TSTP Solution File: SEU346+1 by SRASS---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SRASS---0.1
% Problem : SEU346+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : SRASS -q2 -a 0 10 10 10 -i3 -n60 %s
% Computer : art01.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Thu Dec 30 03:51:40 EST 2010
% Result : Theorem 31.31s
% Output : Solution 31.31s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Reading problem from /tmp/SystemOnTPTP27402/SEU346+1.tptp
% Adding relevance values
% Extracting the conjecture
% Sorting axioms by relevance
% Looking for THM ...
% found
% SZS status THM for /tmp/SystemOnTPTP27402/SEU346+1.tptp
% SZS output start Solution for /tmp/SystemOnTPTP27402/SEU346+1.tptp
% TreeLimitedRun: ----------------------------------------------------------
% TreeLimitedRun: /home/graph/tptp/Systems/EP---1.2/eproof --print-statistics -xAuto -tAuto --cpu-limit=60 --proof-time-unlimited --memory-limit=Auto --tstp-in --tstp-out /tmp/SRASS.s.p
% TreeLimitedRun: CPU time limit is 60s
% TreeLimitedRun: WC time limit is 120s
% TreeLimitedRun: PID is 27498
% TreeLimitedRun: ----------------------------------------------------------
% PrfWatch: 0.00 CPU 0.01 WC
% PrfWatch: 1.95 CPU 2.02 WC
% PrfWatch: 3.94 CPU 4.03 WC
% PrfWatch: 5.93 CPU 6.04 WC
% PrfWatch: 7.92 CPU 8.04 WC
% PrfWatch: 9.91 CPU 10.05 WC
% PrfWatch: 11.90 CPU 12.06 WC
% PrfWatch: 13.89 CPU 14.06 WC
% PrfWatch: 15.88 CPU 16.07 WC
% PrfWatch: 17.86 CPU 18.08 WC
% PrfWatch: 19.45 CPU 20.08 WC
% PrfWatch: 21.08 CPU 22.09 WC
% # Preprocessing time : 0.027 s
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% PrfWatch: 23.06 CPU 24.10 WC
% PrfWatch: 25.05 CPU 26.11 WC
% PrfWatch: 27.04 CPU 28.11 WC
% PrfWatch: 29.03 CPU 30.12 WC
% # SZS output start CNFRefutation.
% fof(1, axiom,![X1]:![X2]:((((~(empty_carrier(X1))&lattice(X1))&latt_str(X1))&element(X2,the_carrier(X1)))=>element(cast_to_el_of_LattPOSet(X1,X2),the_carrier(poset_of_lattice(X1)))),file('/tmp/SRASS.s.p', dt_k4_lattice3)).
% fof(4, axiom,![X1]:(((~(empty_carrier(X1))&lattice(X1))&latt_str(X1))=>![X2]:(element(X2,the_carrier(X1))=>cast_to_el_of_LattPOSet(X1,X2)=X2)),file('/tmp/SRASS.s.p', d3_lattice3)).
% fof(7, axiom,![X1]:(((~(empty_carrier(X1))&lattice(X1))&latt_str(X1))=>![X2]:(element(X2,the_carrier(X1))=>![X3]:(element(X3,the_carrier(X1))=>(in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))<=>below_refl(X1,X2,X3))))),file('/tmp/SRASS.s.p', t32_filter_1)).
% fof(9, axiom,![X1]:(((~(empty_carrier(X1))&lattice(X1))&latt_str(X1))=>poset_of_lattice(X1)=rel_str_of(the_carrier(X1),k2_lattice3(X1))),file('/tmp/SRASS.s.p', d2_lattice3)).
% fof(13, axiom,![X1]:![X2]:![X3]:(((((~(empty_carrier(X1))&reflexive_relstr(X1))&rel_str(X1))&element(X2,the_carrier(X1)))&element(X3,the_carrier(X1)))=>(related_reflexive(X1,X2,X3)<=>related(X1,X2,X3))),file('/tmp/SRASS.s.p', redefinition_r3_orders_2)).
% fof(19, axiom,![X1]:(((~(empty_carrier(X1))&lattice(X1))&latt_str(X1))=>((((~(empty_carrier(poset_of_lattice(X1)))&strict_rel_str(poset_of_lattice(X1)))&reflexive_relstr(poset_of_lattice(X1)))&transitive_relstr(poset_of_lattice(X1)))&antisymmetric_relstr(poset_of_lattice(X1)))),file('/tmp/SRASS.s.p', fc4_lattice3)).
% fof(20, axiom,![X1]:((~(empty_carrier(X1))&one_sorted_str(X1))=>~(empty(the_carrier(X1)))),file('/tmp/SRASS.s.p', fc1_struct_0)).
% fof(23, axiom,![X1]:(((~(empty_carrier(X1))&lattice(X1))&latt_str(X1))=>k2_lattice3(X1)=relation_of_lattice(X1)),file('/tmp/SRASS.s.p', redefinition_k2_lattice3)).
% fof(26, axiom,![X1]:(((~(empty_carrier(X1))&lattice(X1))&latt_str(X1))=>((((strict_rel_str(poset_of_lattice(X1))&reflexive_relstr(poset_of_lattice(X1)))&transitive_relstr(poset_of_lattice(X1)))&antisymmetric_relstr(poset_of_lattice(X1)))&rel_str(poset_of_lattice(X1)))),file('/tmp/SRASS.s.p', dt_k3_lattice3)).
% fof(28, axiom,![X1]:(((~(empty_carrier(X1))&lattice(X1))&latt_str(X1))=>((((reflexive(k2_lattice3(X1))&antisymmetric(k2_lattice3(X1)))&transitive(k2_lattice3(X1)))&v1_partfun1(k2_lattice3(X1),the_carrier(X1),the_carrier(X1)))&relation_of2_as_subset(k2_lattice3(X1),the_carrier(X1),the_carrier(X1)))),file('/tmp/SRASS.s.p', dt_k2_lattice3)).
% fof(29, axiom,![X1]:![X2]:(element(X1,X2)=>(empty(X2)|in(X1,X2))),file('/tmp/SRASS.s.p', t2_subset)).
% fof(34, axiom,![X1]:![X2]:(relation_of2(X2,X1,X1)=>![X3]:![X4]:(rel_str_of(X1,X2)=rel_str_of(X3,X4)=>(X1=X3&X2=X4))),file('/tmp/SRASS.s.p', free_g1_orders_2)).
% fof(38, axiom,![X1]:![X2]:![X3]:![X4]:((((~(empty(X1))&~(empty(X2)))&element(X3,X1))&element(X4,X2))=>ordered_pair_as_product_element(X1,X2,X3,X4)=ordered_pair(X3,X4)),file('/tmp/SRASS.s.p', redefinition_k1_domain_1)).
% fof(42, axiom,![X1]:(rel_str(X1)=>![X2]:(element(X2,the_carrier(X1))=>![X3]:(element(X3,the_carrier(X1))=>(related(X1,X2,X3)<=>in(ordered_pair(X2,X3),the_InternalRel(X1)))))),file('/tmp/SRASS.s.p', d9_orders_2)).
% fof(43, axiom,![X1]:![X2]:~((in(X1,X2)&empty(X2))),file('/tmp/SRASS.s.p', t7_boole)).
% fof(46, axiom,![X1]:![X2]:(relation_of2(X2,X1,X1)=>(strict_rel_str(rel_str_of(X1,X2))&rel_str(rel_str_of(X1,X2)))),file('/tmp/SRASS.s.p', dt_g1_orders_2)).
% fof(51, axiom,![X1]:(rel_str(X1)=>(strict_rel_str(X1)=>X1=rel_str_of(the_carrier(X1),the_InternalRel(X1)))),file('/tmp/SRASS.s.p', abstractness_v1_orders_2)).
% fof(53, axiom,![X1]:![X2]:unordered_pair(X1,X2)=unordered_pair(X2,X1),file('/tmp/SRASS.s.p', commutativity_k2_tarski)).
% fof(54, axiom,![X1]:![X2]:ordered_pair(X1,X2)=unordered_pair(unordered_pair(X1,X2),singleton(X1)),file('/tmp/SRASS.s.p', d5_tarski)).
% fof(55, axiom,![X1]:(rel_str(X1)=>one_sorted_str(X1)),file('/tmp/SRASS.s.p', dt_l1_orders_2)).
% fof(60, axiom,![X1]:(rel_str(X1)=>relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1))),file('/tmp/SRASS.s.p', dt_u1_orders_2)).
% fof(69, axiom,![X1]:![X2]:(((((reflexive(X2)&antisymmetric(X2))&transitive(X2))&v1_partfun1(X2,X1,X1))&relation_of2(X2,X1,X1))=>(((strict_rel_str(rel_str_of(X1,X2))&reflexive_relstr(rel_str_of(X1,X2)))&transitive_relstr(rel_str_of(X1,X2)))&antisymmetric_relstr(rel_str_of(X1,X2)))),file('/tmp/SRASS.s.p', fc3_orders_2)).
% fof(71, axiom,![X1]:![X2]:((~(empty(X1))&relation_of2(X2,X1,X1))=>(~(empty_carrier(rel_str_of(X1,X2)))&strict_rel_str(rel_str_of(X1,X2)))),file('/tmp/SRASS.s.p', fc1_orders_2)).
% fof(73, axiom,![X1]:![X2]:![X3]:(relation_of2_as_subset(X3,X1,X2)<=>relation_of2(X3,X1,X2)),file('/tmp/SRASS.s.p', redefinition_m2_relset_1)).
% fof(93, conjecture,![X1]:(((~(empty_carrier(X1))&lattice(X1))&latt_str(X1))=>![X2]:(element(X2,the_carrier(X1))=>![X3]:(element(X3,the_carrier(X1))=>(below_refl(X1,X2,X3)<=>related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3)))))),file('/tmp/SRASS.s.p', t7_lattice3)).
% fof(94, negated_conjecture,~(![X1]:(((~(empty_carrier(X1))&lattice(X1))&latt_str(X1))=>![X2]:(element(X2,the_carrier(X1))=>![X3]:(element(X3,the_carrier(X1))=>(below_refl(X1,X2,X3)<=>related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3))))))),inference(assume_negation,[status(cth)],[93])).
% fof(95, plain,![X1]:![X2]:((((~(empty_carrier(X1))&lattice(X1))&latt_str(X1))&element(X2,the_carrier(X1)))=>element(cast_to_el_of_LattPOSet(X1,X2),the_carrier(poset_of_lattice(X1)))),inference(fof_simplification,[status(thm)],[1,theory(equality)])).
% fof(96, plain,![X1]:(((~(empty_carrier(X1))&lattice(X1))&latt_str(X1))=>![X2]:(element(X2,the_carrier(X1))=>cast_to_el_of_LattPOSet(X1,X2)=X2)),inference(fof_simplification,[status(thm)],[4,theory(equality)])).
% fof(99, plain,![X1]:(((~(empty_carrier(X1))&lattice(X1))&latt_str(X1))=>![X2]:(element(X2,the_carrier(X1))=>![X3]:(element(X3,the_carrier(X1))=>(in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))<=>below_refl(X1,X2,X3))))),inference(fof_simplification,[status(thm)],[7,theory(equality)])).
% fof(101, plain,![X1]:(((~(empty_carrier(X1))&lattice(X1))&latt_str(X1))=>poset_of_lattice(X1)=rel_str_of(the_carrier(X1),k2_lattice3(X1))),inference(fof_simplification,[status(thm)],[9,theory(equality)])).
% fof(105, plain,![X1]:![X2]:![X3]:(((((~(empty_carrier(X1))&reflexive_relstr(X1))&rel_str(X1))&element(X2,the_carrier(X1)))&element(X3,the_carrier(X1)))=>(related_reflexive(X1,X2,X3)<=>related(X1,X2,X3))),inference(fof_simplification,[status(thm)],[13,theory(equality)])).
% fof(109, plain,![X1]:(((~(empty_carrier(X1))&lattice(X1))&latt_str(X1))=>((((~(empty_carrier(poset_of_lattice(X1)))&strict_rel_str(poset_of_lattice(X1)))&reflexive_relstr(poset_of_lattice(X1)))&transitive_relstr(poset_of_lattice(X1)))&antisymmetric_relstr(poset_of_lattice(X1)))),inference(fof_simplification,[status(thm)],[19,theory(equality)])).
% fof(110, plain,![X1]:((~(empty_carrier(X1))&one_sorted_str(X1))=>~(empty(the_carrier(X1)))),inference(fof_simplification,[status(thm)],[20,theory(equality)])).
% fof(112, plain,![X1]:(((~(empty_carrier(X1))&lattice(X1))&latt_str(X1))=>k2_lattice3(X1)=relation_of_lattice(X1)),inference(fof_simplification,[status(thm)],[23,theory(equality)])).
% fof(114, plain,![X1]:(((~(empty_carrier(X1))&lattice(X1))&latt_str(X1))=>((((strict_rel_str(poset_of_lattice(X1))&reflexive_relstr(poset_of_lattice(X1)))&transitive_relstr(poset_of_lattice(X1)))&antisymmetric_relstr(poset_of_lattice(X1)))&rel_str(poset_of_lattice(X1)))),inference(fof_simplification,[status(thm)],[26,theory(equality)])).
% fof(116, plain,![X1]:(((~(empty_carrier(X1))&lattice(X1))&latt_str(X1))=>((((reflexive(k2_lattice3(X1))&antisymmetric(k2_lattice3(X1)))&transitive(k2_lattice3(X1)))&v1_partfun1(k2_lattice3(X1),the_carrier(X1),the_carrier(X1)))&relation_of2_as_subset(k2_lattice3(X1),the_carrier(X1),the_carrier(X1)))),inference(fof_simplification,[status(thm)],[28,theory(equality)])).
% fof(118, plain,![X1]:![X2]:![X3]:![X4]:((((~(empty(X1))&~(empty(X2)))&element(X3,X1))&element(X4,X2))=>ordered_pair_as_product_element(X1,X2,X3,X4)=ordered_pair(X3,X4)),inference(fof_simplification,[status(thm)],[38,theory(equality)])).
% fof(128, plain,![X1]:![X2]:((~(empty(X1))&relation_of2(X2,X1,X1))=>(~(empty_carrier(rel_str_of(X1,X2)))&strict_rel_str(rel_str_of(X1,X2)))),inference(fof_simplification,[status(thm)],[71,theory(equality)])).
% fof(134, negated_conjecture,~(![X1]:(((~(empty_carrier(X1))&lattice(X1))&latt_str(X1))=>![X2]:(element(X2,the_carrier(X1))=>![X3]:(element(X3,the_carrier(X1))=>(below_refl(X1,X2,X3)<=>related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3))))))),inference(fof_simplification,[status(thm)],[94,theory(equality)])).
% fof(135, plain,![X1]:![X2]:((((empty_carrier(X1)|~(lattice(X1)))|~(latt_str(X1)))|~(element(X2,the_carrier(X1))))|element(cast_to_el_of_LattPOSet(X1,X2),the_carrier(poset_of_lattice(X1)))),inference(fof_nnf,[status(thm)],[95])).
% fof(136, plain,![X3]:![X4]:((((empty_carrier(X3)|~(lattice(X3)))|~(latt_str(X3)))|~(element(X4,the_carrier(X3))))|element(cast_to_el_of_LattPOSet(X3,X4),the_carrier(poset_of_lattice(X3)))),inference(variable_rename,[status(thm)],[135])).
% cnf(137,plain,(element(cast_to_el_of_LattPOSet(X1,X2),the_carrier(poset_of_lattice(X1)))|empty_carrier(X1)|~element(X2,the_carrier(X1))|~latt_str(X1)|~lattice(X1)),inference(split_conjunct,[status(thm)],[136])).
% fof(144, plain,![X1]:(((empty_carrier(X1)|~(lattice(X1)))|~(latt_str(X1)))|![X2]:(~(element(X2,the_carrier(X1)))|cast_to_el_of_LattPOSet(X1,X2)=X2)),inference(fof_nnf,[status(thm)],[96])).
% fof(145, plain,![X3]:(((empty_carrier(X3)|~(lattice(X3)))|~(latt_str(X3)))|![X4]:(~(element(X4,the_carrier(X3)))|cast_to_el_of_LattPOSet(X3,X4)=X4)),inference(variable_rename,[status(thm)],[144])).
% fof(146, plain,![X3]:![X4]:((~(element(X4,the_carrier(X3)))|cast_to_el_of_LattPOSet(X3,X4)=X4)|((empty_carrier(X3)|~(lattice(X3)))|~(latt_str(X3)))),inference(shift_quantors,[status(thm)],[145])).
% cnf(147,plain,(empty_carrier(X1)|cast_to_el_of_LattPOSet(X1,X2)=X2|~latt_str(X1)|~lattice(X1)|~element(X2,the_carrier(X1))),inference(split_conjunct,[status(thm)],[146])).
% fof(154, plain,![X1]:(((empty_carrier(X1)|~(lattice(X1)))|~(latt_str(X1)))|![X2]:(~(element(X2,the_carrier(X1)))|![X3]:(~(element(X3,the_carrier(X1)))|((~(in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1)))|below_refl(X1,X2,X3))&(~(below_refl(X1,X2,X3))|in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))))))),inference(fof_nnf,[status(thm)],[99])).
% fof(155, plain,![X4]:(((empty_carrier(X4)|~(lattice(X4)))|~(latt_str(X4)))|![X5]:(~(element(X5,the_carrier(X4)))|![X6]:(~(element(X6,the_carrier(X4)))|((~(in(ordered_pair_as_product_element(the_carrier(X4),the_carrier(X4),X5,X6),relation_of_lattice(X4)))|below_refl(X4,X5,X6))&(~(below_refl(X4,X5,X6))|in(ordered_pair_as_product_element(the_carrier(X4),the_carrier(X4),X5,X6),relation_of_lattice(X4))))))),inference(variable_rename,[status(thm)],[154])).
% fof(156, plain,![X4]:![X5]:![X6]:(((~(element(X6,the_carrier(X4)))|((~(in(ordered_pair_as_product_element(the_carrier(X4),the_carrier(X4),X5,X6),relation_of_lattice(X4)))|below_refl(X4,X5,X6))&(~(below_refl(X4,X5,X6))|in(ordered_pair_as_product_element(the_carrier(X4),the_carrier(X4),X5,X6),relation_of_lattice(X4)))))|~(element(X5,the_carrier(X4))))|((empty_carrier(X4)|~(lattice(X4)))|~(latt_str(X4)))),inference(shift_quantors,[status(thm)],[155])).
% fof(157, plain,![X4]:![X5]:![X6]:(((((~(in(ordered_pair_as_product_element(the_carrier(X4),the_carrier(X4),X5,X6),relation_of_lattice(X4)))|below_refl(X4,X5,X6))|~(element(X6,the_carrier(X4))))|~(element(X5,the_carrier(X4))))|((empty_carrier(X4)|~(lattice(X4)))|~(latt_str(X4))))&((((~(below_refl(X4,X5,X6))|in(ordered_pair_as_product_element(the_carrier(X4),the_carrier(X4),X5,X6),relation_of_lattice(X4)))|~(element(X6,the_carrier(X4))))|~(element(X5,the_carrier(X4))))|((empty_carrier(X4)|~(lattice(X4)))|~(latt_str(X4))))),inference(distribute,[status(thm)],[156])).
% cnf(158,plain,(empty_carrier(X1)|in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))|~latt_str(X1)|~lattice(X1)|~element(X2,the_carrier(X1))|~element(X3,the_carrier(X1))|~below_refl(X1,X2,X3)),inference(split_conjunct,[status(thm)],[157])).
% cnf(159,plain,(empty_carrier(X1)|below_refl(X1,X2,X3)|~latt_str(X1)|~lattice(X1)|~element(X2,the_carrier(X1))|~element(X3,the_carrier(X1))|~in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))),inference(split_conjunct,[status(thm)],[157])).
% fof(165, plain,![X1]:(((empty_carrier(X1)|~(lattice(X1)))|~(latt_str(X1)))|poset_of_lattice(X1)=rel_str_of(the_carrier(X1),k2_lattice3(X1))),inference(fof_nnf,[status(thm)],[101])).
% fof(166, plain,![X2]:(((empty_carrier(X2)|~(lattice(X2)))|~(latt_str(X2)))|poset_of_lattice(X2)=rel_str_of(the_carrier(X2),k2_lattice3(X2))),inference(variable_rename,[status(thm)],[165])).
% cnf(167,plain,(poset_of_lattice(X1)=rel_str_of(the_carrier(X1),k2_lattice3(X1))|empty_carrier(X1)|~latt_str(X1)|~lattice(X1)),inference(split_conjunct,[status(thm)],[166])).
% fof(177, plain,![X1]:![X2]:![X3]:(((((empty_carrier(X1)|~(reflexive_relstr(X1)))|~(rel_str(X1)))|~(element(X2,the_carrier(X1))))|~(element(X3,the_carrier(X1))))|((~(related_reflexive(X1,X2,X3))|related(X1,X2,X3))&(~(related(X1,X2,X3))|related_reflexive(X1,X2,X3)))),inference(fof_nnf,[status(thm)],[105])).
% fof(178, plain,![X4]:![X5]:![X6]:(((((empty_carrier(X4)|~(reflexive_relstr(X4)))|~(rel_str(X4)))|~(element(X5,the_carrier(X4))))|~(element(X6,the_carrier(X4))))|((~(related_reflexive(X4,X5,X6))|related(X4,X5,X6))&(~(related(X4,X5,X6))|related_reflexive(X4,X5,X6)))),inference(variable_rename,[status(thm)],[177])).
% fof(179, plain,![X4]:![X5]:![X6]:(((~(related_reflexive(X4,X5,X6))|related(X4,X5,X6))|((((empty_carrier(X4)|~(reflexive_relstr(X4)))|~(rel_str(X4)))|~(element(X5,the_carrier(X4))))|~(element(X6,the_carrier(X4)))))&((~(related(X4,X5,X6))|related_reflexive(X4,X5,X6))|((((empty_carrier(X4)|~(reflexive_relstr(X4)))|~(rel_str(X4)))|~(element(X5,the_carrier(X4))))|~(element(X6,the_carrier(X4)))))),inference(distribute,[status(thm)],[178])).
% cnf(180,plain,(empty_carrier(X2)|related_reflexive(X2,X3,X1)|~element(X1,the_carrier(X2))|~element(X3,the_carrier(X2))|~rel_str(X2)|~reflexive_relstr(X2)|~related(X2,X3,X1)),inference(split_conjunct,[status(thm)],[179])).
% cnf(181,plain,(empty_carrier(X2)|related(X2,X3,X1)|~element(X1,the_carrier(X2))|~element(X3,the_carrier(X2))|~rel_str(X2)|~reflexive_relstr(X2)|~related_reflexive(X2,X3,X1)),inference(split_conjunct,[status(thm)],[179])).
% fof(198, plain,![X1]:(((empty_carrier(X1)|~(lattice(X1)))|~(latt_str(X1)))|((((~(empty_carrier(poset_of_lattice(X1)))&strict_rel_str(poset_of_lattice(X1)))&reflexive_relstr(poset_of_lattice(X1)))&transitive_relstr(poset_of_lattice(X1)))&antisymmetric_relstr(poset_of_lattice(X1)))),inference(fof_nnf,[status(thm)],[109])).
% fof(199, plain,![X2]:(((empty_carrier(X2)|~(lattice(X2)))|~(latt_str(X2)))|((((~(empty_carrier(poset_of_lattice(X2)))&strict_rel_str(poset_of_lattice(X2)))&reflexive_relstr(poset_of_lattice(X2)))&transitive_relstr(poset_of_lattice(X2)))&antisymmetric_relstr(poset_of_lattice(X2)))),inference(variable_rename,[status(thm)],[198])).
% fof(200, plain,![X2]:(((((~(empty_carrier(poset_of_lattice(X2)))|((empty_carrier(X2)|~(lattice(X2)))|~(latt_str(X2))))&(strict_rel_str(poset_of_lattice(X2))|((empty_carrier(X2)|~(lattice(X2)))|~(latt_str(X2)))))&(reflexive_relstr(poset_of_lattice(X2))|((empty_carrier(X2)|~(lattice(X2)))|~(latt_str(X2)))))&(transitive_relstr(poset_of_lattice(X2))|((empty_carrier(X2)|~(lattice(X2)))|~(latt_str(X2)))))&(antisymmetric_relstr(poset_of_lattice(X2))|((empty_carrier(X2)|~(lattice(X2)))|~(latt_str(X2))))),inference(distribute,[status(thm)],[199])).
% cnf(204,plain,(empty_carrier(X1)|strict_rel_str(poset_of_lattice(X1))|~latt_str(X1)|~lattice(X1)),inference(split_conjunct,[status(thm)],[200])).
% cnf(205,plain,(empty_carrier(X1)|~latt_str(X1)|~lattice(X1)|~empty_carrier(poset_of_lattice(X1))),inference(split_conjunct,[status(thm)],[200])).
% fof(206, plain,![X1]:((empty_carrier(X1)|~(one_sorted_str(X1)))|~(empty(the_carrier(X1)))),inference(fof_nnf,[status(thm)],[110])).
% fof(207, plain,![X2]:((empty_carrier(X2)|~(one_sorted_str(X2)))|~(empty(the_carrier(X2)))),inference(variable_rename,[status(thm)],[206])).
% cnf(208,plain,(empty_carrier(X1)|~empty(the_carrier(X1))|~one_sorted_str(X1)),inference(split_conjunct,[status(thm)],[207])).
% fof(219, plain,![X1]:(((empty_carrier(X1)|~(lattice(X1)))|~(latt_str(X1)))|k2_lattice3(X1)=relation_of_lattice(X1)),inference(fof_nnf,[status(thm)],[112])).
% fof(220, plain,![X2]:(((empty_carrier(X2)|~(lattice(X2)))|~(latt_str(X2)))|k2_lattice3(X2)=relation_of_lattice(X2)),inference(variable_rename,[status(thm)],[219])).
% cnf(221,plain,(k2_lattice3(X1)=relation_of_lattice(X1)|empty_carrier(X1)|~latt_str(X1)|~lattice(X1)),inference(split_conjunct,[status(thm)],[220])).
% fof(229, plain,![X1]:(((empty_carrier(X1)|~(lattice(X1)))|~(latt_str(X1)))|((((strict_rel_str(poset_of_lattice(X1))&reflexive_relstr(poset_of_lattice(X1)))&transitive_relstr(poset_of_lattice(X1)))&antisymmetric_relstr(poset_of_lattice(X1)))&rel_str(poset_of_lattice(X1)))),inference(fof_nnf,[status(thm)],[114])).
% fof(230, plain,![X2]:(((empty_carrier(X2)|~(lattice(X2)))|~(latt_str(X2)))|((((strict_rel_str(poset_of_lattice(X2))&reflexive_relstr(poset_of_lattice(X2)))&transitive_relstr(poset_of_lattice(X2)))&antisymmetric_relstr(poset_of_lattice(X2)))&rel_str(poset_of_lattice(X2)))),inference(variable_rename,[status(thm)],[229])).
% fof(231, plain,![X2]:(((((strict_rel_str(poset_of_lattice(X2))|((empty_carrier(X2)|~(lattice(X2)))|~(latt_str(X2))))&(reflexive_relstr(poset_of_lattice(X2))|((empty_carrier(X2)|~(lattice(X2)))|~(latt_str(X2)))))&(transitive_relstr(poset_of_lattice(X2))|((empty_carrier(X2)|~(lattice(X2)))|~(latt_str(X2)))))&(antisymmetric_relstr(poset_of_lattice(X2))|((empty_carrier(X2)|~(lattice(X2)))|~(latt_str(X2)))))&(rel_str(poset_of_lattice(X2))|((empty_carrier(X2)|~(lattice(X2)))|~(latt_str(X2))))),inference(distribute,[status(thm)],[230])).
% cnf(232,plain,(empty_carrier(X1)|rel_str(poset_of_lattice(X1))|~latt_str(X1)|~lattice(X1)),inference(split_conjunct,[status(thm)],[231])).
% fof(242, plain,![X1]:(((empty_carrier(X1)|~(lattice(X1)))|~(latt_str(X1)))|((((reflexive(k2_lattice3(X1))&antisymmetric(k2_lattice3(X1)))&transitive(k2_lattice3(X1)))&v1_partfun1(k2_lattice3(X1),the_carrier(X1),the_carrier(X1)))&relation_of2_as_subset(k2_lattice3(X1),the_carrier(X1),the_carrier(X1)))),inference(fof_nnf,[status(thm)],[116])).
% fof(243, plain,![X2]:(((empty_carrier(X2)|~(lattice(X2)))|~(latt_str(X2)))|((((reflexive(k2_lattice3(X2))&antisymmetric(k2_lattice3(X2)))&transitive(k2_lattice3(X2)))&v1_partfun1(k2_lattice3(X2),the_carrier(X2),the_carrier(X2)))&relation_of2_as_subset(k2_lattice3(X2),the_carrier(X2),the_carrier(X2)))),inference(variable_rename,[status(thm)],[242])).
% fof(244, plain,![X2]:(((((reflexive(k2_lattice3(X2))|((empty_carrier(X2)|~(lattice(X2)))|~(latt_str(X2))))&(antisymmetric(k2_lattice3(X2))|((empty_carrier(X2)|~(lattice(X2)))|~(latt_str(X2)))))&(transitive(k2_lattice3(X2))|((empty_carrier(X2)|~(lattice(X2)))|~(latt_str(X2)))))&(v1_partfun1(k2_lattice3(X2),the_carrier(X2),the_carrier(X2))|((empty_carrier(X2)|~(lattice(X2)))|~(latt_str(X2)))))&(relation_of2_as_subset(k2_lattice3(X2),the_carrier(X2),the_carrier(X2))|((empty_carrier(X2)|~(lattice(X2)))|~(latt_str(X2))))),inference(distribute,[status(thm)],[243])).
% cnf(245,plain,(empty_carrier(X1)|relation_of2_as_subset(k2_lattice3(X1),the_carrier(X1),the_carrier(X1))|~latt_str(X1)|~lattice(X1)),inference(split_conjunct,[status(thm)],[244])).
% cnf(246,plain,(empty_carrier(X1)|v1_partfun1(k2_lattice3(X1),the_carrier(X1),the_carrier(X1))|~latt_str(X1)|~lattice(X1)),inference(split_conjunct,[status(thm)],[244])).
% cnf(247,plain,(empty_carrier(X1)|transitive(k2_lattice3(X1))|~latt_str(X1)|~lattice(X1)),inference(split_conjunct,[status(thm)],[244])).
% cnf(248,plain,(empty_carrier(X1)|antisymmetric(k2_lattice3(X1))|~latt_str(X1)|~lattice(X1)),inference(split_conjunct,[status(thm)],[244])).
% cnf(249,plain,(empty_carrier(X1)|reflexive(k2_lattice3(X1))|~latt_str(X1)|~lattice(X1)),inference(split_conjunct,[status(thm)],[244])).
% fof(250, plain,![X1]:![X2]:(~(element(X1,X2))|(empty(X2)|in(X1,X2))),inference(fof_nnf,[status(thm)],[29])).
% fof(251, plain,![X3]:![X4]:(~(element(X3,X4))|(empty(X4)|in(X3,X4))),inference(variable_rename,[status(thm)],[250])).
% cnf(252,plain,(in(X1,X2)|empty(X2)|~element(X1,X2)),inference(split_conjunct,[status(thm)],[251])).
% fof(265, plain,![X1]:![X2]:(~(relation_of2(X2,X1,X1))|![X3]:![X4]:(~(rel_str_of(X1,X2)=rel_str_of(X3,X4))|(X1=X3&X2=X4))),inference(fof_nnf,[status(thm)],[34])).
% fof(266, plain,![X5]:![X6]:(~(relation_of2(X6,X5,X5))|![X7]:![X8]:(~(rel_str_of(X5,X6)=rel_str_of(X7,X8))|(X5=X7&X6=X8))),inference(variable_rename,[status(thm)],[265])).
% fof(267, plain,![X5]:![X6]:![X7]:![X8]:((~(rel_str_of(X5,X6)=rel_str_of(X7,X8))|(X5=X7&X6=X8))|~(relation_of2(X6,X5,X5))),inference(shift_quantors,[status(thm)],[266])).
% fof(268, plain,![X5]:![X6]:![X7]:![X8]:(((X5=X7|~(rel_str_of(X5,X6)=rel_str_of(X7,X8)))|~(relation_of2(X6,X5,X5)))&((X6=X8|~(rel_str_of(X5,X6)=rel_str_of(X7,X8)))|~(relation_of2(X6,X5,X5)))),inference(distribute,[status(thm)],[267])).
% cnf(269,plain,(X1=X4|~relation_of2(X1,X2,X2)|rel_str_of(X2,X1)!=rel_str_of(X3,X4)),inference(split_conjunct,[status(thm)],[268])).
% cnf(270,plain,(X2=X3|~relation_of2(X1,X2,X2)|rel_str_of(X2,X1)!=rel_str_of(X3,X4)),inference(split_conjunct,[status(thm)],[268])).
% fof(280, plain,![X1]:![X2]:![X3]:![X4]:((((empty(X1)|empty(X2))|~(element(X3,X1)))|~(element(X4,X2)))|ordered_pair_as_product_element(X1,X2,X3,X4)=ordered_pair(X3,X4)),inference(fof_nnf,[status(thm)],[118])).
% fof(281, plain,![X5]:![X6]:![X7]:![X8]:((((empty(X5)|empty(X6))|~(element(X7,X5)))|~(element(X8,X6)))|ordered_pair_as_product_element(X5,X6,X7,X8)=ordered_pair(X7,X8)),inference(variable_rename,[status(thm)],[280])).
% cnf(282,plain,(ordered_pair_as_product_element(X1,X2,X3,X4)=ordered_pair(X3,X4)|empty(X2)|empty(X1)|~element(X4,X2)|~element(X3,X1)),inference(split_conjunct,[status(thm)],[281])).
% fof(303, plain,![X1]:(~(rel_str(X1))|![X2]:(~(element(X2,the_carrier(X1)))|![X3]:(~(element(X3,the_carrier(X1)))|((~(related(X1,X2,X3))|in(ordered_pair(X2,X3),the_InternalRel(X1)))&(~(in(ordered_pair(X2,X3),the_InternalRel(X1)))|related(X1,X2,X3)))))),inference(fof_nnf,[status(thm)],[42])).
% fof(304, plain,![X4]:(~(rel_str(X4))|![X5]:(~(element(X5,the_carrier(X4)))|![X6]:(~(element(X6,the_carrier(X4)))|((~(related(X4,X5,X6))|in(ordered_pair(X5,X6),the_InternalRel(X4)))&(~(in(ordered_pair(X5,X6),the_InternalRel(X4)))|related(X4,X5,X6)))))),inference(variable_rename,[status(thm)],[303])).
% fof(305, plain,![X4]:![X5]:![X6]:(((~(element(X6,the_carrier(X4)))|((~(related(X4,X5,X6))|in(ordered_pair(X5,X6),the_InternalRel(X4)))&(~(in(ordered_pair(X5,X6),the_InternalRel(X4)))|related(X4,X5,X6))))|~(element(X5,the_carrier(X4))))|~(rel_str(X4))),inference(shift_quantors,[status(thm)],[304])).
% fof(306, plain,![X4]:![X5]:![X6]:(((((~(related(X4,X5,X6))|in(ordered_pair(X5,X6),the_InternalRel(X4)))|~(element(X6,the_carrier(X4))))|~(element(X5,the_carrier(X4))))|~(rel_str(X4)))&((((~(in(ordered_pair(X5,X6),the_InternalRel(X4)))|related(X4,X5,X6))|~(element(X6,the_carrier(X4))))|~(element(X5,the_carrier(X4))))|~(rel_str(X4)))),inference(distribute,[status(thm)],[305])).
% cnf(307,plain,(related(X1,X2,X3)|~rel_str(X1)|~element(X2,the_carrier(X1))|~element(X3,the_carrier(X1))|~in(ordered_pair(X2,X3),the_InternalRel(X1))),inference(split_conjunct,[status(thm)],[306])).
% cnf(308,plain,(in(ordered_pair(X2,X3),the_InternalRel(X1))|~rel_str(X1)|~element(X2,the_carrier(X1))|~element(X3,the_carrier(X1))|~related(X1,X2,X3)),inference(split_conjunct,[status(thm)],[306])).
% fof(309, plain,![X1]:![X2]:(~(in(X1,X2))|~(empty(X2))),inference(fof_nnf,[status(thm)],[43])).
% fof(310, plain,![X3]:![X4]:(~(in(X3,X4))|~(empty(X4))),inference(variable_rename,[status(thm)],[309])).
% cnf(311,plain,(~empty(X1)|~in(X2,X1)),inference(split_conjunct,[status(thm)],[310])).
% fof(318, plain,![X1]:![X2]:(~(relation_of2(X2,X1,X1))|(strict_rel_str(rel_str_of(X1,X2))&rel_str(rel_str_of(X1,X2)))),inference(fof_nnf,[status(thm)],[46])).
% fof(319, plain,![X3]:![X4]:(~(relation_of2(X4,X3,X3))|(strict_rel_str(rel_str_of(X3,X4))&rel_str(rel_str_of(X3,X4)))),inference(variable_rename,[status(thm)],[318])).
% fof(320, plain,![X3]:![X4]:((strict_rel_str(rel_str_of(X3,X4))|~(relation_of2(X4,X3,X3)))&(rel_str(rel_str_of(X3,X4))|~(relation_of2(X4,X3,X3)))),inference(distribute,[status(thm)],[319])).
% cnf(321,plain,(rel_str(rel_str_of(X2,X1))|~relation_of2(X1,X2,X2)),inference(split_conjunct,[status(thm)],[320])).
% cnf(322,plain,(strict_rel_str(rel_str_of(X2,X1))|~relation_of2(X1,X2,X2)),inference(split_conjunct,[status(thm)],[320])).
% fof(334, plain,![X1]:(~(rel_str(X1))|(~(strict_rel_str(X1))|X1=rel_str_of(the_carrier(X1),the_InternalRel(X1)))),inference(fof_nnf,[status(thm)],[51])).
% fof(335, plain,![X2]:(~(rel_str(X2))|(~(strict_rel_str(X2))|X2=rel_str_of(the_carrier(X2),the_InternalRel(X2)))),inference(variable_rename,[status(thm)],[334])).
% cnf(336,plain,(X1=rel_str_of(the_carrier(X1),the_InternalRel(X1))|~strict_rel_str(X1)|~rel_str(X1)),inference(split_conjunct,[status(thm)],[335])).
% fof(340, plain,![X3]:![X4]:unordered_pair(X3,X4)=unordered_pair(X4,X3),inference(variable_rename,[status(thm)],[53])).
% cnf(341,plain,(unordered_pair(X1,X2)=unordered_pair(X2,X1)),inference(split_conjunct,[status(thm)],[340])).
% fof(342, plain,![X3]:![X4]:ordered_pair(X3,X4)=unordered_pair(unordered_pair(X3,X4),singleton(X3)),inference(variable_rename,[status(thm)],[54])).
% cnf(343,plain,(ordered_pair(X1,X2)=unordered_pair(unordered_pair(X1,X2),singleton(X1))),inference(split_conjunct,[status(thm)],[342])).
% fof(344, plain,![X1]:(~(rel_str(X1))|one_sorted_str(X1)),inference(fof_nnf,[status(thm)],[55])).
% fof(345, plain,![X2]:(~(rel_str(X2))|one_sorted_str(X2)),inference(variable_rename,[status(thm)],[344])).
% cnf(346,plain,(one_sorted_str(X1)|~rel_str(X1)),inference(split_conjunct,[status(thm)],[345])).
% fof(369, plain,![X1]:(~(rel_str(X1))|relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1))),inference(fof_nnf,[status(thm)],[60])).
% fof(370, plain,![X2]:(~(rel_str(X2))|relation_of2_as_subset(the_InternalRel(X2),the_carrier(X2),the_carrier(X2))),inference(variable_rename,[status(thm)],[369])).
% cnf(371,plain,(relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1))|~rel_str(X1)),inference(split_conjunct,[status(thm)],[370])).
% fof(402, plain,![X1]:![X2]:(((((~(reflexive(X2))|~(antisymmetric(X2)))|~(transitive(X2)))|~(v1_partfun1(X2,X1,X1)))|~(relation_of2(X2,X1,X1)))|(((strict_rel_str(rel_str_of(X1,X2))&reflexive_relstr(rel_str_of(X1,X2)))&transitive_relstr(rel_str_of(X1,X2)))&antisymmetric_relstr(rel_str_of(X1,X2)))),inference(fof_nnf,[status(thm)],[69])).
% fof(403, plain,![X3]:![X4]:(((((~(reflexive(X4))|~(antisymmetric(X4)))|~(transitive(X4)))|~(v1_partfun1(X4,X3,X3)))|~(relation_of2(X4,X3,X3)))|(((strict_rel_str(rel_str_of(X3,X4))&reflexive_relstr(rel_str_of(X3,X4)))&transitive_relstr(rel_str_of(X3,X4)))&antisymmetric_relstr(rel_str_of(X3,X4)))),inference(variable_rename,[status(thm)],[402])).
% fof(404, plain,![X3]:![X4]:((((strict_rel_str(rel_str_of(X3,X4))|((((~(reflexive(X4))|~(antisymmetric(X4)))|~(transitive(X4)))|~(v1_partfun1(X4,X3,X3)))|~(relation_of2(X4,X3,X3))))&(reflexive_relstr(rel_str_of(X3,X4))|((((~(reflexive(X4))|~(antisymmetric(X4)))|~(transitive(X4)))|~(v1_partfun1(X4,X3,X3)))|~(relation_of2(X4,X3,X3)))))&(transitive_relstr(rel_str_of(X3,X4))|((((~(reflexive(X4))|~(antisymmetric(X4)))|~(transitive(X4)))|~(v1_partfun1(X4,X3,X3)))|~(relation_of2(X4,X3,X3)))))&(antisymmetric_relstr(rel_str_of(X3,X4))|((((~(reflexive(X4))|~(antisymmetric(X4)))|~(transitive(X4)))|~(v1_partfun1(X4,X3,X3)))|~(relation_of2(X4,X3,X3))))),inference(distribute,[status(thm)],[403])).
% cnf(407,plain,(reflexive_relstr(rel_str_of(X2,X1))|~relation_of2(X1,X2,X2)|~v1_partfun1(X1,X2,X2)|~transitive(X1)|~antisymmetric(X1)|~reflexive(X1)),inference(split_conjunct,[status(thm)],[404])).
% fof(412, plain,![X1]:![X2]:((empty(X1)|~(relation_of2(X2,X1,X1)))|(~(empty_carrier(rel_str_of(X1,X2)))&strict_rel_str(rel_str_of(X1,X2)))),inference(fof_nnf,[status(thm)],[128])).
% fof(413, plain,![X3]:![X4]:((empty(X3)|~(relation_of2(X4,X3,X3)))|(~(empty_carrier(rel_str_of(X3,X4)))&strict_rel_str(rel_str_of(X3,X4)))),inference(variable_rename,[status(thm)],[412])).
% fof(414, plain,![X3]:![X4]:((~(empty_carrier(rel_str_of(X3,X4)))|(empty(X3)|~(relation_of2(X4,X3,X3))))&(strict_rel_str(rel_str_of(X3,X4))|(empty(X3)|~(relation_of2(X4,X3,X3))))),inference(distribute,[status(thm)],[413])).
% cnf(416,plain,(empty(X2)|~relation_of2(X1,X2,X2)|~empty_carrier(rel_str_of(X2,X1))),inference(split_conjunct,[status(thm)],[414])).
% fof(425, plain,![X1]:![X2]:![X3]:((~(relation_of2_as_subset(X3,X1,X2))|relation_of2(X3,X1,X2))&(~(relation_of2(X3,X1,X2))|relation_of2_as_subset(X3,X1,X2))),inference(fof_nnf,[status(thm)],[73])).
% fof(426, plain,![X4]:![X5]:![X6]:((~(relation_of2_as_subset(X6,X4,X5))|relation_of2(X6,X4,X5))&(~(relation_of2(X6,X4,X5))|relation_of2_as_subset(X6,X4,X5))),inference(variable_rename,[status(thm)],[425])).
% cnf(428,plain,(relation_of2(X1,X2,X3)|~relation_of2_as_subset(X1,X2,X3)),inference(split_conjunct,[status(thm)],[426])).
% fof(500, negated_conjecture,?[X1]:(((~(empty_carrier(X1))&lattice(X1))&latt_str(X1))&?[X2]:(element(X2,the_carrier(X1))&?[X3]:(element(X3,the_carrier(X1))&((~(below_refl(X1,X2,X3))|~(related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3))))&(below_refl(X1,X2,X3)|related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3))))))),inference(fof_nnf,[status(thm)],[134])).
% fof(501, negated_conjecture,?[X4]:(((~(empty_carrier(X4))&lattice(X4))&latt_str(X4))&?[X5]:(element(X5,the_carrier(X4))&?[X6]:(element(X6,the_carrier(X4))&((~(below_refl(X4,X5,X6))|~(related_reflexive(poset_of_lattice(X4),cast_to_el_of_LattPOSet(X4,X5),cast_to_el_of_LattPOSet(X4,X6))))&(below_refl(X4,X5,X6)|related_reflexive(poset_of_lattice(X4),cast_to_el_of_LattPOSet(X4,X5),cast_to_el_of_LattPOSet(X4,X6))))))),inference(variable_rename,[status(thm)],[500])).
% fof(502, negated_conjecture,(((~(empty_carrier(esk20_0))&lattice(esk20_0))&latt_str(esk20_0))&(element(esk21_0,the_carrier(esk20_0))&(element(esk22_0,the_carrier(esk20_0))&((~(below_refl(esk20_0,esk21_0,esk22_0))|~(related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),cast_to_el_of_LattPOSet(esk20_0,esk22_0))))&(below_refl(esk20_0,esk21_0,esk22_0)|related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),cast_to_el_of_LattPOSet(esk20_0,esk22_0))))))),inference(skolemize,[status(esa)],[501])).
% cnf(503,negated_conjecture,(related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),cast_to_el_of_LattPOSet(esk20_0,esk22_0))|below_refl(esk20_0,esk21_0,esk22_0)),inference(split_conjunct,[status(thm)],[502])).
% cnf(504,negated_conjecture,(~related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),cast_to_el_of_LattPOSet(esk20_0,esk22_0))|~below_refl(esk20_0,esk21_0,esk22_0)),inference(split_conjunct,[status(thm)],[502])).
% cnf(505,negated_conjecture,(element(esk22_0,the_carrier(esk20_0))),inference(split_conjunct,[status(thm)],[502])).
% cnf(506,negated_conjecture,(element(esk21_0,the_carrier(esk20_0))),inference(split_conjunct,[status(thm)],[502])).
% cnf(507,negated_conjecture,(latt_str(esk20_0)),inference(split_conjunct,[status(thm)],[502])).
% cnf(508,negated_conjecture,(lattice(esk20_0)),inference(split_conjunct,[status(thm)],[502])).
% cnf(509,negated_conjecture,(~empty_carrier(esk20_0)),inference(split_conjunct,[status(thm)],[502])).
% cnf(510,plain,(ordered_pair_as_product_element(X1,X2,X3,X4)=unordered_pair(unordered_pair(X3,X4),singleton(X3))|empty(X2)|empty(X1)|~element(X4,X2)|~element(X3,X1)),inference(rw,[status(thm)],[282,343,theory(equality)]),['unfolding']).
% cnf(511,plain,(related(X1,X2,X3)|~rel_str(X1)|~element(X3,the_carrier(X1))|~element(X2,the_carrier(X1))|~in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),the_InternalRel(X1))),inference(rw,[status(thm)],[307,343,theory(equality)]),['unfolding']).
% cnf(512,plain,(in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),the_InternalRel(X1))|~rel_str(X1)|~related(X1,X2,X3)|~element(X3,the_carrier(X1))|~element(X2,the_carrier(X1))),inference(rw,[status(thm)],[308,343,theory(equality)]),['unfolding']).
% cnf(535,plain,(unordered_pair(singleton(X3),unordered_pair(X3,X4))=ordered_pair_as_product_element(X1,X2,X3,X4)|empty(X2)|empty(X1)|~element(X4,X2)|~element(X3,X1)),inference(rw,[status(thm)],[510,341,theory(equality)])).
% cnf(536,plain,(in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),the_InternalRel(X1))|~rel_str(X1)|~related(X1,X2,X3)|~element(X3,the_carrier(X1))|~element(X2,the_carrier(X1))),inference(rw,[status(thm)],[512,341,theory(equality)])).
% cnf(537,plain,(related(X1,X2,X3)|~rel_str(X1)|~element(X3,the_carrier(X1))|~element(X2,the_carrier(X1))|~in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),the_InternalRel(X1))),inference(rw,[status(thm)],[511,341,theory(equality)])).
% cnf(609,negated_conjecture,(relation_of_lattice(esk20_0)=k2_lattice3(esk20_0)|empty_carrier(esk20_0)|~latt_str(esk20_0)),inference(spm,[status(thm)],[221,508,theory(equality)])).
% cnf(611,negated_conjecture,(relation_of_lattice(esk20_0)=k2_lattice3(esk20_0)|empty_carrier(esk20_0)|$false),inference(rw,[status(thm)],[609,507,theory(equality)])).
% cnf(612,negated_conjecture,(relation_of_lattice(esk20_0)=k2_lattice3(esk20_0)|empty_carrier(esk20_0)),inference(cn,[status(thm)],[611,theory(equality)])).
% cnf(613,negated_conjecture,(relation_of_lattice(esk20_0)=k2_lattice3(esk20_0)),inference(sr,[status(thm)],[612,509,theory(equality)])).
% cnf(625,negated_conjecture,(cast_to_el_of_LattPOSet(esk20_0,esk22_0)=esk22_0|empty_carrier(esk20_0)|~latt_str(esk20_0)|~lattice(esk20_0)),inference(spm,[status(thm)],[147,505,theory(equality)])).
% cnf(626,negated_conjecture,(cast_to_el_of_LattPOSet(esk20_0,esk21_0)=esk21_0|empty_carrier(esk20_0)|~latt_str(esk20_0)|~lattice(esk20_0)),inference(spm,[status(thm)],[147,506,theory(equality)])).
% cnf(629,negated_conjecture,(cast_to_el_of_LattPOSet(esk20_0,esk22_0)=esk22_0|empty_carrier(esk20_0)|$false|~lattice(esk20_0)),inference(rw,[status(thm)],[625,507,theory(equality)])).
% cnf(630,negated_conjecture,(cast_to_el_of_LattPOSet(esk20_0,esk22_0)=esk22_0|empty_carrier(esk20_0)|$false|$false),inference(rw,[status(thm)],[629,508,theory(equality)])).
% cnf(631,negated_conjecture,(cast_to_el_of_LattPOSet(esk20_0,esk22_0)=esk22_0|empty_carrier(esk20_0)),inference(cn,[status(thm)],[630,theory(equality)])).
% cnf(632,negated_conjecture,(cast_to_el_of_LattPOSet(esk20_0,esk22_0)=esk22_0),inference(sr,[status(thm)],[631,509,theory(equality)])).
% cnf(633,negated_conjecture,(cast_to_el_of_LattPOSet(esk20_0,esk21_0)=esk21_0|empty_carrier(esk20_0)|$false|~lattice(esk20_0)),inference(rw,[status(thm)],[626,507,theory(equality)])).
% cnf(634,negated_conjecture,(cast_to_el_of_LattPOSet(esk20_0,esk21_0)=esk21_0|empty_carrier(esk20_0)|$false|$false),inference(rw,[status(thm)],[633,508,theory(equality)])).
% cnf(635,negated_conjecture,(cast_to_el_of_LattPOSet(esk20_0,esk21_0)=esk21_0|empty_carrier(esk20_0)),inference(cn,[status(thm)],[634,theory(equality)])).
% cnf(636,negated_conjecture,(cast_to_el_of_LattPOSet(esk20_0,esk21_0)=esk21_0),inference(sr,[status(thm)],[635,509,theory(equality)])).
% cnf(650,plain,(relation_of2(the_InternalRel(X1),the_carrier(X1),the_carrier(X1))|~rel_str(X1)),inference(spm,[status(thm)],[428,371,theory(equality)])).
% cnf(651,plain,(empty(the_carrier(poset_of_lattice(X1)))|in(cast_to_el_of_LattPOSet(X1,X2),the_carrier(poset_of_lattice(X1)))|empty_carrier(X1)|~element(X2,the_carrier(X1))|~latt_str(X1)|~lattice(X1)),inference(spm,[status(thm)],[252,137,theory(equality)])).
% cnf(676,plain,(empty(the_carrier(X1))|~relation_of2(the_InternalRel(X1),the_carrier(X1),the_carrier(X1))|~empty_carrier(X1)|~strict_rel_str(X1)|~rel_str(X1)),inference(spm,[status(thm)],[416,336,theory(equality)])).
% cnf(679,plain,(relation_of2(k2_lattice3(X1),the_carrier(X1),the_carrier(X1))|empty_carrier(X1)|~latt_str(X1)|~lattice(X1)),inference(spm,[status(thm)],[428,245,theory(equality)])).
% cnf(712,plain,(reflexive_relstr(rel_str_of(the_carrier(X1),k2_lattice3(X1)))|empty_carrier(X1)|~relation_of2(k2_lattice3(X1),the_carrier(X1),the_carrier(X1))|~transitive(k2_lattice3(X1))|~antisymmetric(k2_lattice3(X1))|~reflexive(k2_lattice3(X1))|~latt_str(X1)|~lattice(X1)),inference(spm,[status(thm)],[407,246,theory(equality)])).
% cnf(726,plain,(in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),relation_of_lattice(X1))|empty_carrier(X1)|empty(the_carrier(X1))|~below_refl(X1,X2,X3)|~element(X3,the_carrier(X1))|~element(X2,the_carrier(X1))|~latt_str(X1)|~lattice(X1)),inference(spm,[status(thm)],[158,535,theory(equality)])).
% cnf(727,plain,(below_refl(X1,X2,X3)|empty_carrier(X1)|empty(the_carrier(X1))|~in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),relation_of_lattice(X1))|~element(X3,the_carrier(X1))|~element(X2,the_carrier(X1))|~latt_str(X1)|~lattice(X1)),inference(spm,[status(thm)],[159,535,theory(equality)])).
% cnf(770,negated_conjecture,(element(esk22_0,the_carrier(poset_of_lattice(esk20_0)))|empty_carrier(esk20_0)|~element(esk22_0,the_carrier(esk20_0))|~latt_str(esk20_0)|~lattice(esk20_0)),inference(spm,[status(thm)],[137,632,theory(equality)])).
% cnf(771,negated_conjecture,(~below_refl(esk20_0,esk21_0,esk22_0)|~related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),esk22_0)),inference(rw,[status(thm)],[504,632,theory(equality)])).
% cnf(772,negated_conjecture,(below_refl(esk20_0,esk21_0,esk22_0)|related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),esk22_0)),inference(rw,[status(thm)],[503,632,theory(equality)])).
% cnf(773,negated_conjecture,(element(esk22_0,the_carrier(poset_of_lattice(esk20_0)))|empty_carrier(esk20_0)|$false|~latt_str(esk20_0)|~lattice(esk20_0)),inference(rw,[status(thm)],[770,505,theory(equality)])).
% cnf(774,negated_conjecture,(element(esk22_0,the_carrier(poset_of_lattice(esk20_0)))|empty_carrier(esk20_0)|$false|$false|~lattice(esk20_0)),inference(rw,[status(thm)],[773,507,theory(equality)])).
% cnf(775,negated_conjecture,(element(esk22_0,the_carrier(poset_of_lattice(esk20_0)))|empty_carrier(esk20_0)|$false|$false|$false),inference(rw,[status(thm)],[774,508,theory(equality)])).
% cnf(776,negated_conjecture,(element(esk22_0,the_carrier(poset_of_lattice(esk20_0)))|empty_carrier(esk20_0)),inference(cn,[status(thm)],[775,theory(equality)])).
% cnf(777,negated_conjecture,(element(esk22_0,the_carrier(poset_of_lattice(esk20_0)))),inference(sr,[status(thm)],[776,509,theory(equality)])).
% cnf(778,negated_conjecture,(element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))|empty_carrier(esk20_0)|~element(esk21_0,the_carrier(esk20_0))|~latt_str(esk20_0)|~lattice(esk20_0)),inference(spm,[status(thm)],[137,636,theory(equality)])).
% cnf(779,negated_conjecture,(element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))|empty_carrier(esk20_0)|$false|~latt_str(esk20_0)|~lattice(esk20_0)),inference(rw,[status(thm)],[778,506,theory(equality)])).
% cnf(780,negated_conjecture,(element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))|empty_carrier(esk20_0)|$false|$false|~lattice(esk20_0)),inference(rw,[status(thm)],[779,507,theory(equality)])).
% cnf(781,negated_conjecture,(element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))|empty_carrier(esk20_0)|$false|$false|$false),inference(rw,[status(thm)],[780,508,theory(equality)])).
% cnf(782,negated_conjecture,(element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))|empty_carrier(esk20_0)),inference(cn,[status(thm)],[781,theory(equality)])).
% cnf(783,negated_conjecture,(element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))),inference(sr,[status(thm)],[782,509,theory(equality)])).
% cnf(785,negated_conjecture,(~below_refl(esk20_0,esk21_0,esk22_0)|~related_reflexive(poset_of_lattice(esk20_0),esk21_0,esk22_0)),inference(rw,[status(thm)],[771,636,theory(equality)])).
% cnf(786,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|~below_refl(esk20_0,esk21_0,esk22_0)|~related(poset_of_lattice(esk20_0),esk21_0,esk22_0)|~rel_str(poset_of_lattice(esk20_0))|~reflexive_relstr(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))|~element(esk22_0,the_carrier(poset_of_lattice(esk20_0)))),inference(spm,[status(thm)],[785,180,theory(equality)])).
% cnf(787,negated_conjecture,(below_refl(esk20_0,esk21_0,esk22_0)|related_reflexive(poset_of_lattice(esk20_0),esk21_0,esk22_0)),inference(rw,[status(thm)],[772,636,theory(equality)])).
% cnf(987,plain,(the_carrier(X1)=X2|rel_str_of(the_carrier(X1),the_InternalRel(X1))!=rel_str_of(X2,X3)|~rel_str(X1)),inference(spm,[status(thm)],[270,650,theory(equality)])).
% cnf(988,plain,(the_InternalRel(X1)=X2|rel_str_of(the_carrier(X1),the_InternalRel(X1))!=rel_str_of(X3,X2)|~rel_str(X1)),inference(spm,[status(thm)],[269,650,theory(equality)])).
% cnf(1210,plain,(empty(the_carrier(X1))|~strict_rel_str(X1)|~rel_str(X1)|~empty_carrier(X1)),inference(csr,[status(thm)],[676,650])).
% cnf(1238,plain,(rel_str(rel_str_of(the_carrier(X1),k2_lattice3(X1)))|empty_carrier(X1)|~latt_str(X1)|~lattice(X1)),inference(spm,[status(thm)],[321,679,theory(equality)])).
% cnf(1239,plain,(strict_rel_str(rel_str_of(the_carrier(X1),k2_lattice3(X1)))|empty_carrier(X1)|~latt_str(X1)|~lattice(X1)),inference(spm,[status(thm)],[322,679,theory(equality)])).
% cnf(1240,plain,(the_carrier(X1)=X2|empty_carrier(X1)|rel_str_of(the_carrier(X1),k2_lattice3(X1))!=rel_str_of(X2,X3)|~latt_str(X1)|~lattice(X1)),inference(spm,[status(thm)],[270,679,theory(equality)])).
% cnf(1241,plain,(k2_lattice3(X1)=X2|empty_carrier(X1)|rel_str_of(the_carrier(X1),k2_lattice3(X1))!=rel_str_of(X3,X2)|~latt_str(X1)|~lattice(X1)),inference(spm,[status(thm)],[269,679,theory(equality)])).
% cnf(1433,plain,(reflexive_relstr(rel_str_of(the_carrier(X1),k2_lattice3(X1)))|empty_carrier(X1)|~relation_of2(k2_lattice3(X1),the_carrier(X1),the_carrier(X1))|~transitive(k2_lattice3(X1))|~antisymmetric(k2_lattice3(X1))|~latt_str(X1)|~lattice(X1)),inference(csr,[status(thm)],[712,249])).
% cnf(1434,plain,(reflexive_relstr(rel_str_of(the_carrier(X1),k2_lattice3(X1)))|empty_carrier(X1)|~relation_of2(k2_lattice3(X1),the_carrier(X1),the_carrier(X1))|~transitive(k2_lattice3(X1))|~latt_str(X1)|~lattice(X1)),inference(csr,[status(thm)],[1433,248])).
% cnf(1435,plain,(reflexive_relstr(rel_str_of(the_carrier(X1),k2_lattice3(X1)))|empty_carrier(X1)|~relation_of2(k2_lattice3(X1),the_carrier(X1),the_carrier(X1))|~latt_str(X1)|~lattice(X1)),inference(csr,[status(thm)],[1434,247])).
% cnf(1436,plain,(reflexive_relstr(rel_str_of(the_carrier(X1),k2_lattice3(X1)))|empty_carrier(X1)|~latt_str(X1)|~lattice(X1)),inference(csr,[status(thm)],[1435,679])).
% cnf(1473,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|~below_refl(esk20_0,esk21_0,esk22_0)|~related(poset_of_lattice(esk20_0),esk21_0,esk22_0)|~rel_str(poset_of_lattice(esk20_0))|~reflexive_relstr(poset_of_lattice(esk20_0))|$false|~element(esk22_0,the_carrier(poset_of_lattice(esk20_0)))),inference(rw,[status(thm)],[786,783,theory(equality)])).
% cnf(1474,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|~below_refl(esk20_0,esk21_0,esk22_0)|~related(poset_of_lattice(esk20_0),esk21_0,esk22_0)|~rel_str(poset_of_lattice(esk20_0))|~reflexive_relstr(poset_of_lattice(esk20_0))|$false|$false),inference(rw,[status(thm)],[1473,777,theory(equality)])).
% cnf(1475,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|~below_refl(esk20_0,esk21_0,esk22_0)|~related(poset_of_lattice(esk20_0),esk21_0,esk22_0)|~rel_str(poset_of_lattice(esk20_0))|~reflexive_relstr(poset_of_lattice(esk20_0))),inference(cn,[status(thm)],[1474,theory(equality)])).
% cnf(1654,negated_conjecture,(empty(the_carrier(esk20_0))|in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),k2_lattice3(esk20_0))|empty_carrier(esk20_0)|~below_refl(esk20_0,X1,X2)|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))|~latt_str(esk20_0)|~lattice(esk20_0)),inference(spm,[status(thm)],[726,613,theory(equality)])).
% cnf(1662,negated_conjecture,(empty(the_carrier(esk20_0))|in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),k2_lattice3(esk20_0))|empty_carrier(esk20_0)|~below_refl(esk20_0,X1,X2)|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))|$false|~lattice(esk20_0)),inference(rw,[status(thm)],[1654,507,theory(equality)])).
% cnf(1663,negated_conjecture,(empty(the_carrier(esk20_0))|in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),k2_lattice3(esk20_0))|empty_carrier(esk20_0)|~below_refl(esk20_0,X1,X2)|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))|$false|$false),inference(rw,[status(thm)],[1662,508,theory(equality)])).
% cnf(1664,negated_conjecture,(empty(the_carrier(esk20_0))|in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),k2_lattice3(esk20_0))|empty_carrier(esk20_0)|~below_refl(esk20_0,X1,X2)|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))),inference(cn,[status(thm)],[1663,theory(equality)])).
% cnf(1665,negated_conjecture,(empty(the_carrier(esk20_0))|in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),k2_lattice3(esk20_0))|~below_refl(esk20_0,X1,X2)|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))),inference(sr,[status(thm)],[1664,509,theory(equality)])).
% cnf(1673,negated_conjecture,(empty(the_carrier(esk20_0))|below_refl(esk20_0,X1,X2)|empty_carrier(esk20_0)|~in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),k2_lattice3(esk20_0))|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))|~latt_str(esk20_0)|~lattice(esk20_0)),inference(spm,[status(thm)],[727,613,theory(equality)])).
% cnf(1682,negated_conjecture,(empty(the_carrier(esk20_0))|below_refl(esk20_0,X1,X2)|empty_carrier(esk20_0)|~in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),k2_lattice3(esk20_0))|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))|$false|~lattice(esk20_0)),inference(rw,[status(thm)],[1673,507,theory(equality)])).
% cnf(1683,negated_conjecture,(empty(the_carrier(esk20_0))|below_refl(esk20_0,X1,X2)|empty_carrier(esk20_0)|~in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),k2_lattice3(esk20_0))|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))|$false|$false),inference(rw,[status(thm)],[1682,508,theory(equality)])).
% cnf(1684,negated_conjecture,(empty(the_carrier(esk20_0))|below_refl(esk20_0,X1,X2)|empty_carrier(esk20_0)|~in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),k2_lattice3(esk20_0))|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))),inference(cn,[status(thm)],[1683,theory(equality)])).
% cnf(1685,negated_conjecture,(empty(the_carrier(esk20_0))|below_refl(esk20_0,X1,X2)|~in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),k2_lattice3(esk20_0))|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))),inference(sr,[status(thm)],[1684,509,theory(equality)])).
% cnf(2880,plain,(the_carrier(X1)=X2|X1!=rel_str_of(X2,X3)|~rel_str(X1)|~strict_rel_str(X1)),inference(spm,[status(thm)],[987,336,theory(equality)])).
% cnf(2883,plain,(the_carrier(X1)=the_carrier(X2)|empty_carrier(X2)|X1!=poset_of_lattice(X2)|~strict_rel_str(X1)|~rel_str(X1)|~latt_str(X2)|~lattice(X2)),inference(spm,[status(thm)],[2880,167,theory(equality)])).
% cnf(2926,plain,(the_carrier(poset_of_lattice(X1))=the_carrier(X1)|empty_carrier(X1)|~strict_rel_str(poset_of_lattice(X1))|~rel_str(poset_of_lattice(X1))|~latt_str(X1)|~lattice(X1)),inference(er,[status(thm)],[2883,theory(equality)])).
% cnf(2927,plain,(the_carrier(poset_of_lattice(X1))=the_carrier(X1)|empty_carrier(X1)|~strict_rel_str(poset_of_lattice(X1))|~latt_str(X1)|~lattice(X1)),inference(csr,[status(thm)],[2926,232])).
% cnf(2928,plain,(the_carrier(poset_of_lattice(X1))=the_carrier(X1)|empty_carrier(X1)|~latt_str(X1)|~lattice(X1)),inference(csr,[status(thm)],[2927,204])).
% cnf(2929,plain,(empty_carrier(poset_of_lattice(X1))|empty_carrier(X1)|~empty(the_carrier(X1))|~one_sorted_str(poset_of_lattice(X1))|~latt_str(X1)|~lattice(X1)),inference(spm,[status(thm)],[208,2928,theory(equality)])).
% cnf(2930,plain,(rel_str_of(the_carrier(X1),the_InternalRel(poset_of_lattice(X1)))=poset_of_lattice(X1)|empty_carrier(X1)|~strict_rel_str(poset_of_lattice(X1))|~rel_str(poset_of_lattice(X1))|~latt_str(X1)|~lattice(X1)),inference(spm,[status(thm)],[336,2928,theory(equality)])).
% cnf(3019,plain,(empty(the_carrier(X1))|in(cast_to_el_of_LattPOSet(X1,X2),the_carrier(X1))|empty_carrier(X1)|~element(X2,the_carrier(X1))|~latt_str(X1)|~lattice(X1)),inference(spm,[status(thm)],[651,2928,theory(equality)])).
% cnf(3219,plain,(empty_carrier(X1)|~empty(the_carrier(X1))|~one_sorted_str(poset_of_lattice(X1))|~latt_str(X1)|~lattice(X1)),inference(csr,[status(thm)],[2929,205])).
% cnf(3220,plain,(empty_carrier(X1)|~empty(the_carrier(X1))|~latt_str(X1)|~lattice(X1)|~rel_str(poset_of_lattice(X1))),inference(spm,[status(thm)],[3219,346,theory(equality)])).
% cnf(3223,plain,(empty_carrier(X1)|~empty(the_carrier(X1))|~latt_str(X1)|~lattice(X1)),inference(csr,[status(thm)],[3220,232])).
% cnf(3991,plain,(in(cast_to_el_of_LattPOSet(X1,X2),the_carrier(X1))|empty_carrier(X1)|~element(X2,the_carrier(X1))|~latt_str(X1)|~lattice(X1)),inference(csr,[status(thm)],[3019,3223])).
% cnf(3996,negated_conjecture,(in(esk22_0,the_carrier(esk20_0))|empty_carrier(esk20_0)|~element(esk22_0,the_carrier(esk20_0))|~latt_str(esk20_0)|~lattice(esk20_0)),inference(spm,[status(thm)],[3991,632,theory(equality)])).
% cnf(4010,negated_conjecture,(in(esk22_0,the_carrier(esk20_0))|empty_carrier(esk20_0)|$false|~latt_str(esk20_0)|~lattice(esk20_0)),inference(rw,[status(thm)],[3996,505,theory(equality)])).
% cnf(4011,negated_conjecture,(in(esk22_0,the_carrier(esk20_0))|empty_carrier(esk20_0)|$false|$false|~lattice(esk20_0)),inference(rw,[status(thm)],[4010,507,theory(equality)])).
% cnf(4012,negated_conjecture,(in(esk22_0,the_carrier(esk20_0))|empty_carrier(esk20_0)|$false|$false|$false),inference(rw,[status(thm)],[4011,508,theory(equality)])).
% cnf(4013,negated_conjecture,(in(esk22_0,the_carrier(esk20_0))|empty_carrier(esk20_0)),inference(cn,[status(thm)],[4012,theory(equality)])).
% cnf(4014,negated_conjecture,(in(esk22_0,the_carrier(esk20_0))),inference(sr,[status(thm)],[4013,509,theory(equality)])).
% cnf(4026,negated_conjecture,(~empty(the_carrier(esk20_0))),inference(spm,[status(thm)],[311,4014,theory(equality)])).
% cnf(4290,plain,(the_InternalRel(X1)=X2|X1!=rel_str_of(X3,X2)|~rel_str(X1)|~strict_rel_str(X1)),inference(spm,[status(thm)],[988,336,theory(equality)])).
% cnf(5325,plain,(k2_lattice3(X1)=X2|empty_carrier(X1)|poset_of_lattice(X1)!=rel_str_of(X3,X2)|~latt_str(X1)|~lattice(X1)),inference(spm,[status(thm)],[1241,167,theory(equality)])).
% cnf(8415,plain,(the_InternalRel(rel_str_of(X1,X2))=X2|~strict_rel_str(rel_str_of(X1,X2))|~rel_str(rel_str_of(X1,X2))),inference(er,[status(thm)],[4290,theory(equality)])).
% cnf(10767,plain,(the_InternalRel(poset_of_lattice(X1))=k2_lattice3(X1)|empty_carrier(X1)|~strict_rel_str(poset_of_lattice(X1))|~rel_str(poset_of_lattice(X1))|~latt_str(X1)|~lattice(X1)),inference(spm,[status(thm)],[8415,167,theory(equality)])).
% cnf(10953,plain,(the_InternalRel(poset_of_lattice(X1))=k2_lattice3(X1)|empty_carrier(X1)|~strict_rel_str(poset_of_lattice(X1))|~latt_str(X1)|~lattice(X1)),inference(csr,[status(thm)],[10767,232])).
% cnf(10954,plain,(the_InternalRel(poset_of_lattice(X1))=k2_lattice3(X1)|empty_carrier(X1)|~latt_str(X1)|~lattice(X1)),inference(csr,[status(thm)],[10953,204])).
% cnf(10961,plain,(related(poset_of_lattice(X1),X2,X3)|empty_carrier(X1)|~in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),k2_lattice3(X1))|~rel_str(poset_of_lattice(X1))|~element(X3,the_carrier(poset_of_lattice(X1)))|~element(X2,the_carrier(poset_of_lattice(X1)))|~latt_str(X1)|~lattice(X1)),inference(spm,[status(thm)],[537,10954,theory(equality)])).
% cnf(10977,plain,(in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),k2_lattice3(X3))|empty_carrier(X3)|~related(poset_of_lattice(X3),X1,X2)|~rel_str(poset_of_lattice(X3))|~element(X2,the_carrier(poset_of_lattice(X3)))|~element(X1,the_carrier(poset_of_lattice(X3)))|~latt_str(X3)|~lattice(X3)),inference(spm,[status(thm)],[536,10954,theory(equality)])).
% cnf(12714,negated_conjecture,(in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),k2_lattice3(esk20_0))|~below_refl(esk20_0,X1,X2)|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))),inference(sr,[status(thm)],[1665,4026,theory(equality)])).
% cnf(13462,negated_conjecture,(below_refl(esk20_0,X1,X2)|~in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),k2_lattice3(esk20_0))|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))),inference(sr,[status(thm)],[1685,4026,theory(equality)])).
% cnf(16358,plain,(rel_str_of(the_carrier(X1),the_InternalRel(poset_of_lattice(X1)))=poset_of_lattice(X1)|empty_carrier(X1)|~strict_rel_str(poset_of_lattice(X1))|~latt_str(X1)|~lattice(X1)),inference(csr,[status(thm)],[2930,232])).
% cnf(16359,plain,(rel_str_of(the_carrier(X1),the_InternalRel(poset_of_lattice(X1)))=poset_of_lattice(X1)|empty_carrier(X1)|~latt_str(X1)|~lattice(X1)),inference(csr,[status(thm)],[16358,204])).
% cnf(16375,plain,(k2_lattice3(X1)=the_InternalRel(poset_of_lattice(X2))|empty_carrier(X1)|empty_carrier(X2)|poset_of_lattice(X1)!=poset_of_lattice(X2)|~latt_str(X1)|~lattice(X1)|~latt_str(X2)|~lattice(X2)),inference(spm,[status(thm)],[5325,16359,theory(equality)])).
% cnf(16800,negated_conjecture,(k2_lattice3(esk20_0)=the_InternalRel(poset_of_lattice(X1))|empty_carrier(X1)|empty_carrier(esk20_0)|poset_of_lattice(esk20_0)!=poset_of_lattice(X1)|~latt_str(esk20_0)|~latt_str(X1)|~lattice(X1)),inference(spm,[status(thm)],[16375,508,theory(equality)])).
% cnf(16803,negated_conjecture,(k2_lattice3(esk20_0)=the_InternalRel(poset_of_lattice(X1))|empty_carrier(X1)|empty_carrier(esk20_0)|poset_of_lattice(esk20_0)!=poset_of_lattice(X1)|$false|~latt_str(X1)|~lattice(X1)),inference(rw,[status(thm)],[16800,507,theory(equality)])).
% cnf(16804,negated_conjecture,(k2_lattice3(esk20_0)=the_InternalRel(poset_of_lattice(X1))|empty_carrier(X1)|empty_carrier(esk20_0)|poset_of_lattice(esk20_0)!=poset_of_lattice(X1)|~latt_str(X1)|~lattice(X1)),inference(cn,[status(thm)],[16803,theory(equality)])).
% cnf(16805,negated_conjecture,(the_InternalRel(poset_of_lattice(X1))=k2_lattice3(esk20_0)|empty_carrier(X1)|poset_of_lattice(esk20_0)!=poset_of_lattice(X1)|~latt_str(X1)|~lattice(X1)),inference(sr,[status(thm)],[16804,509,theory(equality)])).
% cnf(16847,negated_conjecture,(rel_str_of(the_carrier(X1),k2_lattice3(esk20_0))=poset_of_lattice(X1)|empty_carrier(X1)|~latt_str(X1)|~lattice(X1)|poset_of_lattice(esk20_0)!=poset_of_lattice(X1)),inference(spm,[status(thm)],[16359,16805,theory(equality)])).
% cnf(17003,negated_conjecture,(reflexive_relstr(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~latt_str(esk20_0)|~lattice(esk20_0)),inference(spm,[status(thm)],[1436,16847,theory(equality)])).
% cnf(17006,negated_conjecture,(rel_str(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~latt_str(esk20_0)|~lattice(esk20_0)),inference(spm,[status(thm)],[1238,16847,theory(equality)])).
% cnf(17007,negated_conjecture,(strict_rel_str(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~latt_str(esk20_0)|~lattice(esk20_0)),inference(spm,[status(thm)],[1239,16847,theory(equality)])).
% cnf(17008,negated_conjecture,(the_carrier(esk20_0)=X1|empty_carrier(esk20_0)|poset_of_lattice(esk20_0)!=rel_str_of(X1,X2)|~latt_str(esk20_0)|~lattice(esk20_0)),inference(spm,[status(thm)],[1240,16847,theory(equality)])).
% cnf(17021,negated_conjecture,(reflexive_relstr(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|$false|~lattice(esk20_0)),inference(rw,[status(thm)],[17003,507,theory(equality)])).
% cnf(17022,negated_conjecture,(reflexive_relstr(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|$false|$false),inference(rw,[status(thm)],[17021,508,theory(equality)])).
% cnf(17023,negated_conjecture,(reflexive_relstr(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)),inference(cn,[status(thm)],[17022,theory(equality)])).
% cnf(17024,negated_conjecture,(reflexive_relstr(poset_of_lattice(esk20_0))),inference(sr,[status(thm)],[17023,509,theory(equality)])).
% cnf(17033,negated_conjecture,(rel_str(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|$false|~lattice(esk20_0)),inference(rw,[status(thm)],[17006,507,theory(equality)])).
% cnf(17034,negated_conjecture,(rel_str(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|$false|$false),inference(rw,[status(thm)],[17033,508,theory(equality)])).
% cnf(17035,negated_conjecture,(rel_str(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)),inference(cn,[status(thm)],[17034,theory(equality)])).
% cnf(17036,negated_conjecture,(rel_str(poset_of_lattice(esk20_0))),inference(sr,[status(thm)],[17035,509,theory(equality)])).
% cnf(17037,negated_conjecture,(strict_rel_str(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|$false|~lattice(esk20_0)),inference(rw,[status(thm)],[17007,507,theory(equality)])).
% cnf(17038,negated_conjecture,(strict_rel_str(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|$false|$false),inference(rw,[status(thm)],[17037,508,theory(equality)])).
% cnf(17039,negated_conjecture,(strict_rel_str(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)),inference(cn,[status(thm)],[17038,theory(equality)])).
% cnf(17040,negated_conjecture,(strict_rel_str(poset_of_lattice(esk20_0))),inference(sr,[status(thm)],[17039,509,theory(equality)])).
% cnf(17041,negated_conjecture,(the_carrier(esk20_0)=X1|empty_carrier(esk20_0)|poset_of_lattice(esk20_0)!=rel_str_of(X1,X2)|$false|~lattice(esk20_0)),inference(rw,[status(thm)],[17008,507,theory(equality)])).
% cnf(17042,negated_conjecture,(the_carrier(esk20_0)=X1|empty_carrier(esk20_0)|poset_of_lattice(esk20_0)!=rel_str_of(X1,X2)|$false|$false),inference(rw,[status(thm)],[17041,508,theory(equality)])).
% cnf(17043,negated_conjecture,(the_carrier(esk20_0)=X1|empty_carrier(esk20_0)|poset_of_lattice(esk20_0)!=rel_str_of(X1,X2)),inference(cn,[status(thm)],[17042,theory(equality)])).
% cnf(17044,negated_conjecture,(the_carrier(esk20_0)=X1|rel_str_of(X1,X2)!=poset_of_lattice(esk20_0)),inference(sr,[status(thm)],[17043,509,theory(equality)])).
% cnf(17051,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|~related(poset_of_lattice(esk20_0),esk21_0,esk22_0)|~below_refl(esk20_0,esk21_0,esk22_0)|~rel_str(poset_of_lattice(esk20_0))|$false),inference(rw,[status(thm)],[1475,17024,theory(equality)])).
% cnf(17052,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|~related(poset_of_lattice(esk20_0),esk21_0,esk22_0)|~below_refl(esk20_0,esk21_0,esk22_0)|~rel_str(poset_of_lattice(esk20_0))),inference(cn,[status(thm)],[17051,theory(equality)])).
% cnf(17079,negated_conjecture,(the_carrier(esk20_0)=the_carrier(X1)|X1!=poset_of_lattice(esk20_0)|~strict_rel_str(X1)|~rel_str(X1)),inference(spm,[status(thm)],[17044,336,theory(equality)])).
% cnf(17086,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|~related(poset_of_lattice(esk20_0),esk21_0,esk22_0)|~below_refl(esk20_0,esk21_0,esk22_0)|$false),inference(rw,[status(thm)],[17052,17036,theory(equality)])).
% cnf(17087,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|~related(poset_of_lattice(esk20_0),esk21_0,esk22_0)|~below_refl(esk20_0,esk21_0,esk22_0)),inference(cn,[status(thm)],[17086,theory(equality)])).
% cnf(17094,negated_conjecture,(the_carrier(esk20_0)=the_carrier(poset_of_lattice(esk20_0))|~strict_rel_str(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))),inference(er,[status(thm)],[17079,theory(equality)])).
% cnf(17095,negated_conjecture,(the_carrier(esk20_0)=the_carrier(poset_of_lattice(esk20_0))|$false|~rel_str(poset_of_lattice(esk20_0))),inference(rw,[status(thm)],[17094,17040,theory(equality)])).
% cnf(17096,negated_conjecture,(the_carrier(esk20_0)=the_carrier(poset_of_lattice(esk20_0))|$false|$false),inference(rw,[status(thm)],[17095,17036,theory(equality)])).
% cnf(17097,negated_conjecture,(the_carrier(esk20_0)=the_carrier(poset_of_lattice(esk20_0))),inference(cn,[status(thm)],[17096,theory(equality)])).
% cnf(17127,negated_conjecture,(empty(the_carrier(esk20_0))|~strict_rel_str(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~empty_carrier(poset_of_lattice(esk20_0))),inference(spm,[status(thm)],[1210,17097,theory(equality)])).
% cnf(17324,negated_conjecture,(empty(the_carrier(esk20_0))|$false|~rel_str(poset_of_lattice(esk20_0))|~empty_carrier(poset_of_lattice(esk20_0))),inference(rw,[status(thm)],[17127,17040,theory(equality)])).
% cnf(17325,negated_conjecture,(empty(the_carrier(esk20_0))|$false|$false|~empty_carrier(poset_of_lattice(esk20_0))),inference(rw,[status(thm)],[17324,17036,theory(equality)])).
% cnf(17326,negated_conjecture,(empty(the_carrier(esk20_0))|~empty_carrier(poset_of_lattice(esk20_0))),inference(cn,[status(thm)],[17325,theory(equality)])).
% cnf(17327,negated_conjecture,(~empty_carrier(poset_of_lattice(esk20_0))),inference(sr,[status(thm)],[17326,4026,theory(equality)])).
% cnf(469206,plain,(related(poset_of_lattice(X1),X2,X3)|empty_carrier(X1)|~in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),k2_lattice3(X1))|~element(X3,the_carrier(poset_of_lattice(X1)))|~element(X2,the_carrier(poset_of_lattice(X1)))|~latt_str(X1)|~lattice(X1)),inference(csr,[status(thm)],[10961,232])).
% cnf(469273,negated_conjecture,(related(poset_of_lattice(esk20_0),X1,X2)|empty_carrier(esk20_0)|~element(X2,the_carrier(poset_of_lattice(esk20_0)))|~element(X1,the_carrier(poset_of_lattice(esk20_0)))|~latt_str(esk20_0)|~lattice(esk20_0)|~below_refl(esk20_0,X1,X2)|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))),inference(spm,[status(thm)],[469206,12714,theory(equality)])).
% cnf(469278,negated_conjecture,(related(poset_of_lattice(esk20_0),X1,X2)|empty_carrier(esk20_0)|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(poset_of_lattice(esk20_0)))|~latt_str(esk20_0)|~lattice(esk20_0)|~below_refl(esk20_0,X1,X2)|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))),inference(rw,[status(thm)],[469273,17097,theory(equality)])).
% cnf(469279,negated_conjecture,(related(poset_of_lattice(esk20_0),X1,X2)|empty_carrier(esk20_0)|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))|~latt_str(esk20_0)|~lattice(esk20_0)|~below_refl(esk20_0,X1,X2)|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))),inference(rw,[status(thm)],[469278,17097,theory(equality)])).
% cnf(469280,negated_conjecture,(related(poset_of_lattice(esk20_0),X1,X2)|empty_carrier(esk20_0)|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))|$false|~lattice(esk20_0)|~below_refl(esk20_0,X1,X2)|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))),inference(rw,[status(thm)],[469279,507,theory(equality)])).
% cnf(469281,negated_conjecture,(related(poset_of_lattice(esk20_0),X1,X2)|empty_carrier(esk20_0)|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))|$false|$false|~below_refl(esk20_0,X1,X2)|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))),inference(rw,[status(thm)],[469280,508,theory(equality)])).
% cnf(469282,negated_conjecture,(related(poset_of_lattice(esk20_0),X1,X2)|empty_carrier(esk20_0)|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))|~below_refl(esk20_0,X1,X2)),inference(cn,[status(thm)],[469281,theory(equality)])).
% cnf(469283,negated_conjecture,(related(poset_of_lattice(esk20_0),X1,X2)|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))|~below_refl(esk20_0,X1,X2)),inference(sr,[status(thm)],[469282,509,theory(equality)])).
% cnf(471003,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|~below_refl(esk20_0,esk21_0,esk22_0)|~element(esk22_0,the_carrier(esk20_0))|~element(esk21_0,the_carrier(esk20_0))),inference(spm,[status(thm)],[17087,469283,theory(equality)])).
% cnf(471438,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|~below_refl(esk20_0,esk21_0,esk22_0)|$false|~element(esk21_0,the_carrier(esk20_0))),inference(rw,[status(thm)],[471003,505,theory(equality)])).
% cnf(471439,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|~below_refl(esk20_0,esk21_0,esk22_0)|$false|$false),inference(rw,[status(thm)],[471438,506,theory(equality)])).
% cnf(471440,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|~below_refl(esk20_0,esk21_0,esk22_0)),inference(cn,[status(thm)],[471439,theory(equality)])).
% cnf(471441,negated_conjecture,(~below_refl(esk20_0,esk21_0,esk22_0)),inference(sr,[status(thm)],[471440,17327,theory(equality)])).
% cnf(471443,negated_conjecture,(related_reflexive(poset_of_lattice(esk20_0),esk21_0,esk22_0)),inference(sr,[status(thm)],[787,471441,theory(equality)])).
% cnf(471453,negated_conjecture,(related(poset_of_lattice(esk20_0),esk21_0,esk22_0)|empty_carrier(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~reflexive_relstr(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))|~element(esk22_0,the_carrier(poset_of_lattice(esk20_0)))),inference(spm,[status(thm)],[181,471443,theory(equality)])).
% cnf(471456,negated_conjecture,(related(poset_of_lattice(esk20_0),esk21_0,esk22_0)|empty_carrier(poset_of_lattice(esk20_0))|$false|~reflexive_relstr(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))|~element(esk22_0,the_carrier(poset_of_lattice(esk20_0)))),inference(rw,[status(thm)],[471453,17036,theory(equality)])).
% cnf(471457,negated_conjecture,(related(poset_of_lattice(esk20_0),esk21_0,esk22_0)|empty_carrier(poset_of_lattice(esk20_0))|$false|$false|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))|~element(esk22_0,the_carrier(poset_of_lattice(esk20_0)))),inference(rw,[status(thm)],[471456,17024,theory(equality)])).
% cnf(471458,negated_conjecture,(related(poset_of_lattice(esk20_0),esk21_0,esk22_0)|empty_carrier(poset_of_lattice(esk20_0))|$false|$false|$false|~element(esk22_0,the_carrier(poset_of_lattice(esk20_0)))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[471457,17097,theory(equality)]),506,theory(equality)])).
% cnf(471459,negated_conjecture,(related(poset_of_lattice(esk20_0),esk21_0,esk22_0)|empty_carrier(poset_of_lattice(esk20_0))|$false|$false|$false|$false),inference(rw,[status(thm)],[inference(rw,[status(thm)],[471458,17097,theory(equality)]),505,theory(equality)])).
% cnf(471460,negated_conjecture,(related(poset_of_lattice(esk20_0),esk21_0,esk22_0)|empty_carrier(poset_of_lattice(esk20_0))),inference(cn,[status(thm)],[471459,theory(equality)])).
% cnf(471461,negated_conjecture,(related(poset_of_lattice(esk20_0),esk21_0,esk22_0)),inference(sr,[status(thm)],[471460,17327,theory(equality)])).
% cnf(472013,plain,(in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),k2_lattice3(X3))|empty_carrier(X3)|~related(poset_of_lattice(X3),X1,X2)|~element(X2,the_carrier(poset_of_lattice(X3)))|~element(X1,the_carrier(poset_of_lattice(X3)))|~latt_str(X3)|~lattice(X3)),inference(csr,[status(thm)],[10977,232])).
% cnf(472021,negated_conjecture,(below_refl(esk20_0,X1,X2)|empty_carrier(esk20_0)|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))|~related(poset_of_lattice(esk20_0),X1,X2)|~element(X2,the_carrier(poset_of_lattice(esk20_0)))|~element(X1,the_carrier(poset_of_lattice(esk20_0)))|~latt_str(esk20_0)|~lattice(esk20_0)),inference(spm,[status(thm)],[13462,472013,theory(equality)])).
% cnf(472094,negated_conjecture,(below_refl(esk20_0,X1,X2)|empty_carrier(esk20_0)|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))|~related(poset_of_lattice(esk20_0),X1,X2)|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(poset_of_lattice(esk20_0)))|~latt_str(esk20_0)|~lattice(esk20_0)),inference(rw,[status(thm)],[472021,17097,theory(equality)])).
% cnf(472095,negated_conjecture,(below_refl(esk20_0,X1,X2)|empty_carrier(esk20_0)|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))|~related(poset_of_lattice(esk20_0),X1,X2)|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))|~latt_str(esk20_0)|~lattice(esk20_0)),inference(rw,[status(thm)],[472094,17097,theory(equality)])).
% cnf(472096,negated_conjecture,(below_refl(esk20_0,X1,X2)|empty_carrier(esk20_0)|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))|~related(poset_of_lattice(esk20_0),X1,X2)|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))|$false|~lattice(esk20_0)),inference(rw,[status(thm)],[472095,507,theory(equality)])).
% cnf(472097,negated_conjecture,(below_refl(esk20_0,X1,X2)|empty_carrier(esk20_0)|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))|~related(poset_of_lattice(esk20_0),X1,X2)|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))|$false|$false),inference(rw,[status(thm)],[472096,508,theory(equality)])).
% cnf(472098,negated_conjecture,(below_refl(esk20_0,X1,X2)|empty_carrier(esk20_0)|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))|~related(poset_of_lattice(esk20_0),X1,X2)),inference(cn,[status(thm)],[472097,theory(equality)])).
% cnf(472099,negated_conjecture,(below_refl(esk20_0,X1,X2)|~element(X2,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))|~related(poset_of_lattice(esk20_0),X1,X2)),inference(sr,[status(thm)],[472098,509,theory(equality)])).
% cnf(472152,negated_conjecture,(below_refl(esk20_0,esk21_0,esk22_0)|~element(esk22_0,the_carrier(esk20_0))|~element(esk21_0,the_carrier(esk20_0))),inference(spm,[status(thm)],[472099,471461,theory(equality)])).
% cnf(472380,negated_conjecture,(below_refl(esk20_0,esk21_0,esk22_0)|$false|~element(esk21_0,the_carrier(esk20_0))),inference(rw,[status(thm)],[472152,505,theory(equality)])).
% cnf(472381,negated_conjecture,(below_refl(esk20_0,esk21_0,esk22_0)|$false|$false),inference(rw,[status(thm)],[472380,506,theory(equality)])).
% cnf(472382,negated_conjecture,(below_refl(esk20_0,esk21_0,esk22_0)),inference(cn,[status(thm)],[472381,theory(equality)])).
% cnf(472383,negated_conjecture,($false),inference(sr,[status(thm)],[472382,471441,theory(equality)])).
% cnf(472384,negated_conjecture,($false),472383,['proof']).
% # SZS output end CNFRefutation
% # Processed clauses : 30404
% # ...of these trivial : 116
% # ...subsumed : 25482
% # ...remaining for further processing: 4806
% # Other redundant clauses eliminated : 2
% # Clauses deleted for lack of memory : 0
% # Backward-subsumed : 273
% # Backward-rewritten : 80
% # Generated clauses : 350124
% # ...of the previous two non-trivial : 328439
% # Contextual simplify-reflections : 32285
% # Paramodulations : 350043
% # Factorizations : 0
% # Equation resolutions : 52
% # Current number of processed clauses: 4285
% # Positive orientable unit clauses: 162
% # Positive unorientable unit clauses: 1
% # Negative unit clauses : 42
% # Non-unit-clauses : 4080
% # Current number of unprocessed clauses: 288352
% # ...number of literals in the above : 2294651
% # Clause-clause subsumption calls (NU) : 3377607
% # Rec. Clause-clause subsumption calls : 1206352
% # Unit Clause-clause subsumption calls : 15752
% # Rewrite failures with RHS unbound : 0
% # Indexed BW rewrite attempts : 376
% # Indexed BW rewrite successes : 42
% # Backwards rewriting index: 1463 leaves, 3.49+/-8.451 terms/leaf
% # Paramod-from index: 763 leaves, 2.74+/-5.557 terms/leaf
% # Paramod-into index: 1225 leaves, 3.27+/-8.252 terms/leaf
% # -------------------------------------------------
% # User time : 22.099 s
% # System time : 0.601 s
% # Total time : 22.700 s
% # Maximum resident set size: 0 pages
% PrfWatch: 29.95 CPU 31.07 WC
% FINAL PrfWatch: 29.95 CPU 31.07 WC
% SZS output end Solution for /tmp/SystemOnTPTP27402/SEU346+1.tptp
%
%------------------------------------------------------------------------------