TSTP Solution File: SEU346+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU346+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 07:29:02 EDT 2022
% Result : Theorem 20.84s 13.68s
% Output : Proof 21.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU346+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Sep 3 11:48:54 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 20.84/13.68 % SZS status Theorem
% 20.84/13.68 % SZS output start Proof
% 20.84/13.68 tff(related_type, type, (
% 20.84/13.68 related: ( $i * $i * $i ) > $o)).
% 20.84/13.68 tff(tptp_fun_C_21_type, type, (
% 20.84/13.68 tptp_fun_C_21: $i)).
% 20.84/13.68 tff(tptp_fun_B_20_type, type, (
% 20.84/13.68 tptp_fun_B_20: $i)).
% 20.84/13.68 tff(rel_str_of_type, type, (
% 20.84/13.68 rel_str_of: ( $i * $i ) > $i)).
% 20.84/13.68 tff(k2_lattice3_type, type, (
% 20.84/13.68 k2_lattice3: $i > $i)).
% 20.84/13.68 tff(tptp_fun_A_19_type, type, (
% 20.84/13.68 tptp_fun_A_19: $i)).
% 20.84/13.68 tff(the_carrier_type, type, (
% 20.84/13.68 the_carrier: $i > $i)).
% 20.84/13.68 tff(cast_to_el_of_LattPOSet_type, type, (
% 20.84/13.68 cast_to_el_of_LattPOSet: ( $i * $i ) > $i)).
% 20.84/13.68 tff(poset_of_lattice_type, type, (
% 20.84/13.68 poset_of_lattice: $i > $i)).
% 20.84/13.68 tff(element_type, type, (
% 20.84/13.68 element: ( $i * $i ) > $o)).
% 20.84/13.68 tff(latt_str_type, type, (
% 20.84/13.68 latt_str: $i > $o)).
% 20.84/13.68 tff(related_reflexive_type, type, (
% 20.84/13.68 related_reflexive: ( $i * $i * $i ) > $o)).
% 20.84/13.68 tff(below_refl_type, type, (
% 20.84/13.68 below_refl: ( $i * $i * $i ) > $o)).
% 20.84/13.68 tff(lattice_type, type, (
% 20.84/13.68 lattice: $i > $o)).
% 20.84/13.68 tff(empty_carrier_type, type, (
% 20.84/13.68 empty_carrier: $i > $o)).
% 20.84/13.68 tff(antisymmetric_relstr_type, type, (
% 20.84/13.68 antisymmetric_relstr: $i > $o)).
% 20.84/13.68 tff(transitive_relstr_type, type, (
% 20.84/13.68 transitive_relstr: $i > $o)).
% 20.84/13.68 tff(reflexive_relstr_type, type, (
% 20.84/13.68 reflexive_relstr: $i > $o)).
% 20.84/13.68 tff(strict_rel_str_type, type, (
% 20.84/13.68 strict_rel_str: $i > $o)).
% 20.84/13.68 tff(rel_str_type, type, (
% 20.84/13.68 rel_str: $i > $o)).
% 20.84/13.68 tff(in_type, type, (
% 20.84/13.68 in: ( $i * $i ) > $o)).
% 20.84/13.68 tff(the_InternalRel_type, type, (
% 20.84/13.68 the_InternalRel: $i > $i)).
% 20.84/13.68 tff(ordered_pair_type, type, (
% 20.84/13.68 ordered_pair: ( $i * $i ) > $i)).
% 20.84/13.68 tff(relation_of_lattice_type, type, (
% 20.84/13.68 relation_of_lattice: $i > $i)).
% 20.84/13.68 tff(ordered_pair_as_product_element_type, type, (
% 20.84/13.68 ordered_pair_as_product_element: ( $i * $i * $i * $i ) > $i)).
% 20.84/13.68 tff(relation_of2_type, type, (
% 20.84/13.68 relation_of2: ( $i * $i * $i ) > $o)).
% 20.84/13.68 tff(relation_of2_as_subset_type, type, (
% 20.84/13.68 relation_of2_as_subset: ( $i * $i * $i ) > $o)).
% 20.84/13.68 tff(v1_partfun1_type, type, (
% 20.84/13.68 v1_partfun1: ( $i * $i * $i ) > $o)).
% 20.84/13.68 tff(transitive_type, type, (
% 20.84/13.68 transitive: $i > $o)).
% 20.84/13.68 tff(antisymmetric_type, type, (
% 20.84/13.68 antisymmetric: $i > $o)).
% 20.84/13.68 tff(reflexive_type, type, (
% 20.84/13.68 reflexive: $i > $o)).
% 20.84/13.68 tff(empty_type, type, (
% 20.84/13.68 empty: $i > $o)).
% 20.84/13.68 tff(one_sorted_str_type, type, (
% 20.84/13.68 one_sorted_str: $i > $o)).
% 20.84/13.68 tff(join_semilatt_str_type, type, (
% 20.84/13.68 join_semilatt_str: $i > $o)).
% 20.84/13.68 tff(meet_semilatt_str_type, type, (
% 20.84/13.68 meet_semilatt_str: $i > $o)).
% 20.84/13.68 tff(1,plain,
% 20.84/13.68 ((((~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))))))),
% 20.84/13.68 inference(rewrite,[status(thm)],[])).
% 20.84/13.68 tff(2,plain,
% 20.84/13.68 (((~(~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)))))) <=> (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))))))),
% 20.84/13.68 inference(rewrite,[status(thm)],[])).
% 20.84/13.68 tff(3,plain,
% 20.84/13.68 ((~(~((~empty_carrier(A!19)) & lattice(A!19) & latt_str(A!19)))) <=> ((~empty_carrier(A!19)) & lattice(A!19) & latt_str(A!19))),
% 20.84/13.68 inference(rewrite,[status(thm)],[])).
% 20.84/13.68 tff(4,plain,
% 20.84/13.68 (((~(~((~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)))))))),
% 20.84/13.68 inference(monotonicity,[status(thm)],[3, 2])).
% 20.84/13.68 tff(5,plain,
% 20.84/13.68 (((~(~((~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))))))),
% 20.84/13.68 inference(transitivity,[status(thm)],[4, 1])).
% 20.84/13.68 tff(6,plain,
% 20.84/13.68 ((~![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)))))))),
% 20.84/13.68 inference(rewrite,[status(thm)],[])).
% 20.84/13.68 tff(7,plain,
% 20.84/13.68 ((~![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)))))))),
% 20.84/13.68 inference(rewrite,[status(thm)],[])).
% 20.84/13.68 tff(8,axiom,(~![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t7_lattice3')).
% 20.84/13.68 tff(9,plain,
% 20.84/13.68 (~![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))))))),
% 20.84/13.68 inference(modus_ponens,[status(thm)],[8, 7])).
% 20.84/13.68 tff(10,plain,
% 20.84/13.68 (~![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))))))),
% 20.84/13.68 inference(modus_ponens,[status(thm)],[9, 6])).
% 20.84/13.68 tff(11,plain,
% 20.84/13.68 (~![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))))))),
% 20.84/13.68 inference(modus_ponens,[status(thm)],[10, 6])).
% 20.84/13.68 tff(12,plain,
% 20.84/13.68 (~![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))))))),
% 20.84/13.68 inference(modus_ponens,[status(thm)],[11, 6])).
% 20.84/13.68 tff(13,plain,
% 20.84/13.68 (~![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))))))),
% 20.84/13.68 inference(modus_ponens,[status(thm)],[12, 6])).
% 20.84/13.68 tff(14,plain,
% 20.84/13.68 (~![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))))))),
% 20.84/13.68 inference(modus_ponens,[status(thm)],[13, 6])).
% 20.84/13.68 tff(15,plain,
% 20.84/13.68 (~![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))))))),
% 20.84/13.68 inference(modus_ponens,[status(thm)],[14, 6])).
% 20.84/13.68 tff(16,plain,
% 20.84/13.68 ((~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)))))),
% 20.84/13.68 inference(modus_ponens,[status(thm)],[15, 5])).
% 20.84/13.68 tff(17,plain,
% 20.84/13.68 (latt_str(A!19)),
% 20.84/13.68 inference(and_elim,[status(thm)],[16])).
% 20.84/13.68 tff(18,plain,
% 20.84/13.68 (lattice(A!19)),
% 20.84/13.68 inference(and_elim,[status(thm)],[16])).
% 20.84/13.68 tff(19,plain,
% 20.84/13.68 (~empty_carrier(A!19)),
% 20.84/13.68 inference(and_elim,[status(thm)],[16])).
% 20.84/13.68 tff(20,plain,
% 20.84/13.68 (^[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))))),
% 20.84/13.68 inference(bind,[status(th)],[])).
% 20.84/13.68 tff(21,plain,
% 20.84/13.68 (![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)))),
% 20.84/13.68 inference(quant_intro,[status(thm)],[20])).
% 20.84/13.68 tff(22,plain,
% 20.84/13.68 (^[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))))),
% 20.84/13.68 inference(bind,[status(th)],[])).
% 20.84/13.68 tff(23,plain,
% 20.84/13.68 (![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)))),
% 20.84/13.68 inference(quant_intro,[status(thm)],[22])).
% 20.84/13.68 tff(24,plain,
% 20.84/13.68 (^[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))))),
% 20.84/13.68 inference(bind,[status(th)],[])).
% 20.84/13.68 tff(25,plain,
% 20.84/13.68 (![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)))),
% 20.84/13.68 inference(quant_intro,[status(thm)],[24])).
% 20.84/13.68 tff(26,plain,
% 20.84/13.68 (![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)))),
% 20.84/13.68 inference(transitivity,[status(thm)],[25, 23])).
% 20.84/13.68 tff(27,plain,
% 20.84/13.68 (^[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)))))),
% 20.84/13.68 inference(bind,[status(th)],[])).
% 20.84/13.68 tff(28,plain,
% 20.84/13.68 (![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)))),
% 20.84/13.68 inference(quant_intro,[status(thm)],[27])).
% 20.84/13.68 tff(29,plain,
% 20.84/13.68 (![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)))),
% 20.84/13.68 inference(rewrite,[status(thm)],[])).
% 20.84/13.68 tff(30,plain,
% 20.84/13.68 (^[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)))))),
% 20.84/13.68 inference(bind,[status(th)],[])).
% 20.84/13.68 tff(31,plain,
% 20.84/13.68 (![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)))),
% 20.84/13.68 inference(quant_intro,[status(thm)],[30])).
% 20.84/13.68 tff(32,axiom,(![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => (cast_to_el_of_LattPOSet(A, B) = B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_lattice3')).
% 20.84/13.68 tff(33,plain,
% 20.84/13.68 (![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)))),
% 20.84/13.68 inference(modus_ponens,[status(thm)],[32, 31])).
% 20.84/13.68 tff(34,plain,
% 20.84/13.68 (![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)))),
% 20.84/13.68 inference(modus_ponens,[status(thm)],[33, 29])).
% 20.84/13.68 tff(35,plain,(
% 20.84/13.68 ![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)))),
% 20.84/13.68 inference(skolemize,[status(sab)],[34])).
% 20.84/13.68 tff(36,plain,
% 20.84/13.68 (![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)))),
% 20.84/13.68 inference(modus_ponens,[status(thm)],[35, 28])).
% 20.84/13.68 tff(37,plain,
% 20.84/13.68 (![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)))),
% 20.84/13.69 inference(modus_ponens,[status(thm)],[36, 26])).
% 20.84/13.69 tff(38,plain,
% 20.84/13.69 (![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)))),
% 20.84/13.69 inference(modus_ponens,[status(thm)],[37, 21])).
% 20.84/13.69 tff(39,plain,
% 20.84/13.69 (((~![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)))),
% 20.84/13.69 inference(rewrite,[status(thm)],[])).
% 20.84/13.69 tff(40,plain,
% 20.84/13.69 ((~![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)))),
% 20.84/13.69 inference(quant_inst,[status(thm)],[])).
% 20.84/13.69 tff(41,plain,
% 20.84/13.69 ((~![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))),
% 20.84/13.69 inference(modus_ponens,[status(thm)],[40, 39])).
% 20.84/13.69 tff(42,plain,
% 20.84/13.69 (![B: $i] : ((~element(B, the_carrier(A!19))) | (cast_to_el_of_LattPOSet(A!19, B) = B))),
% 20.84/13.69 inference(unit_resolution,[status(thm)],[41, 38, 19, 18, 17])).
% 20.84/13.69 tff(43,plain,
% 20.84/13.69 (~((~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))))),
% 20.84/13.69 inference(and_elim,[status(thm)],[16])).
% 20.84/13.69 tff(44,plain,
% 20.84/13.69 (element(C!21, the_carrier(A!19))),
% 20.84/13.69 inference(or_elim,[status(thm)],[43])).
% 20.84/13.69 tff(45,plain,
% 20.84/13.69 (((~![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))),
% 20.84/13.69 inference(rewrite,[status(thm)],[])).
% 20.84/13.69 tff(46,plain,
% 20.84/13.69 ((~![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))),
% 20.84/13.69 inference(quant_inst,[status(thm)],[])).
% 20.84/13.69 tff(47,plain,
% 20.84/13.69 ((~![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)),
% 20.84/13.69 inference(modus_ponens,[status(thm)],[46, 45])).
% 20.84/13.69 tff(48,plain,
% 20.84/13.69 (cast_to_el_of_LattPOSet(A!19, C!21) = C!21),
% 20.84/13.69 inference(unit_resolution,[status(thm)],[47, 44, 42])).
% 20.84/13.69 tff(49,plain,
% 20.84/13.69 (C!21 = cast_to_el_of_LattPOSet(A!19, C!21)),
% 20.84/13.69 inference(symmetry,[status(thm)],[48])).
% 20.84/13.69 tff(50,plain,
% 20.84/13.69 (element(B!20, the_carrier(A!19))),
% 20.84/13.69 inference(and_elim,[status(thm)],[16])).
% 20.84/13.69 tff(51,plain,
% 20.84/13.69 (((~![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))),
% 20.84/13.69 inference(rewrite,[status(thm)],[])).
% 20.84/13.69 tff(52,plain,
% 20.84/13.69 ((~![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))),
% 20.84/13.69 inference(quant_inst,[status(thm)],[])).
% 20.84/13.69 tff(53,plain,
% 20.84/13.69 ((~![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)),
% 20.84/13.69 inference(modus_ponens,[status(thm)],[52, 51])).
% 20.84/13.69 tff(54,plain,
% 20.84/13.69 (cast_to_el_of_LattPOSet(A!19, B!20) = B!20),
% 20.84/13.69 inference(unit_resolution,[status(thm)],[53, 50, 42])).
% 20.84/13.69 tff(55,plain,
% 20.84/13.69 (B!20 = cast_to_el_of_LattPOSet(A!19, B!20)),
% 20.84/13.69 inference(symmetry,[status(thm)],[54])).
% 20.84/13.69 tff(56,plain,
% 20.84/13.69 (^[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))))),
% 20.84/13.69 inference(bind,[status(th)],[])).
% 20.84/13.69 tff(57,plain,
% 20.84/13.69 (![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)))),
% 20.84/13.69 inference(quant_intro,[status(thm)],[56])).
% 20.84/13.69 tff(58,plain,
% 20.84/13.69 (^[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)))))),
% 20.84/13.69 inference(bind,[status(th)],[])).
% 20.84/13.69 tff(59,plain,
% 20.84/13.69 (![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)))),
% 20.84/13.69 inference(quant_intro,[status(thm)],[58])).
% 20.84/13.69 tff(60,plain,
% 20.84/13.69 (![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))))),
% 20.84/13.69 inference(rewrite,[status(thm)],[])).
% 20.84/13.69 tff(61,plain,
% 20.84/13.69 (^[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))))))),
% 20.84/13.69 inference(bind,[status(th)],[])).
% 20.84/13.69 tff(62,plain,
% 20.84/13.69 (![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))))),
% 20.84/13.69 inference(quant_intro,[status(thm)],[61])).
% 20.84/13.69 tff(63,axiom,(![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_lattice3')).
% 20.84/13.69 tff(64,plain,
% 20.84/13.69 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))))),
% 20.84/13.69 inference(modus_ponens,[status(thm)],[63, 62])).
% 20.84/13.69 tff(65,plain,
% 20.84/13.69 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))))),
% 20.84/13.69 inference(modus_ponens,[status(thm)],[64, 60])).
% 20.84/13.69 tff(66,plain,(
% 20.84/13.69 ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))))),
% 20.84/13.69 inference(skolemize,[status(sab)],[65])).
% 20.84/13.69 tff(67,plain,
% 20.84/13.69 (![A: $i] : (empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A)))),
% 20.84/13.69 inference(modus_ponens,[status(thm)],[66, 59])).
% 20.84/13.69 tff(68,plain,
% 20.84/13.69 (![A: $i] : (empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A)))),
% 20.84/13.69 inference(modus_ponens,[status(thm)],[67, 57])).
% 20.84/13.69 tff(69,plain,
% 20.84/13.69 (((~![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) | (~latt_str(A!19)) | (~lattice(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) | (~latt_str(A!19)) | (~lattice(A!19)) | (poset_of_lattice(A!19) = rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))),
% 20.84/13.69 inference(rewrite,[status(thm)],[])).
% 20.84/13.69 tff(70,plain,
% 20.84/13.69 ((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) | (~latt_str(A!19)) | (~lattice(A!19)) | (poset_of_lattice(A!19) = rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))),
% 20.84/13.69 inference(rewrite,[status(thm)],[])).
% 20.84/13.69 tff(71,plain,
% 20.84/13.69 (((~![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) | (~latt_str(A!19)) | (~lattice(A!19)) | (poset_of_lattice(A!19) = rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))),
% 20.84/13.69 inference(monotonicity,[status(thm)],[70])).
% 20.84/13.69 tff(72,plain,
% 20.84/13.69 (((~![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) | (~latt_str(A!19)) | (~lattice(A!19)) | (poset_of_lattice(A!19) = rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))),
% 20.84/13.69 inference(transitivity,[status(thm)],[71, 69])).
% 20.84/13.69 tff(73,plain,
% 20.84/13.69 ((~![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)))),
% 20.84/13.69 inference(quant_inst,[status(thm)],[])).
% 20.84/13.69 tff(74,plain,
% 20.84/13.69 ((~![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) | (~latt_str(A!19)) | (~lattice(A!19)) | (poset_of_lattice(A!19) = rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))),
% 20.84/13.69 inference(modus_ponens,[status(thm)],[73, 72])).
% 20.84/13.69 tff(75,plain,
% 20.84/13.69 (poset_of_lattice(A!19) = rel_str_of(the_carrier(A!19), k2_lattice3(A!19))),
% 20.84/13.69 inference(unit_resolution,[status(thm)],[74, 68, 19, 18, 17])).
% 20.84/13.69 tff(76,plain,
% 20.84/13.69 (rel_str_of(the_carrier(A!19), k2_lattice3(A!19)) = poset_of_lattice(A!19)),
% 20.84/13.69 inference(symmetry,[status(thm)],[75])).
% 20.84/13.69 tff(77,plain,
% 20.84/13.69 (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))),
% 20.84/13.69 inference(monotonicity,[status(thm)],[76, 55, 49])).
% 20.84/13.69 tff(78,plain,
% 20.84/13.69 (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)),
% 20.84/13.69 inference(symmetry,[status(thm)],[77])).
% 20.84/13.69 tff(79,plain,
% 20.84/13.69 ((~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))),
% 20.84/13.69 inference(monotonicity,[status(thm)],[78])).
% 20.84/13.69 tff(80,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)).
% 20.84/13.69 tff(81,plain,
% 20.84/13.69 (^[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)))))))),
% 20.84/13.69 inference(bind,[status(th)],[])).
% 20.84/13.69 tff(82,plain,
% 20.84/13.69 (![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))))))),
% 20.84/13.69 inference(quant_intro,[status(thm)],[81])).
% 20.84/13.69 tff(83,plain,
% 20.84/13.69 (^[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))))))))),
% 20.84/13.69 inference(bind,[status(th)],[])).
% 20.84/13.69 tff(84,plain,
% 20.84/13.69 (![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))))))),
% 20.84/13.69 inference(quant_intro,[status(thm)],[83])).
% 20.84/13.69 tff(85,plain,
% 20.84/13.69 (![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))))),
% 20.84/13.69 inference(rewrite,[status(thm)],[])).
% 20.84/13.69 tff(86,plain,
% 20.84/13.69 (^[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))))))),
% 20.84/13.69 inference(bind,[status(th)],[])).
% 20.84/13.69 tff(87,plain,
% 20.84/13.69 (![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))))),
% 20.84/13.69 inference(quant_intro,[status(thm)],[86])).
% 20.84/13.69 tff(88,axiom,(![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => (((((~empty_carrier(poset_of_lattice(A))) & strict_rel_str(poset_of_lattice(A))) & reflexive_relstr(poset_of_lattice(A))) & transitive_relstr(poset_of_lattice(A))) & antisymmetric_relstr(poset_of_lattice(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc4_lattice3')).
% 20.84/13.69 tff(89,plain,
% 20.84/13.69 (![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))))),
% 20.84/13.69 inference(modus_ponens,[status(thm)],[88, 87])).
% 20.84/13.69 tff(90,plain,
% 20.84/13.69 (![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))))),
% 20.84/13.69 inference(modus_ponens,[status(thm)],[89, 85])).
% 20.84/13.69 tff(91,plain,(
% 20.84/13.69 ![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))))),
% 20.84/13.69 inference(skolemize,[status(sab)],[90])).
% 20.84/13.69 tff(92,plain,
% 20.84/13.69 (![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))))))),
% 20.84/13.69 inference(modus_ponens,[status(thm)],[91, 84])).
% 20.84/13.69 tff(93,plain,
% 20.84/13.69 (![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))))))),
% 20.84/13.69 inference(modus_ponens,[status(thm)],[92, 82])).
% 20.84/13.69 tff(94,plain,
% 20.84/13.69 (((~![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))))))),
% 20.84/13.69 inference(rewrite,[status(thm)],[])).
% 20.84/13.69 tff(95,plain,
% 20.84/13.69 ((~![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))))))),
% 20.84/13.69 inference(quant_inst,[status(thm)],[])).
% 20.84/13.69 tff(96,plain,
% 20.84/13.69 ((~![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)))))),
% 20.84/13.69 inference(modus_ponens,[status(thm)],[95, 94])).
% 20.84/13.69 tff(97,plain,
% 20.84/13.69 (~(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))))),
% 20.84/13.69 inference(unit_resolution,[status(thm)],[96, 93, 19, 18, 17])).
% 20.84/13.69 tff(98,plain,
% 20.84/13.69 ((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)))),
% 20.84/13.69 inference(tautology,[status(thm)],[])).
% 20.84/13.69 tff(99,plain,
% 20.84/13.69 (~empty_carrier(poset_of_lattice(A!19))),
% 20.84/13.69 inference(unit_resolution,[status(thm)],[98, 97])).
% 20.84/13.69 tff(100,plain,
% 20.84/13.69 (^[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)))))))),
% 20.84/13.69 inference(bind,[status(th)],[])).
% 20.84/13.69 tff(101,plain,
% 20.84/13.69 (![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))))))),
% 20.84/13.69 inference(quant_intro,[status(thm)],[100])).
% 20.84/13.69 tff(102,plain,
% 20.84/13.69 (^[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))))))))),
% 20.84/13.69 inference(bind,[status(th)],[])).
% 20.84/13.69 tff(103,plain,
% 20.84/13.69 (![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))))))),
% 20.84/13.69 inference(quant_intro,[status(thm)],[102])).
% 20.84/13.69 tff(104,plain,
% 20.84/13.69 (![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))))),
% 20.84/13.69 inference(rewrite,[status(thm)],[])).
% 20.84/13.69 tff(105,plain,
% 20.84/13.69 (^[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))))))),
% 20.84/13.69 inference(bind,[status(th)],[])).
% 20.84/13.69 tff(106,plain,
% 20.84/13.69 (![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))))),
% 20.84/13.69 inference(quant_intro,[status(thm)],[105])).
% 20.84/13.69 tff(107,axiom,(![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ((((strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A))) & transitive_relstr(poset_of_lattice(A))) & antisymmetric_relstr(poset_of_lattice(A))) & rel_str(poset_of_lattice(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k3_lattice3')).
% 20.84/13.69 tff(108,plain,
% 20.84/13.69 (![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))))),
% 20.84/13.69 inference(modus_ponens,[status(thm)],[107, 106])).
% 20.84/13.69 tff(109,plain,
% 20.84/13.69 (![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))))),
% 20.84/13.69 inference(modus_ponens,[status(thm)],[108, 104])).
% 20.84/13.69 tff(110,plain,(
% 20.84/13.69 ![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))))),
% 20.84/13.69 inference(skolemize,[status(sab)],[109])).
% 20.84/13.69 tff(111,plain,
% 20.84/13.69 (![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))))))),
% 20.84/13.69 inference(modus_ponens,[status(thm)],[110, 103])).
% 20.84/13.69 tff(112,plain,
% 20.84/13.69 (![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))))))),
% 20.84/13.69 inference(modus_ponens,[status(thm)],[111, 101])).
% 20.84/13.69 tff(113,plain,
% 20.84/13.69 (((~![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))))))),
% 20.84/13.69 inference(rewrite,[status(thm)],[])).
% 20.84/13.69 tff(114,plain,
% 20.84/13.69 ((~![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))))))),
% 20.84/13.69 inference(quant_inst,[status(thm)],[])).
% 20.84/13.69 tff(115,plain,
% 20.84/13.69 ((~![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)))))),
% 20.84/13.69 inference(modus_ponens,[status(thm)],[114, 113])).
% 20.84/13.69 tff(116,plain,
% 20.84/13.69 (~((~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))))),
% 20.84/13.69 inference(unit_resolution,[status(thm)],[115, 112, 19, 18, 17])).
% 20.84/13.69 tff(117,plain,
% 20.84/13.69 (((~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))),
% 20.84/13.69 inference(tautology,[status(thm)],[])).
% 20.84/13.69 tff(118,plain,
% 20.84/13.69 (rel_str(poset_of_lattice(A!19))),
% 20.84/13.69 inference(unit_resolution,[status(thm)],[117, 116])).
% 20.84/13.69 tff(119,plain,
% 20.84/13.69 ((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))),
% 20.84/13.69 inference(tautology,[status(thm)],[])).
% 20.84/13.69 tff(120,plain,
% 20.84/13.69 (reflexive_relstr(poset_of_lattice(A!19))),
% 20.84/13.69 inference(unit_resolution,[status(thm)],[119, 97])).
% 20.84/13.69 tff(121,plain,
% 20.84/13.69 (^[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))))),
% 20.84/13.69 inference(bind,[status(th)],[])).
% 20.84/13.69 tff(122,plain,
% 20.84/13.69 (![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)))),
% 20.84/13.69 inference(quant_intro,[status(thm)],[121])).
% 20.84/13.69 tff(123,plain,
% 20.84/13.69 (^[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)))))),
% 20.84/13.69 inference(bind,[status(th)],[])).
% 20.84/13.69 tff(124,plain,
% 20.84/13.69 (![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)))),
% 20.84/13.69 inference(quant_intro,[status(thm)],[123])).
% 20.84/13.69 tff(125,plain,
% 20.84/13.69 (![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))))),
% 20.84/13.69 inference(rewrite,[status(thm)],[])).
% 20.84/13.69 tff(126,plain,
% 20.84/13.69 (^[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))))))),
% 20.84/13.69 inference(bind,[status(th)],[])).
% 20.84/13.69 tff(127,plain,
% 20.84/13.69 (![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))))),
% 20.84/13.69 inference(quant_intro,[status(thm)],[126])).
% 20.84/13.69 tff(128,axiom,(![A: $i, B: $i] : (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) & element(B, the_carrier(A))) => element(cast_to_el_of_LattPOSet(A, B), the_carrier(poset_of_lattice(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k4_lattice3')).
% 20.84/13.69 tff(129,plain,
% 20.84/13.69 (![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))))),
% 20.84/13.69 inference(modus_ponens,[status(thm)],[128, 127])).
% 20.84/13.69 tff(130,plain,
% 20.84/13.69 (![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))))),
% 20.84/13.69 inference(modus_ponens,[status(thm)],[129, 125])).
% 20.84/13.69 tff(131,plain,(
% 20.84/13.69 ![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))))),
% 20.84/13.69 inference(skolemize,[status(sab)],[130])).
% 20.84/13.69 tff(132,plain,
% 20.84/13.69 (![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)))),
% 20.84/13.69 inference(modus_ponens,[status(thm)],[131, 124])).
% 20.84/13.69 tff(133,plain,
% 20.84/13.69 (![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)))),
% 20.84/13.69 inference(modus_ponens,[status(thm)],[132, 122])).
% 20.84/13.69 tff(134,plain,
% 20.84/13.69 (((~![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))) | (~latt_str(A!19)) | (~lattice(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))) | (~latt_str(A!19)) | (~lattice(A!19)) | element(cast_to_el_of_LattPOSet(A!19, C!21), the_carrier(poset_of_lattice(A!19))))),
% 20.84/13.69 inference(rewrite,[status(thm)],[])).
% 20.84/13.69 tff(135,plain,
% 20.84/13.69 ((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))) | (~latt_str(A!19)) | (~lattice(A!19)) | element(cast_to_el_of_LattPOSet(A!19, C!21), the_carrier(poset_of_lattice(A!19))))),
% 20.84/13.69 inference(rewrite,[status(thm)],[])).
% 20.84/13.69 tff(136,plain,
% 20.84/13.69 (((~![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))) | (~latt_str(A!19)) | (~lattice(A!19)) | element(cast_to_el_of_LattPOSet(A!19, C!21), the_carrier(poset_of_lattice(A!19)))))),
% 20.84/13.69 inference(monotonicity,[status(thm)],[135])).
% 20.84/13.69 tff(137,plain,
% 20.84/13.69 (((~![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))) | (~latt_str(A!19)) | (~lattice(A!19)) | element(cast_to_el_of_LattPOSet(A!19, C!21), the_carrier(poset_of_lattice(A!19))))),
% 20.84/13.69 inference(transitivity,[status(thm)],[136, 134])).
% 20.84/13.69 tff(138,plain,
% 20.84/13.69 ((~![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)))),
% 20.84/13.69 inference(quant_inst,[status(thm)],[])).
% 20.84/13.69 tff(139,plain,
% 20.84/13.69 ((~![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))) | (~latt_str(A!19)) | (~lattice(A!19)) | element(cast_to_el_of_LattPOSet(A!19, C!21), the_carrier(poset_of_lattice(A!19)))),
% 20.84/13.69 inference(modus_ponens,[status(thm)],[138, 137])).
% 20.84/13.69 tff(140,plain,
% 20.84/13.69 (element(cast_to_el_of_LattPOSet(A!19, C!21), the_carrier(poset_of_lattice(A!19)))),
% 20.84/13.69 inference(unit_resolution,[status(thm)],[139, 133, 19, 18, 17, 44])).
% 20.84/13.69 tff(141,plain,
% 20.84/13.69 (((~![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))) | (~latt_str(A!19)) | (~lattice(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))) | (~latt_str(A!19)) | (~lattice(A!19)) | element(cast_to_el_of_LattPOSet(A!19, B!20), the_carrier(poset_of_lattice(A!19))))),
% 20.84/13.69 inference(rewrite,[status(thm)],[])).
% 20.84/13.69 tff(142,plain,
% 20.84/13.69 ((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))) | (~latt_str(A!19)) | (~lattice(A!19)) | element(cast_to_el_of_LattPOSet(A!19, B!20), the_carrier(poset_of_lattice(A!19))))),
% 20.84/13.69 inference(rewrite,[status(thm)],[])).
% 20.84/13.69 tff(143,plain,
% 20.84/13.69 (((~![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))) | (~latt_str(A!19)) | (~lattice(A!19)) | element(cast_to_el_of_LattPOSet(A!19, B!20), the_carrier(poset_of_lattice(A!19)))))),
% 20.84/13.69 inference(monotonicity,[status(thm)],[142])).
% 20.84/13.69 tff(144,plain,
% 20.84/13.69 (((~![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))) | (~latt_str(A!19)) | (~lattice(A!19)) | element(cast_to_el_of_LattPOSet(A!19, B!20), the_carrier(poset_of_lattice(A!19))))),
% 20.84/13.69 inference(transitivity,[status(thm)],[143, 141])).
% 20.84/13.69 tff(145,plain,
% 20.84/13.69 ((~![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)))),
% 20.84/13.69 inference(quant_inst,[status(thm)],[])).
% 20.84/13.69 tff(146,plain,
% 20.84/13.69 ((~![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))) | (~latt_str(A!19)) | (~lattice(A!19)) | element(cast_to_el_of_LattPOSet(A!19, B!20), the_carrier(poset_of_lattice(A!19)))),
% 20.84/13.69 inference(modus_ponens,[status(thm)],[145, 144])).
% 20.84/13.69 tff(147,plain,
% 20.84/13.69 (element(cast_to_el_of_LattPOSet(A!19, B!20), the_carrier(poset_of_lattice(A!19)))),
% 20.84/13.69 inference(unit_resolution,[status(thm)],[146, 133, 19, 18, 17, 50])).
% 20.84/13.69 tff(148,plain,
% 20.84/13.69 (^[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))))),
% 20.84/13.70 inference(bind,[status(th)],[])).
% 20.84/13.70 tff(149,plain,
% 20.84/13.70 (![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)))),
% 20.84/13.70 inference(quant_intro,[status(thm)],[148])).
% 20.84/13.70 tff(150,plain,
% 20.84/13.70 (^[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)))))),
% 20.84/13.70 inference(bind,[status(th)],[])).
% 20.84/13.70 tff(151,plain,
% 20.84/13.70 (![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)))),
% 20.84/13.70 inference(quant_intro,[status(thm)],[150])).
% 20.84/13.70 tff(152,plain,
% 20.84/13.70 (![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)))),
% 20.84/13.70 inference(rewrite,[status(thm)],[])).
% 20.84/13.70 tff(153,plain,
% 20.84/13.70 (^[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)))))),
% 20.84/13.70 inference(bind,[status(th)],[])).
% 20.84/13.70 tff(154,plain,
% 20.84/13.70 (![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)))),
% 20.84/13.70 inference(quant_intro,[status(thm)],[153])).
% 20.84/13.70 tff(155,axiom,(![A: $i, B: $i, C: $i] : ((((((~empty_carrier(A)) & reflexive_relstr(A)) & rel_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => (related_reflexive(A, B, C) <=> related(A, B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_r3_orders_2')).
% 20.84/13.70 tff(156,plain,
% 20.84/13.70 (![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)))),
% 20.84/13.70 inference(modus_ponens,[status(thm)],[155, 154])).
% 20.84/13.70 tff(157,plain,
% 20.84/13.70 (![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)))),
% 20.84/13.70 inference(modus_ponens,[status(thm)],[156, 152])).
% 20.84/13.70 tff(158,plain,(
% 20.84/13.70 ![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)))),
% 20.84/13.70 inference(skolemize,[status(sab)],[157])).
% 20.84/13.70 tff(159,plain,
% 20.84/13.70 (![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)))),
% 20.84/13.70 inference(modus_ponens,[status(thm)],[158, 151])).
% 20.84/13.70 tff(160,plain,
% 20.84/13.70 (![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)))),
% 20.84/13.70 inference(modus_ponens,[status(thm)],[159, 149])).
% 20.84/13.70 tff(161,plain,
% 20.84/13.70 (((~![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)))))),
% 20.84/13.70 inference(rewrite,[status(thm)],[])).
% 20.84/13.70 tff(162,plain,
% 20.84/13.70 ((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)))))),
% 20.84/13.70 inference(rewrite,[status(thm)],[])).
% 20.84/13.70 tff(163,plain,
% 20.84/13.70 (((~![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))))))),
% 20.84/13.70 inference(monotonicity,[status(thm)],[162])).
% 20.84/13.70 tff(164,plain,
% 20.84/13.70 (((~![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)))))),
% 20.84/13.70 inference(transitivity,[status(thm)],[163, 161])).
% 20.84/13.70 tff(165,plain,
% 20.84/13.70 ((~![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))))),
% 20.84/13.70 inference(quant_inst,[status(thm)],[])).
% 20.84/13.70 tff(166,plain,
% 20.84/13.70 ((~![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))))),
% 20.84/13.70 inference(modus_ponens,[status(thm)],[165, 164])).
% 20.84/13.70 tff(167,plain,
% 20.84/13.70 (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)))),
% 20.97/13.70 inference(unit_resolution,[status(thm)],[166, 160, 147, 140])).
% 20.97/13.70 tff(168,plain,
% 20.97/13.70 (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))),
% 20.97/13.70 inference(unit_resolution,[status(thm)],[167, 120, 118, 99])).
% 20.97/13.70 tff(169,plain,
% 20.97/13.70 ((~(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)))),
% 20.97/13.70 inference(tautology,[status(thm)],[])).
% 20.97/13.70 tff(170,plain,
% 20.97/13.70 (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)))),
% 20.97/13.70 inference(unit_resolution,[status(thm)],[169, 168])).
% 20.97/13.70 tff(171,plain,
% 20.97/13.70 (~related(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21))),
% 20.97/13.70 inference(unit_resolution,[status(thm)],[170, 80])).
% 20.97/13.70 tff(172,plain,
% 20.97/13.70 (~related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C!21)),
% 20.97/13.70 inference(modus_ponens,[status(thm)],[171, 79])).
% 20.97/13.70 tff(173,plain,
% 20.97/13.70 (the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))) = the_carrier(poset_of_lattice(A!19))),
% 20.97/13.70 inference(monotonicity,[status(thm)],[76])).
% 20.97/13.70 tff(174,plain,
% 20.97/13.70 (the_carrier(poset_of_lattice(A!19)) = the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))),
% 20.97/13.70 inference(symmetry,[status(thm)],[173])).
% 20.97/13.70 tff(175,plain,
% 20.97/13.70 (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))))),
% 20.97/13.70 inference(monotonicity,[status(thm)],[174])).
% 20.97/13.70 tff(176,plain,
% 20.97/13.70 (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))))),
% 20.97/13.70 inference(symmetry,[status(thm)],[175])).
% 20.97/13.70 tff(177,plain,
% 20.97/13.70 (strict_rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))) <=> strict_rel_str(poset_of_lattice(A!19))),
% 20.97/13.70 inference(monotonicity,[status(thm)],[76])).
% 20.97/13.70 tff(178,plain,
% 20.97/13.70 (strict_rel_str(poset_of_lattice(A!19)) <=> strict_rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))),
% 20.97/13.70 inference(symmetry,[status(thm)],[177])).
% 20.97/13.70 tff(179,plain,
% 20.97/13.70 ((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))),
% 20.97/13.70 inference(tautology,[status(thm)],[])).
% 20.97/13.70 tff(180,plain,
% 20.97/13.70 (strict_rel_str(poset_of_lattice(A!19))),
% 20.97/13.70 inference(unit_resolution,[status(thm)],[179, 97])).
% 20.97/13.70 tff(181,plain,
% 20.97/13.70 (strict_rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))),
% 20.97/13.70 inference(modus_ponens,[status(thm)],[180, 178])).
% 20.97/13.70 tff(182,plain,
% 20.97/13.70 (rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))) <=> rel_str(poset_of_lattice(A!19))),
% 20.97/13.70 inference(monotonicity,[status(thm)],[76])).
% 20.97/13.70 tff(183,plain,
% 20.97/13.70 (rel_str(poset_of_lattice(A!19)) <=> rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))),
% 20.97/13.70 inference(symmetry,[status(thm)],[182])).
% 20.97/13.70 tff(184,plain,
% 20.97/13.70 (rel_str(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))),
% 20.97/13.70 inference(modus_ponens,[status(thm)],[118, 183])).
% 20.97/13.70 tff(185,plain,
% 20.97/13.70 (^[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))))),
% 20.97/13.70 inference(bind,[status(th)],[])).
% 20.97/13.70 tff(186,plain,
% 20.97/13.70 (![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)))),
% 20.97/13.70 inference(quant_intro,[status(thm)],[185])).
% 20.97/13.70 tff(187,plain,
% 20.97/13.70 (![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)))),
% 20.97/13.70 inference(rewrite,[status(thm)],[])).
% 20.97/13.70 tff(188,plain,
% 20.97/13.70 (^[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)))))),
% 20.97/13.70 inference(bind,[status(th)],[])).
% 20.97/13.70 tff(189,plain,
% 20.97/13.70 (![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)))),
% 20.97/13.70 inference(quant_intro,[status(thm)],[188])).
% 20.97/13.70 tff(190,axiom,(![A: $i] : (rel_str(A) => (strict_rel_str(A) => (A = rel_str_of(the_carrier(A), the_InternalRel(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','abstractness_v1_orders_2')).
% 20.97/13.70 tff(191,plain,
% 20.97/13.70 (![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 20.97/13.70 inference(modus_ponens,[status(thm)],[190, 189])).
% 20.97/13.70 tff(192,plain,
% 20.97/13.70 (![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 20.97/13.70 inference(modus_ponens,[status(thm)],[191, 187])).
% 20.97/13.70 tff(193,plain,(
% 20.97/13.70 ![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 20.97/13.70 inference(skolemize,[status(sab)],[192])).
% 20.97/13.70 tff(194,plain,
% 20.97/13.70 (![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 20.97/13.70 inference(modus_ponens,[status(thm)],[193, 186])).
% 20.97/13.70 tff(195,plain,
% 20.97/13.70 (((~![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)))))),
% 20.97/13.70 inference(rewrite,[status(thm)],[])).
% 20.97/13.70 tff(196,plain,
% 20.97/13.70 (((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)))))),
% 20.97/13.70 inference(rewrite,[status(thm)],[])).
% 20.97/13.70 tff(197,plain,
% 20.97/13.70 (((~![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))))))),
% 20.97/13.70 inference(monotonicity,[status(thm)],[196])).
% 20.97/13.70 tff(198,plain,
% 20.97/13.70 (((~![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)))))),
% 20.97/13.70 inference(transitivity,[status(thm)],[197, 195])).
% 20.97/13.70 tff(199,plain,
% 20.97/13.70 ((~![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)))))),
% 20.97/13.70 inference(quant_inst,[status(thm)],[])).
% 20.97/13.70 tff(200,plain,
% 20.97/13.70 ((~![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))))),
% 20.97/13.70 inference(modus_ponens,[status(thm)],[199, 198])).
% 20.97/13.70 tff(201,plain,
% 20.97/13.70 ((~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))))),
% 20.97/13.70 inference(unit_resolution,[status(thm)],[200, 194])).
% 20.97/13.70 tff(202,plain,
% 20.97/13.70 (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))))),
% 20.97/13.70 inference(unit_resolution,[status(thm)],[201, 184, 181])).
% 20.97/13.70 tff(203,plain,
% 20.97/13.70 (^[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))))),
% 20.97/13.70 inference(bind,[status(th)],[])).
% 20.97/13.70 tff(204,plain,
% 20.97/13.70 (![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)))),
% 20.97/13.70 inference(quant_intro,[status(thm)],[203])).
% 20.97/13.70 tff(205,plain,
% 20.97/13.70 (^[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)))))),
% 20.97/13.70 inference(bind,[status(th)],[])).
% 20.97/13.70 tff(206,plain,
% 20.97/13.70 (![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)))),
% 20.97/13.70 inference(quant_intro,[status(thm)],[205])).
% 20.97/13.70 tff(207,plain,
% 20.97/13.70 (![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)))),
% 20.97/13.70 inference(rewrite,[status(thm)],[])).
% 20.97/13.70 tff(208,plain,
% 20.97/13.70 (^[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)))))),
% 20.97/13.70 inference(bind,[status(th)],[])).
% 20.97/13.70 tff(209,plain,
% 20.97/13.70 (![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)))),
% 20.97/13.70 inference(quant_intro,[status(thm)],[208])).
% 20.97/13.70 tff(210,axiom,(![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => (k2_lattice3(A) = relation_of_lattice(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k2_lattice3')).
% 20.97/13.70 tff(211,plain,
% 20.97/13.70 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (k2_lattice3(A) = relation_of_lattice(A)))),
% 20.97/13.70 inference(modus_ponens,[status(thm)],[210, 209])).
% 20.97/13.70 tff(212,plain,
% 20.97/13.70 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (k2_lattice3(A) = relation_of_lattice(A)))),
% 20.97/13.70 inference(modus_ponens,[status(thm)],[211, 207])).
% 20.97/13.70 tff(213,plain,(
% 20.97/13.70 ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (k2_lattice3(A) = relation_of_lattice(A)))),
% 20.97/13.70 inference(skolemize,[status(sab)],[212])).
% 20.97/13.70 tff(214,plain,
% 20.97/13.70 (![A: $i] : (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))),
% 20.97/13.70 inference(modus_ponens,[status(thm)],[213, 206])).
% 20.97/13.70 tff(215,plain,
% 20.97/13.70 (![A: $i] : (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))),
% 20.97/13.70 inference(modus_ponens,[status(thm)],[214, 204])).
% 20.97/13.70 tff(216,plain,
% 20.97/13.70 (((~![A: $i] : (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))) | (empty_carrier(A!19) | (~latt_str(A!19)) | (~lattice(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) | (~latt_str(A!19)) | (~lattice(A!19)) | (k2_lattice3(A!19) = relation_of_lattice(A!19)))),
% 20.97/13.70 inference(rewrite,[status(thm)],[])).
% 20.97/13.70 tff(217,plain,
% 20.97/13.70 ((empty_carrier(A!19) | (k2_lattice3(A!19) = relation_of_lattice(A!19)) | (~latt_str(A!19)) | (~lattice(A!19))) <=> (empty_carrier(A!19) | (~latt_str(A!19)) | (~lattice(A!19)) | (k2_lattice3(A!19) = relation_of_lattice(A!19)))),
% 20.97/13.70 inference(rewrite,[status(thm)],[])).
% 20.97/13.70 tff(218,plain,
% 20.97/13.70 (((~![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) | (~latt_str(A!19)) | (~lattice(A!19)) | (k2_lattice3(A!19) = relation_of_lattice(A!19))))),
% 20.97/13.70 inference(monotonicity,[status(thm)],[217])).
% 20.97/13.70 tff(219,plain,
% 20.97/13.70 (((~![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) | (~latt_str(A!19)) | (~lattice(A!19)) | (k2_lattice3(A!19) = relation_of_lattice(A!19)))),
% 20.97/13.70 inference(transitivity,[status(thm)],[218, 216])).
% 20.97/13.70 tff(220,plain,
% 20.97/13.70 ((~![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)))),
% 20.97/13.70 inference(quant_inst,[status(thm)],[])).
% 20.97/13.70 tff(221,plain,
% 20.97/13.70 ((~![A: $i] : (empty_carrier(A) | (k2_lattice3(A) = relation_of_lattice(A)) | (~latt_str(A)) | (~lattice(A)))) | empty_carrier(A!19) | (~latt_str(A!19)) | (~lattice(A!19)) | (k2_lattice3(A!19) = relation_of_lattice(A!19))),
% 20.97/13.70 inference(modus_ponens,[status(thm)],[220, 219])).
% 20.97/13.70 tff(222,plain,
% 20.97/13.70 (k2_lattice3(A!19) = relation_of_lattice(A!19)),
% 20.97/13.70 inference(unit_resolution,[status(thm)],[221, 215, 19, 18, 17])).
% 20.97/13.70 tff(223,plain,
% 20.97/13.70 (relation_of_lattice(A!19) = k2_lattice3(A!19)),
% 20.97/13.70 inference(symmetry,[status(thm)],[222])).
% 20.97/13.70 tff(224,plain,
% 20.97/13.70 (rel_str_of(the_carrier(A!19), relation_of_lattice(A!19)) = rel_str_of(the_carrier(A!19), k2_lattice3(A!19))),
% 20.97/13.70 inference(monotonicity,[status(thm)],[223])).
% 20.97/13.70 tff(225,plain,
% 20.97/13.70 (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))))),
% 20.97/13.70 inference(transitivity,[status(thm)],[224, 202, 176])).
% 20.97/13.70 tff(226,plain,
% 20.97/13.70 (^[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)))),
% 20.97/13.70 inference(bind,[status(th)],[])).
% 20.97/13.70 tff(227,plain,
% 20.97/13.70 (![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))),
% 20.97/13.70 inference(quant_intro,[status(thm)],[226])).
% 20.97/13.70 tff(228,plain,
% 20.97/13.70 (![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))),
% 20.97/13.70 inference(rewrite,[status(thm)],[])).
% 20.97/13.70 tff(229,axiom,(![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 20.97/13.70 tff(230,plain,
% 20.97/13.70 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 20.97/13.70 inference(modus_ponens,[status(thm)],[229, 228])).
% 20.97/13.70 tff(231,plain,(
% 20.97/13.70 ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 20.97/13.70 inference(skolemize,[status(sab)],[230])).
% 20.97/13.70 tff(232,plain,
% 20.97/13.70 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 20.97/13.70 inference(modus_ponens,[status(thm)],[231, 227])).
% 20.97/13.70 tff(233,plain,
% 20.97/13.70 ((~![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)))),
% 20.97/13.70 inference(quant_inst,[status(thm)],[])).
% 20.97/13.70 tff(234,plain,
% 20.97/13.70 (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))),
% 20.97/13.70 inference(unit_resolution,[status(thm)],[233, 232])).
% 20.97/13.70 tff(235,plain,
% 20.97/13.70 (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))),
% 20.97/13.70 inference(monotonicity,[status(thm)],[223])).
% 20.97/13.70 tff(236,plain,
% 20.97/13.70 (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))),
% 20.97/13.70 inference(symmetry,[status(thm)],[235])).
% 20.97/13.70 tff(237,plain,
% 20.97/13.70 (^[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)))))))),
% 20.97/13.70 inference(bind,[status(th)],[])).
% 20.97/13.70 tff(238,plain,
% 20.97/13.70 (![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))))))),
% 20.97/13.70 inference(quant_intro,[status(thm)],[237])).
% 20.97/13.70 tff(239,plain,
% 20.97/13.70 (^[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))))))))),
% 20.97/13.70 inference(bind,[status(th)],[])).
% 20.97/13.70 tff(240,plain,
% 20.97/13.70 (![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))))))),
% 20.97/13.70 inference(quant_intro,[status(thm)],[239])).
% 20.97/13.70 tff(241,plain,
% 20.97/13.70 (![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))))),
% 20.97/13.70 inference(rewrite,[status(thm)],[])).
% 20.97/13.70 tff(242,plain,
% 20.97/13.70 (^[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))))))),
% 20.97/13.70 inference(bind,[status(th)],[])).
% 20.97/13.70 tff(243,plain,
% 20.97/13.70 (![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))))),
% 20.97/13.70 inference(quant_intro,[status(thm)],[242])).
% 20.97/13.70 tff(244,axiom,(![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ((((reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A))) & transitive(k2_lattice3(A))) & v1_partfun1(k2_lattice3(A), the_carrier(A), the_carrier(A))) & relation_of2_as_subset(k2_lattice3(A), the_carrier(A), the_carrier(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k2_lattice3')).
% 20.97/13.70 tff(245,plain,
% 20.97/13.70 (![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))))),
% 20.97/13.70 inference(modus_ponens,[status(thm)],[244, 243])).
% 20.97/13.70 tff(246,plain,
% 20.97/13.70 (![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))))),
% 20.97/13.70 inference(modus_ponens,[status(thm)],[245, 241])).
% 20.97/13.70 tff(247,plain,(
% 20.97/13.70 ![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))))),
% 20.97/13.70 inference(skolemize,[status(sab)],[246])).
% 20.97/13.70 tff(248,plain,
% 20.97/13.70 (![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))))))),
% 20.97/13.70 inference(modus_ponens,[status(thm)],[247, 240])).
% 20.97/13.70 tff(249,plain,
% 20.97/13.70 (![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))))))),
% 20.97/13.70 inference(modus_ponens,[status(thm)],[248, 238])).
% 20.97/13.70 tff(250,plain,
% 20.97/13.70 (((~![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))))))),
% 20.97/13.70 inference(rewrite,[status(thm)],[])).
% 20.97/13.70 tff(251,plain,
% 20.97/13.70 ((~![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))))))),
% 20.97/13.71 inference(quant_inst,[status(thm)],[])).
% 20.97/13.71 tff(252,plain,
% 20.97/13.71 ((~![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)))))),
% 20.97/13.71 inference(modus_ponens,[status(thm)],[251, 250])).
% 20.97/13.71 tff(253,plain,
% 20.97/13.71 (~((~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))))),
% 20.97/13.71 inference(unit_resolution,[status(thm)],[252, 249, 19, 18, 17])).
% 20.97/13.71 tff(254,plain,
% 20.97/13.71 (((~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))),
% 20.97/13.71 inference(tautology,[status(thm)],[])).
% 20.97/13.71 tff(255,plain,
% 20.97/13.71 (relation_of2_as_subset(k2_lattice3(A!19), the_carrier(A!19), the_carrier(A!19))),
% 20.97/13.71 inference(unit_resolution,[status(thm)],[254, 253])).
% 20.97/13.71 tff(256,plain,
% 20.97/13.71 (relation_of2_as_subset(relation_of_lattice(A!19), the_carrier(A!19), the_carrier(A!19))),
% 20.97/13.71 inference(modus_ponens,[status(thm)],[255, 236])).
% 20.97/13.71 tff(257,plain,
% 20.97/13.71 ((~(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))),
% 20.97/13.71 inference(tautology,[status(thm)],[])).
% 20.97/13.71 tff(258,plain,
% 20.97/13.71 (relation_of2(relation_of_lattice(A!19), the_carrier(A!19), the_carrier(A!19))),
% 20.97/13.71 inference(unit_resolution,[status(thm)],[257, 256, 234])).
% 20.97/13.71 tff(259,plain,
% 20.97/13.71 (^[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)))))))),
% 20.97/13.71 inference(bind,[status(th)],[])).
% 20.97/13.71 tff(260,plain,
% 20.97/13.71 (![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))))))),
% 20.97/13.71 inference(quant_intro,[status(thm)],[259])).
% 20.97/13.71 tff(261,plain,
% 20.97/13.71 (^[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)))))))),
% 20.97/13.71 inference(bind,[status(th)],[])).
% 20.97/13.71 tff(262,plain,
% 20.97/13.71 (![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))))))),
% 20.97/13.71 inference(quant_intro,[status(thm)],[261])).
% 20.97/13.71 tff(263,plain,
% 20.97/13.71 (![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))))))),
% 20.97/13.71 inference(transitivity,[status(thm)],[262, 260])).
% 20.97/13.71 tff(264,plain,
% 20.97/13.71 (^[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)))))))),
% 20.97/13.71 inference(bind,[status(th)],[])).
% 20.97/13.71 tff(265,plain,
% 20.97/13.71 (![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))))))),
% 20.97/13.71 inference(quant_intro,[status(thm)],[264])).
% 20.97/13.71 tff(266,plain,
% 20.97/13.71 (![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))))),
% 20.97/13.71 inference(rewrite,[status(thm)],[])).
% 20.97/13.71 tff(267,plain,
% 20.97/13.71 (^[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))))))),
% 20.97/13.71 inference(bind,[status(th)],[])).
% 20.97/13.71 tff(268,plain,
% 20.97/13.71 (![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))))),
% 20.97/13.71 inference(quant_intro,[status(thm)],[267])).
% 20.97/13.71 tff(269,axiom,(![A: $i, B: $i] : (relation_of2(B, A, A) => ![C: $i, D: $i] : ((rel_str_of(A, B) = rel_str_of(C, D)) => ((A = C) & (B = D))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','free_g1_orders_2')).
% 20.97/13.71 tff(270,plain,
% 20.97/13.71 (![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))))),
% 20.97/13.71 inference(modus_ponens,[status(thm)],[269, 268])).
% 20.97/13.71 tff(271,plain,
% 20.97/13.71 (![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))))),
% 20.97/13.71 inference(modus_ponens,[status(thm)],[270, 266])).
% 20.97/13.71 tff(272,plain,(
% 20.97/13.71 ![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))))),
% 20.97/13.71 inference(skolemize,[status(sab)],[271])).
% 20.97/13.71 tff(273,plain,
% 20.97/13.71 (![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))))))),
% 20.97/13.71 inference(modus_ponens,[status(thm)],[272, 265])).
% 20.97/13.71 tff(274,plain,
% 20.97/13.71 (![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))))))),
% 20.97/13.71 inference(modus_ponens,[status(thm)],[273, 263])).
% 20.97/13.71 tff(275,plain,
% 20.97/13.71 (((~![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))))))),
% 20.97/13.71 inference(rewrite,[status(thm)],[])).
% 20.97/13.71 tff(276,plain,
% 20.97/13.71 ((~![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))))))),
% 20.97/13.71 inference(quant_inst,[status(thm)],[])).
% 20.97/13.71 tff(277,plain,
% 20.97/13.71 ((~![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)))))),
% 20.97/13.71 inference(modus_ponens,[status(thm)],[276, 275])).
% 20.97/13.71 tff(278,plain,
% 20.97/13.71 ((~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)))))),
% 20.97/13.71 inference(unit_resolution,[status(thm)],[277, 274])).
% 20.97/13.71 tff(279,plain,
% 20.97/13.71 (![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)))))),
% 20.97/13.71 inference(unit_resolution,[status(thm)],[278, 258])).
% 20.97/13.71 tff(280,plain,
% 20.97/13.71 (((~![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))))))))),
% 20.97/13.71 inference(rewrite,[status(thm)],[])).
% 20.97/13.71 tff(281,plain,
% 20.97/13.71 ((~![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))))))))),
% 20.97/13.71 inference(quant_inst,[status(thm)],[])).
% 20.97/13.71 tff(282,plain,
% 20.97/13.71 ((~![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)))))))),
% 20.97/13.71 inference(modus_ponens,[status(thm)],[281, 280])).
% 20.97/13.71 tff(283,plain,
% 20.97/13.71 ((~(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)))))))),
% 20.97/13.71 inference(unit_resolution,[status(thm)],[282, 279])).
% 20.97/13.71 tff(284,plain,
% 20.97/13.71 (~((~(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))))))),
% 20.97/13.71 inference(unit_resolution,[status(thm)],[283, 225])).
% 20.97/13.71 tff(285,plain,
% 20.97/13.71 (((~(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))))),
% 20.97/13.71 inference(tautology,[status(thm)],[])).
% 20.97/13.71 tff(286,plain,
% 20.97/13.71 (relation_of_lattice(A!19) = the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))),
% 20.97/13.71 inference(unit_resolution,[status(thm)],[285, 284])).
% 20.97/13.71 tff(287,plain,
% 20.97/13.71 (the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))) = relation_of_lattice(A!19)),
% 20.97/13.71 inference(symmetry,[status(thm)],[286])).
% 20.97/13.71 tff(288,plain,
% 20.97/13.71 (^[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))))))),
% 20.97/13.71 inference(bind,[status(th)],[])).
% 20.97/13.71 tff(289,plain,
% 20.97/13.71 (![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)))))),
% 20.97/13.71 inference(quant_intro,[status(thm)],[288])).
% 20.97/13.71 tff(290,plain,
% 20.97/13.71 (^[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))))))),
% 20.97/13.71 inference(bind,[status(th)],[])).
% 20.97/13.71 tff(291,plain,
% 20.97/13.71 (![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)))))),
% 20.97/13.71 inference(quant_intro,[status(thm)],[290])).
% 20.97/13.71 tff(292,plain,
% 20.97/13.71 (![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)))),
% 20.97/13.71 inference(rewrite,[status(thm)],[])).
% 20.97/13.71 tff(293,plain,
% 20.97/13.71 (^[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))))),
% 20.97/13.71 inference(bind,[status(th)],[])).
% 20.97/13.71 tff(294,plain,
% 20.97/13.71 (![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)))),
% 20.97/13.71 inference(quant_intro,[status(thm)],[293])).
% 20.97/13.71 tff(295,axiom,(![A: $i] : (latt_str(A) => (meet_semilatt_str(A) & join_semilatt_str(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l3_lattices')).
% 20.97/13.71 tff(296,plain,
% 20.97/13.71 (![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A)))),
% 20.97/13.71 inference(modus_ponens,[status(thm)],[295, 294])).
% 20.97/13.71 tff(297,plain,
% 20.97/13.71 (![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A)))),
% 20.97/13.71 inference(modus_ponens,[status(thm)],[296, 292])).
% 20.97/13.71 tff(298,plain,(
% 20.97/13.71 ![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A)))),
% 20.97/13.71 inference(skolemize,[status(sab)],[297])).
% 20.97/13.71 tff(299,plain,
% 20.97/13.71 (![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))),
% 20.97/13.71 inference(modus_ponens,[status(thm)],[298, 291])).
% 20.97/13.71 tff(300,plain,
% 20.97/13.71 (![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))),
% 20.97/13.71 inference(modus_ponens,[status(thm)],[299, 289])).
% 20.97/13.71 tff(301,plain,
% 20.97/13.71 (((~![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)))))),
% 20.97/13.71 inference(rewrite,[status(thm)],[])).
% 20.97/13.71 tff(302,plain,
% 20.97/13.71 ((~![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)))))),
% 20.97/13.71 inference(quant_inst,[status(thm)],[])).
% 20.97/13.71 tff(303,plain,
% 20.97/13.71 ((~![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))))),
% 20.97/13.71 inference(modus_ponens,[status(thm)],[302, 301])).
% 20.97/13.71 tff(304,plain,
% 20.97/13.71 (~((~meet_semilatt_str(A!19)) | (~join_semilatt_str(A!19)))),
% 20.97/13.71 inference(unit_resolution,[status(thm)],[303, 300, 17])).
% 20.97/13.71 tff(305,plain,
% 20.97/13.71 (((~meet_semilatt_str(A!19)) | (~join_semilatt_str(A!19))) | join_semilatt_str(A!19)),
% 20.97/13.71 inference(tautology,[status(thm)],[])).
% 20.97/13.71 tff(306,plain,
% 20.97/13.71 (join_semilatt_str(A!19)),
% 20.97/13.71 inference(unit_resolution,[status(thm)],[305, 304])).
% 20.97/13.71 tff(307,plain,
% 20.97/13.71 (^[A: $i] : refl((one_sorted_str(A) | (~join_semilatt_str(A))) <=> (one_sorted_str(A) | (~join_semilatt_str(A))))),
% 20.97/13.71 inference(bind,[status(th)],[])).
% 20.97/13.71 tff(308,plain,
% 20.97/13.71 (![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A))) <=> ![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A)))),
% 20.97/13.71 inference(quant_intro,[status(thm)],[307])).
% 20.97/13.71 tff(309,plain,
% 20.97/13.71 (![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A))) <=> ![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A)))),
% 20.97/13.71 inference(rewrite,[status(thm)],[])).
% 20.97/13.71 tff(310,plain,
% 20.97/13.71 (^[A: $i] : rewrite((join_semilatt_str(A) => one_sorted_str(A)) <=> (one_sorted_str(A) | (~join_semilatt_str(A))))),
% 20.97/13.71 inference(bind,[status(th)],[])).
% 20.97/13.71 tff(311,plain,
% 20.97/13.71 (![A: $i] : (join_semilatt_str(A) => one_sorted_str(A)) <=> ![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A)))),
% 20.97/13.71 inference(quant_intro,[status(thm)],[310])).
% 20.97/13.71 tff(312,axiom,(![A: $i] : (join_semilatt_str(A) => one_sorted_str(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l2_lattices')).
% 20.97/13.71 tff(313,plain,
% 20.97/13.71 (![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A)))),
% 20.97/13.71 inference(modus_ponens,[status(thm)],[312, 311])).
% 20.97/13.71 tff(314,plain,
% 20.97/13.71 (![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A)))),
% 20.97/13.71 inference(modus_ponens,[status(thm)],[313, 309])).
% 20.97/13.71 tff(315,plain,(
% 20.97/13.71 ![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A)))),
% 20.97/13.71 inference(skolemize,[status(sab)],[314])).
% 20.97/13.71 tff(316,plain,
% 20.97/13.71 (![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A)))),
% 20.97/13.71 inference(modus_ponens,[status(thm)],[315, 308])).
% 20.97/13.71 tff(317,plain,
% 20.97/13.71 (((~![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)))),
% 20.97/13.71 inference(rewrite,[status(thm)],[])).
% 20.97/13.71 tff(318,plain,
% 20.97/13.71 ((~![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A)))) | (one_sorted_str(A!19) | (~join_semilatt_str(A!19)))),
% 20.97/13.71 inference(quant_inst,[status(thm)],[])).
% 20.97/13.71 tff(319,plain,
% 20.97/13.71 ((~![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A)))) | one_sorted_str(A!19) | (~join_semilatt_str(A!19))),
% 20.97/13.71 inference(modus_ponens,[status(thm)],[318, 317])).
% 20.97/13.71 tff(320,plain,
% 20.97/13.71 (one_sorted_str(A!19)),
% 20.97/13.71 inference(unit_resolution,[status(thm)],[319, 316, 306])).
% 20.97/13.71 tff(321,plain,
% 20.97/13.71 (^[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))))),
% 20.97/13.71 inference(bind,[status(th)],[])).
% 20.97/13.71 tff(322,plain,
% 20.97/13.71 (![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)))),
% 20.97/13.71 inference(quant_intro,[status(thm)],[321])).
% 20.97/13.71 tff(323,plain,
% 20.97/13.71 (^[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)))))),
% 20.97/13.71 inference(bind,[status(th)],[])).
% 20.97/13.71 tff(324,plain,
% 20.97/13.71 (![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)))),
% 20.97/13.71 inference(quant_intro,[status(thm)],[323])).
% 20.97/13.71 tff(325,plain,
% 20.97/13.71 (![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))))),
% 20.97/13.71 inference(rewrite,[status(thm)],[])).
% 20.97/13.71 tff(326,plain,
% 20.97/13.71 (^[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)))))),
% 20.97/13.71 inference(bind,[status(th)],[])).
% 20.97/13.71 tff(327,plain,
% 20.97/13.71 (![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))))),
% 20.97/13.71 inference(quant_intro,[status(thm)],[326])).
% 20.97/13.71 tff(328,axiom,(![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => (~empty(the_carrier(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_struct_0')).
% 20.97/13.71 tff(329,plain,
% 20.97/13.71 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 20.97/13.71 inference(modus_ponens,[status(thm)],[328, 327])).
% 20.97/13.71 tff(330,plain,
% 20.97/13.71 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 20.97/13.71 inference(modus_ponens,[status(thm)],[329, 325])).
% 20.97/13.71 tff(331,plain,(
% 20.97/13.71 ![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 20.97/13.71 inference(skolemize,[status(sab)],[330])).
% 20.97/13.71 tff(332,plain,
% 20.97/13.71 (![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))),
% 20.97/13.71 inference(modus_ponens,[status(thm)],[331, 324])).
% 20.97/13.71 tff(333,plain,
% 20.97/13.71 (![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))),
% 20.97/13.71 inference(modus_ponens,[status(thm)],[332, 322])).
% 20.97/13.71 tff(334,plain,
% 20.97/13.71 (((~![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))))),
% 20.97/13.71 inference(rewrite,[status(thm)],[])).
% 20.97/13.71 tff(335,plain,
% 20.97/13.71 ((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))))),
% 20.97/13.71 inference(rewrite,[status(thm)],[])).
% 20.97/13.71 tff(336,plain,
% 20.97/13.71 (((~![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)))))),
% 20.97/13.71 inference(monotonicity,[status(thm)],[335])).
% 20.97/13.71 tff(337,plain,
% 20.97/13.71 (((~![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))))),
% 20.97/13.71 inference(transitivity,[status(thm)],[336, 334])).
% 20.97/13.71 tff(338,plain,
% 20.97/13.71 ((~![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)))),
% 20.97/13.71 inference(quant_inst,[status(thm)],[])).
% 20.97/13.71 tff(339,plain,
% 20.97/13.71 ((~![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)))),
% 20.97/13.71 inference(modus_ponens,[status(thm)],[338, 337])).
% 20.97/13.71 tff(340,plain,
% 20.97/13.71 ((~one_sorted_str(A!19)) | (~empty(the_carrier(A!19)))),
% 20.97/13.71 inference(unit_resolution,[status(thm)],[339, 333, 19])).
% 20.97/13.71 tff(341,plain,
% 20.97/13.71 (~empty(the_carrier(A!19))),
% 20.97/13.71 inference(unit_resolution,[status(thm)],[340, 320])).
% 20.97/13.71 tff(342,plain,
% 20.97/13.71 (^[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))))),
% 20.97/13.71 inference(bind,[status(th)],[])).
% 20.97/13.71 tff(343,plain,
% 20.97/13.71 (![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)))),
% 20.97/13.71 inference(quant_intro,[status(thm)],[342])).
% 20.97/13.71 tff(344,plain,
% 20.97/13.71 (^[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)))))),
% 20.97/13.71 inference(bind,[status(th)],[])).
% 20.97/13.71 tff(345,plain,
% 20.97/13.71 (![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)))),
% 20.97/13.71 inference(quant_intro,[status(thm)],[344])).
% 20.97/13.71 tff(346,plain,
% 20.97/13.71 (![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)))),
% 20.97/13.71 inference(rewrite,[status(thm)],[])).
% 20.97/13.71 tff(347,plain,
% 20.97/13.71 (^[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)))))),
% 20.97/13.71 inference(bind,[status(th)],[])).
% 20.97/13.71 tff(348,plain,
% 20.97/13.71 (![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)))),
% 20.97/13.71 inference(quant_intro,[status(thm)],[347])).
% 20.97/13.71 tff(349,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/sandbox2/benchmark/theBenchmark.p','redefinition_k1_domain_1')).
% 20.97/13.71 tff(350,plain,
% 20.97/13.71 (![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)))),
% 20.97/13.71 inference(modus_ponens,[status(thm)],[349, 348])).
% 20.97/13.71 tff(351,plain,
% 20.97/13.71 (![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)))),
% 20.97/13.71 inference(modus_ponens,[status(thm)],[350, 346])).
% 20.97/13.71 tff(352,plain,(
% 20.97/13.71 ![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)))),
% 20.97/13.71 inference(skolemize,[status(sab)],[351])).
% 20.97/13.71 tff(353,plain,
% 20.97/13.71 (![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)))),
% 20.97/13.71 inference(modus_ponens,[status(thm)],[352, 345])).
% 20.97/13.71 tff(354,plain,
% 20.97/13.71 (![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)))),
% 20.97/13.71 inference(modus_ponens,[status(thm)],[353, 343])).
% 20.97/13.71 tff(355,plain,
% 20.97/13.71 (((~![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)))),
% 20.97/13.71 inference(rewrite,[status(thm)],[])).
% 20.97/13.71 tff(356,plain,
% 20.97/13.71 ((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)))),
% 20.97/13.71 inference(rewrite,[status(thm)],[])).
% 20.97/13.71 tff(357,plain,
% 20.97/13.71 (((~![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))))),
% 20.97/13.71 inference(monotonicity,[status(thm)],[356])).
% 20.97/13.71 tff(358,plain,
% 20.97/13.71 (((~![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)))),
% 20.97/13.71 inference(transitivity,[status(thm)],[357, 355])).
% 20.97/13.71 tff(359,plain,
% 20.97/13.71 ((~![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))))),
% 20.97/13.71 inference(quant_inst,[status(thm)],[])).
% 20.97/13.71 tff(360,plain,
% 20.97/13.71 ((~![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))),
% 20.97/13.71 inference(modus_ponens,[status(thm)],[359, 358])).
% 20.97/13.71 tff(361,plain,
% 20.97/13.71 (ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C!21) = ordered_pair(B!20, C!21)),
% 20.97/13.71 inference(unit_resolution,[status(thm)],[360, 354, 50, 44, 341])).
% 20.97/13.71 tff(362,plain,
% 20.97/13.71 (ordered_pair(B!20, C!21) = ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C!21)),
% 20.97/13.71 inference(symmetry,[status(thm)],[361])).
% 20.97/13.71 tff(363,plain,
% 20.97/13.71 (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))),
% 20.97/13.71 inference(monotonicity,[status(thm)],[362, 287])).
% 20.97/13.71 tff(364,plain,
% 20.97/13.71 (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))))),
% 20.97/13.71 inference(symmetry,[status(thm)],[363])).
% 20.97/13.71 tff(365,plain,
% 20.97/13.71 ((~(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)))),
% 20.97/13.71 inference(rewrite,[status(thm)],[])).
% 20.97/13.71 tff(366,plain,
% 20.97/13.71 (~(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)))),
% 20.97/13.71 inference(or_elim,[status(thm)],[43])).
% 20.97/13.71 tff(367,plain,
% 20.97/13.71 ((~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))),
% 20.97/13.71 inference(modus_ponens,[status(thm)],[366, 365])).
% 20.97/13.71 tff(368,plain,
% 20.97/13.71 (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))))),
% 20.97/13.71 inference(tautology,[status(thm)],[])).
% 20.97/13.71 tff(369,plain,
% 20.97/13.71 (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))),
% 20.97/13.71 inference(unit_resolution,[status(thm)],[368, 367])).
% 20.97/13.71 tff(370,plain,
% 20.97/13.71 (below_refl(A!19, B!20, C!21)),
% 20.97/13.71 inference(unit_resolution,[status(thm)],[369, 80])).
% 20.97/13.71 tff(371,plain,
% 20.97/13.71 (^[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))))))),
% 20.97/13.71 inference(bind,[status(th)],[])).
% 20.97/13.71 tff(372,plain,
% 20.97/13.71 (![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)))))),
% 20.97/13.71 inference(quant_intro,[status(thm)],[371])).
% 20.97/13.71 tff(373,plain,
% 20.97/13.71 (^[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))))),
% 20.97/13.71 inference(bind,[status(th)],[])).
% 20.97/13.71 tff(374,plain,
% 20.97/13.71 (![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)))),
% 20.97/13.72 inference(quant_intro,[status(thm)],[373])).
% 20.97/13.72 tff(375,plain,
% 20.97/13.72 (^[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))))),
% 20.97/13.72 inference(bind,[status(th)],[])).
% 20.97/13.72 tff(376,plain,
% 20.97/13.72 (![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)))),
% 20.97/13.72 inference(quant_intro,[status(thm)],[375])).
% 20.97/13.72 tff(377,plain,
% 20.97/13.72 (![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)))),
% 20.97/13.72 inference(transitivity,[status(thm)],[376, 374])).
% 20.97/13.72 tff(378,plain,
% 20.97/13.72 (^[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)))))),
% 20.97/13.72 inference(bind,[status(th)],[])).
% 20.97/13.72 tff(379,plain,
% 20.97/13.72 (![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)))),
% 20.97/13.72 inference(quant_intro,[status(thm)],[378])).
% 20.97/13.72 tff(380,plain,
% 20.97/13.72 (![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)))))),
% 20.97/13.72 inference(rewrite,[status(thm)],[])).
% 20.97/13.72 tff(381,plain,
% 20.97/13.72 (^[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)))))))),
% 20.97/13.72 inference(bind,[status(th)],[])).
% 20.97/13.72 tff(382,plain,
% 20.97/13.72 (![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)))))),
% 20.97/13.72 inference(quant_intro,[status(thm)],[381])).
% 20.97/13.72 tff(383,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/sandbox2/benchmark/theBenchmark.p','t32_filter_1')).
% 20.97/13.72 tff(384,plain,
% 20.97/13.72 (![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)))))),
% 20.97/13.72 inference(modus_ponens,[status(thm)],[383, 382])).
% 20.97/13.72 tff(385,plain,
% 20.97/13.72 (![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)))))),
% 20.97/13.72 inference(modus_ponens,[status(thm)],[384, 380])).
% 20.97/13.72 tff(386,plain,(
% 20.97/13.72 ![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)))))),
% 20.97/13.72 inference(skolemize,[status(sab)],[385])).
% 20.97/13.72 tff(387,plain,
% 20.97/13.72 (![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)))),
% 20.97/13.72 inference(modus_ponens,[status(thm)],[386, 379])).
% 20.97/13.72 tff(388,plain,
% 20.97/13.72 (![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)))),
% 20.97/13.72 inference(modus_ponens,[status(thm)],[387, 377])).
% 20.97/13.72 tff(389,plain,
% 20.97/13.72 (![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)))))),
% 20.97/13.72 inference(modus_ponens,[status(thm)],[388, 372])).
% 20.97/13.72 tff(390,plain,
% 20.97/13.72 (((~![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)))))),
% 20.97/13.72 inference(rewrite,[status(thm)],[])).
% 20.97/13.72 tff(391,plain,
% 20.97/13.72 ((~![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)))))),
% 20.97/13.72 inference(quant_inst,[status(thm)],[])).
% 20.97/13.72 tff(392,plain,
% 20.97/13.72 ((~![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))))),
% 20.97/13.72 inference(modus_ponens,[status(thm)],[391, 390])).
% 20.97/13.72 tff(393,plain,
% 20.97/13.72 (![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))))),
% 20.97/13.72 inference(unit_resolution,[status(thm)],[392, 389, 19, 18, 17])).
% 20.97/13.72 tff(394,plain,
% 20.97/13.72 (((~![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))))),
% 20.97/13.72 inference(rewrite,[status(thm)],[])).
% 20.97/13.72 tff(395,plain,
% 20.97/13.72 ((~![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))))),
% 20.97/13.72 inference(quant_inst,[status(thm)],[])).
% 20.97/13.72 tff(396,plain,
% 20.97/13.72 ((~![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)))),
% 20.97/13.72 inference(modus_ponens,[status(thm)],[395, 394])).
% 20.97/13.72 tff(397,plain,
% 20.97/13.72 (![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)))),
% 20.97/13.72 inference(unit_resolution,[status(thm)],[396, 50, 393])).
% 20.97/13.72 tff(398,plain,
% 20.97/13.72 (((~![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)))),
% 20.97/13.72 inference(rewrite,[status(thm)],[])).
% 20.97/13.72 tff(399,plain,
% 20.97/13.72 ((~![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)))),
% 20.97/13.72 inference(quant_inst,[status(thm)],[])).
% 20.97/13.72 tff(400,plain,
% 20.97/13.72 ((~![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))),
% 20.97/13.72 inference(modus_ponens,[status(thm)],[399, 398])).
% 20.97/13.72 tff(401,plain,
% 20.97/13.72 (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)),
% 20.97/13.72 inference(unit_resolution,[status(thm)],[400, 44, 397])).
% 20.97/13.72 tff(402,plain,
% 20.97/13.72 ((~(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))),
% 20.97/13.72 inference(tautology,[status(thm)],[])).
% 20.97/13.72 tff(403,plain,
% 20.97/13.72 (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))),
% 20.97/13.72 inference(unit_resolution,[status(thm)],[402, 401])).
% 20.97/13.72 tff(404,plain,
% 20.97/13.72 (in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C!21), relation_of_lattice(A!19))),
% 20.97/13.72 inference(unit_resolution,[status(thm)],[403, 370])).
% 20.97/13.72 tff(405,plain,
% 20.97/13.72 (in(ordered_pair(B!20, C!21), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))),
% 20.97/13.72 inference(modus_ponens,[status(thm)],[404, 364])).
% 20.97/13.72 tff(406,plain,
% 20.97/13.72 (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)))),
% 20.97/13.72 inference(monotonicity,[status(thm)],[49, 173])).
% 20.97/13.72 tff(407,plain,
% 20.97/13.72 (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))))),
% 20.97/13.72 inference(symmetry,[status(thm)],[406])).
% 20.97/13.72 tff(408,plain,
% 20.97/13.72 (element(C!21, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))),
% 20.97/13.72 inference(modus_ponens,[status(thm)],[140, 407])).
% 20.97/13.72 tff(409,plain,
% 20.97/13.72 (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)))),
% 20.97/13.72 inference(monotonicity,[status(thm)],[55, 173])).
% 20.97/13.72 tff(410,plain,
% 20.97/13.72 (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))))),
% 20.97/13.72 inference(symmetry,[status(thm)],[409])).
% 20.97/13.72 tff(411,plain,
% 20.97/13.72 (element(B!20, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))),
% 20.97/13.72 inference(modus_ponens,[status(thm)],[147, 410])).
% 20.97/13.72 tff(412,plain,
% 20.97/13.72 (^[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)))))))),
% 20.97/13.72 inference(bind,[status(th)],[])).
% 20.97/13.72 tff(413,plain,
% 20.97/13.72 (![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))))))),
% 20.97/13.72 inference(quant_intro,[status(thm)],[412])).
% 20.97/13.72 tff(414,plain,
% 20.97/13.72 (^[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)))))))),
% 20.97/13.72 inference(bind,[status(th)],[])).
% 20.97/13.72 tff(415,plain,
% 20.97/13.72 (![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))))))),
% 20.97/13.72 inference(quant_intro,[status(thm)],[414])).
% 20.97/13.72 tff(416,plain,
% 20.97/13.72 (![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))))))),
% 20.97/13.72 inference(transitivity,[status(thm)],[415, 413])).
% 20.97/13.72 tff(417,plain,
% 20.97/13.72 (![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))))))),
% 20.97/13.72 inference(rewrite,[status(thm)],[])).
% 20.97/13.72 tff(418,plain,
% 20.97/13.72 (^[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))))))))),
% 20.97/13.72 inference(bind,[status(th)],[])).
% 20.97/13.72 tff(419,plain,
% 20.97/13.72 (![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))))))),
% 20.97/13.72 inference(quant_intro,[status(thm)],[418])).
% 20.97/13.72 tff(420,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/sandbox2/benchmark/theBenchmark.p','d9_orders_2')).
% 20.97/13.72 tff(421,plain,
% 20.97/13.72 (![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))))))),
% 20.97/13.72 inference(modus_ponens,[status(thm)],[420, 419])).
% 20.97/13.72 tff(422,plain,
% 20.97/13.72 (![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))))))),
% 20.97/13.72 inference(modus_ponens,[status(thm)],[421, 417])).
% 20.97/13.72 tff(423,plain,(
% 20.97/13.72 ![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))))))),
% 20.97/13.72 inference(skolemize,[status(sab)],[422])).
% 20.97/13.72 tff(424,plain,
% 20.97/13.72 (![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))))))),
% 20.97/13.72 inference(modus_ponens,[status(thm)],[423, 416])).
% 20.97/13.72 tff(425,plain,
% 20.97/13.72 (((~![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))))))))),
% 20.97/13.72 inference(rewrite,[status(thm)],[])).
% 20.97/13.72 tff(426,plain,
% 20.97/13.72 ((~![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))))))))),
% 20.97/13.72 inference(quant_inst,[status(thm)],[])).
% 20.97/13.72 tff(427,plain,
% 20.97/13.72 ((~![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)))))))),
% 20.97/13.72 inference(modus_ponens,[status(thm)],[426, 425])).
% 20.97/13.72 tff(428,plain,
% 20.97/13.72 ((~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)))))))),
% 20.97/13.72 inference(unit_resolution,[status(thm)],[427, 424])).
% 20.97/13.72 tff(429,plain,
% 20.97/13.72 (![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)))))))),
% 20.97/13.72 inference(unit_resolution,[status(thm)],[428, 184])).
% 20.97/13.72 tff(430,plain,
% 20.97/13.72 (((~![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)))))))),
% 20.97/13.72 inference(rewrite,[status(thm)],[])).
% 20.97/13.72 tff(431,plain,
% 20.97/13.72 ((~![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)))))))),
% 20.97/13.72 inference(quant_inst,[status(thm)],[])).
% 20.97/13.72 tff(432,plain,
% 20.97/13.72 ((~![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))))))),
% 20.97/13.72 inference(modus_ponens,[status(thm)],[431, 430])).
% 20.97/13.72 tff(433,plain,
% 20.97/13.72 ((~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))))))),
% 20.97/13.72 inference(unit_resolution,[status(thm)],[432, 429])).
% 20.97/13.72 tff(434,plain,
% 20.97/13.72 (![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))))))),
% 20.97/13.72 inference(unit_resolution,[status(thm)],[433, 411])).
% 20.97/13.72 tff(435,plain,
% 20.97/13.72 (((~![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))))))),
% 20.97/13.72 inference(rewrite,[status(thm)],[])).
% 20.97/13.72 tff(436,plain,
% 20.97/13.72 ((~![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))))))),
% 20.97/13.72 inference(quant_inst,[status(thm)],[])).
% 20.97/13.72 tff(437,plain,
% 20.97/13.72 ((~![C: $i] : ((~element(C, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C) <=> in(ordered_pair(B!20, C), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))))) | (~element(C!21, the_carrier(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))) | (related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C!21) <=> in(ordered_pair(B!20, C!21), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))),
% 20.97/13.72 inference(modus_ponens,[status(thm)],[436, 435])).
% 20.97/13.72 tff(438,plain,
% 20.97/13.72 (related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C!21) <=> in(ordered_pair(B!20, C!21), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))),
% 20.97/13.72 inference(unit_resolution,[status(thm)],[437, 434, 408])).
% 20.97/13.72 tff(439,plain,
% 20.97/13.72 ((~(related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C!21) <=> in(ordered_pair(B!20, C!21), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))) | related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C!21) | (~in(ordered_pair(B!20, C!21), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))),
% 20.97/13.72 inference(tautology,[status(thm)],[])).
% 20.97/13.72 tff(440,plain,
% 20.97/13.72 (related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C!21) | (~in(ordered_pair(B!20, C!21), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)))))),
% 20.97/13.72 inference(unit_resolution,[status(thm)],[439, 438])).
% 20.97/13.72 tff(441,plain,
% 20.97/13.72 ($false),
% 20.97/13.72 inference(unit_resolution,[status(thm)],[440, 405, 172])).
% 20.97/13.72 tff(442,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,[]))).
% 20.97/13.72 tff(443,plain,
% 20.97/13.72 ((~(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))),
% 21.06/13.79 inference(tautology,[status(thm)],[])).
% 21.06/13.79 tff(444,plain,
% 21.06/13.79 ((~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))),
% 21.06/13.79 inference(unit_resolution,[status(thm)],[443, 168])).
% 21.06/13.79 tff(445,plain,
% 21.06/13.79 (related(poset_of_lattice(A!19), cast_to_el_of_LattPOSet(A!19, B!20), cast_to_el_of_LattPOSet(A!19, C!21))),
% 21.06/13.79 inference(unit_resolution,[status(thm)],[444, 442])).
% 21.06/13.79 tff(446,plain,
% 21.06/13.79 (related(rel_str_of(the_carrier(A!19), k2_lattice3(A!19)), B!20, C!21)),
% 21.06/13.79 inference(modus_ponens,[status(thm)],[445, 78])).
% 21.06/13.79 tff(447,plain,
% 21.06/13.79 ((~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)))))),
% 21.06/13.79 inference(monotonicity,[status(thm)],[364])).
% 21.06/13.79 tff(448,plain,
% 21.06/13.79 ((~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))))),
% 21.06/13.79 inference(tautology,[status(thm)],[])).
% 21.06/13.79 tff(449,plain,
% 21.06/13.79 ((~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)))),
% 21.06/13.79 inference(unit_resolution,[status(thm)],[448, 367])).
% 21.06/13.79 tff(450,plain,
% 21.06/13.79 (~below_refl(A!19, B!20, C!21)),
% 21.06/13.79 inference(unit_resolution,[status(thm)],[449, 442])).
% 21.06/13.79 tff(451,plain,
% 21.06/13.79 ((~(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)),
% 21.06/13.79 inference(tautology,[status(thm)],[])).
% 21.06/13.79 tff(452,plain,
% 21.06/13.79 ((~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)),
% 21.06/13.79 inference(unit_resolution,[status(thm)],[451, 401])).
% 21.06/13.79 tff(453,plain,
% 21.06/13.79 (~in(ordered_pair_as_product_element(the_carrier(A!19), the_carrier(A!19), B!20, C!21), relation_of_lattice(A!19))),
% 21.06/13.79 inference(unit_resolution,[status(thm)],[452, 450])).
% 21.06/13.79 tff(454,plain,
% 21.06/13.79 (~in(ordered_pair(B!20, C!21), the_InternalRel(rel_str_of(the_carrier(A!19), k2_lattice3(A!19))))),
% 21.06/13.79 inference(modus_ponens,[status(thm)],[453, 447])).
% 21.06/13.79 tff(455,plain,
% 21.06/13.79 ((~(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))))),
% 21.06/13.79 inference(tautology,[status(thm)],[])).
% 21.06/13.79 tff(456,plain,
% 21.06/13.79 ((~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))))),
% 21.06/13.79 inference(unit_resolution,[status(thm)],[455, 438])).
% 21.06/13.79 tff(457,plain,
% 21.06/13.79 ($false),
% 21.06/13.79 inference(unit_resolution,[status(thm)],[456, 454, 446])).
% 21.06/13.79 % SZS output end Proof
%------------------------------------------------------------------------------