%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU346+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 14.57s 14.73s
% Output : Proof 14.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU346+1 : TPTP v9.0.0. Released v3.3.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 06:51:31 EDT 2025
% 0.12/0.34 % CPUTime :
% 14.57/14.73 % SZS status Theorem
% 14.57/14.73 % SZS output start Proof
% 14.57/14.73 tff(related_type, type, (
% 14.57/14.73 related: ( $i * $i * $i ) > $o)).
% 14.57/14.73 tff(tptp_fun_C_21_type, type, (
% 14.57/14.73 tptp_fun_C_21: $i)).
% 14.57/14.73 tff(tptp_fun_B_20_type, type, (
% 14.57/14.73 tptp_fun_B_20: $i)).
% 14.57/14.73 tff(rel_str_of_type, type, (
% 14.57/14.73 rel_str_of: ( $i * $i ) > $i)).
% 14.57/14.73 tff(k2_lattice3_type, type, (
% 14.57/14.73 k2_lattice3: $i > $i)).
% 14.57/14.73 tff(tptp_fun_A_19_type, type, (
% 14.57/14.73 tptp_fun_A_19: $i)).
% 14.57/14.73 tff(the_carrier_type, type, (
% 14.57/14.73 the_carrier: $i > $i)).
% 14.57/14.73 tff(cast_to_el_of_LattPOSet_type, type, (
% 14.57/14.73 cast_to_el_of_LattPOSet: ( $i * $i ) > $i)).
% 14.57/14.73 tff(poset_of_lattice_type, type, (
% 14.57/14.73 poset_of_lattice: $i > $i)).
% 14.57/14.73 tff(element_type, type, (
% 14.57/14.73 element: ( $i * $i ) > $o)).
% 14.57/14.73 tff(latt_str_type, type, (
% 14.57/14.73 latt_str: $i > $o)).
% 14.57/14.73 tff(related_reflexive_type, type, (
% 14.57/14.73 related_reflexive: ( $i * $i * $i ) > $o)).
% 14.57/14.73 tff(below_refl_type, type, (
% 14.57/14.73 below_refl: ( $i * $i * $i ) > $o)).
% 14.57/14.73 tff(lattice_type, type, (
% 14.57/14.73 lattice: $i > $o)).
% 14.57/14.73 tff(empty_carrier_type, type, (
% 14.57/14.73 empty_carrier: $i > $o)).
% 14.57/14.73 tff(antisymmetric_relstr_type, type, (
% 14.57/14.73 antisymmetric_relstr: $i > $o)).
% 14.57/14.73 tff(transitive_relstr_type, type, (
% 14.57/14.73 transitive_relstr: $i > $o)).
% 14.57/14.73 tff(reflexive_relstr_type, type, (
% 14.57/14.73 reflexive_relstr: $i > $o)).
% 14.57/14.73 tff(strict_rel_str_type, type, (
% 14.57/14.73 strict_rel_str: $i > $o)).
% 14.57/14.73 tff(rel_str_type, type, (
% 14.57/14.73 rel_str: $i > $o)).
% 14.57/14.73 tff(in_type, type, (
% 14.57/14.73 in: ( $i * $i ) > $o)).
% 14.57/14.73 tff(the_InternalRel_type, type, (
% 14.57/14.73 the_InternalRel: $i > $i)).
% 14.57/14.73 tff(ordered_pair_type, type, (
% 14.57/14.73 ordered_pair: ( $i * $i ) > $i)).
% 14.57/14.73 tff(relation_of_lattice_type, type, (
% 14.57/14.73 relation_of_lattice: $i > $i)).
% 14.57/14.73 tff(ordered_pair_as_product_element_type, type, (
% 14.57/14.73 ordered_pair_as_product_element: ( $i * $i * $i * $i ) > $i)).
% 14.57/14.73 tff(relation_of2_type, type, (
% 14.57/14.73 relation_of2: ( $i * $i * $i ) > $o)).
% 14.57/14.73 tff(relation_of2_as_subset_type, type, (
% 14.57/14.73 relation_of2_as_subset: ( $i * $i * $i ) > $o)).
% 14.57/14.73 tff(v1_partfun1_type, type, (
% 14.57/14.73 v1_partfun1: ( $i * $i * $i ) > $o)).
% 14.57/14.73 tff(transitive_type, type, (
% 14.57/14.73 transitive: $i > $o)).
% 14.57/14.73 tff(antisymmetric_type, type, (
% 14.57/14.73 antisymmetric: $i > $o)).
% 14.57/14.73 tff(reflexive_type, type, (
% 14.57/14.73 reflexive: $i > $o)).
% 14.57/14.73 tff(empty_type, type, (
% 14.57/14.73 empty: $i > $o)).
% 14.57/14.73 tff(one_sorted_str_type, type, (
% 14.57/14.73 one_sorted_str: $i > $o)).
% 14.57/14.73 tff(join_semilatt_str_type, type, (
% 14.57/14.73 join_semilatt_str: $i > $o)).
% 14.57/14.73 tff(meet_semilatt_str_type, type, (
% 14.57/14.73 meet_semilatt_str: $i > $o)).
% 14.57/14.73 tff(1,plain,
% 14.57/14.73 ((((~empty_carrier(A!19)) & lattice(A!19) & latt_str(A!19)) & (element(B!20, the_carrier(A!19)) & (~((~element(C!21, the_carrier(A!19))) | (below_refl(A!19, B!20, C!21) <=> related_reflexive(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21))))))) <=> ((~empty_carrier(A!19)) & lattice(A!19) & latt_str(A!19) & element(B!20, the_carrier(A!19)) & (~((~element(C!21, the_carrier(A!19))) | (below_refl(A!19, B!20, C!21) <=> related_reflexive(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21))))))),
% 14.57/14.73 inference(rewrite,[status(thm)],[])).
% 14.57/14.73 tff(2,plain,
% 14.57/14.73 ((~![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)))))))),
% 14.57/14.73 inference(rewrite,[status(thm)],[])).
% 14.57/14.73 tff(3,plain,
% 14.57/14.73 ((~![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)))))))),
% 14.57/14.73 inference(rewrite,[status(thm)],[])).
% 14.57/14.73 tff(4,axiom,(~![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t7_lattice3')).
% 14.57/14.73 tff(5,plain,
% 14.57/14.73 (~![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))))))),
% 14.57/14.73 inference(modus_ponens,[status(thm)],[4, 3])).
% 14.57/14.73 tff(6,plain,
% 14.57/14.73 (~![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))))))),
% 14.57/14.73 inference(modus_ponens,[status(thm)],[5, 2])).
% 14.57/14.73 tff(7,plain,
% 14.57/14.73 (~![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))))))),
% 14.57/14.73 inference(modus_ponens,[status(thm)],[6, 2])).
% 14.57/14.73 tff(8,plain,
% 14.57/14.73 (~![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))))))),
% 14.57/14.73 inference(modus_ponens,[status(thm)],[7, 2])).
% 14.57/14.73 tff(9,plain,
% 14.57/14.73 ((~empty_carrier(A!19)) & lattice(A!19) & latt_str(A!19) & element(B!20, the_carrier(A!19)) & (~((~element(C!21, the_carrier(A!19))) | (below_refl(A!19, B!20, C!21) <=> related_reflexive(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21)))))),
% 14.57/14.73 inference(modus_ponens,[status(thm)],[8, 1])).
% 14.57/14.73 tff(10,plain,
% 14.57/14.73 (latt_str(A!19)),
% 14.57/14.73 inference(and_elim,[status(thm)],[9])).
% 14.57/14.73 tff(11,plain,
% 14.57/14.73 (lattice(A!19)),
% 14.57/14.73 inference(and_elim,[status(thm)],[9])).
% 14.57/14.73 tff(12,plain,
% 14.57/14.73 (~empty_carrier(A!19)),
% 14.57/14.73 inference(and_elim,[status(thm)],[9])).
% 14.57/14.73 tff(13,plain,
% 14.57/14.73 (^[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))))),
% 14.57/14.73 inference(bind,[status(th)],[])).
% 14.57/14.73 tff(14,plain,
% 14.57/14.73 (![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)))),
% 14.57/14.73 inference(quant_intro,[status(thm)],[13])).
% 14.57/14.73 tff(15,plain,
% 14.57/14.73 (^[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))))),
% 14.57/14.73 inference(bind,[status(th)],[])).
% 14.57/14.73 tff(16,plain,
% 14.57/14.73 (![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)))),
% 14.57/14.73 inference(quant_intro,[status(thm)],[15])).
% 14.57/14.73 tff(17,plain,
% 14.57/14.73 (^[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))))),
% 14.57/14.73 inference(bind,[status(th)],[])).
% 14.57/14.73 tff(18,plain,
% 14.57/14.73 (![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)))),
% 14.57/14.73 inference(quant_intro,[status(thm)],[17])).
% 14.57/14.73 tff(19,plain,
% 14.57/14.73 (![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)))),
% 14.57/14.73 inference(transitivity,[status(thm)],[18, 16])).
% 14.57/14.73 tff(20,plain,
% 14.57/14.73 (^[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)))))),
% 14.57/14.73 inference(bind,[status(th)],[])).
% 14.57/14.73 tff(21,plain,
% 14.57/14.73 (![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)))),
% 14.57/14.73 inference(quant_intro,[status(thm)],[20])).
% 14.57/14.73 tff(22,plain,
% 14.57/14.73 (![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)))),
% 14.57/14.73 inference(rewrite,[status(thm)],[])).
% 14.57/14.73 tff(23,plain,
% 14.57/14.73 (^[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)))))),
% 14.57/14.73 inference(bind,[status(th)],[])).
% 14.57/14.73 tff(24,plain,
% 14.57/14.73 (![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)))),
% 14.57/14.73 inference(quant_intro,[status(thm)],[23])).
% 14.57/14.73 tff(25,axiom,(![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => (cast_to_el_of_LattPOSet(A, B) = B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_lattice3')).
% 14.57/14.73 tff(26,plain,
% 14.57/14.73 (![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)))),
% 14.57/14.73 inference(modus_ponens,[status(thm)],[25, 24])).
% 14.57/14.73 tff(27,plain,
% 14.57/14.73 (![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)))),
% 14.57/14.73 inference(modus_ponens,[status(thm)],[26, 22])).
% 14.57/14.73 tff(28,plain,(
% 14.57/14.73 ![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)))),
% 14.57/14.73 inference(skolemize,[status(sab)],[27])).
% 14.57/14.73 tff(29,plain,
% 14.57/14.73 (![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)))),
% 14.57/14.73 inference(modus_ponens,[status(thm)],[28, 21])).
% 14.57/14.73 tff(30,plain,
% 14.57/14.73 (![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)))),
% 14.57/14.73 inference(modus_ponens,[status(thm)],[29, 19])).
% 14.57/14.73 tff(31,plain,
% 14.57/14.73 (![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)))),
% 14.57/14.73 inference(modus_ponens,[status(thm)],[30, 14])).
% 14.57/14.73 tff(32,plain,
% 14.57/14.73 (((~![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(A!19) | (~latt_str(A!19)) | (~lattice(A!19)) | ![B: $i] : ((~element(B, the_carrier(A!19))) | (cast_to_el_of_LattPOSet(A!19, 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(A!19) | (~latt_str(A!19)) | (~lattice(A!19)) | ![B: $i] : ((~element(B, the_carrier(A!19))) | (cast_to_el_of_LattPOSet(A!19, B) = B)))),
% 14.57/14.73 inference(rewrite,[status(thm)],[])).
% 14.57/14.73 tff(33,plain,
% 14.57/14.73 ((~![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(A!19) | (~latt_str(A!19)) | (~lattice(A!19)) | ![B: $i] : ((~element(B, the_carrier(A!19))) | (cast_to_el_of_LattPOSet(A!19, B) = B)))),
% 14.57/14.73 inference(quant_inst,[status(thm)],[])).
% 14.57/14.73 tff(34,plain,
% 14.57/14.73 ((~![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(A!19) | (~latt_str(A!19)) | (~lattice(A!19)) | ![B: $i] : ((~element(B, the_carrier(A!19))) | (cast_to_el_of_LattPOSet(A!19, B) = B))),
% 14.57/14.73 inference(modus_ponens,[status(thm)],[33, 32])).
% 14.57/14.73 tff(35,plain,
% 14.57/14.73 (![B: $i] : ((~element(B, the_carrier(A!19))) | (cast_to_el_of_LattPOSet(A!19, B) = B))),
% 14.57/14.73 inference(unit_resolution,[status(thm)],[34, 31, 12, 11, 10])).
% 14.57/14.73 tff(36,plain,
% 14.57/14.73 (~((~element(C!21, the_carrier(A!19))) | (below_refl(A!19, B!20, C!21) <=> related_reflexive(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21))))),
% 14.57/14.73 inference(and_elim,[status(thm)],[9])).
% 14.57/14.73 tff(37,plain,
% 14.57/14.73 (element(C!21, the_carrier(A!19))),
% 14.57/14.73 inference(or_elim,[status(thm)],[36])).
% 14.57/14.73 tff(38,plain,
% 14.57/14.73 (((~![B: $i] : ((~element(B, the_carrier(A!19))) | (cast_to_el_of_LattPOSet(A!19, B) = B))) | ((~element(C!21, the_carrier(A!19))) | (cast_to_el_of_LattPOSet(A!19, C!21) = C!21))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!19))) | (cast_to_el_of_LattPOSet(A!19, B) = B))) | (~element(C!21, the_carrier(A!19))) | (cast_to_el_of_LattPOSet(A!19, C!21) = C!21))),
% 14.57/14.73 inference(rewrite,[status(thm)],[])).
% 14.57/14.73 tff(39,plain,
% 14.57/14.73 ((~![B: $i] : ((~element(B, the_carrier(A!19))) | (cast_to_el_of_LattPOSet(A!19, B) = B))) | ((~element(C!21, the_carrier(A!19))) | (cast_to_el_of_LattPOSet(A!19, C!21) = C!21))),
% 14.57/14.73 inference(quant_inst,[status(thm)],[])).
% 14.57/14.73 tff(40,plain,
% 14.57/14.73 ((~![B: $i] : ((~element(B, the_carrier(A!19))) | (cast_to_el_of_LattPOSet(A!19, B) = B))) | (~element(C!21, the_carrier(A!19))) | (cast_to_el_of_LattPOSet(A!19, C!21) = C!21)),
% 14.57/14.73 inference(modus_ponens,[status(thm)],[39, 38])).
% 14.57/14.73 tff(41,plain,
% 14.57/14.73 (cast_to_el_of_LattPOSet(A!19, C!21) = C!21),
% 14.57/14.73 inference(unit_resolution,[status(thm)],[40, 37, 35])).
% 14.57/14.73 tff(42,plain,
% 14.57/14.73 (C!21 = cast_to_el_of_LattPOSet(A!19, C!21)),
% 14.57/14.73 inference(symmetry,[status(thm)],[41])).
% 14.57/14.73 tff(43,plain,
% 14.57/14.73 (element(B!20, the_carrier(A!19))),
% 14.57/14.73 inference(and_elim,[status(thm)],[9])).
% 14.57/14.73 tff(44,plain,
% 14.57/14.73 (((~![B: $i] : ((~element(B, the_carrier(A!19))) | (cast_to_el_of_LattPOSet(A!19, B) = B))) | ((~element(B!20, the_carrier(A!19))) | (cast_to_el_of_LattPOSet(A!19, B!20) = B!20))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!19))) | (cast_to_el_of_LattPOSet(A!19, B) = B))) | (~element(B!20, the_carrier(A!19))) | (cast_to_el_of_LattPOSet(A!19, B!20) = B!20))),
% 14.57/14.73 inference(rewrite,[status(thm)],[])).
% 14.57/14.73 tff(45,plain,
% 14.57/14.73 ((~![B: $i] : ((~element(B, the_carrier(A!19))) | (cast_to_el_of_LattPOSet(A!19, B) = B))) | ((~element(B!20, the_carrier(A!19))) | (cast_to_el_of_LattPOSet(A!19, B!20) = B!20))),
% 14.57/14.73 inference(quant_inst,[status(thm)],[])).
% 14.57/14.73 tff(46,plain,
% 14.57/14.73 ((~![B: $i] : ((~element(B, the_carrier(A!19))) | (cast_to_el_of_LattPOSet(A!19, B) = B))) | (~element(B!20, the_carrier(A!19))) | (cast_to_el_of_LattPOSet(A!19, B!20) = B!20)),
% 14.57/14.73 inference(modus_ponens,[status(thm)],[45, 44])).
% 14.57/14.73 tff(47,plain,
% 14.57/14.73 (cast_to_el_of_LattPOSet(A!19, B!20) = B!20),
% 14.57/14.73 inference(unit_resolution,[status(thm)],[46, 43, 35])).
% 14.57/14.73 tff(48,plain,
% 14.57/14.73 (B!20 = cast_to_el_of_LattPOSet(A!19, B!20)),
% 14.57/14.73 inference(symmetry,[status(thm)],[47])).
% 14.57/14.73 tff(49,plain,
% 14.57/14.73 (^[A: $i] : refl((empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A))) <=> (empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A))))),
% 14.57/14.73 inference(bind,[status(th)],[])).
% 14.57/14.73 tff(50,plain,
% 14.57/14.73 (![A: $i] : (empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A)))),
% 14.57/14.73 inference(quant_intro,[status(thm)],[49])).
% 14.57/14.73 tff(51,plain,
% 14.57/14.73 (^[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)))) <=> (empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(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) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A)))))),
% 14.57/14.73 inference(bind,[status(th)],[])).
% 14.57/14.73 tff(52,plain,
% 14.57/14.73 (![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) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A)))),
% 14.57/14.73 inference(quant_intro,[status(thm)],[51])).
% 14.57/14.73 tff(53,plain,
% 14.57/14.73 (![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))))),
% 14.57/14.73 inference(rewrite,[status(thm)],[])).
% 14.57/14.73 tff(54,plain,
% 14.57/14.73 (^[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))))))),
% 14.57/14.73 inference(bind,[status(th)],[])).
% 14.57/14.73 tff(55,plain,
% 14.57/14.73 (![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))))),
% 14.57/14.73 inference(quant_intro,[status(thm)],[54])).
% 14.57/14.73 tff(56,axiom,(![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_lattice3')).
% 14.57/14.73 tff(57,plain,
% 14.57/14.73 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))))),
% 14.57/14.73 inference(modus_ponens,[status(thm)],[56, 55])).
% 14.57/14.73 tff(58,plain,
% 14.57/14.73 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))))),
% 14.57/14.73 inference(modus_ponens,[status(thm)],[57, 53])).
% 14.57/14.73 tff(59,plain,(
% 14.57/14.73 ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))))),
% 14.57/14.73 inference(skolemize,[status(sab)],[58])).
% 14.57/14.73 tff(60,plain,
% 14.57/14.73 (![A: $i] : (empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A)))),
% 14.57/14.73 inference(modus_ponens,[status(thm)],[59, 52])).
% 14.57/14.73 tff(61,plain,
% 14.57/14.73 (![A: $i] : (empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A)))),
% 14.57/14.73 inference(modus_ponens,[status(thm)],[60, 50])).
% 14.57/14.73 tff(62,plain,
% 14.57/14.73 (((~![A: $i] : (empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A)))) | (empty_carrier(A!19) | (~lattice(A!19)) | (~latt_str(A!19)) | (poset_of_lattice(A!19) = rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) <=> ((~![A: $i] : (empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A)))) | empty_carrier(A!19) | (~lattice(A!19)) | (~latt_str(A!19)) | (poset_of_lattice(A!19) = rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))),
% 14.57/14.73 inference(rewrite,[status(thm)],[])).
% 14.57/14.73 tff(63,plain,
% 14.57/14.73 ((empty_carrier(A!19) | (poset_of_lattice(A!19) = rel_str_of(the_carrier(A!19), k2_lattice3(A!19))) | (~latt_str(A!19)) | (~lattice(A!19))) <=> (empty_carrier(A!19) | (~lattice(A!19)) | (~latt_str(A!19)) | (poset_of_lattice(A!19) = rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))),
% 14.57/14.73 inference(rewrite,[status(thm)],[])).
% 14.57/14.73 tff(64,plain,
% 14.57/14.73 (((~![A: $i] : (empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A)))) | (empty_carrier(A!19) | (poset_of_lattice(A!19) = rel_str_of(the_carrier(A!19), k2_lattice3(A!19))) | (~latt_str(A!19)) | (~lattice(A!19)))) <=> ((~![A: $i] : (empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A)))) | (empty_carrier(A!19) | (~lattice(A!19)) | (~latt_str(A!19)) | (poset_of_lattice(A!19) = rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))),
% 14.57/14.73 inference(monotonicity,[status(thm)],[63])).
% 14.57/14.73 tff(65,plain,
% 14.57/14.73 (((~![A: $i] : (empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A)))) | (empty_carrier(A!19) | (poset_of_lattice(A!19) = rel_str_of(the_carrier(A!19), k2_lattice3(A!19))) | (~latt_str(A!19)) | (~lattice(A!19)))) <=> ((~![A: $i] : (empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A)))) | empty_carrier(A!19) | (~lattice(A!19)) | (~latt_str(A!19)) | (poset_of_lattice(A!19) = rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))),
% 14.57/14.73 inference(transitivity,[status(thm)],[64, 62])).
% 14.57/14.73 tff(66,plain,
% 14.57/14.73 ((~![A: $i] : (empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A)))) | (empty_carrier(A!19) | (poset_of_lattice(A!19) = rel_str_of(the_carrier(A!19), k2_lattice3(A!19))) | (~latt_str(A!19)) | (~lattice(A!19)))),
% 14.57/14.73 inference(quant_inst,[status(thm)],[])).
% 14.57/14.73 tff(67,plain,
% 14.57/14.73 ((~![A: $i] : (empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A)))) | empty_carrier(A!19) | (~lattice(A!19)) | (~latt_str(A!19)) | (poset_of_lattice(A!19) = rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))),
% 14.57/14.73 inference(modus_ponens,[status(thm)],[66, 65])).
% 14.57/14.73 tff(68,plain,
% 14.57/14.73 (poset_of_lattice(A!19) = rel_str_of(the_carrier(A!19), k2_lattice3(A!19))),
% 14.57/14.73 inference(unit_resolution,[status(thm)],[67, 61, 12, 11, 10])).
% 14.57/14.73 tff(69,plain,
% 14.57/14.73 (rel_str_of(the_carrier(A!19), k2_lattice3(A!19)) = poset_of_lattice(A!19)),
% 14.57/14.73 inference(symmetry,[status(thm)],[68])).
% 14.57/14.73 tff(70,plain,
% 14.57/14.73 (related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C!21) <=> related(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21))),
% 14.57/14.73 inference(monotonicity,[status(thm)],[69, 48, 42])).
% 14.57/14.73 tff(71,plain,
% 14.57/14.73 (related(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21)) <=> related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C!21)),
% 14.57/14.73 inference(symmetry,[status(thm)],[70])).
% 14.57/14.73 tff(72,plain,
% 14.57/14.73 ((~related(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21))) <=> (~related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C!21))),
% 14.57/14.73 inference(monotonicity,[status(thm)],[71])).
% 14.57/14.73 tff(73,assumption,(~related_reflexive(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21))), introduced(assumption)).
% 14.57/14.73 tff(74,plain,
% 14.57/14.73 (^[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)))))))),
% 14.57/14.73 inference(bind,[status(th)],[])).
% 14.57/14.73 tff(75,plain,
% 14.57/14.73 (![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))))))),
% 14.57/14.73 inference(quant_intro,[status(thm)],[74])).
% 14.57/14.73 tff(76,plain,
% 14.57/14.73 (^[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))))))))),
% 14.57/14.73 inference(bind,[status(th)],[])).
% 14.57/14.73 tff(77,plain,
% 14.57/14.73 (![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))))))),
% 14.57/14.73 inference(quant_intro,[status(thm)],[76])).
% 14.57/14.73 tff(78,plain,
% 14.57/14.73 (![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))))),
% 14.57/14.73 inference(rewrite,[status(thm)],[])).
% 14.57/14.73 tff(79,plain,
% 14.57/14.73 (^[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))))))),
% 14.57/14.73 inference(bind,[status(th)],[])).
% 14.57/14.73 tff(80,plain,
% 14.57/14.73 (![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))))),
% 14.57/14.73 inference(quant_intro,[status(thm)],[79])).
% 14.57/14.73 tff(81,axiom,(![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => (((((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A))) & reflexive_relstr(poset_of_lattice(A))) & transitive_relstr(poset_of_lattice(A))) & antisymmetric_relstr(poset_of_lattice(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc4_lattice3')).
% 14.57/14.73 tff(82,plain,
% 14.57/14.73 (![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))))),
% 14.57/14.73 inference(modus_ponens,[status(thm)],[81, 80])).
% 14.57/14.73 tff(83,plain,
% 14.57/14.73 (![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))))),
% 14.57/14.73 inference(modus_ponens,[status(thm)],[82, 78])).
% 14.57/14.73 tff(84,plain,(
% 14.57/14.73 ![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))))),
% 14.57/14.73 inference(skolemize,[status(sab)],[83])).
% 14.57/14.73 tff(85,plain,
% 14.57/14.73 (![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))))))),
% 14.57/14.73 inference(modus_ponens,[status(thm)],[84, 77])).
% 14.57/14.73 tff(86,plain,
% 14.57/14.73 (![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))))))),
% 14.57/14.73 inference(modus_ponens,[status(thm)],[85, 75])).
% 14.57/14.73 tff(87,plain,
% 14.57/14.73 (((~![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(A!19) | (~latt_str(A!19)) | (~lattice(A!19)) | (~(empty_carrier(poset_of_lattice(A!19)) | (~strict_rel_str(poset_of_lattice(A!19))) | (~reflexive_relstr(poset_of_lattice(A!19))) | (~transitive_relstr(poset_of_lattice(A!19))) | (~antisymmetric_relstr(poset_of_lattice(A!19))))))) <=> ((~![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(A!19) | (~latt_str(A!19)) | (~lattice(A!19)) | (~(empty_carrier(poset_of_lattice(A!19)) | (~strict_rel_str(poset_of_lattice(A!19))) | (~reflexive_relstr(poset_of_lattice(A!19))) | (~transitive_relstr(poset_of_lattice(A!19))) | (~antisymmetric_relstr(poset_of_lattice(A!19))))))),
% 14.57/14.74 inference(rewrite,[status(thm)],[])).
% 14.57/14.74 tff(88,plain,
% 14.57/14.74 ((~![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(A!19) | (~latt_str(A!19)) | (~lattice(A!19)) | (~(empty_carrier(poset_of_lattice(A!19)) | (~strict_rel_str(poset_of_lattice(A!19))) | (~reflexive_relstr(poset_of_lattice(A!19))) | (~transitive_relstr(poset_of_lattice(A!19))) | (~antisymmetric_relstr(poset_of_lattice(A!19))))))),
% 14.57/14.74 inference(quant_inst,[status(thm)],[])).
% 14.57/14.74 tff(89,plain,
% 14.57/14.74 ((~![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(A!19) | (~latt_str(A!19)) | (~lattice(A!19)) | (~(empty_carrier(poset_of_lattice(A!19)) | (~strict_rel_str(poset_of_lattice(A!19))) | (~reflexive_relstr(poset_of_lattice(A!19))) | (~transitive_relstr(poset_of_lattice(A!19))) | (~antisymmetric_relstr(poset_of_lattice(A!19)))))),
% 14.57/14.74 inference(modus_ponens,[status(thm)],[88, 87])).
% 14.57/14.74 tff(90,plain,
% 14.57/14.74 (~(empty_carrier(poset_of_lattice(A!19)) | (~strict_rel_str(poset_of_lattice(A!19))) | (~reflexive_relstr(poset_of_lattice(A!19))) | (~transitive_relstr(poset_of_lattice(A!19))) | (~antisymmetric_relstr(poset_of_lattice(A!19))))),
% 14.57/14.74 inference(unit_resolution,[status(thm)],[89, 86, 12, 11, 10])).
% 14.57/14.74 tff(91,plain,
% 14.57/14.74 ((empty_carrier(poset_of_lattice(A!19)) | (~strict_rel_str(poset_of_lattice(A!19))) | (~reflexive_relstr(poset_of_lattice(A!19))) | (~transitive_relstr(poset_of_lattice(A!19))) | (~antisymmetric_relstr(poset_of_lattice(A!19)))) | (~empty_carrier(poset_of_lattice(A!19)))),
% 14.57/14.74 inference(tautology,[status(thm)],[])).
% 14.57/14.74 tff(92,plain,
% 14.57/14.74 (~empty_carrier(poset_of_lattice(A!19))),
% 14.57/14.74 inference(unit_resolution,[status(thm)],[91, 90])).
% 14.57/14.74 tff(93,plain,
% 14.57/14.74 (^[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)))))))),
% 14.57/14.74 inference(bind,[status(th)],[])).
% 14.57/14.74 tff(94,plain,
% 14.57/14.74 (![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))))))),
% 14.57/14.74 inference(quant_intro,[status(thm)],[93])).
% 14.57/14.74 tff(95,plain,
% 14.57/14.74 (^[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))))))))),
% 14.57/14.74 inference(bind,[status(th)],[])).
% 14.57/14.74 tff(96,plain,
% 14.57/14.74 (![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))))))),
% 14.57/14.74 inference(quant_intro,[status(thm)],[95])).
% 14.57/14.74 tff(97,plain,
% 14.57/14.74 (![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))))),
% 14.57/14.74 inference(rewrite,[status(thm)],[])).
% 14.57/14.74 tff(98,plain,
% 14.57/14.74 (^[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))))))),
% 14.57/14.74 inference(bind,[status(th)],[])).
% 14.57/14.74 tff(99,plain,
% 14.57/14.74 (![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))))),
% 14.57/14.74 inference(quant_intro,[status(thm)],[98])).
% 14.57/14.74 tff(100,axiom,(![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ((((strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A))) & transitive_relstr(poset_of_lattice(A))) & antisymmetric_relstr(poset_of_lattice(A))) & rel_str(poset_of_lattice(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k3_lattice3')).
% 14.57/14.74 tff(101,plain,
% 14.57/14.74 (![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))))),
% 14.57/14.74 inference(modus_ponens,[status(thm)],[100, 99])).
% 14.57/14.74 tff(102,plain,
% 14.57/14.74 (![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))))),
% 14.57/14.74 inference(modus_ponens,[status(thm)],[101, 97])).
% 14.57/14.74 tff(103,plain,(
% 14.57/14.74 ![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))))),
% 14.57/14.74 inference(skolemize,[status(sab)],[102])).
% 14.57/14.74 tff(104,plain,
% 14.57/14.74 (![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))))))),
% 14.57/14.74 inference(modus_ponens,[status(thm)],[103, 96])).
% 14.57/14.74 tff(105,plain,
% 14.57/14.74 (![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))))))),
% 14.57/14.74 inference(modus_ponens,[status(thm)],[104, 94])).
% 14.57/14.74 tff(106,plain,
% 14.57/14.74 (((~![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(A!19) | (~latt_str(A!19)) | (~lattice(A!19)) | (~((~strict_rel_str(poset_of_lattice(A!19))) | (~reflexive_relstr(poset_of_lattice(A!19))) | (~transitive_relstr(poset_of_lattice(A!19))) | (~antisymmetric_relstr(poset_of_lattice(A!19))) | (~rel_str(poset_of_lattice(A!19))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~((~strict_rel_str(poset_of_lattice(A))) | (~reflexive_relstr(poset_of_lattice(A))) | (~transitive_relstr(poset_of_lattice(A))) | (~antisymmetric_relstr(poset_of_lattice(A))) | (~rel_str(poset_of_lattice(A))))))) | empty_carrier(A!19) | (~latt_str(A!19)) | (~lattice(A!19)) | (~((~strict_rel_str(poset_of_lattice(A!19))) | (~reflexive_relstr(poset_of_lattice(A!19))) | (~transitive_relstr(poset_of_lattice(A!19))) | (~antisymmetric_relstr(poset_of_lattice(A!19))) | (~rel_str(poset_of_lattice(A!19))))))),
% 14.57/14.74 inference(rewrite,[status(thm)],[])).
% 14.57/14.74 tff(107,plain,
% 14.57/14.74 ((~![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(A!19) | (~latt_str(A!19)) | (~lattice(A!19)) | (~((~strict_rel_str(poset_of_lattice(A!19))) | (~reflexive_relstr(poset_of_lattice(A!19))) | (~transitive_relstr(poset_of_lattice(A!19))) | (~antisymmetric_relstr(poset_of_lattice(A!19))) | (~rel_str(poset_of_lattice(A!19))))))),
% 14.57/14.74 inference(quant_inst,[status(thm)],[])).
% 14.57/14.74 tff(108,plain,
% 14.57/14.74 ((~![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(A!19) | (~latt_str(A!19)) | (~lattice(A!19)) | (~((~strict_rel_str(poset_of_lattice(A!19))) | (~reflexive_relstr(poset_of_lattice(A!19))) | (~transitive_relstr(poset_of_lattice(A!19))) | (~antisymmetric_relstr(poset_of_lattice(A!19))) | (~rel_str(poset_of_lattice(A!19)))))),
% 14.57/14.74 inference(modus_ponens,[status(thm)],[107, 106])).
% 14.57/14.74 tff(109,plain,
% 14.57/14.74 (~((~strict_rel_str(poset_of_lattice(A!19))) | (~reflexive_relstr(poset_of_lattice(A!19))) | (~transitive_relstr(poset_of_lattice(A!19))) | (~antisymmetric_relstr(poset_of_lattice(A!19))) | (~rel_str(poset_of_lattice(A!19))))),
% 14.57/14.74 inference(unit_resolution,[status(thm)],[108, 105, 12, 11, 10])).
% 14.57/14.74 tff(110,plain,
% 14.57/14.74 (((~strict_rel_str(poset_of_lattice(A!19))) | (~reflexive_relstr(poset_of_lattice(A!19))) | (~transitive_relstr(poset_of_lattice(A!19))) | (~antisymmetric_relstr(poset_of_lattice(A!19))) | (~rel_str(poset_of_lattice(A!19)))) | rel_str(poset_of_lattice(A!19))),
% 14.57/14.74 inference(tautology,[status(thm)],[])).
% 14.57/14.74 tff(111,plain,
% 14.57/14.74 (rel_str(poset_of_lattice(A!19))),
% 14.57/14.74 inference(unit_resolution,[status(thm)],[110, 109])).
% 14.57/14.74 tff(112,plain,
% 14.57/14.74 ((empty_carrier(poset_of_lattice(A!19)) | (~strict_rel_str(poset_of_lattice(A!19))) | (~reflexive_relstr(poset_of_lattice(A!19))) | (~transitive_relstr(poset_of_lattice(A!19))) | (~antisymmetric_relstr(poset_of_lattice(A!19)))) | reflexive_relstr(poset_of_lattice(A!19))),
% 14.57/14.74 inference(tautology,[status(thm)],[])).
% 14.57/14.74 tff(113,plain,
% 14.57/14.74 (reflexive_relstr(poset_of_lattice(A!19))),
% 14.57/14.74 inference(unit_resolution,[status(thm)],[112, 90])).
% 14.57/14.74 tff(114,plain,
% 14.57/14.74 (^[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))))),
% 14.57/14.74 inference(bind,[status(th)],[])).
% 14.57/14.74 tff(115,plain,
% 14.57/14.74 (![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)))),
% 14.57/14.74 inference(quant_intro,[status(thm)],[114])).
% 14.57/14.74 tff(116,plain,
% 14.57/14.74 (^[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)))))),
% 14.57/14.74 inference(bind,[status(th)],[])).
% 14.57/14.74 tff(117,plain,
% 14.57/14.74 (![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)))),
% 14.57/14.74 inference(quant_intro,[status(thm)],[116])).
% 14.57/14.74 tff(118,plain,
% 14.57/14.74 (![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))))),
% 14.57/14.74 inference(rewrite,[status(thm)],[])).
% 14.57/14.74 tff(119,plain,
% 14.57/14.74 (^[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))))))),
% 14.57/14.74 inference(bind,[status(th)],[])).
% 14.57/14.74 tff(120,plain,
% 14.57/14.74 (![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))))),
% 14.57/14.74 inference(quant_intro,[status(thm)],[119])).
% 14.57/14.74 tff(121,axiom,(![A: $i, B: $i] : (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) & element(B, the_carrier(A))) => element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k4_lattice3')).
% 14.57/14.74 tff(122,plain,
% 14.57/14.74 (![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))))),
% 14.57/14.74 inference(modus_ponens,[status(thm)],[121, 120])).
% 14.57/14.74 tff(123,plain,
% 14.57/14.74 (![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))))),
% 14.57/14.74 inference(modus_ponens,[status(thm)],[122, 118])).
% 14.57/14.74 tff(124,plain,(
% 14.57/14.74 ![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))))),
% 14.57/14.74 inference(skolemize,[status(sab)],[123])).
% 14.57/14.74 tff(125,plain,
% 14.57/14.74 (![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)))),
% 14.57/14.74 inference(modus_ponens,[status(thm)],[124, 117])).
% 14.57/14.74 tff(126,plain,
% 14.57/14.74 (![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)))),
% 14.57/14.74 inference(modus_ponens,[status(thm)],[125, 115])).
% 14.57/14.74 tff(127,plain,
% 14.57/14.74 (((~![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(A!19) | (~element(C!21, the_carrier(A!19))) | (~lattice(A!19)) | (~latt_str(A!19)) | element(cast_to_el_of_LattPOSet(A!19, C!21), the_carrier(poset_of_lattice(A!19))))) <=> ((~![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(A!19) | (~element(C!21, the_carrier(A!19))) | (~lattice(A!19)) | (~latt_str(A!19)) | element(cast_to_el_of_LattPOSet(A!19, C!21), the_carrier(poset_of_lattice(A!19))))),
% 14.57/14.74 inference(rewrite,[status(thm)],[])).
% 14.57/14.74 tff(128,plain,
% 14.57/14.74 ((element(cast_to_el_of_LattPOSet(A!19, C!21), the_carrier(poset_of_lattice(A!19))) | empty_carrier(A!19) | (~element(C!21, the_carrier(A!19))) | (~lattice(A!19)) | (~latt_str(A!19))) <=> (empty_carrier(A!19) | (~element(C!21, the_carrier(A!19))) | (~lattice(A!19)) | (~latt_str(A!19)) | element(cast_to_el_of_LattPOSet(A!19, C!21), the_carrier(poset_of_lattice(A!19))))),
% 14.57/14.74 inference(rewrite,[status(thm)],[])).
% 14.57/14.74 tff(129,plain,
% 14.57/14.74 (((~![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(A!19, C!21), the_carrier(poset_of_lattice(A!19))) | empty_carrier(A!19) | (~element(C!21, the_carrier(A!19))) | (~lattice(A!19)) | (~latt_str(A!19)))) <=> ((~![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(A!19) | (~element(C!21, the_carrier(A!19))) | (~lattice(A!19)) | (~latt_str(A!19)) | element(cast_to_el_of_LattPOSet(A!19, C!21), the_carrier(poset_of_lattice(A!19)))))),
% 14.57/14.74 inference(monotonicity,[status(thm)],[128])).
% 14.57/14.74 tff(130,plain,
% 14.57/14.74 (((~![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(A!19, C!21), the_carrier(poset_of_lattice(A!19))) | empty_carrier(A!19) | (~element(C!21, the_carrier(A!19))) | (~lattice(A!19)) | (~latt_str(A!19)))) <=> ((~![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(A!19) | (~element(C!21, the_carrier(A!19))) | (~lattice(A!19)) | (~latt_str(A!19)) | element(cast_to_el_of_LattPOSet(A!19, C!21), the_carrier(poset_of_lattice(A!19))))),
% 14.57/14.74 inference(transitivity,[status(thm)],[129, 127])).
% 14.57/14.74 tff(131,plain,
% 14.57/14.74 ((~![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(A!19, C!21), the_carrier(poset_of_lattice(A!19))) | empty_carrier(A!19) | (~element(C!21, the_carrier(A!19))) | (~lattice(A!19)) | (~latt_str(A!19)))),
% 14.57/14.74 inference(quant_inst,[status(thm)],[])).
% 14.57/14.74 tff(132,plain,
% 14.57/14.74 ((~![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(A!19) | (~element(C!21, the_carrier(A!19))) | (~lattice(A!19)) | (~latt_str(A!19)) | element(cast_to_el_of_LattPOSet(A!19, C!21), the_carrier(poset_of_lattice(A!19)))),
% 14.57/14.74 inference(modus_ponens,[status(thm)],[131, 130])).
% 14.57/14.74 tff(133,plain,
% 14.57/14.74 (element(cast_to_el_of_LattPOSet(A!19, C!21), the_carrier(poset_of_lattice(A!19)))),
% 14.57/14.74 inference(unit_resolution,[status(thm)],[132, 126, 12, 11, 10, 37])).
% 14.57/14.74 tff(134,plain,
% 14.57/14.74 (((~![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(A!19) | (~element(B!20, the_carrier(A!19))) | (~lattice(A!19)) | (~latt_str(A!19)) | element(cast_to_el_of_LattPOSet(A!19, B!20), the_carrier(poset_of_lattice(A!19))))) <=> ((~![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(A!19) | (~element(B!20, the_carrier(A!19))) | (~lattice(A!19)) | (~latt_str(A!19)) | element(cast_to_el_of_LattPOSet(A!19, B!20), the_carrier(poset_of_lattice(A!19))))),
% 14.57/14.74 inference(rewrite,[status(thm)],[])).
% 14.57/14.74 tff(135,plain,
% 14.57/14.74 ((element(cast_to_el_of_LattPOSet(A!19, B!20), the_carrier(poset_of_lattice(A!19))) | empty_carrier(A!19) | (~element(B!20, the_carrier(A!19))) | (~lattice(A!19)) | (~latt_str(A!19))) <=> (empty_carrier(A!19) | (~element(B!20, the_carrier(A!19))) | (~lattice(A!19)) | (~latt_str(A!19)) | element(cast_to_el_of_LattPOSet(A!19, B!20), the_carrier(poset_of_lattice(A!19))))),
% 14.57/14.74 inference(rewrite,[status(thm)],[])).
% 14.57/14.74 tff(136,plain,
% 14.57/14.74 (((~![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(A!19, B!20), the_carrier(poset_of_lattice(A!19))) | empty_carrier(A!19) | (~element(B!20, the_carrier(A!19))) | (~lattice(A!19)) | (~latt_str(A!19)))) <=> ((~![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(A!19) | (~element(B!20, the_carrier(A!19))) | (~lattice(A!19)) | (~latt_str(A!19)) | element(cast_to_el_of_LattPOSet(A!19, B!20), the_carrier(poset_of_lattice(A!19)))))),
% 14.57/14.74 inference(monotonicity,[status(thm)],[135])).
% 14.57/14.74 tff(137,plain,
% 14.57/14.74 (((~![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(A!19, B!20), the_carrier(poset_of_lattice(A!19))) | empty_carrier(A!19) | (~element(B!20, the_carrier(A!19))) | (~lattice(A!19)) | (~latt_str(A!19)))) <=> ((~![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(A!19) | (~element(B!20, the_carrier(A!19))) | (~lattice(A!19)) | (~latt_str(A!19)) | element(cast_to_el_of_LattPOSet(A!19, B!20), the_carrier(poset_of_lattice(A!19))))),
% 14.57/14.74 inference(transitivity,[status(thm)],[136, 134])).
% 14.57/14.74 tff(138,plain,
% 14.57/14.74 ((~![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(A!19, B!20), the_carrier(poset_of_lattice(A!19))) | empty_carrier(A!19) | (~element(B!20, the_carrier(A!19))) | (~lattice(A!19)) | (~latt_str(A!19)))),
% 14.57/14.74 inference(quant_inst,[status(thm)],[])).
% 14.57/14.74 tff(139,plain,
% 14.57/14.74 ((~![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(A!19) | (~element(B!20, the_carrier(A!19))) | (~lattice(A!19)) | (~latt_str(A!19)) | element(cast_to_el_of_LattPOSet(A!19, B!20), the_carrier(poset_of_lattice(A!19)))),
% 14.57/14.74 inference(modus_ponens,[status(thm)],[138, 137])).
% 14.57/14.74 tff(140,plain,
% 14.57/14.74 (element(cast_to_el_of_LattPOSet(A!19, B!20), the_carrier(poset_of_lattice(A!19)))),
% 14.57/14.74 inference(unit_resolution,[status(thm)],[139, 126, 12, 11, 10, 43])).
% 14.57/14.74 tff(141,plain,
% 14.57/14.74 (^[A: $i, B: $i, C: $i] : refl((empty_carrier(A) | (related_reflexive(A, B, C) <=> related(A, B, C)) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A))) <=> (empty_carrier(A) | (related_reflexive(A, B, C) <=> related(A, B, C)) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A))))),
% 14.57/14.74 inference(bind,[status(th)],[])).
% 14.57/14.74 tff(142,plain,
% 14.57/14.74 (![A: $i, B: $i, C: $i] : (empty_carrier(A) | (related_reflexive(A, B, C) <=> related(A, B, C)) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A))) <=> ![A: $i, B: $i, C: $i] : (empty_carrier(A) | (related_reflexive(A, B, C) <=> related(A, B, C)) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))),
% 14.57/14.74 inference(quant_intro,[status(thm)],[141])).
% 14.57/14.74 tff(143,plain,
% 14.57/14.74 (^[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))) <=> (empty_carrier(A) | (related_reflexive(A, B, C) <=> related(A, B, C)) | (~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) | (related_reflexive(A, B, C) <=> related(A, B, C)) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))))),
% 14.57/14.74 inference(bind,[status(th)],[])).
% 14.57/14.74 tff(144,plain,
% 14.57/14.74 (![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) | (related_reflexive(A, B, C) <=> related(A, B, C)) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))),
% 14.57/14.74 inference(quant_intro,[status(thm)],[143])).
% 14.57/14.74 tff(145,plain,
% 14.57/14.74 (![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)))),
% 14.57/14.74 inference(rewrite,[status(thm)],[])).
% 14.57/14.74 tff(146,plain,
% 14.57/14.74 (^[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)))))),
% 14.57/14.74 inference(bind,[status(th)],[])).
% 14.57/14.74 tff(147,plain,
% 14.57/14.74 (![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)))),
% 14.57/14.74 inference(quant_intro,[status(thm)],[146])).
% 14.57/14.74 tff(148,axiom,(![A: $i, B: $i, C: $i] : ((((((~empty_carrier(A)) & reflexive_relstr(A)) & rel_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => (related_reflexive(A, B, C) <=> related(A, B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_r3_orders_2')).
% 14.57/14.74 tff(149,plain,
% 14.57/14.74 (![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)))),
% 14.57/14.74 inference(modus_ponens,[status(thm)],[148, 147])).
% 14.57/14.74 tff(150,plain,
% 14.57/14.74 (![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)))),
% 14.57/14.74 inference(modus_ponens,[status(thm)],[149, 145])).
% 14.57/14.74 tff(151,plain,(
% 14.57/14.74 ![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)))),
% 14.57/14.74 inference(skolemize,[status(sab)],[150])).
% 14.57/14.74 tff(152,plain,
% 14.57/14.74 (![A: $i, B: $i, C: $i] : (empty_carrier(A) | (related_reflexive(A, B, C) <=> related(A, B, C)) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))),
% 14.57/14.74 inference(modus_ponens,[status(thm)],[151, 144])).
% 14.57/14.74 tff(153,plain,
% 14.57/14.74 (![A: $i, B: $i, C: $i] : (empty_carrier(A) | (related_reflexive(A, B, C) <=> related(A, B, C)) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))),
% 14.57/14.74 inference(modus_ponens,[status(thm)],[152, 142])).
% 14.57/14.74 tff(154,plain,
% 14.57/14.74 (((~![A: $i, B: $i, C: $i] : (empty_carrier(A) | (related_reflexive(A, B, C) <=> related(A, B, C)) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))) | (empty_carrier(poset_of_lattice(A!19)) | (~reflexive_relstr(poset_of_lattice(A!19))) | (~rel_str(poset_of_lattice(A!19))) | (related_reflexive(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21)) <=> related(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21))) | (~element(cast_to_el_of_LattPOSet(A!19, C!21), the_carrier(poset_of_lattice(A!19)))) | (~element(cast_to_el_of_LattPOSet(A!19, B!20), the_carrier(poset_of_lattice(A!19)))))) <=> ((~![A: $i, B: $i, C: $i] : (empty_carrier(A) | (related_reflexive(A, B, C) <=> related(A, B, C)) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))) | empty_carrier(poset_of_lattice(A!19)) | (~reflexive_relstr(poset_of_lattice(A!19))) | (~rel_str(poset_of_lattice(A!19))) | (related_reflexive(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21)) <=> related(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21))) | (~element(cast_to_el_of_LattPOSet(A!19, C!21), the_carrier(poset_of_lattice(A!19)))) | (~element(cast_to_el_of_LattPOSet(A!19, B!20), the_carrier(poset_of_lattice(A!19)))))),
% 14.57/14.74 inference(rewrite,[status(thm)],[])).
% 14.57/14.74 tff(155,plain,
% 14.57/14.74 ((empty_carrier(poset_of_lattice(A!19)) | (related_reflexive(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21)) <=> related(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21))) | (~element(cast_to_el_of_LattPOSet(A!19, C!21), the_carrier(poset_of_lattice(A!19)))) | (~element(cast_to_el_of_LattPOSet(A!19, B!20), the_carrier(poset_of_lattice(A!19)))) | (~reflexive_relstr(poset_of_lattice(A!19))) | (~rel_str(poset_of_lattice(A!19)))) <=> (empty_carrier(poset_of_lattice(A!19)) | (~reflexive_relstr(poset_of_lattice(A!19))) | (~rel_str(poset_of_lattice(A!19))) | (related_reflexive(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21)) <=> related(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21))) | (~element(cast_to_el_of_LattPOSet(A!19, C!21), the_carrier(poset_of_lattice(A!19)))) | (~element(cast_to_el_of_LattPOSet(A!19, B!20), the_carrier(poset_of_lattice(A!19)))))),
% 14.57/14.74 inference(rewrite,[status(thm)],[])).
% 14.57/14.74 tff(156,plain,
% 14.57/14.74 (((~![A: $i, B: $i, C: $i] : (empty_carrier(A) | (related_reflexive(A, B, C) <=> related(A, B, C)) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))) | (empty_carrier(poset_of_lattice(A!19)) | (related_reflexive(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21)) <=> related(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21))) | (~element(cast_to_el_of_LattPOSet(A!19, C!21), the_carrier(poset_of_lattice(A!19)))) | (~element(cast_to_el_of_LattPOSet(A!19, B!20), the_carrier(poset_of_lattice(A!19)))) | (~reflexive_relstr(poset_of_lattice(A!19))) | (~rel_str(poset_of_lattice(A!19))))) <=> ((~![A: $i, B: $i, C: $i] : (empty_carrier(A) | (related_reflexive(A, B, C) <=> related(A, B, C)) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))) | (empty_carrier(poset_of_lattice(A!19)) | (~reflexive_relstr(poset_of_lattice(A!19))) | (~rel_str(poset_of_lattice(A!19))) | (related_reflexive(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21)) <=> related(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21))) | (~element(cast_to_el_of_LattPOSet(A!19, C!21), the_carrier(poset_of_lattice(A!19)))) | (~element(cast_to_el_of_LattPOSet(A!19, B!20), the_carrier(poset_of_lattice(A!19))))))),
% 14.57/14.74 inference(monotonicity,[status(thm)],[155])).
% 14.57/14.74 tff(157,plain,
% 14.57/14.74 (((~![A: $i, B: $i, C: $i] : (empty_carrier(A) | (related_reflexive(A, B, C) <=> related(A, B, C)) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))) | (empty_carrier(poset_of_lattice(A!19)) | (related_reflexive(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21)) <=> related(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21))) | (~element(cast_to_el_of_LattPOSet(A!19, C!21), the_carrier(poset_of_lattice(A!19)))) | (~element(cast_to_el_of_LattPOSet(A!19, B!20), the_carrier(poset_of_lattice(A!19)))) | (~reflexive_relstr(poset_of_lattice(A!19))) | (~rel_str(poset_of_lattice(A!19))))) <=> ((~![A: $i, B: $i, C: $i] : (empty_carrier(A) | (related_reflexive(A, B, C) <=> related(A, B, C)) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))) | empty_carrier(poset_of_lattice(A!19)) | (~reflexive_relstr(poset_of_lattice(A!19))) | (~rel_str(poset_of_lattice(A!19))) | (related_reflexive(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21)) <=> related(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21))) | (~element(cast_to_el_of_LattPOSet(A!19, C!21), the_carrier(poset_of_lattice(A!19)))) | (~element(cast_to_el_of_LattPOSet(A!19, B!20), the_carrier(poset_of_lattice(A!19)))))),
% 14.57/14.74 inference(transitivity,[status(thm)],[156, 154])).
% 14.57/14.74 tff(158,plain,
% 14.57/14.74 ((~![A: $i, B: $i, C: $i] : (empty_carrier(A) | (related_reflexive(A, B, C) <=> related(A, B, C)) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))) | (empty_carrier(poset_of_lattice(A!19)) | (related_reflexive(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21)) <=> related(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21))) | (~element(cast_to_el_of_LattPOSet(A!19, C!21), the_carrier(poset_of_lattice(A!19)))) | (~element(cast_to_el_of_LattPOSet(A!19, B!20), the_carrier(poset_of_lattice(A!19)))) | (~reflexive_relstr(poset_of_lattice(A!19))) | (~rel_str(poset_of_lattice(A!19))))),
% 14.57/14.74 inference(quant_inst,[status(thm)],[])).
% 14.57/14.74 tff(159,plain,
% 14.57/14.74 ((~![A: $i, B: $i, C: $i] : (empty_carrier(A) | (related_reflexive(A, B, C) <=> related(A, B, C)) | (~element(C, the_carrier(A))) | (~element(B, the_carrier(A))) | (~reflexive_relstr(A)) | (~rel_str(A)))) | empty_carrier(poset_of_lattice(A!19)) | (~reflexive_relstr(poset_of_lattice(A!19))) | (~rel_str(poset_of_lattice(A!19))) | (related_reflexive(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21)) <=> related(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21))) | (~element(cast_to_el_of_LattPOSet(A!19, C!21), the_carrier(poset_of_lattice(A!19)))) | (~element(cast_to_el_of_LattPOSet(A!19, B!20), the_carrier(poset_of_lattice(A!19))))),
% 14.57/14.74 inference(modus_ponens,[status(thm)],[158, 157])).
% 14.57/14.74 tff(160,plain,
% 14.57/14.74 (empty_carrier(poset_of_lattice(A!19)) | (~reflexive_relstr(poset_of_lattice(A!19))) | (~rel_str(poset_of_lattice(A!19))) | (related_reflexive(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21)) <=> related(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21)))),
% 14.57/14.74 inference(unit_resolution,[status(thm)],[159, 153, 140, 133])).
% 14.57/14.74 tff(161,plain,
% 14.57/14.74 (related_reflexive(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21)) <=> related(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21))),
% 14.57/14.74 inference(unit_resolution,[status(thm)],[160, 113, 111, 92])).
% 14.57/14.74 tff(162,plain,
% 14.57/14.74 ((~(related_reflexive(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21)) <=> related(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21)))) | related_reflexive(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21)) | (~related(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21)))),
% 14.57/14.74 inference(tautology,[status(thm)],[])).
% 14.57/14.74 tff(163,plain,
% 14.57/14.74 (related_reflexive(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21)) | (~related(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21)))),
% 14.57/14.74 inference(unit_resolution,[status(thm)],[162, 161])).
% 14.57/14.74 tff(164,plain,
% 14.57/14.74 (~related(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21))),
% 14.57/14.74 inference(unit_resolution,[status(thm)],[163, 73])).
% 14.57/14.74 tff(165,plain,
% 14.57/14.74 (~related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C!21)),
% 14.57/14.74 inference(modus_ponens,[status(thm)],[164, 72])).
% 14.57/14.74 tff(166,plain,
% 14.57/14.74 (the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))) = the_carrier(poset_of_lattice(A!19))),
% 14.57/14.74 inference(monotonicity,[status(thm)],[69])).
% 14.57/14.74 tff(167,plain,
% 14.57/14.74 (the_carrier(poset_of_lattice(A!19)) = the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))),
% 14.57/14.74 inference(symmetry,[status(thm)],[166])).
% 14.57/14.74 tff(168,plain,
% 14.57/14.74 (rel_str_of(the_carrier(poset_of_lattice(A!19)), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))) = rel_str_of(the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))),
% 14.57/14.74 inference(monotonicity,[status(thm)],[167])).
% 14.57/14.74 tff(169,plain,
% 14.57/14.74 (rel_str_of(the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))) = rel_str_of(the_carrier(poset_of_lattice(A!19)), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))),
% 14.57/14.74 inference(symmetry,[status(thm)],[168])).
% 14.57/14.74 tff(170,plain,
% 14.57/14.74 (strict_rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))) <=> strict_rel_str(poset_of_lattice(A!19))),
% 14.57/14.74 inference(monotonicity,[status(thm)],[69])).
% 14.57/14.74 tff(171,plain,
% 14.57/14.74 (strict_rel_str(poset_of_lattice(A!19)) <=> strict_rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))),
% 14.57/14.74 inference(symmetry,[status(thm)],[170])).
% 14.57/14.74 tff(172,plain,
% 14.57/14.74 ((empty_carrier(poset_of_lattice(A!19)) | (~strict_rel_str(poset_of_lattice(A!19))) | (~reflexive_relstr(poset_of_lattice(A!19))) | (~transitive_relstr(poset_of_lattice(A!19))) | (~antisymmetric_relstr(poset_of_lattice(A!19)))) | strict_rel_str(poset_of_lattice(A!19))),
% 14.57/14.75 inference(tautology,[status(thm)],[])).
% 14.57/14.75 tff(173,plain,
% 14.57/14.75 (strict_rel_str(poset_of_lattice(A!19))),
% 14.57/14.75 inference(unit_resolution,[status(thm)],[172, 90])).
% 14.57/14.75 tff(174,plain,
% 14.57/14.75 (strict_rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))),
% 14.57/14.75 inference(modus_ponens,[status(thm)],[173, 171])).
% 14.57/14.75 tff(175,plain,
% 14.57/14.75 (rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))) <=> rel_str(poset_of_lattice(A!19))),
% 14.57/14.75 inference(monotonicity,[status(thm)],[69])).
% 14.57/14.75 tff(176,plain,
% 14.57/14.75 (rel_str(poset_of_lattice(A!19)) <=> rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))),
% 14.57/14.75 inference(symmetry,[status(thm)],[175])).
% 14.57/14.75 tff(177,plain,
% 14.57/14.75 (rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))),
% 14.57/14.75 inference(modus_ponens,[status(thm)],[111, 176])).
% 14.57/14.75 tff(178,plain,
% 14.57/14.75 (^[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))))),
% 14.57/14.75 inference(bind,[status(th)],[])).
% 14.57/14.75 tff(179,plain,
% 14.57/14.75 (![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)))),
% 14.57/14.75 inference(quant_intro,[status(thm)],[178])).
% 14.57/14.75 tff(180,plain,
% 14.57/14.75 (![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)))),
% 14.57/14.75 inference(rewrite,[status(thm)],[])).
% 14.57/14.75 tff(181,plain,
% 14.57/14.75 (^[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)))))),
% 14.57/14.75 inference(bind,[status(th)],[])).
% 14.57/14.75 tff(182,plain,
% 14.57/14.75 (![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)))),
% 14.57/14.75 inference(quant_intro,[status(thm)],[181])).
% 14.57/14.75 tff(183,axiom,(![A: $i] : (rel_str(A) => (strict_rel_str(A) => (A = rel_str_of(the_carrier(A), the_InternalRel(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','abstractness_v1_orders_2')).
% 14.57/14.75 tff(184,plain,
% 14.57/14.75 (![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 14.57/14.75 inference(modus_ponens,[status(thm)],[183, 182])).
% 14.57/14.75 tff(185,plain,
% 14.57/14.75 (![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 14.57/14.75 inference(modus_ponens,[status(thm)],[184, 180])).
% 14.57/14.75 tff(186,plain,(
% 14.57/14.75 ![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 14.57/14.75 inference(skolemize,[status(sab)],[185])).
% 14.57/14.75 tff(187,plain,
% 14.57/14.75 (![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 14.57/14.75 inference(modus_ponens,[status(thm)],[186, 179])).
% 14.57/14.75 tff(188,plain,
% 14.57/14.75 (((~![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(A!19), k2_lattice3(A!19)))) | (rel_str_of(the_carrier(A!19), k2_lattice3(A!19)) = rel_str_of(the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (~strict_rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))) <=> ((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | (~rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))) | (rel_str_of(the_carrier(A!19), k2_lattice3(A!19)) = rel_str_of(the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (~strict_rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))),
% 14.57/14.75 inference(rewrite,[status(thm)],[])).
% 14.57/14.75 tff(189,plain,
% 14.57/14.75 (((rel_str_of(the_carrier(A!19), k2_lattice3(A!19)) = rel_str_of(the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (~strict_rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))) | (~rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) <=> ((~rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))) | (rel_str_of(the_carrier(A!19), k2_lattice3(A!19)) = rel_str_of(the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (~strict_rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))),
% 14.57/14.75 inference(rewrite,[status(thm)],[])).
% 14.57/14.75 tff(190,plain,
% 14.57/14.75 (((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | ((rel_str_of(the_carrier(A!19), k2_lattice3(A!19)) = rel_str_of(the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (~strict_rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))) | (~rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))) <=> ((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | ((~rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))) | (rel_str_of(the_carrier(A!19), k2_lattice3(A!19)) = rel_str_of(the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (~strict_rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))))),
% 14.57/14.75 inference(monotonicity,[status(thm)],[189])).
% 14.57/14.75 tff(191,plain,
% 14.57/14.75 (((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | ((rel_str_of(the_carrier(A!19), k2_lattice3(A!19)) = rel_str_of(the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (~strict_rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))) | (~rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))) <=> ((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | (~rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))) | (rel_str_of(the_carrier(A!19), k2_lattice3(A!19)) = rel_str_of(the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (~strict_rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))),
% 14.57/14.75 inference(transitivity,[status(thm)],[190, 188])).
% 14.57/14.75 tff(192,plain,
% 14.57/14.75 ((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | ((rel_str_of(the_carrier(A!19), k2_lattice3(A!19)) = rel_str_of(the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (~strict_rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))) | (~rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))),
% 14.57/14.75 inference(quant_inst,[status(thm)],[])).
% 14.57/14.75 tff(193,plain,
% 14.57/14.75 ((~![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(A!19), k2_lattice3(A!19)))) | (rel_str_of(the_carrier(A!19), k2_lattice3(A!19)) = rel_str_of(the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (~strict_rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))),
% 14.57/14.75 inference(modus_ponens,[status(thm)],[192, 191])).
% 14.57/14.75 tff(194,plain,
% 14.57/14.75 ((~rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))) | (rel_str_of(the_carrier(A!19), k2_lattice3(A!19)) = rel_str_of(the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (~strict_rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))),
% 14.57/14.75 inference(unit_resolution,[status(thm)],[193, 187])).
% 14.57/14.75 tff(195,plain,
% 14.57/14.75 (rel_str_of(the_carrier(A!19), k2_lattice3(A!19)) = rel_str_of(the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))),
% 14.57/14.75 inference(unit_resolution,[status(thm)],[194, 177, 174])).
% 14.57/14.75 tff(196,plain,
% 14.57/14.75 (^[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))))),
% 14.57/14.75 inference(bind,[status(th)],[])).
% 14.57/14.75 tff(197,plain,
% 14.57/14.75 (![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)))),
% 14.57/14.75 inference(quant_intro,[status(thm)],[196])).
% 14.57/14.75 tff(198,plain,
% 14.57/14.75 (^[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)))))),
% 14.57/14.75 inference(bind,[status(th)],[])).
% 14.57/14.75 tff(199,plain,
% 14.57/14.75 (![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)))),
% 14.57/14.75 inference(quant_intro,[status(thm)],[198])).
% 14.57/14.75 tff(200,plain,
% 14.57/14.75 (![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)))),
% 14.57/14.75 inference(rewrite,[status(thm)],[])).
% 14.57/14.75 tff(201,plain,
% 14.57/14.75 (^[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)))))),
% 14.57/14.75 inference(bind,[status(th)],[])).
% 14.57/14.75 tff(202,plain,
% 14.57/14.75 (![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)))),
% 14.57/14.75 inference(quant_intro,[status(thm)],[201])).
% 14.57/14.75 tff(203,axiom,(![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => (k2_lattice3(A) = relation_of_lattice(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k2_lattice3')).
% 14.57/14.75 tff(204,plain,
% 14.57/14.75 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (k2_lattice3(A) = relation_of_lattice(A)))),
% 14.57/14.75 inference(modus_ponens,[status(thm)],[203, 202])).
% 14.57/14.75 tff(205,plain,
% 14.57/14.75 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (k2_lattice3(A) = relation_of_lattice(A)))),
% 14.57/14.75 inference(modus_ponens,[status(thm)],[204, 200])).
% 14.57/14.75 tff(206,plain,(
% 14.57/14.75 ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (k2_lattice3(A) = relation_of_lattice(A)))),
% 14.57/14.75 inference(skolemize,[status(sab)],[205])).
% 14.57/14.75 tff(207,plain,
% 14.57/14.75 (![A: $i] : (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))),
% 14.57/14.75 inference(modus_ponens,[status(thm)],[206, 199])).
% 14.57/14.75 tff(208,plain,
% 14.57/14.75 (![A: $i] : (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))),
% 14.57/14.75 inference(modus_ponens,[status(thm)],[207, 197])).
% 14.57/14.75 tff(209,plain,
% 14.57/14.75 (((~![A: $i] : (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))) | (empty_carrier(A!19) | (~lattice(A!19)) | (~latt_str(A!19)) | (k2_lattice3(A!19) = relation_of_lattice(A!19)))) <=> ((~![A: $i] : (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))) | empty_carrier(A!19) | (~lattice(A!19)) | (~latt_str(A!19)) | (k2_lattice3(A!19) = relation_of_lattice(A!19)))),
% 14.57/14.75 inference(rewrite,[status(thm)],[])).
% 14.57/14.75 tff(210,plain,
% 14.57/14.75 ((empty_carrier(A!19) | (k2_lattice3(A!19) = relation_of_lattice(A!19)) | (~latt_str(A!19)) | (~lattice(A!19))) <=> (empty_carrier(A!19) | (~lattice(A!19)) | (~latt_str(A!19)) | (k2_lattice3(A!19) = relation_of_lattice(A!19)))),
% 14.57/14.75 inference(rewrite,[status(thm)],[])).
% 14.57/14.75 tff(211,plain,
% 14.57/14.75 (((~![A: $i] : (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))) | (empty_carrier(A!19) | (k2_lattice3(A!19) = relation_of_lattice(A!19)) | (~latt_str(A!19)) | (~lattice(A!19)))) <=> ((~![A: $i] : (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))) | (empty_carrier(A!19) | (~lattice(A!19)) | (~latt_str(A!19)) | (k2_lattice3(A!19) = relation_of_lattice(A!19))))),
% 14.57/14.75 inference(monotonicity,[status(thm)],[210])).
% 14.57/14.75 tff(212,plain,
% 14.57/14.75 (((~![A: $i] : (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))) | (empty_carrier(A!19) | (k2_lattice3(A!19) = relation_of_lattice(A!19)) | (~latt_str(A!19)) | (~lattice(A!19)))) <=> ((~![A: $i] : (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))) | empty_carrier(A!19) | (~lattice(A!19)) | (~latt_str(A!19)) | (k2_lattice3(A!19) = relation_of_lattice(A!19)))),
% 14.57/14.75 inference(transitivity,[status(thm)],[211, 209])).
% 14.57/14.75 tff(213,plain,
% 14.57/14.75 ((~![A: $i] : (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))) | (empty_carrier(A!19) | (k2_lattice3(A!19) = relation_of_lattice(A!19)) | (~latt_str(A!19)) | (~lattice(A!19)))),
% 14.57/14.75 inference(quant_inst,[status(thm)],[])).
% 14.57/14.75 tff(214,plain,
% 14.57/14.75 ((~![A: $i] : (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))) | empty_carrier(A!19) | (~lattice(A!19)) | (~latt_str(A!19)) | (k2_lattice3(A!19) = relation_of_lattice(A!19))),
% 14.57/14.75 inference(modus_ponens,[status(thm)],[213, 212])).
% 14.57/14.75 tff(215,plain,
% 14.57/14.75 (k2_lattice3(A!19) = relation_of_lattice(A!19)),
% 14.57/14.75 inference(unit_resolution,[status(thm)],[214, 208, 12, 11, 10])).
% 14.57/14.75 tff(216,plain,
% 14.57/14.75 (relation_of_lattice(A!19) = k2_lattice3(A!19)),
% 14.57/14.75 inference(symmetry,[status(thm)],[215])).
% 14.57/14.75 tff(217,plain,
% 14.57/14.75 (rel_str_of(the_carrier(A!19), relation_of_lattice(A!19)) = rel_str_of(the_carrier(A!19), k2_lattice3(A!19))),
% 14.57/14.75 inference(monotonicity,[status(thm)],[216])).
% 14.57/14.75 tff(218,plain,
% 14.57/14.75 (rel_str_of(the_carrier(A!19), relation_of_lattice(A!19)) = rel_str_of(the_carrier(poset_of_lattice(A!19)), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))),
% 14.57/14.75 inference(transitivity,[status(thm)],[217, 195, 169])).
% 14.57/14.75 tff(219,plain,
% 14.57/14.75 (^[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)))),
% 14.57/14.75 inference(bind,[status(th)],[])).
% 14.57/14.75 tff(220,plain,
% 14.57/14.75 (![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))),
% 14.57/14.75 inference(quant_intro,[status(thm)],[219])).
% 14.57/14.75 tff(221,plain,
% 14.57/14.75 (![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))),
% 14.57/14.75 inference(rewrite,[status(thm)],[])).
% 14.57/14.75 tff(222,axiom,(![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 14.57/14.75 tff(223,plain,
% 14.57/14.75 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 14.57/14.75 inference(modus_ponens,[status(thm)],[222, 221])).
% 14.57/14.75 tff(224,plain,(
% 14.57/14.75 ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 14.57/14.75 inference(skolemize,[status(sab)],[223])).
% 14.57/14.75 tff(225,plain,
% 14.57/14.75 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 14.57/14.75 inference(modus_ponens,[status(thm)],[224, 220])).
% 14.57/14.75 tff(226,plain,
% 14.57/14.75 ((~![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(A!19), the_carrier(A!19), the_carrier(A!19)) <=> relation_of2(relation_of_lattice(A!19), the_carrier(A!19), the_carrier(A!19)))),
% 14.57/14.75 inference(quant_inst,[status(thm)],[])).
% 14.57/14.75 tff(227,plain,
% 14.57/14.75 (relation_of2_as_subset(relation_of_lattice(A!19), the_carrier(A!19), the_carrier(A!19)) <=> relation_of2(relation_of_lattice(A!19), the_carrier(A!19), the_carrier(A!19))),
% 14.57/14.75 inference(unit_resolution,[status(thm)],[226, 225])).
% 14.57/14.75 tff(228,plain,
% 14.57/14.75 (relation_of2_as_subset(relation_of_lattice(A!19), the_carrier(A!19), the_carrier(A!19)) <=> relation_of2_as_subset(k2_lattice3(A!19), the_carrier(A!19), the_carrier(A!19))),
% 14.57/14.75 inference(monotonicity,[status(thm)],[216])).
% 14.57/14.75 tff(229,plain,
% 14.57/14.75 (relation_of2_as_subset(k2_lattice3(A!19), the_carrier(A!19), the_carrier(A!19)) <=> relation_of2_as_subset(relation_of_lattice(A!19), the_carrier(A!19), the_carrier(A!19))),
% 14.57/14.75 inference(symmetry,[status(thm)],[228])).
% 14.57/14.75 tff(230,plain,
% 14.57/14.75 (^[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)))))))),
% 14.57/14.75 inference(bind,[status(th)],[])).
% 14.57/14.75 tff(231,plain,
% 14.57/14.75 (![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))))))),
% 14.57/14.75 inference(quant_intro,[status(thm)],[230])).
% 14.57/14.75 tff(232,plain,
% 14.57/14.75 (^[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))))))))),
% 14.57/14.75 inference(bind,[status(th)],[])).
% 14.57/14.75 tff(233,plain,
% 14.57/14.75 (![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))))))),
% 14.57/14.75 inference(quant_intro,[status(thm)],[232])).
% 14.57/14.75 tff(234,plain,
% 14.57/14.75 (![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))))),
% 14.57/14.75 inference(rewrite,[status(thm)],[])).
% 14.57/14.75 tff(235,plain,
% 14.57/14.75 (^[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))))))),
% 14.57/14.75 inference(bind,[status(th)],[])).
% 14.57/14.75 tff(236,plain,
% 14.57/14.75 (![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))))),
% 14.57/14.75 inference(quant_intro,[status(thm)],[235])).
% 14.57/14.75 tff(237,axiom,(![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ((((reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A))) & transitive(k2_lattice3(A))) & v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A))) & relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k2_lattice3')).
% 14.57/14.75 tff(238,plain,
% 14.57/14.75 (![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))))),
% 14.57/14.75 inference(modus_ponens,[status(thm)],[237, 236])).
% 14.57/14.75 tff(239,plain,
% 14.57/14.75 (![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))))),
% 14.57/14.75 inference(modus_ponens,[status(thm)],[238, 234])).
% 14.57/14.75 tff(240,plain,(
% 14.57/14.75 ![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))))),
% 14.57/14.75 inference(skolemize,[status(sab)],[239])).
% 14.57/14.75 tff(241,plain,
% 14.57/14.75 (![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))))))),
% 14.57/14.75 inference(modus_ponens,[status(thm)],[240, 233])).
% 14.57/14.75 tff(242,plain,
% 14.57/14.75 (![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))))))),
% 14.57/14.75 inference(modus_ponens,[status(thm)],[241, 231])).
% 14.57/14.75 tff(243,plain,
% 14.57/14.75 (((~![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(A!19) | (~latt_str(A!19)) | (~lattice(A!19)) | (~((~reflexive(k2_lattice3(A!19))) | (~antisymmetric(k2_lattice3(A!19))) | (~transitive(k2_lattice3(A!19))) | (~v1_partfun1(k2_lattice3(A!19), the_carrier(A!19), the_carrier(A!19))) | (~relation_of2_as_subset(k2_lattice3(A!19), the_carrier(A!19), the_carrier(A!19))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~((~reflexive(k2_lattice3(A))) | (~antisymmetric(k2_lattice3(A))) | (~transitive(k2_lattice3(A))) | (~v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A))) | (~relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A))))))) | empty_carrier(A!19) | (~latt_str(A!19)) | (~lattice(A!19)) | (~((~reflexive(k2_lattice3(A!19))) | (~antisymmetric(k2_lattice3(A!19))) | (~transitive(k2_lattice3(A!19))) | (~v1_partfun1(k2_lattice3(A!19), the_carrier(A!19), the_carrier(A!19))) | (~relation_of2_as_subset(k2_lattice3(A!19), the_carrier(A!19), the_carrier(A!19))))))),
% 14.57/14.75 inference(rewrite,[status(thm)],[])).
% 14.57/14.75 tff(244,plain,
% 14.57/14.75 ((~![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(A!19) | (~latt_str(A!19)) | (~lattice(A!19)) | (~((~reflexive(k2_lattice3(A!19))) | (~antisymmetric(k2_lattice3(A!19))) | (~transitive(k2_lattice3(A!19))) | (~v1_partfun1(k2_lattice3(A!19), the_carrier(A!19), the_carrier(A!19))) | (~relation_of2_as_subset(k2_lattice3(A!19), the_carrier(A!19), the_carrier(A!19))))))),
% 14.57/14.75 inference(quant_inst,[status(thm)],[])).
% 14.57/14.75 tff(245,plain,
% 14.57/14.75 ((~![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(A!19) | (~latt_str(A!19)) | (~lattice(A!19)) | (~((~reflexive(k2_lattice3(A!19))) | (~antisymmetric(k2_lattice3(A!19))) | (~transitive(k2_lattice3(A!19))) | (~v1_partfun1(k2_lattice3(A!19), the_carrier(A!19), the_carrier(A!19))) | (~relation_of2_as_subset(k2_lattice3(A!19), the_carrier(A!19), the_carrier(A!19)))))),
% 14.57/14.75 inference(modus_ponens,[status(thm)],[244, 243])).
% 14.57/14.75 tff(246,plain,
% 14.57/14.75 (~((~reflexive(k2_lattice3(A!19))) | (~antisymmetric(k2_lattice3(A!19))) | (~transitive(k2_lattice3(A!19))) | (~v1_partfun1(k2_lattice3(A!19), the_carrier(A!19), the_carrier(A!19))) | (~relation_of2_as_subset(k2_lattice3(A!19), the_carrier(A!19), the_carrier(A!19))))),
% 14.57/14.75 inference(unit_resolution,[status(thm)],[245, 242, 12, 11, 10])).
% 14.57/14.75 tff(247,plain,
% 14.57/14.75 (((~reflexive(k2_lattice3(A!19))) | (~antisymmetric(k2_lattice3(A!19))) | (~transitive(k2_lattice3(A!19))) | (~v1_partfun1(k2_lattice3(A!19), the_carrier(A!19), the_carrier(A!19))) | (~relation_of2_as_subset(k2_lattice3(A!19), the_carrier(A!19), the_carrier(A!19)))) | relation_of2_as_subset(k2_lattice3(A!19), the_carrier(A!19), the_carrier(A!19))),
% 14.57/14.75 inference(tautology,[status(thm)],[])).
% 14.57/14.75 tff(248,plain,
% 14.57/14.75 (relation_of2_as_subset(k2_lattice3(A!19), the_carrier(A!19), the_carrier(A!19))),
% 14.57/14.75 inference(unit_resolution,[status(thm)],[247, 246])).
% 14.57/14.75 tff(249,plain,
% 14.57/14.75 (relation_of2_as_subset(relation_of_lattice(A!19), the_carrier(A!19), the_carrier(A!19))),
% 14.57/14.75 inference(modus_ponens,[status(thm)],[248, 229])).
% 14.57/14.75 tff(250,plain,
% 14.57/14.75 ((~(relation_of2_as_subset(relation_of_lattice(A!19), the_carrier(A!19), the_carrier(A!19)) <=> relation_of2(relation_of_lattice(A!19), the_carrier(A!19), the_carrier(A!19)))) | (~relation_of2_as_subset(relation_of_lattice(A!19), the_carrier(A!19), the_carrier(A!19))) | relation_of2(relation_of_lattice(A!19), the_carrier(A!19), the_carrier(A!19))),
% 14.57/14.75 inference(tautology,[status(thm)],[])).
% 14.57/14.75 tff(251,plain,
% 14.57/14.75 (relation_of2(relation_of_lattice(A!19), the_carrier(A!19), the_carrier(A!19))),
% 14.57/14.75 inference(unit_resolution,[status(thm)],[250, 249, 227])).
% 14.57/14.75 tff(252,plain,
% 14.57/14.75 (^[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)))))))),
% 14.57/14.75 inference(bind,[status(th)],[])).
% 14.57/14.75 tff(253,plain,
% 14.57/14.75 (![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))))))),
% 14.57/14.75 inference(quant_intro,[status(thm)],[252])).
% 14.57/14.75 tff(254,plain,
% 14.57/14.75 (^[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)))))))),
% 14.57/14.75 inference(bind,[status(th)],[])).
% 14.57/14.75 tff(255,plain,
% 14.57/14.75 (![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))))))),
% 14.57/14.75 inference(quant_intro,[status(thm)],[254])).
% 14.57/14.75 tff(256,plain,
% 14.57/14.75 (![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))))))),
% 14.57/14.75 inference(transitivity,[status(thm)],[255, 253])).
% 14.57/14.75 tff(257,plain,
% 14.57/14.75 (^[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)))))))),
% 14.57/14.75 inference(bind,[status(th)],[])).
% 14.57/14.75 tff(258,plain,
% 14.57/14.75 (![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))))))),
% 14.57/14.75 inference(quant_intro,[status(thm)],[257])).
% 14.57/14.75 tff(259,plain,
% 14.57/14.75 (![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))))),
% 14.57/14.75 inference(rewrite,[status(thm)],[])).
% 14.57/14.75 tff(260,plain,
% 14.57/14.75 (^[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))))))),
% 14.57/14.75 inference(bind,[status(th)],[])).
% 14.57/14.75 tff(261,plain,
% 14.57/14.75 (![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))))),
% 14.57/14.75 inference(quant_intro,[status(thm)],[260])).
% 14.57/14.75 tff(262,axiom,(![A: $i, B: $i] : (relation_of2(B, A, A) => ![C: $i, D: $i] : ((rel_str_of(A, B) = rel_str_of(C, D)) => ((A = C) & (B = D))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','free_g1_orders_2')).
% 14.57/14.75 tff(263,plain,
% 14.57/14.75 (![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))))),
% 14.57/14.75 inference(modus_ponens,[status(thm)],[262, 261])).
% 14.57/14.75 tff(264,plain,
% 14.57/14.75 (![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))))),
% 14.57/14.75 inference(modus_ponens,[status(thm)],[263, 259])).
% 14.57/14.75 tff(265,plain,(
% 14.57/14.75 ![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))))),
% 14.57/14.75 inference(skolemize,[status(sab)],[264])).
% 14.57/14.75 tff(266,plain,
% 14.57/14.75 (![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))))))),
% 14.57/14.75 inference(modus_ponens,[status(thm)],[265, 258])).
% 14.57/14.75 tff(267,plain,
% 14.57/14.75 (![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))))))),
% 14.57/14.75 inference(modus_ponens,[status(thm)],[266, 256])).
% 14.57/14.75 tff(268,plain,
% 14.57/14.75 (((~![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(A!19), the_carrier(A!19), the_carrier(A!19))) | ![C: $i, D: $i] : ((~(rel_str_of(the_carrier(A!19), relation_of_lattice(A!19)) = rel_str_of(C, D))) | (~((~(the_carrier(A!19) = C)) | (~(relation_of_lattice(A!19) = 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(A!19), the_carrier(A!19), the_carrier(A!19))) | ![C: $i, D: $i] : ((~(rel_str_of(the_carrier(A!19), relation_of_lattice(A!19)) = rel_str_of(C, D))) | (~((~(the_carrier(A!19) = C)) | (~(relation_of_lattice(A!19) = D))))))),
% 14.57/14.75 inference(rewrite,[status(thm)],[])).
% 14.57/14.75 tff(269,plain,
% 14.57/14.75 ((~![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(A!19), the_carrier(A!19), the_carrier(A!19))) | ![C: $i, D: $i] : ((~(rel_str_of(the_carrier(A!19), relation_of_lattice(A!19)) = rel_str_of(C, D))) | (~((~(the_carrier(A!19) = C)) | (~(relation_of_lattice(A!19) = D))))))),
% 14.57/14.75 inference(quant_inst,[status(thm)],[])).
% 14.57/14.75 tff(270,plain,
% 14.57/14.75 ((~![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(A!19), the_carrier(A!19), the_carrier(A!19))) | ![C: $i, D: $i] : ((~(rel_str_of(the_carrier(A!19), relation_of_lattice(A!19)) = rel_str_of(C, D))) | (~((~(the_carrier(A!19) = C)) | (~(relation_of_lattice(A!19) = D)))))),
% 14.57/14.75 inference(modus_ponens,[status(thm)],[269, 268])).
% 14.57/14.75 tff(271,plain,
% 14.57/14.75 ((~relation_of2(relation_of_lattice(A!19), the_carrier(A!19), the_carrier(A!19))) | ![C: $i, D: $i] : ((~(rel_str_of(the_carrier(A!19), relation_of_lattice(A!19)) = rel_str_of(C, D))) | (~((~(the_carrier(A!19) = C)) | (~(relation_of_lattice(A!19) = D)))))),
% 14.57/14.75 inference(unit_resolution,[status(thm)],[270, 267])).
% 14.57/14.75 tff(272,plain,
% 14.57/14.75 (![C: $i, D: $i] : ((~(rel_str_of(the_carrier(A!19), relation_of_lattice(A!19)) = rel_str_of(C, D))) | (~((~(the_carrier(A!19) = C)) | (~(relation_of_lattice(A!19) = D)))))),
% 14.57/14.75 inference(unit_resolution,[status(thm)],[271, 251])).
% 14.57/14.75 tff(273,plain,
% 14.57/14.75 (((~![C: $i, D: $i] : ((~(rel_str_of(the_carrier(A!19), relation_of_lattice(A!19)) = rel_str_of(C, D))) | (~((~(the_carrier(A!19) = C)) | (~(relation_of_lattice(A!19) = D)))))) | ((~(rel_str_of(the_carrier(A!19), relation_of_lattice(A!19)) = rel_str_of(the_carrier(poset_of_lattice(A!19)), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))) | (~((~(the_carrier(A!19) = the_carrier(poset_of_lattice(A!19)))) | (~(relation_of_lattice(A!19) = the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))))))) <=> ((~![C: $i, D: $i] : ((~(rel_str_of(the_carrier(A!19), relation_of_lattice(A!19)) = rel_str_of(C, D))) | (~((~(the_carrier(A!19) = C)) | (~(relation_of_lattice(A!19) = D)))))) | (~(rel_str_of(the_carrier(A!19), relation_of_lattice(A!19)) = rel_str_of(the_carrier(poset_of_lattice(A!19)), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))) | (~((~(the_carrier(A!19) = the_carrier(poset_of_lattice(A!19)))) | (~(relation_of_lattice(A!19) = the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))))))),
% 14.57/14.75 inference(rewrite,[status(thm)],[])).
% 14.57/14.75 tff(274,plain,
% 14.57/14.75 ((~![C: $i, D: $i] : ((~(rel_str_of(the_carrier(A!19), relation_of_lattice(A!19)) = rel_str_of(C, D))) | (~((~(the_carrier(A!19) = C)) | (~(relation_of_lattice(A!19) = D)))))) | ((~(rel_str_of(the_carrier(A!19), relation_of_lattice(A!19)) = rel_str_of(the_carrier(poset_of_lattice(A!19)), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))) | (~((~(the_carrier(A!19) = the_carrier(poset_of_lattice(A!19)))) | (~(relation_of_lattice(A!19) = the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))))))),
% 14.57/14.75 inference(quant_inst,[status(thm)],[])).
% 14.57/14.75 tff(275,plain,
% 14.57/14.75 ((~![C: $i, D: $i] : ((~(rel_str_of(the_carrier(A!19), relation_of_lattice(A!19)) = rel_str_of(C, D))) | (~((~(the_carrier(A!19) = C)) | (~(relation_of_lattice(A!19) = D)))))) | (~(rel_str_of(the_carrier(A!19), relation_of_lattice(A!19)) = rel_str_of(the_carrier(poset_of_lattice(A!19)), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))) | (~((~(the_carrier(A!19) = the_carrier(poset_of_lattice(A!19)))) | (~(relation_of_lattice(A!19) = the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))))),
% 14.57/14.75 inference(modus_ponens,[status(thm)],[274, 273])).
% 14.57/14.75 tff(276,plain,
% 14.57/14.75 ((~(rel_str_of(the_carrier(A!19), relation_of_lattice(A!19)) = rel_str_of(the_carrier(poset_of_lattice(A!19)), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))) | (~((~(the_carrier(A!19) = the_carrier(poset_of_lattice(A!19)))) | (~(relation_of_lattice(A!19) = the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))))),
% 14.57/14.75 inference(unit_resolution,[status(thm)],[275, 272])).
% 14.57/14.75 tff(277,plain,
% 14.57/14.75 (~((~(the_carrier(A!19) = the_carrier(poset_of_lattice(A!19)))) | (~(relation_of_lattice(A!19) = the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))))),
% 14.57/14.75 inference(unit_resolution,[status(thm)],[276, 218])).
% 14.57/14.75 tff(278,plain,
% 14.57/14.75 (((~(the_carrier(A!19) = the_carrier(poset_of_lattice(A!19)))) | (~(relation_of_lattice(A!19) = the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))) | (relation_of_lattice(A!19) = the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))),
% 14.57/14.75 inference(tautology,[status(thm)],[])).
% 14.57/14.75 tff(279,plain,
% 14.57/14.75 (relation_of_lattice(A!19) = the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))),
% 14.57/14.75 inference(unit_resolution,[status(thm)],[278, 277])).
% 14.57/14.75 tff(280,plain,
% 14.57/14.75 (the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))) = relation_of_lattice(A!19)),
% 14.57/14.75 inference(symmetry,[status(thm)],[279])).
% 14.57/14.75 tff(281,plain,
% 14.57/14.75 (^[A: $i] : refl(((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A))))) <=> ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A))))))),
% 14.57/14.75 inference(bind,[status(th)],[])).
% 14.57/14.75 tff(282,plain,
% 14.57/14.75 (![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A))))) <=> ![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))),
% 14.57/14.75 inference(quant_intro,[status(thm)],[281])).
% 14.57/14.75 tff(283,plain,
% 14.57/14.75 (^[A: $i] : rewrite(((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A))) <=> ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A))))))),
% 14.57/14.75 inference(bind,[status(th)],[])).
% 14.57/14.75 tff(284,plain,
% 14.57/14.75 (![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A))) <=> ![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))),
% 14.57/14.75 inference(quant_intro,[status(thm)],[283])).
% 14.57/14.75 tff(285,plain,
% 14.57/14.75 (![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A))) <=> ![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A)))),
% 14.57/14.76 inference(rewrite,[status(thm)],[])).
% 14.57/14.76 tff(286,plain,
% 14.57/14.76 (^[A: $i] : rewrite((latt_str(A) => (meet_semilatt_str(A) & join_semilatt_str(A))) <=> ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A))))),
% 14.57/14.76 inference(bind,[status(th)],[])).
% 14.57/14.76 tff(287,plain,
% 14.57/14.76 (![A: $i] : (latt_str(A) => (meet_semilatt_str(A) & join_semilatt_str(A))) <=> ![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A)))),
% 14.57/14.76 inference(quant_intro,[status(thm)],[286])).
% 14.57/14.76 tff(288,axiom,(![A: $i] : (latt_str(A) => (meet_semilatt_str(A) & join_semilatt_str(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l3_lattices')).
% 14.57/14.76 tff(289,plain,
% 14.57/14.76 (![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A)))),
% 14.57/14.76 inference(modus_ponens,[status(thm)],[288, 287])).
% 14.57/14.76 tff(290,plain,
% 14.57/14.76 (![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A)))),
% 14.57/14.76 inference(modus_ponens,[status(thm)],[289, 285])).
% 14.57/14.76 tff(291,plain,(
% 14.57/14.76 ![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A)))),
% 14.57/14.76 inference(skolemize,[status(sab)],[290])).
% 14.57/14.76 tff(292,plain,
% 14.57/14.76 (![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))),
% 14.57/14.76 inference(modus_ponens,[status(thm)],[291, 284])).
% 14.57/14.76 tff(293,plain,
% 14.57/14.76 (![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))),
% 14.57/14.76 inference(modus_ponens,[status(thm)],[292, 282])).
% 14.57/14.76 tff(294,plain,
% 14.57/14.76 (((~![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))) | ((~latt_str(A!19)) | (~((~meet_semilatt_str(A!19)) | (~join_semilatt_str(A!19)))))) <=> ((~![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))) | (~latt_str(A!19)) | (~((~meet_semilatt_str(A!19)) | (~join_semilatt_str(A!19)))))),
% 14.57/14.76 inference(rewrite,[status(thm)],[])).
% 14.57/14.76 tff(295,plain,
% 14.57/14.76 ((~![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))) | ((~latt_str(A!19)) | (~((~meet_semilatt_str(A!19)) | (~join_semilatt_str(A!19)))))),
% 14.57/14.76 inference(quant_inst,[status(thm)],[])).
% 14.57/14.76 tff(296,plain,
% 14.57/14.76 ((~![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))) | (~latt_str(A!19)) | (~((~meet_semilatt_str(A!19)) | (~join_semilatt_str(A!19))))),
% 14.57/14.76 inference(modus_ponens,[status(thm)],[295, 294])).
% 14.57/14.76 tff(297,plain,
% 14.57/14.76 (~((~meet_semilatt_str(A!19)) | (~join_semilatt_str(A!19)))),
% 14.57/14.76 inference(unit_resolution,[status(thm)],[296, 293, 10])).
% 14.57/14.76 tff(298,plain,
% 14.57/14.76 (((~meet_semilatt_str(A!19)) | (~join_semilatt_str(A!19))) | join_semilatt_str(A!19)),
% 14.57/14.76 inference(tautology,[status(thm)],[])).
% 14.57/14.76 tff(299,plain,
% 14.57/14.76 (join_semilatt_str(A!19)),
% 14.57/14.76 inference(unit_resolution,[status(thm)],[298, 297])).
% 14.57/14.76 tff(300,plain,
% 14.57/14.76 (^[A: $i] : refl((one_sorted_str(A) | (~join_semilatt_str(A))) <=> (one_sorted_str(A) | (~join_semilatt_str(A))))),
% 14.57/14.76 inference(bind,[status(th)],[])).
% 14.57/14.76 tff(301,plain,
% 14.57/14.76 (![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A))) <=> ![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A)))),
% 14.57/14.76 inference(quant_intro,[status(thm)],[300])).
% 14.57/14.76 tff(302,plain,
% 14.57/14.76 (![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A))) <=> ![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A)))),
% 14.57/14.76 inference(rewrite,[status(thm)],[])).
% 14.57/14.76 tff(303,plain,
% 14.57/14.76 (^[A: $i] : rewrite((join_semilatt_str(A) => one_sorted_str(A)) <=> (one_sorted_str(A) | (~join_semilatt_str(A))))),
% 14.57/14.76 inference(bind,[status(th)],[])).
% 14.57/14.76 tff(304,plain,
% 14.57/14.76 (![A: $i] : (join_semilatt_str(A) => one_sorted_str(A)) <=> ![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A)))),
% 14.57/14.76 inference(quant_intro,[status(thm)],[303])).
% 14.57/14.76 tff(305,axiom,(![A: $i] : (join_semilatt_str(A) => one_sorted_str(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l2_lattices')).
% 14.57/14.76 tff(306,plain,
% 14.57/14.76 (![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A)))),
% 14.57/14.76 inference(modus_ponens,[status(thm)],[305, 304])).
% 14.57/14.76 tff(307,plain,
% 14.57/14.76 (![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A)))),
% 14.57/14.76 inference(modus_ponens,[status(thm)],[306, 302])).
% 14.57/14.76 tff(308,plain,(
% 14.57/14.76 ![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A)))),
% 14.57/14.76 inference(skolemize,[status(sab)],[307])).
% 14.57/14.76 tff(309,plain,
% 14.57/14.76 (![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A)))),
% 14.57/14.76 inference(modus_ponens,[status(thm)],[308, 301])).
% 14.57/14.76 tff(310,plain,
% 14.57/14.76 (((~![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A)))) | (one_sorted_str(A!19) | (~join_semilatt_str(A!19)))) <=> ((~![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A)))) | one_sorted_str(A!19) | (~join_semilatt_str(A!19)))),
% 14.57/14.76 inference(rewrite,[status(thm)],[])).
% 14.57/14.76 tff(311,plain,
% 14.57/14.76 ((~![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A)))) | (one_sorted_str(A!19) | (~join_semilatt_str(A!19)))),
% 14.57/14.76 inference(quant_inst,[status(thm)],[])).
% 14.57/14.76 tff(312,plain,
% 14.57/14.76 ((~![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A)))) | one_sorted_str(A!19) | (~join_semilatt_str(A!19))),
% 14.57/14.76 inference(modus_ponens,[status(thm)],[311, 310])).
% 14.57/14.76 tff(313,plain,
% 14.57/14.76 (one_sorted_str(A!19)),
% 14.57/14.76 inference(unit_resolution,[status(thm)],[312, 309, 299])).
% 14.57/14.76 tff(314,plain,
% 14.57/14.76 (^[A: $i] : refl((empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A))) <=> (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A))))),
% 14.57/14.76 inference(bind,[status(th)],[])).
% 14.57/14.76 tff(315,plain,
% 14.57/14.76 (![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A))) <=> ![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))),
% 14.57/14.76 inference(quant_intro,[status(thm)],[314])).
% 14.57/14.76 tff(316,plain,
% 14.57/14.76 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & one_sorted_str(A)) <=> (~(empty_carrier(A) | (~one_sorted_str(A))))), ((~((~empty_carrier(A)) & one_sorted_str(A))) <=> (~(~(empty_carrier(A) | (~one_sorted_str(A))))))), rewrite((~(~(empty_carrier(A) | (~one_sorted_str(A))))) <=> (empty_carrier(A) | (~one_sorted_str(A)))), ((~((~empty_carrier(A)) & one_sorted_str(A))) <=> (empty_carrier(A) | (~one_sorted_str(A))))), (((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> ((~empty(the_carrier(A))) | (empty_carrier(A) | (~one_sorted_str(A)))))), rewrite(((~empty(the_carrier(A))) | (empty_carrier(A) | (~one_sorted_str(A)))) <=> (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))), (((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))))),
% 14.57/14.76 inference(bind,[status(th)],[])).
% 14.57/14.76 tff(317,plain,
% 14.57/14.76 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> ![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))),
% 14.57/14.76 inference(quant_intro,[status(thm)],[316])).
% 14.57/14.76 tff(318,plain,
% 14.57/14.76 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> ![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 14.57/14.76 inference(rewrite,[status(thm)],[])).
% 14.57/14.76 tff(319,plain,
% 14.57/14.76 (^[A: $i] : rewrite((((~empty_carrier(A)) & one_sorted_str(A)) => (~empty(the_carrier(A)))) <=> ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))))),
% 14.57/14.76 inference(bind,[status(th)],[])).
% 14.57/14.76 tff(320,plain,
% 14.57/14.76 (![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => (~empty(the_carrier(A)))) <=> ![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 14.57/14.76 inference(quant_intro,[status(thm)],[319])).
% 14.57/14.76 tff(321,axiom,(![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => (~empty(the_carrier(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_struct_0')).
% 14.57/14.76 tff(322,plain,
% 14.57/14.76 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 14.57/14.76 inference(modus_ponens,[status(thm)],[321, 320])).
% 14.57/14.76 tff(323,plain,
% 14.57/14.76 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 14.57/14.76 inference(modus_ponens,[status(thm)],[322, 318])).
% 14.57/14.76 tff(324,plain,(
% 14.57/14.76 ![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 14.57/14.76 inference(skolemize,[status(sab)],[323])).
% 14.57/14.76 tff(325,plain,
% 14.57/14.76 (![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))),
% 14.57/14.76 inference(modus_ponens,[status(thm)],[324, 317])).
% 14.57/14.76 tff(326,plain,
% 14.57/14.76 (![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))),
% 14.57/14.76 inference(modus_ponens,[status(thm)],[325, 315])).
% 14.57/14.76 tff(327,plain,
% 14.57/14.76 (((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | (empty_carrier(A!19) | (~one_sorted_str(A!19)) | (~empty(the_carrier(A!19))))) <=> ((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | empty_carrier(A!19) | (~one_sorted_str(A!19)) | (~empty(the_carrier(A!19))))),
% 14.57/14.76 inference(rewrite,[status(thm)],[])).
% 14.57/14.76 tff(328,plain,
% 14.57/14.76 ((empty_carrier(A!19) | (~empty(the_carrier(A!19))) | (~one_sorted_str(A!19))) <=> (empty_carrier(A!19) | (~one_sorted_str(A!19)) | (~empty(the_carrier(A!19))))),
% 14.57/14.76 inference(rewrite,[status(thm)],[])).
% 14.57/14.76 tff(329,plain,
% 14.57/14.76 (((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | (empty_carrier(A!19) | (~empty(the_carrier(A!19))) | (~one_sorted_str(A!19)))) <=> ((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | (empty_carrier(A!19) | (~one_sorted_str(A!19)) | (~empty(the_carrier(A!19)))))),
% 14.57/14.76 inference(monotonicity,[status(thm)],[328])).
% 14.57/14.76 tff(330,plain,
% 14.57/14.76 (((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | (empty_carrier(A!19) | (~empty(the_carrier(A!19))) | (~one_sorted_str(A!19)))) <=> ((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | empty_carrier(A!19) | (~one_sorted_str(A!19)) | (~empty(the_carrier(A!19))))),
% 14.57/14.76 inference(transitivity,[status(thm)],[329, 327])).
% 14.57/14.76 tff(331,plain,
% 14.57/14.76 ((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | (empty_carrier(A!19) | (~empty(the_carrier(A!19))) | (~one_sorted_str(A!19)))),
% 14.57/14.76 inference(quant_inst,[status(thm)],[])).
% 14.57/14.76 tff(332,plain,
% 14.57/14.76 ((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | empty_carrier(A!19) | (~one_sorted_str(A!19)) | (~empty(the_carrier(A!19)))),
% 14.57/14.76 inference(modus_ponens,[status(thm)],[331, 330])).
% 14.57/14.76 tff(333,plain,
% 14.57/14.76 ((~one_sorted_str(A!19)) | (~empty(the_carrier(A!19)))),
% 14.57/14.76 inference(unit_resolution,[status(thm)],[332, 326, 12])).
% 14.57/14.76 tff(334,plain,
% 14.57/14.76 (~empty(the_carrier(A!19))),
% 14.57/14.76 inference(unit_resolution,[status(thm)],[333, 313])).
% 14.57/14.76 tff(335,plain,
% 14.57/14.76 (^[A: $i, B: $i, C: $i, D: $i] : refl((empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B))) <=> (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B))))),
% 14.57/14.76 inference(bind,[status(th)],[])).
% 14.57/14.76 tff(336,plain,
% 14.57/14.76 (![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B))) <=> ![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))),
% 14.57/14.76 inference(quant_intro,[status(thm)],[335])).
% 14.57/14.76 tff(337,plain,
% 14.57/14.76 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B)) <=> (~(empty(B) | empty(A) | (~element(C, A)) | (~element(D, B))))), ((~((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B))) <=> (~(~(empty(B) | empty(A) | (~element(C, A)) | (~element(D, B))))))), rewrite((~(~(empty(B) | empty(A) | (~element(C, A)) | (~element(D, B))))) <=> (empty(B) | empty(A) | (~element(C, A)) | (~element(D, B)))), ((~((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B))) <=> (empty(B) | empty(A) | (~element(C, A)) | (~element(D, B))))), (((~((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B))) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D))) <=> ((empty(B) | empty(A) | (~element(C, A)) | (~element(D, B))) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D))))), rewrite(((empty(B) | empty(A) | (~element(C, A)) | (~element(D, B))) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D))) <=> (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))), (((~((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B))) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D))) <=> (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))))),
% 14.57/14.76 inference(bind,[status(th)],[])).
% 14.57/14.76 tff(338,plain,
% 14.57/14.76 (![A: $i, B: $i, C: $i, D: $i] : ((~((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B))) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))),
% 14.57/14.76 inference(quant_intro,[status(thm)],[337])).
% 14.57/14.76 tff(339,plain,
% 14.57/14.76 (![A: $i, B: $i, C: $i, D: $i] : ((~((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B))) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B))) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)))),
% 14.57/14.76 inference(rewrite,[status(thm)],[])).
% 14.57/14.76 tff(340,plain,
% 14.57/14.76 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~empty(A)) & (~empty(B))) & element(C, A)) <=> ((~empty(A)) & (~empty(B)) & element(C, A))), (((((~empty(A)) & (~empty(B))) & element(C, A)) & element(D, B)) <=> (((~empty(A)) & (~empty(B)) & element(C, A)) & element(D, B)))), rewrite((((~empty(A)) & (~empty(B)) & element(C, A)) & element(D, B)) <=> ((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B))), (((((~empty(A)) & (~empty(B))) & element(C, A)) & element(D, B)) <=> ((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B)))), ((((((~empty(A)) & (~empty(B))) & element(C, A)) & element(D, B)) => (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D))) <=> (((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B)) => (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D))))), rewrite((((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B)) => (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D))) <=> ((~((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B))) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)))), ((((((~empty(A)) & (~empty(B))) & element(C, A)) & element(D, B)) => (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D))) <=> ((~((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B))) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)))))),
% 14.57/14.76 inference(bind,[status(th)],[])).
% 14.57/14.76 tff(341,plain,
% 14.57/14.76 (![A: $i, B: $i, C: $i, D: $i] : (((((~empty(A)) & (~empty(B))) & element(C, A)) & element(D, B)) => (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B))) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)))),
% 14.57/14.76 inference(quant_intro,[status(thm)],[340])).
% 14.57/14.76 tff(342,axiom,(![A: $i, B: $i, C: $i, D: $i] : (((((~empty(A)) & (~empty(B))) & element(C, A)) & element(D, B)) => (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k1_domain_1')).
% 14.57/14.76 tff(343,plain,
% 14.57/14.76 (![A: $i, B: $i, C: $i, D: $i] : ((~((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B))) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)))),
% 14.57/14.76 inference(modus_ponens,[status(thm)],[342, 341])).
% 14.57/14.76 tff(344,plain,
% 14.57/14.76 (![A: $i, B: $i, C: $i, D: $i] : ((~((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B))) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)))),
% 14.57/14.76 inference(modus_ponens,[status(thm)],[343, 339])).
% 14.57/14.76 tff(345,plain,(
% 14.57/14.76 ![A: $i, B: $i, C: $i, D: $i] : ((~((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B))) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)))),
% 14.57/14.76 inference(skolemize,[status(sab)],[344])).
% 14.57/14.76 tff(346,plain,
% 14.57/14.76 (![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))),
% 14.57/14.76 inference(modus_ponens,[status(thm)],[345, 338])).
% 14.57/14.76 tff(347,plain,
% 14.57/14.76 (![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))),
% 14.57/14.76 inference(modus_ponens,[status(thm)],[346, 336])).
% 14.57/14.76 tff(348,plain,
% 14.57/14.76 (((~![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))) | ((~element(B!20, the_carrier(A!19))) | (~element(C!21, the_carrier(A!19))) | empty(the_carrier(A!19)) | (ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C!21) = ordered_pair(B!20, C!21)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))) | (~element(B!20, the_carrier(A!19))) | (~element(C!21, the_carrier(A!19))) | empty(the_carrier(A!19)) | (ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C!21) = ordered_pair(B!20, C!21)))),
% 14.57/14.76 inference(rewrite,[status(thm)],[])).
% 14.57/14.76 tff(349,plain,
% 14.57/14.76 ((empty(the_carrier(A!19)) | empty(the_carrier(A!19)) | (ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C!21) = ordered_pair(B!20, C!21)) | (~element(B!20, the_carrier(A!19))) | (~element(C!21, the_carrier(A!19)))) <=> ((~element(B!20, the_carrier(A!19))) | (~element(C!21, the_carrier(A!19))) | empty(the_carrier(A!19)) | (ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C!21) = ordered_pair(B!20, C!21)))),
% 14.57/14.76 inference(rewrite,[status(thm)],[])).
% 14.57/14.76 tff(350,plain,
% 14.57/14.76 (((~![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))) | (empty(the_carrier(A!19)) | empty(the_carrier(A!19)) | (ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C!21) = ordered_pair(B!20, C!21)) | (~element(B!20, the_carrier(A!19))) | (~element(C!21, the_carrier(A!19))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))) | ((~element(B!20, the_carrier(A!19))) | (~element(C!21, the_carrier(A!19))) | empty(the_carrier(A!19)) | (ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C!21) = ordered_pair(B!20, C!21))))),
% 14.57/14.76 inference(monotonicity,[status(thm)],[349])).
% 14.57/14.76 tff(351,plain,
% 14.57/14.76 (((~![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))) | (empty(the_carrier(A!19)) | empty(the_carrier(A!19)) | (ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C!21) = ordered_pair(B!20, C!21)) | (~element(B!20, the_carrier(A!19))) | (~element(C!21, the_carrier(A!19))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))) | (~element(B!20, the_carrier(A!19))) | (~element(C!21, the_carrier(A!19))) | empty(the_carrier(A!19)) | (ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C!21) = ordered_pair(B!20, C!21)))),
% 14.57/14.76 inference(transitivity,[status(thm)],[350, 348])).
% 14.57/14.76 tff(352,plain,
% 14.57/14.76 ((~![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))) | (empty(the_carrier(A!19)) | empty(the_carrier(A!19)) | (ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C!21) = ordered_pair(B!20, C!21)) | (~element(B!20, the_carrier(A!19))) | (~element(C!21, the_carrier(A!19))))),
% 14.57/14.76 inference(quant_inst,[status(thm)],[])).
% 14.57/14.76 tff(353,plain,
% 14.57/14.76 ((~![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))) | (~element(B!20, the_carrier(A!19))) | (~element(C!21, the_carrier(A!19))) | empty(the_carrier(A!19)) | (ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C!21) = ordered_pair(B!20, C!21))),
% 14.57/14.76 inference(modus_ponens,[status(thm)],[352, 351])).
% 14.57/14.76 tff(354,plain,
% 14.57/14.76 (ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C!21) = ordered_pair(B!20, C!21)),
% 14.57/14.76 inference(unit_resolution,[status(thm)],[353, 347, 43, 37, 334])).
% 14.57/14.76 tff(355,plain,
% 14.57/14.76 (ordered_pair(B!20, C!21) = ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C!21)),
% 14.57/14.76 inference(symmetry,[status(thm)],[354])).
% 14.57/14.76 tff(356,plain,
% 14.57/14.76 (in(ordered_pair(B!20, C!21), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))) <=> in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C!21), relation_of_lattice(A!19))),
% 14.57/14.76 inference(monotonicity,[status(thm)],[355, 280])).
% 14.57/14.76 tff(357,plain,
% 14.57/14.76 (in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C!21), relation_of_lattice(A!19)) <=> in(ordered_pair(B!20, C!21), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))),
% 14.57/14.76 inference(symmetry,[status(thm)],[356])).
% 14.57/14.76 tff(358,plain,
% 14.57/14.76 (~(below_refl(A!19, B!20, C!21) <=> related_reflexive(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21)))),
% 14.57/14.76 inference(or_elim,[status(thm)],[36])).
% 14.57/14.76 tff(359,plain,
% 14.57/14.76 ((below_refl(A!19, B!20, C!21) <=> related_reflexive(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21))) | below_refl(A!19, B!20, C!21) | related_reflexive(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21))),
% 14.57/14.76 inference(tautology,[status(thm)],[])).
% 14.57/14.76 tff(360,plain,
% 14.57/14.76 (below_refl(A!19, B!20, C!21) | related_reflexive(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21))),
% 14.57/14.76 inference(unit_resolution,[status(thm)],[359, 358])).
% 14.57/14.76 tff(361,plain,
% 14.57/14.76 (below_refl(A!19, B!20, C!21)),
% 14.57/14.76 inference(unit_resolution,[status(thm)],[360, 73])).
% 14.57/14.76 tff(362,plain,
% 14.57/14.76 (^[A: $i] : rewrite((empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, 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))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C))))))),
% 14.57/14.76 inference(bind,[status(th)],[])).
% 14.57/14.76 tff(363,plain,
% 14.57/14.76 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, 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))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))))),
% 14.57/14.76 inference(quant_intro,[status(thm)],[362])).
% 14.57/14.76 tff(364,plain,
% 14.57/14.76 (^[A: $i] : refl((empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))) | (~lattice(A))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))) | (~lattice(A))))),
% 14.57/14.76 inference(bind,[status(th)],[])).
% 14.57/14.76 tff(365,plain,
% 14.57/14.76 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, 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))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))) | (~lattice(A)))),
% 14.57/14.76 inference(quant_intro,[status(thm)],[364])).
% 14.57/14.76 tff(366,plain,
% 14.57/14.76 (^[A: $i] : rewrite((empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))) | (~lattice(A))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))) | (~lattice(A))))),
% 14.57/14.76 inference(bind,[status(th)],[])).
% 14.57/14.76 tff(367,plain,
% 14.57/14.76 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, 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))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))) | (~lattice(A)))),
% 14.57/14.76 inference(quant_intro,[status(thm)],[366])).
% 14.57/14.76 tff(368,plain,
% 14.57/14.76 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, 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))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))) | (~lattice(A)))),
% 14.57/14.76 inference(transitivity,[status(thm)],[367, 365])).
% 14.57/14.76 tff(369,plain,
% 14.57/14.76 (^[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))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C))))) <=> ((empty_carrier(A) | (~latt_str(A)) | (~lattice(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C))))))), rewrite(((empty_carrier(A) | (~latt_str(A)) | (~lattice(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C))))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, 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))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C))))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))) | (~lattice(A)))))),
% 14.61/14.76 inference(bind,[status(th)],[])).
% 14.61/14.76 tff(370,plain,
% 14.61/14.76 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C))))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))) | (~lattice(A)))),
% 14.61/14.76 inference(quant_intro,[status(thm)],[369])).
% 14.61/14.76 tff(371,plain,
% 14.61/14.76 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, 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))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))))),
% 14.61/14.76 inference(rewrite,[status(thm)],[])).
% 14.61/14.76 tff(372,plain,
% 14.61/14.76 (^[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)) => (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C))) <=> ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C))))), (![C: $i] : (element(C, the_carrier(A)) => (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C))) <=> ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C))))), ((element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))) <=> (element(B, the_carrier(A)) => ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))))), rewrite((element(B, the_carrier(A)) => ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C))))), ((element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C))))))), (![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C))))) <=> (((~empty_carrier(A)) & lattice(A) & latt_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C))))))), rewrite((((~empty_carrier(A)) & lattice(A) & latt_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C))))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C))))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))))))),
% 14.61/14.76 inference(bind,[status(th)],[])).
% 14.61/14.76 tff(373,plain,
% 14.61/14.76 (![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, 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))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))))),
% 14.61/14.76 inference(quant_intro,[status(thm)],[372])).
% 14.61/14.76 tff(374,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)) => (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t32_filter_1')).
% 14.61/14.76 tff(375,plain,
% 14.61/14.76 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))))),
% 14.61/14.76 inference(modus_ponens,[status(thm)],[374, 373])).
% 14.61/14.76 tff(376,plain,
% 14.61/14.76 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))))),
% 14.61/14.76 inference(modus_ponens,[status(thm)],[375, 371])).
% 14.61/14.76 tff(377,plain,(
% 14.61/14.76 ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))))),
% 14.61/14.76 inference(skolemize,[status(sab)],[376])).
% 14.61/14.76 tff(378,plain,
% 14.61/14.76 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))) | (~lattice(A)))),
% 14.61/14.76 inference(modus_ponens,[status(thm)],[377, 370])).
% 14.61/14.76 tff(379,plain,
% 14.61/14.76 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))) | (~lattice(A)))),
% 14.61/14.76 inference(modus_ponens,[status(thm)],[378, 368])).
% 14.61/14.76 tff(380,plain,
% 14.61/14.76 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))))),
% 14.61/14.76 inference(modus_ponens,[status(thm)],[379, 363])).
% 14.61/14.76 tff(381,plain,
% 14.61/14.76 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))))) | (empty_carrier(A!19) | (~latt_str(A!19)) | (~lattice(A!19)) | ![B: $i] : ((~element(B, the_carrier(A!19))) | ![C: $i] : ((~element(C, the_carrier(A!19))) | (in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B, C), relation_of_lattice(A!19)) <=> below_refl(A!19, B, 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))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))))) | empty_carrier(A!19) | (~latt_str(A!19)) | (~lattice(A!19)) | ![B: $i] : ((~element(B, the_carrier(A!19))) | ![C: $i] : ((~element(C, the_carrier(A!19))) | (in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B, C), relation_of_lattice(A!19)) <=> below_refl(A!19, B, C)))))),
% 14.61/14.76 inference(rewrite,[status(thm)],[])).
% 14.61/14.76 tff(382,plain,
% 14.61/14.76 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))))) | (empty_carrier(A!19) | (~latt_str(A!19)) | (~lattice(A!19)) | ![B: $i] : ((~element(B, the_carrier(A!19))) | ![C: $i] : ((~element(C, the_carrier(A!19))) | (in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B, C), relation_of_lattice(A!19)) <=> below_refl(A!19, B, C)))))),
% 14.61/14.76 inference(quant_inst,[status(thm)],[])).
% 14.61/14.76 tff(383,plain,
% 14.61/14.76 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))))) | empty_carrier(A!19) | (~latt_str(A!19)) | (~lattice(A!19)) | ![B: $i] : ((~element(B, the_carrier(A!19))) | ![C: $i] : ((~element(C, the_carrier(A!19))) | (in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B, C), relation_of_lattice(A!19)) <=> below_refl(A!19, B, C))))),
% 14.61/14.76 inference(modus_ponens,[status(thm)],[382, 381])).
% 14.61/14.76 tff(384,plain,
% 14.61/14.76 (![B: $i] : ((~element(B, the_carrier(A!19))) | ![C: $i] : ((~element(C, the_carrier(A!19))) | (in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B, C), relation_of_lattice(A!19)) <=> below_refl(A!19, B, C))))),
% 14.61/14.76 inference(unit_resolution,[status(thm)],[383, 380, 12, 11, 10])).
% 14.61/14.76 tff(385,plain,
% 14.61/14.76 (((~![B: $i] : ((~element(B, the_carrier(A!19))) | ![C: $i] : ((~element(C, the_carrier(A!19))) | (in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B, C), relation_of_lattice(A!19)) <=> below_refl(A!19, B, C))))) | ((~element(B!20, the_carrier(A!19))) | ![C: $i] : ((~element(C, the_carrier(A!19))) | (in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C), relation_of_lattice(A!19)) <=> below_refl(A!19, B!20, C))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!19))) | ![C: $i] : ((~element(C, the_carrier(A!19))) | (in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B, C), relation_of_lattice(A!19)) <=> below_refl(A!19, B, C))))) | (~element(B!20, the_carrier(A!19))) | ![C: $i] : ((~element(C, the_carrier(A!19))) | (in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C), relation_of_lattice(A!19)) <=> below_refl(A!19, B!20, C))))),
% 14.61/14.76 inference(rewrite,[status(thm)],[])).
% 14.61/14.76 tff(386,plain,
% 14.61/14.76 ((~![B: $i] : ((~element(B, the_carrier(A!19))) | ![C: $i] : ((~element(C, the_carrier(A!19))) | (in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B, C), relation_of_lattice(A!19)) <=> below_refl(A!19, B, C))))) | ((~element(B!20, the_carrier(A!19))) | ![C: $i] : ((~element(C, the_carrier(A!19))) | (in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C), relation_of_lattice(A!19)) <=> below_refl(A!19, B!20, C))))),
% 14.61/14.76 inference(quant_inst,[status(thm)],[])).
% 14.61/14.76 tff(387,plain,
% 14.61/14.76 ((~![B: $i] : ((~element(B, the_carrier(A!19))) | ![C: $i] : ((~element(C, the_carrier(A!19))) | (in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B, C), relation_of_lattice(A!19)) <=> below_refl(A!19, B, C))))) | (~element(B!20, the_carrier(A!19))) | ![C: $i] : ((~element(C, the_carrier(A!19))) | (in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C), relation_of_lattice(A!19)) <=> below_refl(A!19, B!20, C)))),
% 14.61/14.76 inference(modus_ponens,[status(thm)],[386, 385])).
% 14.61/14.76 tff(388,plain,
% 14.61/14.76 (![C: $i] : ((~element(C, the_carrier(A!19))) | (in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C), relation_of_lattice(A!19)) <=> below_refl(A!19, B!20, C)))),
% 14.61/14.76 inference(unit_resolution,[status(thm)],[387, 43, 384])).
% 14.61/14.76 tff(389,plain,
% 14.61/14.76 (((~![C: $i] : ((~element(C, the_carrier(A!19))) | (in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C), relation_of_lattice(A!19)) <=> below_refl(A!19, B!20, C)))) | ((~element(C!21, the_carrier(A!19))) | (in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C!21), relation_of_lattice(A!19)) <=> below_refl(A!19, B!20, C!21)))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!19))) | (in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C), relation_of_lattice(A!19)) <=> below_refl(A!19, B!20, C)))) | (~element(C!21, the_carrier(A!19))) | (in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C!21), relation_of_lattice(A!19)) <=> below_refl(A!19, B!20, C!21)))),
% 14.61/14.76 inference(rewrite,[status(thm)],[])).
% 14.61/14.76 tff(390,plain,
% 14.61/14.76 ((~![C: $i] : ((~element(C, the_carrier(A!19))) | (in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C), relation_of_lattice(A!19)) <=> below_refl(A!19, B!20, C)))) | ((~element(C!21, the_carrier(A!19))) | (in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C!21), relation_of_lattice(A!19)) <=> below_refl(A!19, B!20, C!21)))),
% 14.61/14.76 inference(quant_inst,[status(thm)],[])).
% 14.61/14.76 tff(391,plain,
% 14.61/14.76 ((~![C: $i] : ((~element(C, the_carrier(A!19))) | (in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C), relation_of_lattice(A!19)) <=> below_refl(A!19, B!20, C)))) | (~element(C!21, the_carrier(A!19))) | (in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C!21), relation_of_lattice(A!19)) <=> below_refl(A!19, B!20, C!21))),
% 14.61/14.77 inference(modus_ponens,[status(thm)],[390, 389])).
% 14.61/14.77 tff(392,plain,
% 14.61/14.77 (in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C!21), relation_of_lattice(A!19)) <=> below_refl(A!19, B!20, C!21)),
% 14.61/14.77 inference(unit_resolution,[status(thm)],[391, 37, 388])).
% 14.61/14.77 tff(393,plain,
% 14.61/14.77 ((~(in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C!21), relation_of_lattice(A!19)) <=> below_refl(A!19, B!20, C!21))) | in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C!21), relation_of_lattice(A!19)) | (~below_refl(A!19, B!20, C!21))),
% 14.61/14.77 inference(tautology,[status(thm)],[])).
% 14.61/14.77 tff(394,plain,
% 14.61/14.77 (in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C!21), relation_of_lattice(A!19)) | (~below_refl(A!19, B!20, C!21))),
% 14.61/14.77 inference(unit_resolution,[status(thm)],[393, 392])).
% 14.61/14.77 tff(395,plain,
% 14.61/14.77 (in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C!21), relation_of_lattice(A!19))),
% 14.61/14.77 inference(unit_resolution,[status(thm)],[394, 361])).
% 14.61/14.77 tff(396,plain,
% 14.61/14.77 (in(ordered_pair(B!20, C!21), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))),
% 14.61/14.77 inference(modus_ponens,[status(thm)],[395, 357])).
% 14.61/14.77 tff(397,plain,
% 14.61/14.77 (element(C!21, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))) <=> element(cast_to_el_of_LattPOSet(A!19, C!21), the_carrier(poset_of_lattice(A!19)))),
% 14.61/14.77 inference(monotonicity,[status(thm)],[42, 166])).
% 14.61/14.77 tff(398,plain,
% 14.61/14.77 (element(cast_to_el_of_LattPOSet(A!19, C!21), the_carrier(poset_of_lattice(A!19))) <=> element(C!21, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))),
% 14.61/14.77 inference(symmetry,[status(thm)],[397])).
% 14.61/14.77 tff(399,plain,
% 14.61/14.77 (element(C!21, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))),
% 14.61/14.77 inference(modus_ponens,[status(thm)],[133, 398])).
% 14.61/14.77 tff(400,plain,
% 14.61/14.77 (element(B!20, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))) <=> element(cast_to_el_of_LattPOSet(A!19, B!20), the_carrier(poset_of_lattice(A!19)))),
% 14.61/14.77 inference(monotonicity,[status(thm)],[48, 166])).
% 14.61/14.77 tff(401,plain,
% 14.61/14.77 (element(cast_to_el_of_LattPOSet(A!19, B!20), the_carrier(poset_of_lattice(A!19))) <=> element(B!20, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))),
% 14.61/14.77 inference(symmetry,[status(thm)],[400])).
% 14.61/14.77 tff(402,plain,
% 14.61/14.77 (element(B!20, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))),
% 14.61/14.77 inference(modus_ponens,[status(thm)],[140, 401])).
% 14.61/14.77 tff(403,plain,
% 14.61/14.77 (^[A: $i] : refl(((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))))),
% 14.61/14.77 inference(bind,[status(th)],[])).
% 14.61/14.77 tff(404,plain,
% 14.61/14.77 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 14.61/14.77 inference(quant_intro,[status(thm)],[403])).
% 14.61/14.77 tff(405,plain,
% 14.61/14.77 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))))),
% 14.61/14.77 inference(bind,[status(th)],[])).
% 14.61/14.77 tff(406,plain,
% 14.61/14.77 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 14.61/14.77 inference(quant_intro,[status(thm)],[405])).
% 14.61/14.77 tff(407,plain,
% 14.61/14.77 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 14.61/14.77 inference(transitivity,[status(thm)],[406, 404])).
% 14.61/14.77 tff(408,plain,
% 14.61/14.77 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 14.61/14.77 inference(rewrite,[status(thm)],[])).
% 14.61/14.77 tff(409,plain,
% 14.61/14.77 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))) <=> ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))), (![C: $i] : (element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))) <=> ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))), ((element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))) <=> (element(B, the_carrier(A)) => ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))), rewrite((element(B, the_carrier(A)) => ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))), ((element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))))), (![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))), ((rel_str(A) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> (rel_str(A) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))))), rewrite((rel_str(A) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))), ((rel_str(A) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))))),
% 14.61/14.77 inference(bind,[status(th)],[])).
% 14.61/14.77 tff(410,plain,
% 14.61/14.77 (![A: $i] : (rel_str(A) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 14.61/14.77 inference(quant_intro,[status(thm)],[409])).
% 14.61/14.77 tff(411,axiom,(![A: $i] : (rel_str(A) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d9_orders_2')).
% 14.61/14.77 tff(412,plain,
% 14.61/14.77 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 14.61/14.77 inference(modus_ponens,[status(thm)],[411, 410])).
% 14.61/14.77 tff(413,plain,
% 14.61/14.77 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 14.61/14.77 inference(modus_ponens,[status(thm)],[412, 408])).
% 14.61/14.77 tff(414,plain,(
% 14.61/14.77 ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 14.61/14.77 inference(skolemize,[status(sab)],[413])).
% 14.61/14.77 tff(415,plain,
% 14.61/14.77 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 14.61/14.77 inference(modus_ponens,[status(thm)],[414, 407])).
% 14.61/14.77 tff(416,plain,
% 14.61/14.77 (((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))) | ((~rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))) | ![B: $i] : ((~element(B, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | ![C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B, C) <=> in(ordered_pair(B, C), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))) | (~rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))) | ![B: $i] : ((~element(B, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | ![C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B, C) <=> in(ordered_pair(B, C), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))))))),
% 14.61/14.77 inference(rewrite,[status(thm)],[])).
% 14.61/14.77 tff(417,plain,
% 14.61/14.77 ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))) | ((~rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))) | ![B: $i] : ((~element(B, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | ![C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B, C) <=> in(ordered_pair(B, C), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))))))),
% 14.61/14.77 inference(quant_inst,[status(thm)],[])).
% 14.61/14.77 tff(418,plain,
% 14.61/14.77 ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))) | (~rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))) | ![B: $i] : ((~element(B, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | ![C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B, C) <=> in(ordered_pair(B, C), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))))),
% 14.61/14.77 inference(modus_ponens,[status(thm)],[417, 416])).
% 14.61/14.77 tff(419,plain,
% 14.61/14.77 ((~rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))) | ![B: $i] : ((~element(B, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | ![C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B, C) <=> in(ordered_pair(B, C), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))))),
% 14.61/14.77 inference(unit_resolution,[status(thm)],[418, 415])).
% 14.61/14.77 tff(420,plain,
% 14.61/14.77 (![B: $i] : ((~element(B, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | ![C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B, C) <=> in(ordered_pair(B, C), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))))),
% 14.61/14.77 inference(unit_resolution,[status(thm)],[419, 177])).
% 14.61/14.77 tff(421,plain,
% 14.61/14.77 (((~![B: $i] : ((~element(B, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | ![C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B, C) <=> in(ordered_pair(B, C), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))))) | ((~element(B!20, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | ![C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C) <=> in(ordered_pair(B!20, C), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))))) <=> ((~![B: $i] : ((~element(B, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | ![C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B, C) <=> in(ordered_pair(B, C), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))))) | (~element(B!20, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | ![C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C) <=> in(ordered_pair(B!20, C), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))))),
% 14.61/14.77 inference(rewrite,[status(thm)],[])).
% 14.61/14.77 tff(422,plain,
% 14.61/14.77 ((~![B: $i] : ((~element(B, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | ![C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B, C) <=> in(ordered_pair(B, C), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))))) | ((~element(B!20, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | ![C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C) <=> in(ordered_pair(B!20, C), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))))),
% 14.61/14.77 inference(quant_inst,[status(thm)],[])).
% 14.61/14.77 tff(423,plain,
% 14.61/14.77 ((~![B: $i] : ((~element(B, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | ![C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B, C) <=> in(ordered_pair(B, C), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))))) | (~element(B!20, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | ![C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C) <=> in(ordered_pair(B!20, C), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))))),
% 14.61/14.77 inference(modus_ponens,[status(thm)],[422, 421])).
% 14.61/14.77 tff(424,plain,
% 14.61/14.77 ((~element(B!20, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | ![C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C) <=> in(ordered_pair(B!20, C), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))))),
% 14.61/14.77 inference(unit_resolution,[status(thm)],[423, 420])).
% 14.61/14.77 tff(425,plain,
% 14.61/14.77 (![C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C) <=> in(ordered_pair(B!20, C), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))))),
% 14.61/14.77 inference(unit_resolution,[status(thm)],[424, 402])).
% 14.61/14.77 tff(426,plain,
% 14.61/14.77 (((~![C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C) <=> in(ordered_pair(B!20, C), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))))) | ((~element(C!21, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C!21) <=> in(ordered_pair(B!20, C!21), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))))) <=> ((~![C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C) <=> in(ordered_pair(B!20, C), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))))) | (~element(C!21, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C!21) <=> in(ordered_pair(B!20, C!21), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))))),
% 14.61/14.77 inference(rewrite,[status(thm)],[])).
% 14.61/14.77 tff(427,plain,
% 14.61/14.77 ((~![C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C) <=> in(ordered_pair(B!20, C), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))))) | ((~element(C!21, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C!21) <=> in(ordered_pair(B!20, C!21), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))))),
% 14.61/14.77 inference(quant_inst,[status(thm)],[])).
% 14.61/14.77 tff(428,plain,
% 14.61/14.77 ((~![C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C) <=> in(ordered_pair(B!20, C), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))))) | (~element(C!21, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C!21) <=> in(ordered_pair(B!20, C!21), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))),
% 14.61/14.77 inference(modus_ponens,[status(thm)],[427, 426])).
% 14.61/14.77 tff(429,plain,
% 14.61/14.77 (related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C!21) <=> in(ordered_pair(B!20, C!21), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))),
% 14.61/14.77 inference(unit_resolution,[status(thm)],[428, 425, 399])).
% 14.61/14.77 tff(430,plain,
% 14.61/14.77 ((~(related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C!21) <=> in(ordered_pair(B!20, C!21), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))) | related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C!21) | (~in(ordered_pair(B!20, C!21), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))),
% 14.61/14.77 inference(tautology,[status(thm)],[])).
% 14.61/14.77 tff(431,plain,
% 14.61/14.77 (related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C!21) | (~in(ordered_pair(B!20, C!21), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))),
% 14.61/14.77 inference(unit_resolution,[status(thm)],[430, 429])).
% 14.61/14.77 tff(432,plain,
% 14.61/14.77 ($false),
% 14.61/14.77 inference(unit_resolution,[status(thm)],[431, 396, 165])).
% 14.61/14.77 tff(433,plain,(related_reflexive(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21))), inference(lemma,lemma(discharge,[]))).
% 14.68/14.85 tff(434,plain,
% 14.68/14.85 ((~(related_reflexive(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21)) <=> related(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21)))) | (~related_reflexive(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21))) | related(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21))),
% 14.68/14.85 inference(tautology,[status(thm)],[])).
% 14.68/14.85 tff(435,plain,
% 14.68/14.85 ((~related_reflexive(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21))) | related(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21))),
% 14.68/14.85 inference(unit_resolution,[status(thm)],[434, 161])).
% 14.68/14.85 tff(436,plain,
% 14.68/14.85 (related(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21))),
% 14.68/14.85 inference(unit_resolution,[status(thm)],[435, 433])).
% 14.68/14.85 tff(437,plain,
% 14.68/14.85 (related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C!21)),
% 14.68/14.85 inference(modus_ponens,[status(thm)],[436, 71])).
% 14.68/14.85 tff(438,plain,
% 14.68/14.85 ((~in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C!21), relation_of_lattice(A!19))) <=> (~in(ordered_pair(B!20, C!21), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))),
% 14.68/14.85 inference(monotonicity,[status(thm)],[357])).
% 14.68/14.85 tff(439,plain,
% 14.68/14.85 ((below_refl(A!19, B!20, C!21) <=> related_reflexive(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21))) | (~below_refl(A!19, B!20, C!21)) | (~related_reflexive(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21)))),
% 14.68/14.85 inference(tautology,[status(thm)],[])).
% 14.68/14.85 tff(440,plain,
% 14.68/14.85 ((~below_refl(A!19, B!20, C!21)) | (~related_reflexive(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21)))),
% 14.68/14.85 inference(unit_resolution,[status(thm)],[439, 358])).
% 14.68/14.85 tff(441,plain,
% 14.68/14.85 (~below_refl(A!19, B!20, C!21)),
% 14.68/14.85 inference(unit_resolution,[status(thm)],[440, 433])).
% 14.68/14.85 tff(442,plain,
% 14.68/14.85 ((~(in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C!21), relation_of_lattice(A!19)) <=> below_refl(A!19, B!20, C!21))) | (~in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C!21), relation_of_lattice(A!19))) | below_refl(A!19, B!20, C!21)),
% 14.68/14.85 inference(tautology,[status(thm)],[])).
% 14.68/14.85 tff(443,plain,
% 14.68/14.85 ((~in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C!21), relation_of_lattice(A!19))) | below_refl(A!19, B!20, C!21)),
% 14.68/14.85 inference(unit_resolution,[status(thm)],[442, 392])).
% 14.68/14.85 tff(444,plain,
% 14.68/14.85 (~in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C!21), relation_of_lattice(A!19))),
% 14.68/14.85 inference(unit_resolution,[status(thm)],[443, 441])).
% 14.68/14.85 tff(445,plain,
% 14.68/14.85 (~in(ordered_pair(B!20, C!21), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))),
% 14.68/14.85 inference(modus_ponens,[status(thm)],[444, 438])).
% 14.68/14.85 tff(446,plain,
% 14.68/14.85 ((~(related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C!21) <=> in(ordered_pair(B!20, C!21), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))) | (~related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C!21)) | in(ordered_pair(B!20, C!21), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))),
% 14.68/14.85 inference(tautology,[status(thm)],[])).
% 14.68/14.85 tff(447,plain,
% 14.68/14.85 ((~related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C!21)) | in(ordered_pair(B!20, C!21), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))),
% 14.68/14.85 inference(unit_resolution,[status(thm)],[446, 429])).
% 14.68/14.85 tff(448,plain,
% 14.68/14.85 ($false),
% 14.68/14.85 inference(unit_resolution,[status(thm)],[447, 445, 437])).
% 14.68/14.85 % SZS output end Proof
% 14.68/14.86 % E exiting
%------------------------------------------------------------------------------