff(170,plain,
% 4.44/4.58 (relstr_element_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20)) <=> relstr_element_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20))),
% 4.44/4.58 inference(monotonicity,[status(thm)],[33])).
% 4.44/4.58 tff(171,plain,
% 4.44/4.58 (relstr_element_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20)) <=> relstr_element_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20))),
% 4.44/4.58 inference(symmetry,[status(thm)],[170])).
% 4.44/4.58 tff(172,plain,
% 4.44/4.58 ((~relstr_element_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20))) <=> (~relstr_element_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20)))),
% 4.44/4.58 inference(monotonicity,[status(thm)],[171])).
% 4.44/4.58 tff(173,assumption,(~relstr_element_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20))), introduced(assumption)).
% 4.44/4.58 tff(174,plain,
% 4.44/4.58 (~relstr_element_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20))),
% 4.44/4.58 inference(modus_ponens,[status(thm)],[173, 172])).
% 4.44/4.58 tff(175,plain,
% 4.44/4.58 (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)))),
% 4.44/4.58 inference(monotonicity,[status(thm)],[34])).
% 4.44/4.58 tff(176,plain,
% 4.44/4.58 (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))))),
% 4.44/4.58 inference(symmetry,[status(thm)],[175])).
% 4.44/4.58 tff(177,plain,
% 4.44/4.58 (~((~element(C!20, the_carrier(B!18))) | (latt_set_smaller(B!18, C!20, A!19) <=> relstr_element_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20))))),
% 4.44/4.58 inference(and_elim,[status(thm)],[9])).
% 4.44/4.58 tff(178,plain,
% 4.44/4.58 (element(C!20, the_carrier(B!18))),
% 4.44/4.58 inference(or_elim,[status(thm)],[177])).
% 4.44/4.58 tff(179,plain,
% 4.44/4.58 (^[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))))),
% 4.44/4.58 inference(bind,[status(th)],[])).
% 4.44/4.58 tff(180,plain,
% 4.44/4.58 (![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)))),
% 4.44/4.58 inference(quant_intro,[status(thm)],[179])).
% 4.44/4.58 tff(181,plain,
% 4.44/4.58 (^[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)))))),
% 4.44/4.58 inference(bind,[status(th)],[])).
% 4.44/4.58 tff(182,plain,
% 4.44/4.58 (![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)))),
% 4.44/4.58 inference(quant_intro,[status(thm)],[181])).
% 4.44/4.58 tff(183,plain,
% 4.44/4.58 (![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))))),
% 4.44/4.58 inference(rewrite,[status(thm)],[])).
% 4.44/4.58 tff(184,plain,
% 4.44/4.58 (^[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))))))),
% 4.44/4.58 inference(bind,[status(th)],[])).
% 4.44/4.58 tff(185,plain,
% 4.44/4.58 (![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))))),
% 4.44/4.58 inference(quant_intro,[status(thm)],[184])).
% 4.44/4.58 tff(186,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')).
% 4.44/4.58 tff(187,plain,
% 4.44/4.58 (![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))))),
% 4.44/4.58 inference(modus_ponens,[status(thm)],[186, 185])).
% 4.44/4.58 tff(188,plain,
% 4.44/4.58 (![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))))),
% 4.44/4.58 inference(modus_ponens,[status(thm)],[187, 183])).
% 4.44/4.58 tff(189,plain,(
% 4.44/4.58 ![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))))),
% 4.44/4.58 inference(skolemize,[status(sab)],[188])).
% 4.44/4.58 tff(190,plain,
% 4.44/4.58 (![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)))),
% 4.44/4.58 inference(modus_ponens,[status(thm)],[189, 182])).
% 4.44/4.58 tff(191,plain,
% 4.44/4.58 (![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)))),
% 4.44/4.58 inference(modus_ponens,[status(thm)],[190, 180])).
% 4.44/4.58 tff(192,plain,
% 4.44/4.58 (((~![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))))),
% 4.44/4.59 inference(rewrite,[status(thm)],[])).
% 4.44/4.59 tff(193,plain,
% 4.44/4.59 ((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))))),
% 4.44/4.59 inference(rewrite,[status(thm)],[])).
% 4.44/4.59 tff(194,plain,
% 4.44/4.59 (((~![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)))))),
% 4.44/4.59 inference(monotonicity,[status(thm)],[193])).
% 4.44/4.59 tff(195,plain,
% 4.44/4.59 (((~![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))))),
% 4.44/4.59 inference(transitivity,[status(thm)],[194, 192])).
% 4.44/4.59 tff(196,plain,
% 4.44/4.59 ((~![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)))),
% 4.44/4.59 inference(quant_inst,[status(thm)],[])).
% 4.44/4.59 tff(197,plain,
% 4.44/4.59 ((~![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)))),
% 4.44/4.59 inference(modus_ponens,[status(thm)],[196, 195])).
% 4.44/4.59 tff(198,plain,
% 4.44/4.59 (element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(poset_of_lattice(B!18)))),
% 4.44/4.59 inference(unit_resolution,[status(thm)],[197, 191, 12, 11, 10, 178])).
% 4.44/4.59 tff(199,plain,
% 4.44/4.59 (element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 4.44/4.59 inference(modus_ponens,[status(thm)],[198, 176])).
% 4.44/4.59 tff(200,plain,
% 4.44/4.59 (^[A: $i] : refl(((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~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_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B)))))))))))),
% 4.44/4.59 inference(bind,[status(th)],[])).
% 4.44/4.59 tff(201,plain,
% 4.44/4.59 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~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_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B))))))))))),
% 4.44/4.59 inference(quant_intro,[status(thm)],[200])).
% 4.44/4.59 tff(202,plain,
% 4.44/4.59 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~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_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B)))))))))))),
% 4.44/4.59 inference(bind,[status(th)],[])).
% 4.44/4.59 tff(203,plain,
% 4.44/4.59 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~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_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B))))))))))),
% 4.44/4.59 inference(quant_intro,[status(thm)],[202])).
% 4.44/4.59 tff(204,plain,
% 4.44/4.59 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~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_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B))))))))))),
% 4.44/4.59 inference(transitivity,[status(thm)],[203, 201])).
% 4.44/4.59 tff(205,plain,
% 4.44/4.59 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B)))) & (relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~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_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B)))))))))))),
% 4.44/4.59 inference(bind,[status(th)],[])).
% 4.44/4.59 tff(206,plain,
% 4.44/4.59 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B)))) & (relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~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_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B))))))))))),
% 4.44/4.59 inference(quant_intro,[status(thm)],[205])).
% 4.44/4.59 tff(207,plain,
% 4.44/4.59 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B))))))),
% 4.44/4.59 inference(rewrite,[status(thm)],[])).
% 4.44/4.59 tff(208,plain,
% 4.44/4.59 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i, C: $i] : trans(monotonicity(rewrite((relstr_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, C, D)))) <=> (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B))))), ((element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, C, D))))) <=> (element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B))))))), rewrite((element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B))))) <=> ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B)))))), ((element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, C, D))))) <=> ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B)))))))), (![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, C, D))))) <=> ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B))))))), ((rel_str(A) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, C, D)))))) <=> (rel_str(A) => ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B)))))))), rewrite((rel_str(A) => ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B)))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B))))))), ((rel_str(A) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, C, D)))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B))))))))),
% 4.44/4.59 inference(bind,[status(th)],[])).
% 4.44/4.59 tff(209,plain,
% 4.44/4.59 (![A: $i] : (rel_str(A) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, C, D)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B))))))),
% 4.44/4.59 inference(quant_intro,[status(thm)],[208])).
% 4.44/4.59 tff(210,axiom,(![A: $i] : (rel_str(A) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, C, D))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d8_lattice3')).
% 4.44/4.59 tff(211,plain,
% 4.44/4.59 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B))))))),
% 4.44/4.59 inference(modus_ponens,[status(thm)],[210, 209])).
% 4.44/4.59 tff(212,plain,
% 4.44/4.59 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B))))))),
% 4.44/4.59 inference(modus_ponens,[status(thm)],[211, 207])).
% 4.44/4.59 tff(213,plain,(
% 4.44/4.59 ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B)))) & (relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B))))))))),
% 4.44/4.59 inference(skolemize,[status(sab)],[212])).
% 4.44/4.59 tff(214,plain,
% 4.44/4.59 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B))))))))))),
% 4.44/4.59 inference(modus_ponens,[status(thm)],[213, 206])).
% 4.44/4.59 tff(215,plain,
% 4.44/4.59 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_1(C, B, A), B))))))))))),
% 4.44/4.59 inference(modus_ponens,[status(thm)],[214, 204])).
% 4.44/4.59 tff(216,plain,
% 4.44/4.59 (((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~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_element_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)), C, D)))) | (~(relstr_element_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)), C, tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~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_element_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)), C, D)))) | (~(relstr_element_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)), C, tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))))))))))),
% 4.44/4.59 inference(rewrite,[status(thm)],[])).
% 4.44/4.59 tff(217,plain,
% 4.44/4.59 (((~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_element_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)), C, D) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(D, B))))) | (~(relstr_element_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)), C, tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~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_element_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)), C, D)))) | (~(relstr_element_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)), C, tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))))))))))),
% 4.44/4.59 inference(rewrite,[status(thm)],[])).
% 4.44/4.59 tff(218,plain,
% 4.44/4.59 (((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~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_element_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)), C, D) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(D, B))))) | (~(relstr_element_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)), C, tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~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_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~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_element_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)), C, D)))) | (~(relstr_element_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)), C, tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))))))))))),
% 4.44/4.59 inference(monotonicity,[status(thm)],[217])).
% 4.44/4.59 tff(219,plain,
% 4.44/4.59 (((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~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_element_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)), C, D) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(D, B))))) | (~(relstr_element_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)), C, tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~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_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~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_element_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)), C, D)))) | (~(relstr_element_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)), C, tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))))))))))),
% 4.44/4.59 inference(transitivity,[status(thm)],[218, 216])).
% 4.44/4.59 tff(220,plain,
% 4.44/4.59 ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~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_element_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)), C, D) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~in(D, B))))) | (~(relstr_element_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)), C, tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~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))))))))))),
% 4.44/4.59 inference(quant_inst,[status(thm)],[])).
% 4.44/4.59 tff(221,plain,
% 4.44/4.59 ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~in(D, B))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~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_element_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)), C, D)))) | (~(relstr_element_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)), C, tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))))))))),
% 4.44/4.59 inference(modus_ponens,[status(thm)],[220, 219])).
% 4.44/4.59 tff(222,plain,
% 4.44/4.59 ((~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_element_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)), C, D)))) | (~(relstr_element_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)), C, tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))))))))),
% 4.44/4.59 inference(unit_resolution,[status(thm)],[221, 215])).
% 4.44/4.59 tff(223,plain,
% 4.44/4.59 (![B: $i, C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~((~((~relstr_element_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)), C, D)))) | (~(relstr_element_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)), C, tptp_fun_D_1(C, B, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))))))))),
% 4.44/4.59 inference(unit_resolution,[status(thm)],[222, 64])).
% 4.44/4.59 tff(224,plain,
% 4.44/4.59 (((~![B: $i, C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~((~((~relstr_element_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)), C, D)))) | (~(relstr_element_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)), C, tptp_fun_D_1(C, B, 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))))) | (~((~((~relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, 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))))) | (~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_element_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)), C, D)))) | (~(relstr_element_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)), C, tptp_fun_D_1(C, B, 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))))) | (~((~((~relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, 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))))) | (~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)))))))))),
% 4.44/4.59 inference(rewrite,[status(thm)],[])).
% 4.44/4.59 tff(225,plain,
% 4.44/4.59 (((~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~((~((~relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, 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))))) | (~((~((~relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, 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))))) | (~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)))))))))),
% 4.44/4.59 inference(rewrite,[status(thm)],[])).
% 4.44/4.59 tff(226,plain,
% 4.44/4.59 (((~![B: $i, C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~((~((~relstr_element_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)), C, D)))) | (~(relstr_element_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)), C, tptp_fun_D_1(C, B, 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))))) | (~((~((~relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_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, C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~((~((~relstr_element_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)), C, D)))) | (~(relstr_element_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)), C, tptp_fun_D_1(C, B, 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))))) | (~((~((~relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, 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))))) | (~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))))))))))),
% 4.44/4.60 inference(monotonicity,[status(thm)],[225])).
% 4.44/4.60 tff(227,plain,
% 4.44/4.60 (((~![B: $i, C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~((~((~relstr_element_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)), C, D)))) | (~(relstr_element_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)), C, tptp_fun_D_1(C, B, 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))))) | (~((~((~relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_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, C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~((~((~relstr_element_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)), C, D)))) | (~(relstr_element_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)), C, tptp_fun_D_1(C, B, 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))))) | (~((~((~relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, 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))))) | (~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)))))))))),
% 4.44/4.60 inference(transitivity,[status(thm)],[226, 224])).
% 4.44/4.60 tff(228,plain,
% 4.44/4.60 ((~![B: $i, C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~((~((~relstr_element_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)), C, D)))) | (~(relstr_element_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)), C, tptp_fun_D_1(C, B, 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))))) | (~((~((~relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))))))))),
% 4.44/4.60 inference(quant_inst,[status(thm)],[])).
% 4.44/4.60 tff(229,plain,
% 4.44/4.60 ((~![B: $i, C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~((~((~relstr_element_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)), C, D)))) | (~(relstr_element_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)), C, tptp_fun_D_1(C, B, 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))))) | (~((~((~relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, 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))))) | (~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))))))))),
% 4.44/4.60 inference(modus_ponens,[status(thm)],[228, 227])).
% 4.44/4.60 tff(230,plain,
% 4.44/4.60 ((~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | (~((~((~relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, 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))))) | (~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))))))))),
% 4.44/4.60 inference(unit_resolution,[status(thm)],[229, 223])).
% 4.44/4.60 tff(231,plain,
% 4.44/4.60 (~((~((~relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, 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))))) | (~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)))))))),
% 4.44/4.60 inference(unit_resolution,[status(thm)],[230, 199])).
% 4.44/4.60 tff(232,plain,
% 4.44/4.60 (((~((~relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, 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))))) | (~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_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, 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))))) | (~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)))))),
% 4.44/4.60 inference(tautology,[status(thm)],[])).
% 4.44/4.60 tff(233,plain,
% 4.44/4.60 (relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, 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))))) | (~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))))),
% 4.44/4.60 inference(unit_resolution,[status(thm)],[232, 231])).
% 4.44/4.60 tff(234,plain,
% 4.44/4.60 ((~(relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, 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))))) | (~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_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, 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))))) | (~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))))),
% 4.44/4.60 inference(tautology,[status(thm)],[])).
% 4.44/4.60 tff(235,plain,
% 4.44/4.60 (relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, 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))))) | (~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))))),
% 4.44/4.60 inference(unit_resolution,[status(thm)],[234, 233])).
% 4.44/4.60 tff(236,plain,
% 4.44/4.60 (~(related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, 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))))) | (~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)))),
% 4.44/4.60 inference(unit_resolution,[status(thm)],[235, 174])).
% 4.44/4.60 tff(237,plain,
% 4.44/4.60 ((related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, 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))))) | (~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))))),
% 4.44/4.60 inference(tautology,[status(thm)],[])).
% 4.44/4.60 tff(238,plain,
% 4.44/4.60 (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))))),
% 4.44/4.60 inference(unit_resolution,[status(thm)],[237, 236])).
% 4.44/4.60 tff(239,plain,
% 4.44/4.60 (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))),
% 4.44/4.60 inference(modus_ponens,[status(thm)],[238, 169])).
% 4.44/4.60 tff(240,plain,
% 4.44/4.60 (^[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))))),
% 4.44/4.60 inference(bind,[status(th)],[])).
% 4.44/4.60 tff(241,plain,
% 4.44/4.60 (![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)))),
% 4.44/4.60 inference(quant_intro,[status(thm)],[240])).
% 4.44/4.60 tff(242,plain,
% 4.44/4.60 (^[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))))),
% 4.44/4.60 inference(bind,[status(th)],[])).
% 4.44/4.60 tff(243,plain,
% 4.44/4.60 (![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)))),
% 4.44/4.60 inference(quant_intro,[status(thm)],[242])).
% 4.44/4.60 tff(244,plain,
% 4.44/4.60 (^[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))))),
% 4.44/4.60 inference(bind,[status(th)],[])).
% 4.44/4.60 tff(245,plain,
% 4.44/4.60 (![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)))),
% 4.44/4.60 inference(quant_intro,[status(thm)],[244])).
% 4.44/4.60 tff(246,plain,
% 4.44/4.60 (![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)))),
% 4.44/4.60 inference(transitivity,[status(thm)],[245, 243])).
% 4.44/4.60 tff(247,plain,
% 4.44/4.60 (^[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))) | ![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)))))),
% 4.44/4.60 inference(bind,[status(th)],[])).
% 4.44/4.60 tff(248,plain,
% 4.44/4.60 (![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)))),
% 4.44/4.60 inference(quant_intro,[status(thm)],[247])).
% 4.44/4.60 tff(249,plain,
% 4.44/4.60 (![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)))),
% 4.44/4.60 inference(rewrite,[status(thm)],[])).
% 4.44/4.60 tff(250,plain,
% 4.44/4.60 (^[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)))))),
% 4.44/4.60 inference(bind,[status(th)],[])).
% 4.44/4.60 tff(251,plain,
% 4.44/4.60 (![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)))),
% 4.44/4.60 inference(quant_intro,[status(thm)],[250])).
% 4.44/4.60 tff(252,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')).
% 4.44/4.60 tff(253,plain,
% 4.44/4.60 (![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)))),
% 4.44/4.60 inference(modus_ponens,[status(thm)],[252, 251])).
% 4.44/4.60 tff(254,plain,
% 4.44/4.60 (![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)))),
% 4.44/4.60 inference(modus_ponens,[status(thm)],[253, 249])).
% 4.44/4.60 tff(255,plain,(
% 4.44/4.60 ![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)))),
% 4.44/4.60 inference(skolemize,[status(sab)],[254])).
% 4.44/4.60 tff(256,plain,
% 4.44/4.60 (![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)))),
% 4.44/4.60 inference(modus_ponens,[status(thm)],[255, 248])).
% 4.44/4.60 tff(257,plain,
% 4.44/4.60 (![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)))),
% 4.44/4.60 inference(modus_ponens,[status(thm)],[256, 246])).
% 4.44/4.60 tff(258,plain,
% 4.44/4.60 (![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)))),
% 4.44/4.60 inference(modus_ponens,[status(thm)],[257, 241])).
% 4.44/4.60 tff(259,plain,
% 4.44/4.60 (((~![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)))),
% 4.44/4.60 inference(rewrite,[status(thm)],[])).
% 4.44/4.60 tff(260,plain,
% 4.44/4.60 ((~![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)))),
% 4.44/4.60 inference(quant_inst,[status(thm)],[])).
% 4.44/4.60 tff(261,plain,
% 4.44/4.60 ((~![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))),
% 4.44/4.60 inference(modus_ponens,[status(thm)],[260, 259])).
% 4.44/4.60 tff(262,plain,
% 4.44/4.60 (![B: $i] : ((~element(B, the_carrier(poset_of_lattice(B!18)))) | (cast_to_el_of_lattice(B!18, B) = B))),
% 4.44/4.60 inference(unit_resolution,[status(thm)],[261, 258, 12, 11, 10])).
% 4.44/4.60 tff(263,plain,
% 4.44/4.60 (((~![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)))),
% 4.44/4.60 inference(rewrite,[status(thm)],[])).
% 4.44/4.60 tff(264,plain,
% 4.44/4.60 ((~![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)))),
% 4.44/4.60 inference(quant_inst,[status(thm)],[])).
% 4.44/4.60 tff(265,plain,
% 4.44/4.60 ((~![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))),
% 4.44/4.60 inference(modus_ponens,[status(thm)],[264, 263])).
% 4.44/4.60 tff(266,plain,
% 4.44/4.60 (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)),
% 4.44/4.60 inference(unit_resolution,[status(thm)],[265, 262, 198])).
% 4.44/4.60 tff(267,plain,
% 4.44/4.60 (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))),
% 4.44/4.60 inference(symmetry,[status(thm)],[266])).
% 4.44/4.60 tff(268,plain,
% 4.44/4.60 (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))),
% 4.44/4.60 inference(monotonicity,[status(thm)],[267])).
% 4.44/4.60 tff(269,plain,
% 4.44/4.60 (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))),
% 4.44/4.60 inference(symmetry,[status(thm)],[268])).
% 4.44/4.60 tff(270,plain,
% 4.44/4.60 (^[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))))),
% 4.44/4.60 inference(bind,[status(th)],[])).
% 4.44/4.60 tff(271,plain,
% 4.44/4.60 (![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)))),
% 4.44/4.60 inference(quant_intro,[status(thm)],[270])).
% 4.44/4.60 tff(272,plain,
% 4.44/4.60 (^[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)))))),
% 4.44/4.60 inference(bind,[status(th)],[])).
% 4.44/4.60 tff(273,plain,
% 4.44/4.60 (![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)))),
% 4.44/4.60 inference(quant_intro,[status(thm)],[272])).
% 4.44/4.60 tff(274,plain,
% 4.44/4.60 (![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)))),
% 4.44/4.60 inference(rewrite,[status(thm)],[])).
% 4.44/4.60 tff(275,plain,
% 4.44/4.60 (^[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)))))),
% 4.44/4.60 inference(bind,[status(th)],[])).
% 4.44/4.60 tff(276,plain,
% 4.44/4.60 (![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)))),
% 4.44/4.60 inference(quant_intro,[status(thm)],[275])).
% 4.44/4.60 tff(277,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')).
% 4.44/4.60 tff(278,plain,
% 4.44/4.60 (![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)))),
% 4.44/4.60 inference(modus_ponens,[status(thm)],[277, 276])).
% 4.44/4.60 tff(279,plain,
% 4.44/4.60 (![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)))),
% 4.44/4.60 inference(modus_ponens,[status(thm)],[278, 274])).
% 4.44/4.60 tff(280,plain,(
% 4.44/4.60 ![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)))),
% 4.44/4.60 inference(skolemize,[status(sab)],[279])).
% 4.44/4.60 tff(281,plain,
% 4.44/4.60 (![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)))),
% 4.44/4.60 inference(modus_ponens,[status(thm)],[280, 273])).
% 4.44/4.60 tff(282,plain,
% 4.44/4.60 (![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)))),
% 4.44/4.60 inference(modus_ponens,[status(thm)],[281, 271])).
% 4.44/4.60 tff(283,plain,
% 4.44/4.60 (((~![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)))),
% 4.44/4.60 inference(rewrite,[status(thm)],[])).
% 4.44/4.60 tff(284,plain,
% 4.44/4.60 ((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)))),
% 4.44/4.60 inference(rewrite,[status(thm)],[])).
% 4.44/4.60 tff(285,plain,
% 4.44/4.60 (((~![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))))),
% 4.44/4.60 inference(monotonicity,[status(thm)],[284])).
% 4.44/4.60 tff(286,plain,
% 4.44/4.60 (((~![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)))),
% 4.44/4.60 inference(transitivity,[status(thm)],[285, 283])).
% 4.44/4.60 tff(287,plain,
% 4.44/4.60 ((~![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)))),
% 4.44/4.60 inference(quant_inst,[status(thm)],[])).
% 4.44/4.60 tff(288,plain,
% 4.44/4.60 ((~![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))),
% 4.44/4.60 inference(modus_ponens,[status(thm)],[287, 286])).
% 4.44/4.61 tff(289,plain,
% 4.44/4.61 (element(cast_to_el_of_lattice(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), the_carrier(B!18))),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[288, 282, 12, 11, 10, 198])).
% 4.44/4.61 tff(290,plain,
% 4.44/4.61 (element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))),
% 4.44/4.61 inference(modus_ponens,[status(thm)],[289, 269])).
% 4.44/4.61 tff(291,plain,
% 4.44/4.61 (^[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))))),
% 4.44/4.61 inference(bind,[status(th)],[])).
% 4.44/4.61 tff(292,plain,
% 4.44/4.61 (![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)))),
% 4.44/4.61 inference(quant_intro,[status(thm)],[291])).
% 4.44/4.61 tff(293,plain,
% 4.44/4.61 (^[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)))))),
% 4.44/4.61 inference(bind,[status(th)],[])).
% 4.44/4.61 tff(294,plain,
% 4.44/4.61 (![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)))),
% 4.44/4.61 inference(quant_intro,[status(thm)],[293])).
% 4.44/4.61 tff(295,plain,
% 4.44/4.61 (![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)))),
% 4.44/4.61 inference(rewrite,[status(thm)],[])).
% 4.44/4.61 tff(296,plain,
% 4.44/4.61 (^[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)))))),
% 4.44/4.61 inference(bind,[status(th)],[])).
% 4.44/4.61 tff(297,plain,
% 4.44/4.61 (![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)))),
% 4.44/4.61 inference(quant_intro,[status(thm)],[296])).
% 4.44/4.61 tff(298,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')).
% 4.44/4.61 tff(299,plain,
% 4.44/4.61 (![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)))),
% 4.44/4.61 inference(modus_ponens,[status(thm)],[298, 297])).
% 4.44/4.61 tff(300,plain,
% 4.44/4.61 (![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)))),
% 4.44/4.61 inference(modus_ponens,[status(thm)],[299, 295])).
% 4.44/4.61 tff(301,plain,(
% 4.44/4.61 ![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)))),
% 4.44/4.61 inference(skolemize,[status(sab)],[300])).
% 4.44/4.61 tff(302,plain,
% 4.44/4.61 (![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)))),
% 4.44/4.61 inference(modus_ponens,[status(thm)],[301, 294])).
% 4.44/4.61 tff(303,plain,
% 4.44/4.61 (![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)))),
% 4.44/4.61 inference(modus_ponens,[status(thm)],[302, 292])).
% 4.44/4.61 tff(304,plain,
% 4.44/4.61 (((~![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)))))),
% 4.44/4.61 inference(rewrite,[status(thm)],[])).
% 4.44/4.61 tff(305,plain,
% 4.44/4.61 ((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)))))),
% 4.44/4.61 inference(rewrite,[status(thm)],[])).
% 4.44/4.61 tff(306,plain,
% 4.44/4.61 ((~(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))))),
% 4.44/4.61 inference(rewrite,[status(thm)],[])).
% 4.44/4.61 tff(307,plain,
% 4.44/4.61 ((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)))),
% 4.44/4.61 inference(monotonicity,[status(thm)],[306])).
% 4.44/4.61 tff(308,plain,
% 4.44/4.61 ((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)))))),
% 4.44/4.61 inference(transitivity,[status(thm)],[307, 305])).
% 4.44/4.61 tff(309,plain,
% 4.44/4.61 (((~![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))))))),
% 4.44/4.61 inference(monotonicity,[status(thm)],[308])).
% 4.44/4.61 tff(310,plain,
% 4.44/4.61 (((~![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)))))),
% 4.44/4.61 inference(transitivity,[status(thm)],[309, 304])).
% 4.44/4.61 tff(311,plain,
% 4.44/4.61 ((~![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)))),
% 4.44/4.61 inference(quant_inst,[status(thm)],[])).
% 4.44/4.61 tff(312,plain,
% 4.44/4.61 ((~![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))))),
% 4.44/4.61 inference(modus_ponens,[status(thm)],[311, 310])).
% 4.44/4.61 tff(313,plain,
% 4.44/4.61 (~(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)))),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[312, 303, 12, 11, 10])).
% 4.44/4.61 tff(314,plain,
% 4.44/4.61 ((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)),
% 4.44/4.61 inference(tautology,[status(thm)],[])).
% 4.44/4.61 tff(315,plain,
% 4.44/4.61 (join_absorbing(B!18)),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[314, 313])).
% 4.44/4.61 tff(316,plain,
% 4.44/4.61 ((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)),
% 4.44/4.61 inference(tautology,[status(thm)],[])).
% 4.44/4.61 tff(317,plain,
% 4.44/4.61 (meet_absorbing(B!18)),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[316, 313])).
% 4.44/4.61 tff(318,plain,
% 4.44/4.61 ((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)),
% 4.44/4.61 inference(tautology,[status(thm)],[])).
% 4.44/4.61 tff(319,plain,
% 4.44/4.61 (meet_commutative(B!18)),
% 4.44/4.61 inference(unit_resolution,[status(thm)],[318, 313])).
% 4.44/4.61 tff(320,plain,
% 4.44/4.61 (^[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)))))),
% 4.44/4.61 inference(bind,[status(th)],[])).
% 4.44/4.61 tff(321,plain,
% 4.44/4.61 (![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))))),
% 4.44/4.61 inference(quant_intro,[status(thm)],[320])).
% 4.44/4.61 tff(322,plain,
% 4.44/4.61 (^[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))))))),
% 4.47/4.61 inference(bind,[status(th)],[])).
% 4.47/4.61 tff(323,plain,
% 4.47/4.61 (![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))))),
% 4.47/4.61 inference(quant_intro,[status(thm)],[322])).
% 4.47/4.61 tff(324,plain,
% 4.47/4.61 (![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)))),
% 4.47/4.61 inference(rewrite,[status(thm)],[])).
% 4.47/4.61 tff(325,plain,
% 4.47/4.61 (^[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)))))),
% 4.47/4.61 inference(bind,[status(th)],[])).
% 4.47/4.61 tff(326,plain,
% 4.47/4.61 (![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)))),
% 4.47/4.61 inference(quant_intro,[status(thm)],[325])).
% 4.47/4.61 tff(327,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')).
% 4.47/4.61 tff(328,plain,
% 4.47/4.61 (![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)))),
% 4.47/4.61 inference(modus_ponens,[status(thm)],[327, 326])).
% 4.47/4.61 tff(329,plain,
% 4.47/4.61 (![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)))),
% 4.47/4.61 inference(modus_ponens,[status(thm)],[328, 324])).
% 4.47/4.61 tff(330,plain,(
% 4.47/4.61 ![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)))),
% 4.47/4.61 inference(skolemize,[status(sab)],[329])).
% 4.47/4.61 tff(331,plain,
% 4.47/4.61 (![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))))),
% 4.47/4.61 inference(modus_ponens,[status(thm)],[330, 323])).
% 4.47/4.61 tff(332,plain,
% 4.47/4.61 (![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))))),
% 4.47/4.61 inference(modus_ponens,[status(thm)],[331, 321])).
% 4.47/4.61 tff(333,plain,
% 4.47/4.61 (((~![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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_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: $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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))))),
% 4.47/4.61 inference(rewrite,[status(thm)],[])).
% 4.47/4.61 tff(334,plain,
% 4.47/4.61 (((below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | empty_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))) | (~meet_commutative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)) | (~latt_str(B!18)) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), 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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))))),
% 4.47/4.61 inference(rewrite,[status(thm)],[])).
% 4.47/4.61 tff(335,plain,
% 4.47/4.61 (((~![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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | empty_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))) | (~meet_commutative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)) | (~latt_str(B!18)) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), 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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))))),
% 4.47/4.61 inference(monotonicity,[status(thm)],[334])).
% 4.47/4.61 tff(336,plain,
% 4.47/4.61 (((~![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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | empty_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))) | (~meet_commutative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)) | (~latt_str(B!18)) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), 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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))))),
% 4.47/4.61 inference(transitivity,[status(thm)],[335, 333])).
% 4.47/4.61 tff(337,plain,
% 4.47/4.61 ((~![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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | empty_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))) | (~meet_commutative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)) | (~latt_str(B!18)) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))))),
% 4.47/4.61 inference(quant_inst,[status(thm)],[])).
% 4.47/4.61 tff(338,plain,
% 4.47/4.61 ((~![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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))),
% 4.47/4.61 inference(modus_ponens,[status(thm)],[337, 336])).
% 4.47/4.61 tff(339,plain,
% 4.47/4.61 (below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 4.47/4.61 inference(unit_resolution,[status(thm)],[338, 332, 12, 10, 319, 317, 315, 290, 239])).
% 4.47/4.61 tff(340,plain,
% 4.47/4.61 (^[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)))))))),
% 4.47/4.61 inference(bind,[status(th)],[])).
% 4.47/4.61 tff(341,plain,
% 4.47/4.61 (![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))))))),
% 4.47/4.61 inference(quant_intro,[status(thm)],[340])).
% 4.47/4.61 tff(342,plain,
% 4.47/4.61 (^[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))))),
% 4.47/4.61 inference(bind,[status(th)],[])).
% 4.47/4.61 tff(343,plain,
% 4.47/4.61 (![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)))),
% 4.47/4.61 inference(quant_intro,[status(thm)],[342])).
% 4.47/4.61 tff(344,plain,
% 4.47/4.61 (^[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))))),
% 4.47/4.61 inference(bind,[status(th)],[])).
% 4.47/4.61 tff(345,plain,
% 4.47/4.61 (![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)))),
% 4.47/4.61 inference(quant_intro,[status(thm)],[344])).
% 4.47/4.61 tff(346,plain,
% 4.47/4.61 (![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)))),
% 4.47/4.61 inference(transitivity,[status(thm)],[345, 343])).
% 4.47/4.61 tff(347,plain,
% 4.47/4.61 (^[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)))))),
% 4.47/4.61 inference(bind,[status(th)],[])).
% 4.47/4.61 tff(348,plain,
% 4.47/4.61 (![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)))),
% 4.47/4.61 inference(quant_intro,[status(thm)],[347])).
% 4.47/4.61 tff(349,plain,
% 4.47/4.61 (![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))))))),
% 4.47/4.61 inference(rewrite,[status(thm)],[])).
% 4.47/4.61 tff(350,plain,
% 4.47/4.61 (^[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))))))))),
% 4.47/4.62 inference(bind,[status(th)],[])).
% 4.47/4.62 tff(351,plain,
% 4.47/4.62 (![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))))))),
% 4.47/4.62 inference(quant_intro,[status(thm)],[350])).
% 4.47/4.62 tff(352,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')).
% 4.47/4.62 tff(353,plain,
% 4.47/4.62 (![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))))))),
% 4.47/4.62 inference(modus_ponens,[status(thm)],[352, 351])).
% 4.47/4.62 tff(354,plain,
% 4.47/4.62 (![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))))))),
% 4.47/4.62 inference(modus_ponens,[status(thm)],[353, 349])).
% 4.47/4.62 tff(355,plain,(
% 4.47/4.62 ![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))))))),
% 4.47/4.62 inference(skolemize,[status(sab)],[354])).
% 4.47/4.62 tff(356,plain,
% 4.47/4.62 (![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)))),
% 4.47/4.62 inference(modus_ponens,[status(thm)],[355, 348])).
% 4.47/4.62 tff(357,plain,
% 4.47/4.62 (![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)))),
% 4.47/4.62 inference(modus_ponens,[status(thm)],[356, 346])).
% 4.47/4.62 tff(358,plain,
% 4.47/4.62 (![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))))))),
% 4.47/4.62 inference(modus_ponens,[status(thm)],[357, 341])).
% 4.47/4.62 tff(359,plain,
% 4.47/4.62 (((~![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))))))),
% 4.47/4.62 inference(rewrite,[status(thm)],[])).
% 4.47/4.62 tff(360,plain,
% 4.47/4.62 ((~![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))))))),
% 4.47/4.62 inference(quant_inst,[status(thm)],[])).
% 4.47/4.62 tff(361,plain,
% 4.47/4.62 ((~![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)))))),
% 4.47/4.62 inference(modus_ponens,[status(thm)],[360, 359])).
% 4.47/4.62 tff(362,plain,
% 4.47/4.62 (![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)))))),
% 4.47/4.62 inference(unit_resolution,[status(thm)],[361, 12, 11, 10, 358])).
% 4.47/4.62 tff(363,plain,
% 4.47/4.62 (((~![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(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | ![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), cast_to_el_of_LattPOSet(B!18, C)))))) <=> ((~![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(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | ![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), cast_to_el_of_LattPOSet(B!18, C)))))),
% 4.47/4.62 inference(rewrite,[status(thm)],[])).
% 4.47/4.62 tff(364,plain,
% 4.47/4.62 ((~![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(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | ![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), cast_to_el_of_LattPOSet(B!18, C)))))),
% 4.47/4.62 inference(quant_inst,[status(thm)],[])).
% 4.47/4.62 tff(365,plain,
% 4.47/4.62 ((~![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(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | ![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), cast_to_el_of_LattPOSet(B!18, C))))),
% 4.47/4.62 inference(modus_ponens,[status(thm)],[364, 363])).
% 4.47/4.62 tff(366,plain,
% 4.47/4.62 ((~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | ![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), cast_to_el_of_LattPOSet(B!18, C))))),
% 4.47/4.62 inference(unit_resolution,[status(thm)],[365, 362])).
% 4.47/4.62 tff(367,plain,
% 4.47/4.62 (![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), cast_to_el_of_LattPOSet(B!18, C))))),
% 4.47/4.62 inference(unit_resolution,[status(thm)],[366, 290])).
% 4.47/4.62 tff(368,plain,
% 4.47/4.62 (((~![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), cast_to_el_of_LattPOSet(B!18, C))))) | ((~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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), 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)))))))) <=> ((~![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), cast_to_el_of_LattPOSet(B!18, C))))) | (~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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), 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)))))))),
% 4.47/4.62 inference(rewrite,[status(thm)],[])).
% 4.47/4.62 tff(369,plain,
% 4.47/4.62 ((~![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), cast_to_el_of_LattPOSet(B!18, C))))) | ((~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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), 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)))))))),
% 4.47/4.62 inference(quant_inst,[status(thm)],[])).
% 4.47/4.62 tff(370,plain,
% 4.47/4.62 ((~![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), cast_to_el_of_LattPOSet(B!18, C))))) | (~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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), 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))))))),
% 4.47/4.62 inference(modus_ponens,[status(thm)],[369, 368])).
% 4.47/4.62 tff(371,plain,
% 4.47/4.62 ((~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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), 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))))))),
% 4.47/4.62 inference(unit_resolution,[status(thm)],[370, 367])).
% 4.47/4.62 tff(372,plain,
% 4.47/4.62 (below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), 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)))))),
% 4.47/4.62 inference(unit_resolution,[status(thm)],[371, 239])).
% 4.47/4.62 tff(373,plain,
% 4.47/4.62 (^[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))))),
% 4.47/4.62 inference(bind,[status(th)],[])).
% 4.47/4.62 tff(374,plain,
% 4.47/4.62 (![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)))),
% 4.47/4.62 inference(quant_intro,[status(thm)],[373])).
% 4.47/4.62 tff(375,plain,
% 4.47/4.62 (^[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))))),
% 4.47/4.62 inference(bind,[status(th)],[])).
% 4.47/4.62 tff(376,plain,
% 4.47/4.62 (![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)))),
% 4.47/4.62 inference(quant_intro,[status(thm)],[375])).
% 4.47/4.62 tff(377,plain,
% 4.47/4.62 (^[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))))),
% 4.47/4.62 inference(bind,[status(th)],[])).
% 4.47/4.62 tff(378,plain,
% 4.47/4.62 (![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)))),
% 4.47/4.62 inference(quant_intro,[status(thm)],[377])).
% 4.47/4.62 tff(379,plain,
% 4.47/4.62 (![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)))),
% 4.47/4.62 inference(transitivity,[status(thm)],[378, 376])).
% 4.47/4.62 tff(380,plain,
% 4.47/4.62 (^[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)))))),
% 4.47/4.62 inference(bind,[status(th)],[])).
% 4.47/4.62 tff(381,plain,
% 4.47/4.62 (![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)))),
% 4.47/4.62 inference(quant_intro,[status(thm)],[380])).
% 4.47/4.62 tff(382,plain,
% 4.47/4.62 (![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)))),
% 4.47/4.62 inference(rewrite,[status(thm)],[])).
% 4.47/4.62 tff(383,plain,
% 4.47/4.62 (^[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)))))),
% 4.47/4.62 inference(bind,[status(th)],[])).
% 4.47/4.62 tff(384,plain,
% 4.47/4.62 (![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)))),
% 4.47/4.62 inference(quant_intro,[status(thm)],[383])).
% 4.47/4.62 tff(385,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')).
% 4.47/4.62 tff(386,plain,
% 4.47/4.62 (![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)))),
% 4.47/4.62 inference(modus_ponens,[status(thm)],[385, 384])).
% 4.47/4.62 tff(387,plain,
% 4.47/4.62 (![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)))),
% 4.47/4.62 inference(modus_ponens,[status(thm)],[386, 382])).
% 4.47/4.62 tff(388,plain,(
% 4.47/4.62 ![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)))),
% 4.47/4.62 inference(skolemize,[status(sab)],[387])).
% 4.47/4.62 tff(389,plain,
% 4.47/4.62 (![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)))),
% 4.47/4.62 inference(modus_ponens,[status(thm)],[388, 381])).
% 4.47/4.62 tff(390,plain,
% 4.47/4.62 (![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)))),
% 4.47/4.62 inference(modus_ponens,[status(thm)],[389, 379])).
% 4.47/4.62 tff(391,plain,
% 4.47/4.62 (![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)))),
% 4.47/4.62 inference(modus_ponens,[status(thm)],[390, 374])).
% 4.47/4.62 tff(392,plain,
% 4.47/4.62 (((~![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)))),
% 4.47/4.62 inference(rewrite,[status(thm)],[])).
% 4.47/4.62 tff(393,plain,
% 4.47/4.62 ((~![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)))),
% 4.47/4.62 inference(quant_inst,[status(thm)],[])).
% 4.47/4.62 tff(394,plain,
% 4.47/4.62 ((~![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))),
% 4.47/4.62 inference(modus_ponens,[status(thm)],[393, 392])).
% 4.47/4.62 tff(395,plain,
% 4.47/4.62 (![B: $i] : ((~element(B, the_carrier(B!18))) | (cast_to_el_of_LattPOSet(B!18, B) = B))),
% 4.47/4.62 inference(unit_resolution,[status(thm)],[394, 391, 12, 11, 10])).
% 4.47/4.62 tff(396,plain,
% 4.47/4.62 (((~![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)))))),
% 4.47/4.62 inference(rewrite,[status(thm)],[])).
% 4.47/4.62 tff(397,plain,
% 4.47/4.62 ((~![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)))))),
% 4.47/4.62 inference(quant_inst,[status(thm)],[])).
% 4.47/4.62 tff(398,plain,
% 4.47/4.62 ((~![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))))),
% 4.47/4.62 inference(modus_ponens,[status(thm)],[397, 396])).
% 4.47/4.62 tff(399,plain,
% 4.47/4.62 ((~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))))),
% 4.47/4.62 inference(unit_resolution,[status(thm)],[398, 395])).
% 4.47/4.62 tff(400,plain,
% 4.47/4.62 (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)))),
% 4.47/4.62 inference(unit_resolution,[status(thm)],[399, 239])).
% 4.47/4.62 tff(401,plain,
% 4.47/4.62 (tptp_fun_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, tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 4.47/4.62 inference(symmetry,[status(thm)],[400])).
% 4.47/4.62 tff(402,plain,
% 4.47/4.62 (((~![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))),
% 4.47/4.62 inference(rewrite,[status(thm)],[])).
% 4.47/4.62 tff(403,plain,
% 4.47/4.62 ((~![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))),
% 4.47/4.62 inference(quant_inst,[status(thm)],[])).
% 4.47/4.62 tff(404,plain,
% 4.47/4.62 ((~![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)),
% 4.47/4.62 inference(modus_ponens,[status(thm)],[403, 402])).
% 4.47/4.62 tff(405,plain,
% 4.47/4.62 (cast_to_el_of_LattPOSet(B!18, C!20) = C!20),
% 4.47/4.62 inference(unit_resolution,[status(thm)],[404, 178, 395])).
% 4.47/4.62 tff(406,plain,
% 4.47/4.62 (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)),
% 4.47/4.62 inference(monotonicity,[status(thm)],[405])).
% 4.47/4.62 tff(407,plain,
% 4.47/4.62 (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))),
% 4.47/4.62 inference(symmetry,[status(thm)],[406])).
% 4.47/4.62 tff(408,plain,
% 4.47/4.62 (related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), 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)))))),
% 4.47/4.62 inference(monotonicity,[status(thm)],[33, 407, 401])).
% 4.47/4.62 tff(409,plain,
% 4.47/4.62 ((~related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) <=> (~related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), 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))))))),
% 4.47/4.62 inference(monotonicity,[status(thm)],[408])).
% 4.47/4.62 tff(410,plain,
% 4.47/4.62 (reflexive_relstr(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) <=> reflexive_relstr(poset_of_lattice(B!18))),
% 4.47/4.62 inference(monotonicity,[status(thm)],[33])).
% 4.47/4.62 tff(411,plain,
% 4.47/4.62 (reflexive_relstr(poset_of_lattice(B!18)) <=> reflexive_relstr(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))),
% 4.47/4.62 inference(symmetry,[status(thm)],[410])).
% 4.47/4.62 tff(412,plain,
% 4.47/4.62 (((~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))),
% 4.47/4.62 inference(tautology,[status(thm)],[])).
% 4.47/4.62 tff(413,plain,
% 4.47/4.62 (reflexive_relstr(poset_of_lattice(B!18))),
% 4.47/4.62 inference(unit_resolution,[status(thm)],[412, 56])).
% 4.47/4.62 tff(414,plain,
% 4.47/4.62 (reflexive_relstr(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))),
% 4.47/4.62 inference(modus_ponens,[status(thm)],[413, 411])).
% 4.47/4.62 tff(415,plain,
% 4.47/4.62 (empty_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) <=> empty_carrier(poset_of_lattice(B!18))),
% 4.47/4.62 inference(monotonicity,[status(thm)],[33])).
% 4.47/4.62 tff(416,plain,
% 4.47/4.62 (empty_carrier(poset_of_lattice(B!18)) <=> empty_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))),
% 4.47/4.62 inference(symmetry,[status(thm)],[415])).
% 4.47/4.62 tff(417,plain,
% 4.47/4.62 ((~empty_carrier(poset_of_lattice(B!18))) <=> (~empty_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 4.47/4.62 inference(monotonicity,[status(thm)],[416])).
% 4.47/4.62 tff(418,plain,
% 4.47/4.62 (^[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)))))))),
% 4.47/4.62 inference(bind,[status(th)],[])).
% 4.47/4.62 tff(419,plain,
% 4.47/4.62 (![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))))))),
% 4.47/4.62 inference(quant_intro,[status(thm)],[418])).
% 4.47/4.62 tff(420,plain,
% 4.47/4.62 (^[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))))))))),
% 4.47/4.62 inference(bind,[status(th)],[])).
% 4.47/4.62 tff(421,plain,
% 4.47/4.62 (![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))))))),
% 4.47/4.62 inference(quant_intro,[status(thm)],[420])).
% 4.47/4.62 tff(422,plain,
% 4.47/4.62 (![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))))),
% 4.47/4.62 inference(rewrite,[status(thm)],[])).
% 4.47/4.62 tff(423,plain,
% 4.47/4.62 (^[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))))))),
% 4.47/4.62 inference(bind,[status(th)],[])).
% 4.47/4.62 tff(424,plain,
% 4.47/4.62 (![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))))),
% 4.47/4.62 inference(quant_intro,[status(thm)],[423])).
% 4.47/4.62 tff(425,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')).
% 4.47/4.62 tff(426,plain,
% 4.47/4.62 (![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))))),
% 4.47/4.62 inference(modus_ponens,[status(thm)],[425, 424])).
% 4.47/4.62 tff(427,plain,
% 4.47/4.62 (![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))))),
% 4.47/4.62 inference(modus_ponens,[status(thm)],[426, 422])).
% 4.47/4.62 tff(428,plain,(
% 4.47/4.62 ![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))))),
% 4.47/4.62 inference(skolemize,[status(sab)],[427])).
% 4.47/4.62 tff(429,plain,
% 4.47/4.62 (![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))))))),
% 4.47/4.62 inference(modus_ponens,[status(thm)],[428, 421])).
% 4.47/4.62 tff(430,plain,
% 4.47/4.62 (![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))))))),
% 4.47/4.62 inference(modus_ponens,[status(thm)],[429, 419])).
% 4.47/4.62 tff(431,plain,
% 4.47/4.62 (((~![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)))))),
% 4.47/4.62 inference(rewrite,[status(thm)],[])).
% 4.47/4.62 tff(432,plain,
% 4.47/4.62 ((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)))))),
% 4.47/4.62 inference(rewrite,[status(thm)],[])).
% 4.47/4.62 tff(433,plain,
% 4.47/4.62 (((~![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))))))),
% 4.47/4.62 inference(monotonicity,[status(thm)],[432])).
% 4.47/4.62 tff(434,plain,
% 4.47/4.63 (((~![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)))))),
% 4.47/4.63 inference(transitivity,[status(thm)],[433, 431])).
% 4.47/4.63 tff(435,plain,
% 4.47/4.63 ((~![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))))))),
% 4.47/4.63 inference(quant_inst,[status(thm)],[])).
% 4.47/4.63 tff(436,plain,
% 4.47/4.63 ((~![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))))),
% 4.47/4.63 inference(modus_ponens,[status(thm)],[435, 434])).
% 4.47/4.63 tff(437,plain,
% 4.47/4.63 (~((~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)))),
% 4.47/4.63 inference(unit_resolution,[status(thm)],[436, 430, 12, 11, 10])).
% 4.47/4.63 tff(438,plain,
% 4.47/4.63 (((~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)))),
% 4.47/4.63 inference(tautology,[status(thm)],[])).
% 4.47/4.63 tff(439,plain,
% 4.47/4.63 (~empty_carrier(poset_of_lattice(B!18))),
% 4.47/4.63 inference(unit_resolution,[status(thm)],[438, 437])).
% 4.47/4.63 tff(440,plain,
% 4.47/4.63 (~empty_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))),
% 4.47/4.63 inference(modus_ponens,[status(thm)],[439, 417])).
% 4.47/4.63 tff(441,plain,
% 4.47/4.63 (^[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))))),
% 4.47/4.63 inference(bind,[status(th)],[])).
% 4.47/4.63 tff(442,plain,
% 4.47/4.63 (![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)))),
% 4.47/4.63 inference(quant_intro,[status(thm)],[441])).
% 4.47/4.63 tff(443,plain,
% 4.47/4.63 (^[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)))))),
% 4.47/4.63 inference(bind,[status(th)],[])).
% 4.47/4.63 tff(444,plain,
% 4.47/4.63 (![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)))),
% 4.47/4.63 inference(quant_intro,[status(thm)],[443])).
% 4.47/4.63 tff(445,plain,
% 4.47/4.63 (![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)))),
% 4.47/4.63 inference(rewrite,[status(thm)],[])).
% 4.47/4.63 tff(446,plain,
% 4.47/4.63 (^[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)))))),
% 4.47/4.63 inference(bind,[status(th)],[])).
% 4.47/4.63 tff(447,plain,
% 4.47/4.63 (![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)))),
% 4.47/4.63 inference(quant_intro,[status(thm)],[446])).
% 4.47/4.63 tff(448,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')).
% 4.47/4.63 tff(449,plain,
% 4.47/4.63 (![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)))),
% 4.47/4.63 inference(modus_ponens,[status(thm)],[448, 447])).
% 4.47/4.63 tff(450,plain,
% 4.47/4.63 (![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)))),
% 4.47/4.63 inference(modus_ponens,[status(thm)],[449, 445])).
% 4.47/4.63 tff(451,plain,(
% 4.47/4.63 ![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)))),
% 4.47/4.63 inference(skolemize,[status(sab)],[450])).
% 4.47/4.63 tff(452,plain,
% 4.47/4.63 (![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)))),
% 4.47/4.63 inference(modus_ponens,[status(thm)],[451, 444])).
% 4.47/4.63 tff(453,plain,
% 4.47/4.63 (![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)))),
% 4.47/4.63 inference(modus_ponens,[status(thm)],[452, 442])).
% 4.47/4.63 tff(454,plain,
% 4.47/4.63 (((~![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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_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: $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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))))),
% 4.47/4.63 inference(rewrite,[status(thm)],[])).
% 4.47/4.63 tff(455,plain,
% 4.47/4.63 (((related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | empty_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))))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), 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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))))),
% 4.47/4.63 inference(rewrite,[status(thm)],[])).
% 4.47/4.63 tff(456,plain,
% 4.47/4.63 (((~![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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | empty_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))))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), 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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))))),
% 4.47/4.63 inference(monotonicity,[status(thm)],[455])).
% 4.47/4.63 tff(457,plain,
% 4.47/4.63 (((~![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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | empty_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))))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), 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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))))),
% 4.47/4.63 inference(transitivity,[status(thm)],[456, 454])).
% 4.47/4.63 tff(458,plain,
% 4.47/4.63 ((~![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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | empty_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))))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), 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)))))),
% 4.47/4.63 inference(quant_inst,[status(thm)],[])).
% 4.47/4.63 tff(459,plain,
% 4.47/4.63 ((~![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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))),
% 4.47/4.63 inference(modus_ponens,[status(thm)],[458, 457])).
% 4.47/4.63 tff(460,plain,
% 4.47/4.63 (related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 4.47/4.63 inference(unit_resolution,[status(thm)],[459, 453, 440, 64, 414, 199, 238])).
% 4.47/4.63 tff(461,plain,
% 4.47/4.63 ((related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, 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))))) | (~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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))),
% 4.47/4.63 inference(tautology,[status(thm)],[])).
% 4.47/4.63 tff(462,plain,
% 4.47/4.63 (~related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 4.47/4.63 inference(unit_resolution,[status(thm)],[461, 236])).
% 4.47/4.63 tff(463,plain,
% 4.47/4.63 ((~(related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))) | (~related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 4.47/4.63 inference(tautology,[status(thm)],[])).
% 4.47/4.63 tff(464,plain,
% 4.47/4.63 ((~(related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))) | (~related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))),
% 4.47/4.63 inference(unit_resolution,[status(thm)],[463, 462])).
% 4.47/4.63 tff(465,plain,
% 4.47/4.63 (~related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 4.47/4.63 inference(unit_resolution,[status(thm)],[464, 460])).
% 4.47/4.63 tff(466,plain,
% 4.47/4.63 (~related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), 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)))))),
% 4.47/4.63 inference(modus_ponens,[status(thm)],[465, 409])).
% 4.47/4.63 tff(467,plain,
% 4.47/4.63 ((~(below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), 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))))))) | (~below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), 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)))))),
% 4.47/4.63 inference(tautology,[status(thm)],[])).
% 4.47/4.63 tff(468,plain,
% 4.47/4.63 (~below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 4.47/4.63 inference(unit_resolution,[status(thm)],[467, 466, 372])).
% 4.47/4.63 tff(469,plain,
% 4.47/4.63 (latt_set_smaller(B!18, cast_to_el_of_LattPOSet(B!18, C!20), A!19) <=> latt_set_smaller(B!18, C!20, A!19)),
% 4.47/4.63 inference(monotonicity,[status(thm)],[405])).
% 4.47/4.63 tff(470,plain,
% 4.47/4.63 (latt_set_smaller(B!18, C!20, A!19) <=> latt_set_smaller(B!18, cast_to_el_of_LattPOSet(B!18, C!20), A!19)),
% 4.47/4.63 inference(symmetry,[status(thm)],[469])).
% 4.47/4.63 tff(471,plain,
% 4.47/4.63 (~(latt_set_smaller(B!18, C!20, A!19) <=> relstr_element_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20)))),
% 4.47/4.63 inference(or_elim,[status(thm)],[177])).
% 4.47/4.63 tff(472,plain,
% 4.47/4.63 ((latt_set_smaller(B!18, C!20, A!19) <=> relstr_element_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20))) | latt_set_smaller(B!18, C!20, A!19) | relstr_element_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20))),
% 4.47/4.63 inference(tautology,[status(thm)],[])).
% 4.47/4.63 tff(473,plain,
% 4.47/4.63 (latt_set_smaller(B!18, C!20, A!19) | relstr_element_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20))),
% 4.47/4.63 inference(unit_resolution,[status(thm)],[472, 471])).
% 4.47/4.63 tff(474,plain,
% 4.47/4.63 (latt_set_smaller(B!18, C!20, A!19)),
% 4.47/4.63 inference(unit_resolution,[status(thm)],[473, 173])).
% 4.47/4.63 tff(475,plain,
% 4.47/4.63 (latt_set_smaller(B!18, cast_to_el_of_LattPOSet(B!18, C!20), A!19)),
% 4.47/4.63 inference(modus_ponens,[status(thm)],[474, 470])).
% 4.47/4.63 tff(476,plain,
% 4.47/4.63 (^[A: $i] : refl((empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~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_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))))),
% 4.47/4.63 inference(bind,[status(th)],[])).
% 4.47/4.63 tff(477,plain,
% 4.47/4.63 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~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_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))),
% 4.47/4.63 inference(quant_intro,[status(thm)],[476])).
% 4.47/4.63 tff(478,plain,
% 4.47/4.63 (^[A: $i] : rewrite((empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~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_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))))),
% 4.47/4.63 inference(bind,[status(th)],[])).
% 4.47/4.63 tff(479,plain,
% 4.47/4.63 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~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_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))),
% 4.47/4.63 inference(quant_intro,[status(thm)],[478])).
% 4.47/4.63 tff(480,plain,
% 4.47/4.63 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~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_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))),
% 4.47/4.63 inference(transitivity,[status(thm)],[479, 477])).
% 4.47/4.63 tff(481,plain,
% 4.47/4.63 (^[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_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A))))) & (latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))), (![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A))))) & (latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~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_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A))))) & (latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~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_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~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_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~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_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~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_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A))))) & (latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~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_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))))),
% 4.47/4.63 inference(bind,[status(th)],[])).
% 4.47/4.63 tff(482,plain,
% 4.47/4.63 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A))))) & (latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~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_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))),
% 4.47/4.63 inference(quant_intro,[status(thm)],[481])).
% 4.47/4.63 tff(483,plain,
% 4.47/4.63 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A))))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))))),
% 4.47/4.63 inference(rewrite,[status(thm)],[])).
% 4.47/4.63 tff(484,plain,
% 4.47/4.63 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((latt_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, B, D)))) <=> (latt_set_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A))))))), (![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, B, D)))) <=> ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A))))))), ((element(B, the_carrier(A)) => ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, B, D))))) <=> (element(B, the_carrier(A)) => ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))))), rewrite((element(B, the_carrier(A)) => ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A))))))), ((element(B, the_carrier(A)) => ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, B, D))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A))))))))), (![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, B, D))))) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))))), ((((~empty_carrier(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, B, D)))))) <=> (((~empty_carrier(A)) & latt_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A))))))))), rewrite((((~empty_carrier(A)) & latt_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A))))))) <=> ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))))), ((((~empty_carrier(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, B, D)))))) <=> ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))))))),
% 4.47/4.63 inference(bind,[status(th)],[])).
% 4.47/4.63 tff(485,plain,
% 4.47/4.63 (![A: $i] : (((~empty_carrier(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, B, D)))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))))),
% 4.47/4.63 inference(quant_intro,[status(thm)],[484])).
% 4.47/4.63 tff(486,axiom,(![A: $i] : (((~empty_carrier(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, B, D))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d16_lattice3')).
% 4.47/4.63 tff(487,plain,
% 4.47/4.63 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))))),
% 4.47/4.63 inference(modus_ponens,[status(thm)],[486, 485])).
% 4.47/4.63 tff(488,plain,
% 4.47/4.63 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))))),
% 4.47/4.63 inference(modus_ponens,[status(thm)],[487, 483])).
% 4.47/4.63 tff(489,plain,(
% 4.47/4.63 ![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A))))) & (latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))),
% 4.47/4.63 inference(skolemize,[status(sab)],[488])).
% 4.47/4.63 tff(490,plain,
% 4.47/4.63 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))),
% 4.47/4.63 inference(modus_ponens,[status(thm)],[489, 482])).
% 4.47/4.63 tff(491,plain,
% 4.47/4.63 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))),
% 4.47/4.64 inference(modus_ponens,[status(thm)],[490, 480])).
% 4.47/4.64 tff(492,plain,
% 4.47/4.64 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~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_set_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, B, D)))) | (~(latt_set_smaller(B!18, B, C) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, B, tptp_fun_D_0(C, B, B!18)) | (~in(tptp_fun_D_0(C, B, B!18), C))))))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~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_set_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, B, D)))) | (~(latt_set_smaller(B!18, B, C) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, B, tptp_fun_D_0(C, B, B!18)) | (~in(tptp_fun_D_0(C, B, B!18), C))))))))))),
% 4.47/4.64 inference(rewrite,[status(thm)],[])).
% 4.47/4.64 tff(493,plain,
% 4.47/4.64 ((empty_carrier(B!18) | (~latt_str(B!18)) | ![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | below(B!18, B, D) | (~element(D, the_carrier(B!18)))))) | (~(latt_set_smaller(B!18, B, C) | (~((~in(tptp_fun_D_0(C, B, B!18), C)) | below(B!18, B, tptp_fun_D_0(C, B, B!18)) | (~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_set_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, B, D)))) | (~(latt_set_smaller(B!18, B, C) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, B, tptp_fun_D_0(C, B, B!18)) | (~in(tptp_fun_D_0(C, B, B!18), C))))))))))),
% 4.47/4.64 inference(rewrite,[status(thm)],[])).
% 4.47/4.64 tff(494,plain,
% 4.47/4.64 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~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_set_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | below(B!18, B, D) | (~element(D, the_carrier(B!18)))))) | (~(latt_set_smaller(B!18, B, C) | (~((~in(tptp_fun_D_0(C, B, B!18), C)) | below(B!18, B, tptp_fun_D_0(C, B, B!18)) | (~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_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~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_set_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, B, D)))) | (~(latt_set_smaller(B!18, B, C) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, B, tptp_fun_D_0(C, B, B!18)) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))))),
% 4.47/4.64 inference(monotonicity,[status(thm)],[493])).
% 4.47/4.64 tff(495,plain,
% 4.47/4.64 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~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_set_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | below(B!18, B, D) | (~element(D, the_carrier(B!18)))))) | (~(latt_set_smaller(B!18, B, C) | (~((~in(tptp_fun_D_0(C, B, B!18), C)) | below(B!18, B, tptp_fun_D_0(C, B, B!18)) | (~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_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~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_set_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, B, D)))) | (~(latt_set_smaller(B!18, B, C) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, B, tptp_fun_D_0(C, B, B!18)) | (~in(tptp_fun_D_0(C, B, B!18), C))))))))))),
% 4.47/4.64 inference(transitivity,[status(thm)],[494, 492])).
% 4.47/4.64 tff(496,plain,
% 4.47/4.64 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~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_set_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | below(B!18, B, D) | (~element(D, the_carrier(B!18)))))) | (~(latt_set_smaller(B!18, B, C) | (~((~in(tptp_fun_D_0(C, B, B!18), C)) | below(B!18, B, tptp_fun_D_0(C, B, B!18)) | (~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18)))))))))))),
% 4.47/4.64 inference(quant_inst,[status(thm)],[])).
% 4.47/4.64 tff(497,plain,
% 4.47/4.64 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~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_set_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, B, D)))) | (~(latt_set_smaller(B!18, B, C) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, B, tptp_fun_D_0(C, B, B!18)) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))),
% 4.47/4.64 inference(modus_ponens,[status(thm)],[496, 495])).
% 4.47/4.64 tff(498,plain,
% 4.47/4.64 (![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, B, D)))) | (~(latt_set_smaller(B!18, B, C) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, B, tptp_fun_D_0(C, B, B!18)) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))),
% 4.47/4.64 inference(unit_resolution,[status(thm)],[497, 491, 12, 10])).
% 4.47/4.64 tff(499,plain,
% 4.47/4.64 (((~![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, B, D)))) | (~(latt_set_smaller(B!18, B, C) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, B, tptp_fun_D_0(C, B, B!18)) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))) | ((~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18)) | (~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_set_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, B, D)))) | (~(latt_set_smaller(B!18, B, C) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, B, tptp_fun_D_0(C, B, B!18)) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18)) | (~element(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18))))))))))),
% 4.47/4.64 inference(rewrite,[status(thm)],[])).
% 4.47/4.64 tff(500,plain,
% 4.47/4.64 (((~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18)) | (~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_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18)) | (~element(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18))))))))))),
% 4.47/4.64 inference(rewrite,[status(thm)],[])).
% 4.47/4.64 tff(501,plain,
% 4.47/4.64 (((~![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, B, D)))) | (~(latt_set_smaller(B!18, B, C) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, B, tptp_fun_D_0(C, B, B!18)) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))) | ((~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18)) | (~in(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), C)))))))))) <=> ((~![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, B, D)))) | (~(latt_set_smaller(B!18, B, C) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, B, tptp_fun_D_0(C, B, B!18)) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))) | ((~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18)) | (~element(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18)))))))))))),
% 4.47/4.64 inference(monotonicity,[status(thm)],[500])).
% 4.47/4.64 tff(502,plain,
% 4.47/4.64 (((~![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, B, D)))) | (~(latt_set_smaller(B!18, B, C) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, B, tptp_fun_D_0(C, B, B!18)) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))) | ((~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18)) | (~in(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), C)))))))))) <=> ((~![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, B, D)))) | (~(latt_set_smaller(B!18, B, C) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, B, tptp_fun_D_0(C, B, B!18)) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18)) | (~element(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18))))))))))),
% 4.47/4.64 inference(transitivity,[status(thm)],[501, 499])).
% 4.47/4.64 tff(503,plain,
% 4.47/4.64 ((~![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, B, D)))) | (~(latt_set_smaller(B!18, B, C) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, B, tptp_fun_D_0(C, B, B!18)) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))) | ((~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18)) | (~in(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), C)))))))))),
% 4.50/4.64 inference(quant_inst,[status(thm)],[])).
% 4.50/4.64 tff(504,plain,
% 4.50/4.64 ((~![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, B, D)))) | (~(latt_set_smaller(B!18, B, C) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, B, tptp_fun_D_0(C, B, B!18)) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18)) | (~element(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18)))))))))),
% 4.50/4.64 inference(modus_ponens,[status(thm)],[503, 502])).
% 4.50/4.64 tff(505,plain,
% 4.50/4.64 ((~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18)) | (~element(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18)))))))))),
% 4.50/4.64 inference(unit_resolution,[status(thm)],[504, 498])).
% 4.50/4.64 tff(506,plain,
% 4.50/4.64 (![C: $i] : (~((~((~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18)) | (~element(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18)))))))))),
% 4.50/4.64 inference(unit_resolution,[status(thm)],[505, 290])).
% 4.50/4.64 tff(507,plain,
% 4.50/4.64 (((~![C: $i] : (~((~((~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18)) | (~element(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18)))))))))) | (~((~((~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18)) | (~in(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), A!19))))))))) <=> ((~![C: $i] : (~((~((~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18)) | (~element(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18)))))))))) | (~((~((~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18)) | (~in(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), A!19)))))))))),
% 4.50/4.64 inference(rewrite,[status(thm)],[])).
% 4.50/4.64 tff(508,plain,
% 4.50/4.64 ((~((~((~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18)) | (~element(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18))))))))) <=> (~((~((~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18)) | (~in(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), A!19))))))))),
% 4.50/4.64 inference(rewrite,[status(thm)],[])).
% 4.50/4.64 tff(509,plain,
% 4.50/4.64 (((~![C: $i] : (~((~((~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18)) | (~element(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18)))))))))) | (~((~((~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18)) | (~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_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18)) | (~element(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18)))))))))) | (~((~((~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18)) | (~in(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), A!19)))))))))),
% 4.50/4.64 inference(monotonicity,[status(thm)],[508])).
% 4.50/4.64 tff(510,plain,
% 4.50/4.64 (((~![C: $i] : (~((~((~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18)) | (~element(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18)))))))))) | (~((~((~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18)) | (~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_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18)) | (~element(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18)))))))))) | (~((~((~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18)) | (~in(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), A!19)))))))))),
% 4.50/4.64 inference(transitivity,[status(thm)],[509, 507])).
% 4.50/4.64 tff(511,plain,
% 4.50/4.64 ((~![C: $i] : (~((~((~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18)) | (~element(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18)))))))))) | (~((~((~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18)) | (~element(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18)))))))))),
% 4.50/4.64 inference(quant_inst,[status(thm)],[])).
% 4.50/4.64 tff(512,plain,
% 4.50/4.64 ((~![C: $i] : (~((~((~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18)) | (~element(tptp_fun_D_0(C, cast_to_el_of_LattPOSet(B!18, C!20), B!18), the_carrier(B!18)))))))))) | (~((~((~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18)) | (~in(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), A!19))))))))),
% 4.50/4.65 inference(modus_ponens,[status(thm)],[511, 510])).
% 4.50/4.65 tff(513,plain,
% 4.50/4.65 (~((~((~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18)) | (~in(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), A!19)))))))),
% 4.50/4.65 inference(unit_resolution,[status(thm)],[512, 506])).
% 4.50/4.65 tff(514,plain,
% 4.50/4.65 (((~((~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18)) | (~in(tptp_fun_D_0(A!19, cast_to_el_of_LattPOSet(B!18, C!20), B!18), A!19))))))) | ((~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))),
% 4.50/4.65 inference(tautology,[status(thm)],[])).
% 4.50/4.65 tff(515,plain,
% 4.50/4.65 ((~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D))),
% 4.50/4.65 inference(unit_resolution,[status(thm)],[514, 513])).
% 4.50/4.65 tff(516,plain,
% 4.50/4.65 ((~((~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D))),
% 4.50/4.65 inference(tautology,[status(thm)],[])).
% 4.50/4.65 tff(517,plain,
% 4.50/4.65 ((~latt_set_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, cast_to_el_of_LattPOSet(B!18, C!20), D))),
% 4.50/4.65 inference(unit_resolution,[status(thm)],[516, 515])).
% 4.50/4.65 tff(518,plain,
% 4.50/4.65 (![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(B!18))) | below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), D))),
% 4.50/4.65 inference(unit_resolution,[status(thm)],[517, 475])).
% 4.50/4.65 tff(519,plain,
% 4.50/4.65 ((related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, 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))))) | (~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)),
% 4.50/4.65 inference(tautology,[status(thm)],[])).
% 4.50/4.65 tff(520,plain,
% 4.50/4.65 (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)),
% 4.50/4.65 inference(unit_resolution,[status(thm)],[519, 236])).
% 4.50/4.65 tff(521,plain,
% 4.50/4.65 (((~![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(B!18))) | below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), D))) | ((~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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))) <=> ((~![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(B!18))) | below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), D))) | (~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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))),
% 4.50/4.65 inference(rewrite,[status(thm)],[])).
% 4.50/4.65 tff(522,plain,
% 4.50/4.65 ((~![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(B!18))) | below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), D))) | ((~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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))),
% 4.50/4.65 inference(quant_inst,[status(thm)],[])).
% 4.50/4.65 tff(523,plain,
% 4.50/4.65 ((~![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(B!18))) | below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), D))) | (~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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 4.50/4.65 inference(modus_ponens,[status(thm)],[522, 521])).
% 4.50/4.65 tff(524,plain,
% 4.50/4.65 ((~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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 4.50/4.65 inference(unit_resolution,[status(thm)],[523, 520, 518])).
% 4.50/4.65 tff(525,plain,
% 4.50/4.65 (below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 4.50/4.65 inference(unit_resolution,[status(thm)],[524, 239])).
% 4.50/4.65 tff(526,plain,
% 4.50/4.65 ((~(below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))) | below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) | (~below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))),
% 4.50/4.65 inference(tautology,[status(thm)],[])).
% 4.50/4.65 tff(527,plain,
% 4.50/4.65 ((~(below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))) <=> below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18)))))) | below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 4.50/4.65 inference(unit_resolution,[status(thm)],[526, 525])).
% 4.50/4.65 tff(528,plain,
% 4.50/4.65 ($false),
% 4.50/4.65 inference(unit_resolution,[status(thm)],[527, 468, 339])).
% 4.50/4.65 tff(529,plain,(relstr_element_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20))), inference(lemma,lemma(discharge,[]))).
% 4.50/4.65 tff(530,plain,
% 4.50/4.65 ((latt_set_smaller(B!18, C!20, A!19) <=> relstr_element_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20))) | (~latt_set_smaller(B!18, C!20, A!19)) | (~relstr_element_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20)))),
% 4.50/4.65 inference(tautology,[status(thm)],[])).
% 4.50/4.65 tff(531,plain,
% 4.50/4.65 ((~latt_set_smaller(B!18, C!20, A!19)) | (~relstr_element_smaller(poset_of_lattice(B!18), A!19, cast_to_el_of_LattPOSet(B!18, C!20)))),
% 4.50/4.65 inference(unit_resolution,[status(thm)],[530, 471])).
% 4.50/4.65 tff(532,plain,
% 4.50/4.65 (~latt_set_smaller(B!18, C!20, A!19)),
% 4.50/4.65 inference(unit_resolution,[status(thm)],[531, 529])).
% 4.50/4.65 tff(533,plain,
% 4.50/4.65 (((~![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, B, D)))) | (~(latt_set_smaller(B!18, B, C) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, B, tptp_fun_D_0(C, B, B!18)) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))) | ((~element(C!20, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_smaller(B!18, C!20, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, C!20, D)))) | (~(latt_set_smaller(B!18, C!20, C) | (~((~in(tptp_fun_D_0(C, C!20, B!18), C)) | below(B!18, C!20, tptp_fun_D_0(C, C!20, B!18)) | (~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_set_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, B, D)))) | (~(latt_set_smaller(B!18, B, C) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, B, tptp_fun_D_0(C, B, B!18)) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))) | (~element(C!20, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_smaller(B!18, C!20, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, C!20, D)))) | (~(latt_set_smaller(B!18, C!20, C) | (~((~in(tptp_fun_D_0(C, C!20, B!18), C)) | below(B!18, C!20, tptp_fun_D_0(C, C!20, B!18)) | (~element(tptp_fun_D_0(C, C!20, B!18), the_carrier(B!18))))))))))),
% 4.50/4.65 inference(rewrite,[status(thm)],[])).
% 4.50/4.65 tff(534,plain,
% 4.50/4.65 (((~element(C!20, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_smaller(B!18, C!20, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, C!20, D)))) | (~(latt_set_smaller(B!18, C!20, C) | (~((~element(tptp_fun_D_0(C, C!20, B!18), the_carrier(B!18))) | below(B!18, C!20, tptp_fun_D_0(C, C!20, B!18)) | (~in(tptp_fun_D_0(C, C!20, B!18), C))))))))) <=> ((~element(C!20, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_smaller(B!18, C!20, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, C!20, D)))) | (~(latt_set_smaller(B!18, C!20, C) | (~((~in(tptp_fun_D_0(C, C!20, B!18), C)) | below(B!18, C!20, tptp_fun_D_0(C, C!20, B!18)) | (~element(tptp_fun_D_0(C, C!20, B!18), the_carrier(B!18))))))))))),
% 4.50/4.65 inference(rewrite,[status(thm)],[])).
% 4.50/4.65 tff(535,plain,
% 4.50/4.65 (((~![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, B, D)))) | (~(latt_set_smaller(B!18, B, C) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, B, tptp_fun_D_0(C, B, B!18)) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))) | ((~element(C!20, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_smaller(B!18, C!20, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, C!20, D)))) | (~(latt_set_smaller(B!18, C!20, C) | (~((~element(tptp_fun_D_0(C, C!20, B!18), the_carrier(B!18))) | below(B!18, C!20, tptp_fun_D_0(C, C!20, B!18)) | (~in(tptp_fun_D_0(C, C!20, B!18), C)))))))))) <=> ((~![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, B, D)))) | (~(latt_set_smaller(B!18, B, C) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, B, tptp_fun_D_0(C, B, B!18)) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))) | ((~element(C!20, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_smaller(B!18, C!20, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, C!20, D)))) | (~(latt_set_smaller(B!18, C!20, C) | (~((~in(tptp_fun_D_0(C, C!20, B!18), C)) | below(B!18, C!20, tptp_fun_D_0(C, C!20, B!18)) | (~element(tptp_fun_D_0(C, C!20, B!18), the_carrier(B!18)))))))))))),
% 4.50/4.65 inference(monotonicity,[status(thm)],[534])).
% 4.50/4.65 tff(536,plain,
% 4.50/4.65 (((~![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, B, D)))) | (~(latt_set_smaller(B!18, B, C) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, B, tptp_fun_D_0(C, B, B!18)) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))) | ((~element(C!20, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_smaller(B!18, C!20, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, C!20, D)))) | (~(latt_set_smaller(B!18, C!20, C) | (~((~element(tptp_fun_D_0(C, C!20, B!18), the_carrier(B!18))) | below(B!18, C!20, tptp_fun_D_0(C, C!20, B!18)) | (~in(tptp_fun_D_0(C, C!20, B!18), C)))))))))) <=> ((~![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, B, D)))) | (~(latt_set_smaller(B!18, B, C) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, B, tptp_fun_D_0(C, B, B!18)) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))) | (~element(C!20, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_smaller(B!18, C!20, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, C!20, D)))) | (~(latt_set_smaller(B!18, C!20, C) | (~((~in(tptp_fun_D_0(C, C!20, B!18), C)) | below(B!18, C!20, tptp_fun_D_0(C, C!20, B!18)) | (~element(tptp_fun_D_0(C, C!20, B!18), the_carrier(B!18))))))))))),
% 4.50/4.65 inference(transitivity,[status(thm)],[535, 533])).
% 4.50/4.65 tff(537,plain,
% 4.50/4.65 ((~![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, B, D)))) | (~(latt_set_smaller(B!18, B, C) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, B, tptp_fun_D_0(C, B, B!18)) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))) | ((~element(C!20, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_smaller(B!18, C!20, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, C!20, D)))) | (~(latt_set_smaller(B!18, C!20, C) | (~((~element(tptp_fun_D_0(C, C!20, B!18), the_carrier(B!18))) | below(B!18, C!20, tptp_fun_D_0(C, C!20, B!18)) | (~in(tptp_fun_D_0(C, C!20, B!18), C)))))))))),
% 4.50/4.65 inference(quant_inst,[status(thm)],[])).
% 4.50/4.65 tff(538,plain,
% 4.50/4.65 ((~![B: $i] : ((~element(B, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_smaller(B!18, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, B, D)))) | (~(latt_set_smaller(B!18, B, C) | (~((~element(tptp_fun_D_0(C, B, B!18), the_carrier(B!18))) | below(B!18, B, tptp_fun_D_0(C, B, B!18)) | (~in(tptp_fun_D_0(C, B, B!18), C)))))))))) | (~element(C!20, the_carrier(B!18))) | ![C: $i] : (~((~((~latt_set_smaller(B!18, C!20, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, C!20, D)))) | (~(latt_set_smaller(B!18, C!20, C) | (~((~in(tptp_fun_D_0(C, C!20, B!18), C)) | below(B!18, C!20, tptp_fun_D_0(C, C!20, B!18)) | (~element(tptp_fun_D_0(C, C!20, B!18), the_carrier(B!18)))))))))),
% 4.50/4.65 inference(modus_ponens,[status(thm)],[537, 536])).
% 4.50/4.65 tff(539,plain,
% 4.50/4.65 (![C: $i] : (~((~((~latt_set_smaller(B!18, C!20, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, C!20, D)))) | (~(latt_set_smaller(B!18, C!20, C) | (~((~in(tptp_fun_D_0(C, C!20, B!18), C)) | below(B!18, C!20, tptp_fun_D_0(C, C!20, B!18)) | (~element(tptp_fun_D_0(C, C!20, B!18), the_carrier(B!18)))))))))),
% 4.50/4.65 inference(unit_resolution,[status(thm)],[538, 178, 498])).
% 4.50/4.65 tff(540,plain,
% 4.50/4.65 (((~![C: $i] : (~((~((~latt_set_smaller(B!18, C!20, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, C!20, D)))) | (~(latt_set_smaller(B!18, C!20, C) | (~((~in(tptp_fun_D_0(C, C!20, B!18), C)) | below(B!18, C!20, tptp_fun_D_0(C, C!20, B!18)) | (~element(tptp_fun_D_0(C, C!20, B!18), the_carrier(B!18)))))))))) | (~((~((~latt_set_smaller(B!18, C!20, A!19)) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(B!18))) | below(B!18, C!20, D)))) | (~(latt_set_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, C!20, tptp_fun_D_0(A!19, C!20, B!18)) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19))))))))) <=> ((~![C: $i] : (~((~((~latt_set_smaller(B!18, C!20, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, C!20, D)))) | (~(latt_set_smaller(B!18, C!20, C) | (~((~in(tptp_fun_D_0(C, C!20, B!18), C)) | below(B!18, C!20, tptp_fun_D_0(C, C!20, B!18)) | (~element(tptp_fun_D_0(C, C!20, B!18), the_carrier(B!18)))))))))) | (~((~((~latt_set_smaller(B!18, C!20, A!19)) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(B!18))) | below(B!18, C!20, D)))) | (~(latt_set_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, C!20, tptp_fun_D_0(A!19, C!20, B!18)) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19)))))))))),
% 4.50/4.65 inference(rewrite,[status(thm)],[])).
% 4.50/4.65 tff(541,plain,
% 4.50/4.65 ((~((~((~latt_set_smaller(B!18, C!20, A!19)) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(B!18))) | below(B!18, C!20, D)))) | (~(latt_set_smaller(B!18, C!20, A!19) | (~((~in(tptp_fun_D_0(A!19, C!20, B!18), A!19)) | below(B!18, C!20, tptp_fun_D_0(A!19, C!20, B!18)) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))))))))) <=> (~((~((~latt_set_smaller(B!18, C!20, A!19)) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(B!18))) | below(B!18, C!20, D)))) | (~(latt_set_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, C!20, tptp_fun_D_0(A!19, C!20, B!18)) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19))))))))),
% 4.50/4.65 inference(rewrite,[status(thm)],[])).
% 4.50/4.65 tff(542,plain,
% 4.50/4.65 (((~![C: $i] : (~((~((~latt_set_smaller(B!18, C!20, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, C!20, D)))) | (~(latt_set_smaller(B!18, C!20, C) | (~((~in(tptp_fun_D_0(C, C!20, B!18), C)) | below(B!18, C!20, tptp_fun_D_0(C, C!20, B!18)) | (~element(tptp_fun_D_0(C, C!20, B!18), the_carrier(B!18)))))))))) | (~((~((~latt_set_smaller(B!18, C!20, A!19)) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(B!18))) | below(B!18, C!20, D)))) | (~(latt_set_smaller(B!18, C!20, A!19) | (~((~in(tptp_fun_D_0(A!19, C!20, B!18), A!19)) | below(B!18, C!20, tptp_fun_D_0(A!19, C!20, B!18)) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18)))))))))) <=> ((~![C: $i] : (~((~((~latt_set_smaller(B!18, C!20, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, C!20, D)))) | (~(latt_set_smaller(B!18, C!20, C) | (~((~in(tptp_fun_D_0(C, C!20, B!18), C)) | below(B!18, C!20, tptp_fun_D_0(C, C!20, B!18)) | (~element(tptp_fun_D_0(C, C!20, B!18), the_carrier(B!18)))))))))) | (~((~((~latt_set_smaller(B!18, C!20, A!19)) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(B!18))) | below(B!18, C!20, D)))) | (~(latt_set_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, C!20, tptp_fun_D_0(A!19, C!20, B!18)) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19)))))))))),
% 4.50/4.65 inference(monotonicity,[status(thm)],[541])).
% 4.50/4.65 tff(543,plain,
% 4.50/4.65 (((~![C: $i] : (~((~((~latt_set_smaller(B!18, C!20, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, C!20, D)))) | (~(latt_set_smaller(B!18, C!20, C) | (~((~in(tptp_fun_D_0(C, C!20, B!18), C)) | below(B!18, C!20, tptp_fun_D_0(C, C!20, B!18)) | (~element(tptp_fun_D_0(C, C!20, B!18), the_carrier(B!18)))))))))) | (~((~((~latt_set_smaller(B!18, C!20, A!19)) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(B!18))) | below(B!18, C!20, D)))) | (~(latt_set_smaller(B!18, C!20, A!19) | (~((~in(tptp_fun_D_0(A!19, C!20, B!18), A!19)) | below(B!18, C!20, tptp_fun_D_0(A!19, C!20, B!18)) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18)))))))))) <=> ((~![C: $i] : (~((~((~latt_set_smaller(B!18, C!20, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, C!20, D)))) | (~(latt_set_smaller(B!18, C!20, C) | (~((~in(tptp_fun_D_0(C, C!20, B!18), C)) | below(B!18, C!20, tptp_fun_D_0(C, C!20, B!18)) | (~element(tptp_fun_D_0(C, C!20, B!18), the_carrier(B!18)))))))))) | (~((~((~latt_set_smaller(B!18, C!20, A!19)) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(B!18))) | below(B!18, C!20, D)))) | (~(latt_set_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, C!20, tptp_fun_D_0(A!19, C!20, B!18)) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19)))))))))),
% 4.50/4.65 inference(transitivity,[status(thm)],[542, 540])).
% 4.50/4.65 tff(544,plain,
% 4.50/4.65 ((~![C: $i] : (~((~((~latt_set_smaller(B!18, C!20, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, C!20, D)))) | (~(latt_set_smaller(B!18, C!20, C) | (~((~in(tptp_fun_D_0(C, C!20, B!18), C)) | below(B!18, C!20, tptp_fun_D_0(C, C!20, B!18)) | (~element(tptp_fun_D_0(C, C!20, B!18), the_carrier(B!18)))))))))) | (~((~((~latt_set_smaller(B!18, C!20, A!19)) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(B!18))) | below(B!18, C!20, D)))) | (~(latt_set_smaller(B!18, C!20, A!19) | (~((~in(tptp_fun_D_0(A!19, C!20, B!18), A!19)) | below(B!18, C!20, tptp_fun_D_0(A!19, C!20, B!18)) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18)))))))))),
% 4.50/4.65 inference(quant_inst,[status(thm)],[])).
% 4.50/4.65 tff(545,plain,
% 4.50/4.65 ((~![C: $i] : (~((~((~latt_set_smaller(B!18, C!20, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(B!18))) | below(B!18, C!20, D)))) | (~(latt_set_smaller(B!18, C!20, C) | (~((~in(tptp_fun_D_0(C, C!20, B!18), C)) | below(B!18, C!20, tptp_fun_D_0(C, C!20, B!18)) | (~element(tptp_fun_D_0(C, C!20, B!18), the_carrier(B!18)))))))))) | (~((~((~latt_set_smaller(B!18, C!20, A!19)) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(B!18))) | below(B!18, C!20, D)))) | (~(latt_set_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, C!20, tptp_fun_D_0(A!19, C!20, B!18)) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19))))))))),
% 4.50/4.65 inference(modus_ponens,[status(thm)],[544, 543])).
% 4.50/4.65 tff(546,plain,
% 4.50/4.65 (~((~((~latt_set_smaller(B!18, C!20, A!19)) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(B!18))) | below(B!18, C!20, D)))) | (~(latt_set_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, C!20, tptp_fun_D_0(A!19, C!20, B!18)) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19)))))))),
% 4.50/4.65 inference(unit_resolution,[status(thm)],[545, 539])).
% 4.50/4.65 tff(547,plain,
% 4.50/4.65 (((~((~latt_set_smaller(B!18, C!20, A!19)) | ![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(B!18))) | below(B!18, C!20, D)))) | (~(latt_set_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, C!20, tptp_fun_D_0(A!19, C!20, B!18)) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19))))))) | (latt_set_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, C!20, tptp_fun_D_0(A!19, C!20, B!18)) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19)))))),
% 4.50/4.66 inference(tautology,[status(thm)],[])).
% 4.50/4.66 tff(548,plain,
% 4.50/4.66 (latt_set_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, C!20, tptp_fun_D_0(A!19, C!20, B!18)) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19))))),
% 4.50/4.66 inference(unit_resolution,[status(thm)],[547, 546])).
% 4.50/4.66 tff(549,plain,
% 4.50/4.66 ((~(latt_set_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, C!20, tptp_fun_D_0(A!19, C!20, B!18)) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19)))))) | latt_set_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, C!20, tptp_fun_D_0(A!19, C!20, B!18)) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19))))),
% 4.50/4.66 inference(tautology,[status(thm)],[])).
% 4.50/4.66 tff(550,plain,
% 4.50/4.66 (latt_set_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, C!20, tptp_fun_D_0(A!19, C!20, B!18)) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19))))),
% 4.50/4.66 inference(unit_resolution,[status(thm)],[549, 548])).
% 4.50/4.66 tff(551,plain,
% 4.50/4.66 (~((~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | below(B!18, C!20, tptp_fun_D_0(A!19, C!20, B!18)) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19)))),
% 4.50/4.66 inference(unit_resolution,[status(thm)],[550, 532])).
% 4.50/4.66 tff(552,plain,
% 4.50/4.66 (((~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | below(B!18, C!20, tptp_fun_D_0(A!19, C!20, B!18)) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19))) | element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))),
% 4.50/4.66 inference(tautology,[status(thm)],[])).
% 4.50/4.66 tff(553,plain,
% 4.50/4.66 (element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))),
% 4.50/4.66 inference(unit_resolution,[status(thm)],[552, 551])).
% 4.50/4.66 tff(554,plain,
% 4.50/4.66 (((~![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)))),
% 4.50/4.66 inference(rewrite,[status(thm)],[])).
% 4.50/4.66 tff(555,plain,
% 4.50/4.66 ((~![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)))),
% 4.50/4.66 inference(quant_inst,[status(thm)],[])).
% 4.50/4.66 tff(556,plain,
% 4.50/4.66 ((~![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))),
% 4.50/4.66 inference(modus_ponens,[status(thm)],[555, 554])).
% 4.50/4.66 tff(557,plain,
% 4.50/4.66 (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)),
% 4.50/4.66 inference(unit_resolution,[status(thm)],[556, 395, 553])).
% 4.50/4.66 tff(558,plain,
% 4.50/4.66 (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))),
% 4.50/4.66 inference(symmetry,[status(thm)],[557])).
% 4.50/4.66 tff(559,plain,
% 4.50/4.66 (related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18)))),
% 4.50/4.66 inference(monotonicity,[status(thm)],[33, 407, 558])).
% 4.50/4.66 tff(560,plain,
% 4.50/4.66 (related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18))) <=> related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18))),
% 4.50/4.66 inference(symmetry,[status(thm)],[559])).
% 4.50/4.66 tff(561,plain,
% 4.50/4.66 ((~related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18)))) <=> (~related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)))),
% 4.50/4.66 inference(monotonicity,[status(thm)],[560])).
% 4.50/4.66 tff(562,plain,
% 4.50/4.66 (((~![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), cast_to_el_of_LattPOSet(B!18, C))))) | ((~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | (below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18)))))) <=> ((~![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), cast_to_el_of_LattPOSet(B!18, C))))) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | (below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18)))))),
% 4.50/4.66 inference(rewrite,[status(thm)],[])).
% 4.50/4.66 tff(563,plain,
% 4.50/4.66 ((~![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), cast_to_el_of_LattPOSet(B!18, C))))) | ((~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | (below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18)))))),
% 4.50/4.66 inference(quant_inst,[status(thm)],[])).
% 4.50/4.66 tff(564,plain,
% 4.50/4.66 ((~![C: $i] : ((~element(C, the_carrier(B!18))) | (below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), C) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), cast_to_el_of_LattPOSet(B!18, C))))) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | (below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18))))),
% 4.50/4.66 inference(modus_ponens,[status(thm)],[563, 562])).
% 4.50/4.66 tff(565,plain,
% 4.50/4.66 (below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18)))),
% 4.50/4.66 inference(unit_resolution,[status(thm)],[564, 367, 553])).
% 4.50/4.66 tff(566,plain,
% 4.50/4.66 (((~![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_0(A!19, C!20, B!18), the_carrier(B!18))) | (below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) <=> below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, 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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) <=> below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18))))),
% 4.50/4.66 inference(rewrite,[status(thm)],[])).
% 4.50/4.66 tff(567,plain,
% 4.50/4.66 (((below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) <=> below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18))) | empty_carrier(B!18) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | (~meet_commutative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)) | (~latt_str(B!18)) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), 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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) <=> below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18))))),
% 4.50/4.66 inference(rewrite,[status(thm)],[])).
% 4.50/4.66 tff(568,plain,
% 4.50/4.66 (((~![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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) <=> below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18))) | empty_carrier(B!18) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | (~meet_commutative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)) | (~latt_str(B!18)) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), 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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) <=> below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)))))),
% 4.50/4.66 inference(monotonicity,[status(thm)],[567])).
% 4.50/4.66 tff(569,plain,
% 4.50/4.66 (((~![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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) <=> below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18))) | empty_carrier(B!18) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | (~meet_commutative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)) | (~latt_str(B!18)) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), 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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) <=> below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18))))),
% 4.50/4.66 inference(transitivity,[status(thm)],[568, 566])).
% 4.50/4.66 tff(570,plain,
% 4.50/4.66 ((~![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, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) <=> below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18))) | empty_carrier(B!18) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | (~meet_commutative(B!18)) | (~meet_absorbing(B!18)) | (~join_absorbing(B!18)) | (~latt_str(B!18)) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), the_carrier(B!18))))),
% 4.50/4.66 inference(quant_inst,[status(thm)],[])).
% 4.50/4.66 tff(571,plain,
% 4.50/4.66 ((~![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_0(A!19, C!20, B!18), the_carrier(B!18))) | (below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) <=> below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)))),
% 4.50/4.66 inference(modus_ponens,[status(thm)],[570, 569])).
% 4.50/4.66 tff(572,plain,
% 4.50/4.66 (below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) <=> below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18))),
% 4.50/4.66 inference(unit_resolution,[status(thm)],[571, 332, 12, 10, 319, 317, 315, 290, 553])).
% 4.50/4.66 tff(573,plain,
% 4.50/4.66 (below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) <=> below(B!18, C!20, tptp_fun_D_0(A!19, C!20, B!18))),
% 4.50/4.66 inference(monotonicity,[status(thm)],[405])).
% 4.50/4.66 tff(574,plain,
% 4.50/4.66 (below(B!18, C!20, tptp_fun_D_0(A!19, C!20, B!18)) <=> below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18))),
% 4.50/4.66 inference(symmetry,[status(thm)],[573])).
% 4.50/4.66 tff(575,plain,
% 4.50/4.66 ((~below(B!18, C!20, tptp_fun_D_0(A!19, C!20, B!18))) <=> (~below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)))),
% 4.50/4.66 inference(monotonicity,[status(thm)],[574])).
% 4.50/4.66 tff(576,plain,
% 4.50/4.66 (((~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | below(B!18, C!20, tptp_fun_D_0(A!19, C!20, B!18)) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19))) | (~below(B!18, C!20, tptp_fun_D_0(A!19, C!20, B!18)))),
% 4.50/4.66 inference(tautology,[status(thm)],[])).
% 4.50/4.66 tff(577,plain,
% 4.50/4.66 (~below(B!18, C!20, tptp_fun_D_0(A!19, C!20, B!18))),
% 4.50/4.66 inference(unit_resolution,[status(thm)],[576, 551])).
% 4.50/4.66 tff(578,plain,
% 4.50/4.66 (~below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18))),
% 4.50/4.66 inference(modus_ponens,[status(thm)],[577, 575])).
% 4.50/4.66 tff(579,plain,
% 4.50/4.66 ((~(below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) <=> below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)))) | (~below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18))) | below(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18))),
% 4.50/4.66 inference(tautology,[status(thm)],[])).
% 4.50/4.66 tff(580,plain,
% 4.50/4.66 (~below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18))),
% 4.50/4.66 inference(unit_resolution,[status(thm)],[579, 578, 572])).
% 4.50/4.66 tff(581,plain,
% 4.50/4.66 ((~(below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) <=> related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18))))) | below_refl(B!18, cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) | (~related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18))))),
% 4.50/4.66 inference(tautology,[status(thm)],[])).
% 4.50/4.66 tff(582,plain,
% 4.50/4.66 (~related_reflexive(poset_of_lattice(B!18), cast_to_el_of_LattPOSet(B!18, cast_to_el_of_LattPOSet(B!18, C!20)), cast_to_el_of_LattPOSet(B!18, tptp_fun_D_0(A!19, C!20, B!18)))),
% 4.50/4.66 inference(unit_resolution,[status(thm)],[581, 580, 565])).
% 4.50/4.66 tff(583,plain,
% 4.50/4.66 (~related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18))),
% 4.50/4.66 inference(modus_ponens,[status(thm)],[582, 561])).
% 4.50/4.66 tff(584,plain,
% 4.50/4.66 (the_carrier(poset_of_lattice(B!18)) = the_carrier(B!18)),
% 4.50/4.66 inference(symmetry,[status(thm)],[166])).
% 4.50/4.66 tff(585,plain,
% 4.50/4.66 (the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))) = the_carrier(B!18)),
% 4.50/4.66 inference(transitivity,[status(thm)],[34, 584])).
% 4.50/4.66 tff(586,plain,
% 4.50/4.66 (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))),
% 4.50/4.66 inference(monotonicity,[status(thm)],[585])).
% 4.50/4.66 tff(587,plain,
% 4.50/4.66 (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))))),
% 4.50/4.66 inference(symmetry,[status(thm)],[586])).
% 4.50/4.66 tff(588,plain,
% 4.50/4.66 (element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))),
% 4.50/4.66 inference(modus_ponens,[status(thm)],[553, 587])).
% 4.50/4.66 tff(589,plain,
% 4.50/4.66 (((~![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))))) | (related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, 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))))))) <=> ((~![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))))) | (related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, 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))))))),
% 4.50/4.66 inference(rewrite,[status(thm)],[])).
% 4.50/4.66 tff(590,plain,
% 4.50/4.66 (((related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18))) | empty_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))))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), 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))))) | (related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, 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))))))),
% 4.50/4.66 inference(rewrite,[status(thm)],[])).
% 4.50/4.66 tff(591,plain,
% 4.50/4.66 (((~![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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18))) | empty_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))))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), 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))))) | (related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, 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)))))))),
% 4.50/4.66 inference(monotonicity,[status(thm)],[590])).
% 4.50/4.66 tff(592,plain,
% 4.50/4.66 (((~![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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18))) | empty_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))))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), 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))))) | (related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, 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))))))),
% 4.50/4.66 inference(transitivity,[status(thm)],[591, 589])).
% 4.50/4.66 tff(593,plain,
% 4.50/4.66 ((~![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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18))) | empty_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))))) | (~element(cast_to_el_of_LattPOSet(B!18, C!20), 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)))))),
% 4.50/4.66 inference(quant_inst,[status(thm)],[])).
% 4.50/4.66 tff(594,plain,
% 4.50/4.66 ((~![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))))) | (related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, 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)))))),
% 4.50/4.66 inference(modus_ponens,[status(thm)],[593, 592])).
% 4.50/4.66 tff(595,plain,
% 4.50/4.66 ((related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, 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)))))),
% 4.50/4.66 inference(unit_resolution,[status(thm)],[594, 453, 440, 64, 414, 199])).
% 4.50/4.66 tff(596,plain,
% 4.50/4.66 (related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18))),
% 4.50/4.66 inference(unit_resolution,[status(thm)],[595, 588])).
% 4.50/4.66 tff(597,plain,
% 4.50/4.66 (relstr_element_smaller(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), A!19, cast_to_el_of_LattPOSet(B!18, C!20))),
% 4.50/4.66 inference(modus_ponens,[status(thm)],[529, 171])).
% 4.50/4.66 tff(598,plain,
% 4.50/4.67 (((~((~relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~(relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_1(cast_to_el_of_LattPOSet(B!18, C!20), A!19, 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))))) | (~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_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), D)))),
% 4.50/4.67 inference(tautology,[status(thm)],[])).
% 4.50/4.67 tff(599,plain,
% 4.50/4.67 ((~relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), D))),
% 4.50/4.67 inference(unit_resolution,[status(thm)],[598, 231])).
% 4.50/4.67 tff(600,plain,
% 4.50/4.67 ((~((~relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), D)))) | (~relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), D))),
% 4.50/4.67 inference(tautology,[status(thm)],[])).
% 4.50/4.67 tff(601,plain,
% 4.50/4.67 ((~relstr_element_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)), cast_to_el_of_LattPOSet(B!18, C!20), D))),
% 4.50/4.67 inference(unit_resolution,[status(thm)],[600, 599])).
% 4.50/4.67 tff(602,plain,
% 4.50/4.67 (![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)), cast_to_el_of_LattPOSet(B!18, C!20), D))),
% 4.50/4.67 inference(unit_resolution,[status(thm)],[601, 597])).
% 4.50/4.67 tff(603,plain,
% 4.50/4.67 (((~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(B!18))) | below(B!18, C!20, tptp_fun_D_0(A!19, C!20, B!18)) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19))) | in(tptp_fun_D_0(A!19, C!20, B!18), A!19)),
% 4.50/4.67 inference(tautology,[status(thm)],[])).
% 4.50/4.67 tff(604,plain,
% 4.50/4.67 (in(tptp_fun_D_0(A!19, C!20, B!18), A!19)),
% 4.50/4.67 inference(unit_resolution,[status(thm)],[603, 551])).
% 4.50/4.67 tff(605,plain,
% 4.50/4.67 (((~![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)), cast_to_el_of_LattPOSet(B!18, C!20), D))) | ((~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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)))) <=> ((~![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)), cast_to_el_of_LattPOSet(B!18, C!20), D))) | (~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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)))),
% 4.50/4.69 inference(rewrite,[status(thm)],[])).
% 4.50/4.69 tff(606,plain,
% 4.50/4.69 ((~![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)), cast_to_el_of_LattPOSet(B!18, C!20), D))) | ((~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)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)))),
% 4.50/4.69 inference(quant_inst,[status(thm)],[])).
% 4.50/4.69 tff(607,plain,
% 4.50/4.69 ((~![D: $i] : ((~in(D, A!19)) | (~element(D, the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), D))) | (~in(tptp_fun_D_0(A!19, C!20, B!18), A!19)) | (~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18))),
% 4.50/4.69 inference(modus_ponens,[status(thm)],[606, 605])).
% 4.50/4.69 tff(608,plain,
% 4.50/4.69 ((~element(tptp_fun_D_0(A!19, C!20, B!18), the_carrier(rel_str_of(the_carrier(B!18), k2_lattice3(B!18))))) | related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18))),
% 4.50/4.69 inference(unit_resolution,[status(thm)],[607, 604, 602])).
% 4.50/4.69 tff(609,plain,
% 4.50/4.69 (related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18))),
% 4.50/4.69 inference(unit_resolution,[status(thm)],[608, 588])).
% 4.50/4.69 tff(610,plain,
% 4.50/4.69 ((~(related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) <=> related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)))) | related_reflexive(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)) | (~related(rel_str_of(the_carrier(B!18), k2_lattice3(B!18)), cast_to_el_of_LattPOSet(B!18, C!20), tptp_fun_D_0(A!19, C!20, B!18)))),
% 4.50/4.69 inference(tautology,[status(thm)],[])).
% 4.50/4.69 tff(611,plain,
% 4.50/4.69 ($false),
% 4.50/4.69 inference(unit_resolution,[status(thm)],[610, 609, 596, 583])).
% 4.50/4.69 % SZS output end Proof
% 4.50/4.69 % E exiting
%------------------------------------------------------------------------------