%------------------------------------------------------------------------------
% File     : SRASS---0.1
% Problem  : SEU349+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 : art07.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 03:53:36 EST 2010

% Result   : Theorem 2.73s
% Output   : Solution 2.73s
% 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/SystemOnTPTP5776/SEU349+1.tptp
% Adding relevance values
% Extracting the conjecture
% Sorting axioms by relevance
% Looking for THM       ... 
% found
% SZS status THM for /tmp/SystemOnTPTP5776/SEU349+1.tptp
% SZS output start Solution for /tmp/SystemOnTPTP5776/SEU349+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 5872
% TreeLimitedRun: ----------------------------------------------------------
% PrfWatch: 0.00 CPU 0.02 WC
% # Preprocessing time     : 0.020 s
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # 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(5, axiom,![X1]:![X2]:((((~(empty_carrier(X1))&lattice(X1))&latt_str(X1))&element(X2,the_carrier(poset_of_lattice(X1))))=>element(cast_to_el_of_lattice(X1,X2),the_carrier(X1))),file('/tmp/SRASS.s.p', dt_k5_lattice3)).
% fof(6, axiom,![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(7, axiom,![X1]:(((~(empty_carrier(X1))&lattice(X1))&latt_str(X1))=>![X2]:(element(X2,the_carrier(poset_of_lattice(X1)))=>cast_to_el_of_lattice(X1,X2)=X2)),file('/tmp/SRASS.s.p', d4_lattice3)).
% fof(8, axiom,![X1]:((~(empty_carrier(X1))&latt_str(X1))=>![X2]:(element(X2,the_carrier(X1))=>![X3]:(latt_element_smaller(X1,X2,X3)<=>![X4]:(element(X4,the_carrier(X1))=>(in(X4,X3)=>below(X1,X4,X2)))))),file('/tmp/SRASS.s.p', d17_lattice3)).
% 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(15, axiom,![X1]:![X2]:(in(X1,X2)=>element(X1,X2)),file('/tmp/SRASS.s.p', t1_subset)).
% fof(16, axiom,![X1]:(rel_str(X1)=>![X2]:![X3]:(element(X3,the_carrier(X1))=>(relstr_set_smaller(X1,X2,X3)<=>![X4]:(element(X4,the_carrier(X1))=>(in(X4,X2)=>related(X1,X4,X3)))))),file('/tmp/SRASS.s.p', d9_lattice3)).
% fof(18, 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(25, 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(26, axiom,![X1]:![X2]:![X3]:(((((((~(empty_carrier(X1))&meet_commutative(X1))&meet_absorbing(X1))&join_absorbing(X1))&latt_str(X1))&element(X2,the_carrier(X1)))&element(X3,the_carrier(X1)))=>(below_refl(X1,X2,X3)<=>below(X1,X2,X3))),file('/tmp/SRASS.s.p', redefinition_r3_lattices)).
% fof(27, 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(32, 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(35, axiom,![X1]:![X2]:(element(X1,X2)=>(empty(X2)|in(X1,X2))),file('/tmp/SRASS.s.p', t2_subset)).
% fof(38, axiom,![X1]:(latt_str(X1)=>((~(empty_carrier(X1))&lattice(X1))=>((((((~(empty_carrier(X1))&join_commutative(X1))&join_associative(X1))&meet_commutative(X1))&meet_associative(X1))&meet_absorbing(X1))&join_absorbing(X1)))),file('/tmp/SRASS.s.p', cc1_lattices)).
% fof(40, axiom,![X1]:![X2]:~((in(X1,X2)&empty(X2))),file('/tmp/SRASS.s.p', t7_boole)).
% fof(43, 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(52, 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(63, 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(71, conjecture,![X1]:![X2]:(((~(empty_carrier(X2))&lattice(X2))&latt_str(X2))=>![X3]:(element(X3,the_carrier(X2))=>(latt_element_smaller(X2,X3,X1)<=>relstr_set_smaller(poset_of_lattice(X2),X1,cast_to_el_of_LattPOSet(X2,X3))))),file('/tmp/SRASS.s.p', t30_lattice3)).
% fof(72, negated_conjecture,~(![X1]:![X2]:(((~(empty_carrier(X2))&lattice(X2))&latt_str(X2))=>![X3]:(element(X3,the_carrier(X2))=>(latt_element_smaller(X2,X3,X1)<=>relstr_set_smaller(poset_of_lattice(X2),X1,cast_to_el_of_LattPOSet(X2,X3)))))),inference(assume_negation,[status(cth)],[71])).
% fof(73, 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(74, 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(75, plain,![X1]:![X2]:((((~(empty_carrier(X1))&lattice(X1))&latt_str(X1))&element(X2,the_carrier(poset_of_lattice(X1))))=>element(cast_to_el_of_lattice(X1,X2),the_carrier(X1))),inference(fof_simplification,[status(thm)],[5,theory(equality)])).
% fof(76, plain,![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)],[6,theory(equality)])).
% fof(77, plain,![X1]:(((~(empty_carrier(X1))&lattice(X1))&latt_str(X1))=>![X2]:(element(X2,the_carrier(poset_of_lattice(X1)))=>cast_to_el_of_lattice(X1,X2)=X2)),inference(fof_simplification,[status(thm)],[7,theory(equality)])).
% fof(78, plain,![X1]:((~(empty_carrier(X1))&latt_str(X1))=>![X2]:(element(X2,the_carrier(X1))=>![X3]:(latt_element_smaller(X1,X2,X3)<=>![X4]:(element(X4,the_carrier(X1))=>(in(X4,X3)=>below(X1,X4,X2)))))),inference(fof_simplification,[status(thm)],[8,theory(equality)])).
% fof(79, 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(83, 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)],[18,theory(equality)])).
% fof(90, 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)],[25,theory(equality)])).
% fof(91, plain,![X1]:![X2]:![X3]:(((((((~(empty_carrier(X1))&meet_commutative(X1))&meet_absorbing(X1))&join_absorbing(X1))&latt_str(X1))&element(X2,the_carrier(X1)))&element(X3,the_carrier(X1)))=>(below_refl(X1,X2,X3)<=>below(X1,X2,X3))),inference(fof_simplification,[status(thm)],[26,theory(equality)])).
% fof(92, 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)],[27,theory(equality)])).
% fof(95, plain,![X1]:(latt_str(X1)=>((~(empty_carrier(X1))&lattice(X1))=>((((((~(empty_carrier(X1))&join_commutative(X1))&join_associative(X1))&meet_commutative(X1))&meet_associative(X1))&meet_absorbing(X1))&join_absorbing(X1)))),inference(fof_simplification,[status(thm)],[38,theory(equality)])).
% fof(101, negated_conjecture,~(![X1]:![X2]:(((~(empty_carrier(X2))&lattice(X2))&latt_str(X2))=>![X3]:(element(X3,the_carrier(X2))=>(latt_element_smaller(X2,X3,X1)<=>relstr_set_smaller(poset_of_lattice(X2),X1,cast_to_el_of_LattPOSet(X2,X3)))))),inference(fof_simplification,[status(thm)],[72,theory(equality)])).
% fof(102, 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)],[73])).
% fof(103, 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)],[102])).
% cnf(104,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)],[103])).
% fof(111, 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)],[74])).
% fof(112, 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)],[111])).
% fof(113, 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)],[112])).
% cnf(114,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)],[113])).
% fof(115, plain,![X1]:![X2]:((((empty_carrier(X1)|~(lattice(X1)))|~(latt_str(X1)))|~(element(X2,the_carrier(poset_of_lattice(X1)))))|element(cast_to_el_of_lattice(X1,X2),the_carrier(X1))),inference(fof_nnf,[status(thm)],[75])).
% fof(116, plain,![X3]:![X4]:((((empty_carrier(X3)|~(lattice(X3)))|~(latt_str(X3)))|~(element(X4,the_carrier(poset_of_lattice(X3)))))|element(cast_to_el_of_lattice(X3,X4),the_carrier(X3))),inference(variable_rename,[status(thm)],[115])).
% cnf(117,plain,(element(cast_to_el_of_lattice(X1,X2),the_carrier(X1))|empty_carrier(X1)|~element(X2,the_carrier(poset_of_lattice(X1)))|~latt_str(X1)|~lattice(X1)),inference(split_conjunct,[status(thm)],[116])).
% fof(118, plain,![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)))&(~(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)))))),inference(fof_nnf,[status(thm)],[76])).
% fof(119, plain,![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)))&(~(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)))))),inference(variable_rename,[status(thm)],[118])).
% fof(120, plain,![X4]:![X5]:![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)))&(~(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))))|~(element(X5,the_carrier(X4))))|((empty_carrier(X4)|~(lattice(X4)))|~(latt_str(X4)))),inference(shift_quantors,[status(thm)],[119])).
% fof(121, plain,![X4]:![X5]:![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)))|~(element(X6,the_carrier(X4))))|~(element(X5,the_carrier(X4))))|((empty_carrier(X4)|~(lattice(X4)))|~(latt_str(X4))))&((((~(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))|~(element(X6,the_carrier(X4))))|~(element(X5,the_carrier(X4))))|((empty_carrier(X4)|~(lattice(X4)))|~(latt_str(X4))))),inference(distribute,[status(thm)],[120])).
% cnf(122,plain,(empty_carrier(X1)|below_refl(X1,X2,X3)|~latt_str(X1)|~lattice(X1)|~element(X2,the_carrier(X1))|~element(X3,the_carrier(X1))|~related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3))),inference(split_conjunct,[status(thm)],[121])).
% cnf(123,plain,(empty_carrier(X1)|related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3))|~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)],[121])).
% fof(124, plain,![X1]:(((empty_carrier(X1)|~(lattice(X1)))|~(latt_str(X1)))|![X2]:(~(element(X2,the_carrier(poset_of_lattice(X1))))|cast_to_el_of_lattice(X1,X2)=X2)),inference(fof_nnf,[status(thm)],[77])).
% fof(125, plain,![X3]:(((empty_carrier(X3)|~(lattice(X3)))|~(latt_str(X3)))|![X4]:(~(element(X4,the_carrier(poset_of_lattice(X3))))|cast_to_el_of_lattice(X3,X4)=X4)),inference(variable_rename,[status(thm)],[124])).
% fof(126, plain,![X3]:![X4]:((~(element(X4,the_carrier(poset_of_lattice(X3))))|cast_to_el_of_lattice(X3,X4)=X4)|((empty_carrier(X3)|~(lattice(X3)))|~(latt_str(X3)))),inference(shift_quantors,[status(thm)],[125])).
% cnf(127,plain,(empty_carrier(X1)|cast_to_el_of_lattice(X1,X2)=X2|~latt_str(X1)|~lattice(X1)|~element(X2,the_carrier(poset_of_lattice(X1)))),inference(split_conjunct,[status(thm)],[126])).
% fof(128, plain,![X1]:((empty_carrier(X1)|~(latt_str(X1)))|![X2]:(~(element(X2,the_carrier(X1)))|![X3]:((~(latt_element_smaller(X1,X2,X3))|![X4]:(~(element(X4,the_carrier(X1)))|(~(in(X4,X3))|below(X1,X4,X2))))&(?[X4]:(element(X4,the_carrier(X1))&(in(X4,X3)&~(below(X1,X4,X2))))|latt_element_smaller(X1,X2,X3))))),inference(fof_nnf,[status(thm)],[78])).
% fof(129, plain,![X5]:((empty_carrier(X5)|~(latt_str(X5)))|![X6]:(~(element(X6,the_carrier(X5)))|![X7]:((~(latt_element_smaller(X5,X6,X7))|![X8]:(~(element(X8,the_carrier(X5)))|(~(in(X8,X7))|below(X5,X8,X6))))&(?[X9]:(element(X9,the_carrier(X5))&(in(X9,X7)&~(below(X5,X9,X6))))|latt_element_smaller(X5,X6,X7))))),inference(variable_rename,[status(thm)],[128])).
% fof(130, plain,![X5]:((empty_carrier(X5)|~(latt_str(X5)))|![X6]:(~(element(X6,the_carrier(X5)))|![X7]:((~(latt_element_smaller(X5,X6,X7))|![X8]:(~(element(X8,the_carrier(X5)))|(~(in(X8,X7))|below(X5,X8,X6))))&((element(esk3_3(X5,X6,X7),the_carrier(X5))&(in(esk3_3(X5,X6,X7),X7)&~(below(X5,esk3_3(X5,X6,X7),X6))))|latt_element_smaller(X5,X6,X7))))),inference(skolemize,[status(esa)],[129])).
% fof(131, plain,![X5]:![X6]:![X7]:![X8]:(((((~(element(X8,the_carrier(X5)))|(~(in(X8,X7))|below(X5,X8,X6)))|~(latt_element_smaller(X5,X6,X7)))&((element(esk3_3(X5,X6,X7),the_carrier(X5))&(in(esk3_3(X5,X6,X7),X7)&~(below(X5,esk3_3(X5,X6,X7),X6))))|latt_element_smaller(X5,X6,X7)))|~(element(X6,the_carrier(X5))))|(empty_carrier(X5)|~(latt_str(X5)))),inference(shift_quantors,[status(thm)],[130])).
% fof(132, plain,![X5]:![X6]:![X7]:![X8]:(((((~(element(X8,the_carrier(X5)))|(~(in(X8,X7))|below(X5,X8,X6)))|~(latt_element_smaller(X5,X6,X7)))|~(element(X6,the_carrier(X5))))|(empty_carrier(X5)|~(latt_str(X5))))&((((element(esk3_3(X5,X6,X7),the_carrier(X5))|latt_element_smaller(X5,X6,X7))|~(element(X6,the_carrier(X5))))|(empty_carrier(X5)|~(latt_str(X5))))&((((in(esk3_3(X5,X6,X7),X7)|latt_element_smaller(X5,X6,X7))|~(element(X6,the_carrier(X5))))|(empty_carrier(X5)|~(latt_str(X5))))&(((~(below(X5,esk3_3(X5,X6,X7),X6))|latt_element_smaller(X5,X6,X7))|~(element(X6,the_carrier(X5))))|(empty_carrier(X5)|~(latt_str(X5))))))),inference(distribute,[status(thm)],[131])).
% cnf(133,plain,(empty_carrier(X1)|latt_element_smaller(X1,X2,X3)|~latt_str(X1)|~element(X2,the_carrier(X1))|~below(X1,esk3_3(X1,X2,X3),X2)),inference(split_conjunct,[status(thm)],[132])).
% cnf(134,plain,(empty_carrier(X1)|latt_element_smaller(X1,X2,X3)|in(esk3_3(X1,X2,X3),X3)|~latt_str(X1)|~element(X2,the_carrier(X1))),inference(split_conjunct,[status(thm)],[132])).
% cnf(135,plain,(empty_carrier(X1)|latt_element_smaller(X1,X2,X3)|element(esk3_3(X1,X2,X3),the_carrier(X1))|~latt_str(X1)|~element(X2,the_carrier(X1))),inference(split_conjunct,[status(thm)],[132])).
% cnf(136,plain,(empty_carrier(X1)|below(X1,X4,X2)|~latt_str(X1)|~element(X2,the_carrier(X1))|~latt_element_smaller(X1,X2,X3)|~in(X4,X3)|~element(X4,the_carrier(X1))),inference(split_conjunct,[status(thm)],[132])).
% fof(137, 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)],[79])).
% fof(138, 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)],[137])).
% cnf(139,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)],[138])).
% fof(155, plain,![X1]:![X2]:(~(in(X1,X2))|element(X1,X2)),inference(fof_nnf,[status(thm)],[15])).
% fof(156, plain,![X3]:![X4]:(~(in(X3,X4))|element(X3,X4)),inference(variable_rename,[status(thm)],[155])).
% cnf(157,plain,(element(X1,X2)|~in(X1,X2)),inference(split_conjunct,[status(thm)],[156])).
% fof(158, plain,![X1]:(~(rel_str(X1))|![X2]:![X3]:(~(element(X3,the_carrier(X1)))|((~(relstr_set_smaller(X1,X2,X3))|![X4]:(~(element(X4,the_carrier(X1)))|(~(in(X4,X2))|related(X1,X4,X3))))&(?[X4]:(element(X4,the_carrier(X1))&(in(X4,X2)&~(related(X1,X4,X3))))|relstr_set_smaller(X1,X2,X3))))),inference(fof_nnf,[status(thm)],[16])).
% fof(159, plain,![X5]:(~(rel_str(X5))|![X6]:![X7]:(~(element(X7,the_carrier(X5)))|((~(relstr_set_smaller(X5,X6,X7))|![X8]:(~(element(X8,the_carrier(X5)))|(~(in(X8,X6))|related(X5,X8,X7))))&(?[X9]:(element(X9,the_carrier(X5))&(in(X9,X6)&~(related(X5,X9,X7))))|relstr_set_smaller(X5,X6,X7))))),inference(variable_rename,[status(thm)],[158])).
% fof(160, plain,![X5]:(~(rel_str(X5))|![X6]:![X7]:(~(element(X7,the_carrier(X5)))|((~(relstr_set_smaller(X5,X6,X7))|![X8]:(~(element(X8,the_carrier(X5)))|(~(in(X8,X6))|related(X5,X8,X7))))&((element(esk7_3(X5,X6,X7),the_carrier(X5))&(in(esk7_3(X5,X6,X7),X6)&~(related(X5,esk7_3(X5,X6,X7),X7))))|relstr_set_smaller(X5,X6,X7))))),inference(skolemize,[status(esa)],[159])).
% fof(161, plain,![X5]:![X6]:![X7]:![X8]:(((((~(element(X8,the_carrier(X5)))|(~(in(X8,X6))|related(X5,X8,X7)))|~(relstr_set_smaller(X5,X6,X7)))&((element(esk7_3(X5,X6,X7),the_carrier(X5))&(in(esk7_3(X5,X6,X7),X6)&~(related(X5,esk7_3(X5,X6,X7),X7))))|relstr_set_smaller(X5,X6,X7)))|~(element(X7,the_carrier(X5))))|~(rel_str(X5))),inference(shift_quantors,[status(thm)],[160])).
% fof(162, plain,![X5]:![X6]:![X7]:![X8]:(((((~(element(X8,the_carrier(X5)))|(~(in(X8,X6))|related(X5,X8,X7)))|~(relstr_set_smaller(X5,X6,X7)))|~(element(X7,the_carrier(X5))))|~(rel_str(X5)))&((((element(esk7_3(X5,X6,X7),the_carrier(X5))|relstr_set_smaller(X5,X6,X7))|~(element(X7,the_carrier(X5))))|~(rel_str(X5)))&((((in(esk7_3(X5,X6,X7),X6)|relstr_set_smaller(X5,X6,X7))|~(element(X7,the_carrier(X5))))|~(rel_str(X5)))&(((~(related(X5,esk7_3(X5,X6,X7),X7))|relstr_set_smaller(X5,X6,X7))|~(element(X7,the_carrier(X5))))|~(rel_str(X5)))))),inference(distribute,[status(thm)],[161])).
% cnf(163,plain,(relstr_set_smaller(X1,X3,X2)|~rel_str(X1)|~element(X2,the_carrier(X1))|~related(X1,esk7_3(X1,X3,X2),X2)),inference(split_conjunct,[status(thm)],[162])).
% cnf(164,plain,(relstr_set_smaller(X1,X3,X2)|in(esk7_3(X1,X3,X2),X3)|~rel_str(X1)|~element(X2,the_carrier(X1))),inference(split_conjunct,[status(thm)],[162])).
% cnf(165,plain,(relstr_set_smaller(X1,X3,X2)|element(esk7_3(X1,X3,X2),the_carrier(X1))|~rel_str(X1)|~element(X2,the_carrier(X1))),inference(split_conjunct,[status(thm)],[162])).
% cnf(166,plain,(related(X1,X4,X2)|~rel_str(X1)|~element(X2,the_carrier(X1))|~relstr_set_smaller(X1,X3,X2)|~in(X4,X3)|~element(X4,the_carrier(X1))),inference(split_conjunct,[status(thm)],[162])).
% fof(170, 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)],[83])).
% fof(171, 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)],[170])).
% fof(172, 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)],[171])).
% cnf(175,plain,(empty_carrier(X1)|reflexive_relstr(poset_of_lattice(X1))|~latt_str(X1)|~lattice(X1)),inference(split_conjunct,[status(thm)],[172])).
% cnf(176,plain,(empty_carrier(X1)|strict_rel_str(poset_of_lattice(X1))|~latt_str(X1)|~lattice(X1)),inference(split_conjunct,[status(thm)],[172])).
% cnf(177,plain,(empty_carrier(X1)|~latt_str(X1)|~lattice(X1)|~empty_carrier(poset_of_lattice(X1))),inference(split_conjunct,[status(thm)],[172])).
% fof(205, 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)],[90])).
% fof(206, 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)],[205])).
% fof(207, 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)],[206])).
% cnf(208,plain,(empty_carrier(X1)|rel_str(poset_of_lattice(X1))|~latt_str(X1)|~lattice(X1)),inference(split_conjunct,[status(thm)],[207])).
% fof(213, plain,![X1]:![X2]:![X3]:(((((((empty_carrier(X1)|~(meet_commutative(X1)))|~(meet_absorbing(X1)))|~(join_absorbing(X1)))|~(latt_str(X1)))|~(element(X2,the_carrier(X1))))|~(element(X3,the_carrier(X1))))|((~(below_refl(X1,X2,X3))|below(X1,X2,X3))&(~(below(X1,X2,X3))|below_refl(X1,X2,X3)))),inference(fof_nnf,[status(thm)],[91])).
% fof(214, plain,![X4]:![X5]:![X6]:(((((((empty_carrier(X4)|~(meet_commutative(X4)))|~(meet_absorbing(X4)))|~(join_absorbing(X4)))|~(latt_str(X4)))|~(element(X5,the_carrier(X4))))|~(element(X6,the_carrier(X4))))|((~(below_refl(X4,X5,X6))|below(X4,X5,X6))&(~(below(X4,X5,X6))|below_refl(X4,X5,X6)))),inference(variable_rename,[status(thm)],[213])).
% fof(215, plain,![X4]:![X5]:![X6]:(((~(below_refl(X4,X5,X6))|below(X4,X5,X6))|((((((empty_carrier(X4)|~(meet_commutative(X4)))|~(meet_absorbing(X4)))|~(join_absorbing(X4)))|~(latt_str(X4)))|~(element(X5,the_carrier(X4))))|~(element(X6,the_carrier(X4)))))&((~(below(X4,X5,X6))|below_refl(X4,X5,X6))|((((((empty_carrier(X4)|~(meet_commutative(X4)))|~(meet_absorbing(X4)))|~(join_absorbing(X4)))|~(latt_str(X4)))|~(element(X5,the_carrier(X4))))|~(element(X6,the_carrier(X4)))))),inference(distribute,[status(thm)],[214])).
% cnf(216,plain,(empty_carrier(X2)|below_refl(X2,X3,X1)|~element(X1,the_carrier(X2))|~element(X3,the_carrier(X2))|~latt_str(X2)|~join_absorbing(X2)|~meet_absorbing(X2)|~meet_commutative(X2)|~below(X2,X3,X1)),inference(split_conjunct,[status(thm)],[215])).
% cnf(217,plain,(empty_carrier(X2)|below(X2,X3,X1)|~element(X1,the_carrier(X2))|~element(X3,the_carrier(X2))|~latt_str(X2)|~join_absorbing(X2)|~meet_absorbing(X2)|~meet_commutative(X2)|~below_refl(X2,X3,X1)),inference(split_conjunct,[status(thm)],[215])).
% fof(218, 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)],[92])).
% fof(219, 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)],[218])).
% fof(220, 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)],[219])).
% cnf(221,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)],[220])).
% cnf(222,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)],[220])).
% fof(240, 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)],[32])).
% fof(241, 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)],[240])).
% fof(242, 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)],[241])).
% fof(243, 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)],[242])).
% cnf(245,plain,(X2=X3|~relation_of2(X1,X2,X2)|rel_str_of(X2,X1)!=rel_str_of(X3,X4)),inference(split_conjunct,[status(thm)],[243])).
% fof(252, plain,![X1]:![X2]:(~(element(X1,X2))|(empty(X2)|in(X1,X2))),inference(fof_nnf,[status(thm)],[35])).
% fof(253, plain,![X3]:![X4]:(~(element(X3,X4))|(empty(X4)|in(X3,X4))),inference(variable_rename,[status(thm)],[252])).
% cnf(254,plain,(in(X1,X2)|empty(X2)|~element(X1,X2)),inference(split_conjunct,[status(thm)],[253])).
% fof(263, plain,![X1]:(~(latt_str(X1))|((empty_carrier(X1)|~(lattice(X1)))|((((((~(empty_carrier(X1))&join_commutative(X1))&join_associative(X1))&meet_commutative(X1))&meet_associative(X1))&meet_absorbing(X1))&join_absorbing(X1)))),inference(fof_nnf,[status(thm)],[95])).
% fof(264, plain,![X2]:(~(latt_str(X2))|((empty_carrier(X2)|~(lattice(X2)))|((((((~(empty_carrier(X2))&join_commutative(X2))&join_associative(X2))&meet_commutative(X2))&meet_associative(X2))&meet_absorbing(X2))&join_absorbing(X2)))),inference(variable_rename,[status(thm)],[263])).
% fof(265, plain,![X2]:((((((((~(empty_carrier(X2))|(empty_carrier(X2)|~(lattice(X2))))|~(latt_str(X2)))&((join_commutative(X2)|(empty_carrier(X2)|~(lattice(X2))))|~(latt_str(X2))))&((join_associative(X2)|(empty_carrier(X2)|~(lattice(X2))))|~(latt_str(X2))))&((meet_commutative(X2)|(empty_carrier(X2)|~(lattice(X2))))|~(latt_str(X2))))&((meet_associative(X2)|(empty_carrier(X2)|~(lattice(X2))))|~(latt_str(X2))))&((meet_absorbing(X2)|(empty_carrier(X2)|~(lattice(X2))))|~(latt_str(X2))))&((join_absorbing(X2)|(empty_carrier(X2)|~(lattice(X2))))|~(latt_str(X2)))),inference(distribute,[status(thm)],[264])).
% cnf(266,plain,(empty_carrier(X1)|join_absorbing(X1)|~latt_str(X1)|~lattice(X1)),inference(split_conjunct,[status(thm)],[265])).
% cnf(267,plain,(empty_carrier(X1)|meet_absorbing(X1)|~latt_str(X1)|~lattice(X1)),inference(split_conjunct,[status(thm)],[265])).
% cnf(269,plain,(empty_carrier(X1)|meet_commutative(X1)|~latt_str(X1)|~lattice(X1)),inference(split_conjunct,[status(thm)],[265])).
% fof(278, plain,![X1]:![X2]:(~(in(X1,X2))|~(empty(X2))),inference(fof_nnf,[status(thm)],[40])).
% fof(279, plain,![X3]:![X4]:(~(in(X3,X4))|~(empty(X4))),inference(variable_rename,[status(thm)],[278])).
% cnf(280,plain,(~empty(X1)|~in(X2,X1)),inference(split_conjunct,[status(thm)],[279])).
% fof(286, plain,![X1]:(~(rel_str(X1))|(~(strict_rel_str(X1))|X1=rel_str_of(the_carrier(X1),the_InternalRel(X1)))),inference(fof_nnf,[status(thm)],[43])).
% fof(287, plain,![X2]:(~(rel_str(X2))|(~(strict_rel_str(X2))|X2=rel_str_of(the_carrier(X2),the_InternalRel(X2)))),inference(variable_rename,[status(thm)],[286])).
% cnf(288,plain,(X1=rel_str_of(the_carrier(X1),the_InternalRel(X1))|~strict_rel_str(X1)|~rel_str(X1)),inference(split_conjunct,[status(thm)],[287])).
% fof(315, plain,![X1]:(~(rel_str(X1))|relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1))),inference(fof_nnf,[status(thm)],[52])).
% fof(316, plain,![X2]:(~(rel_str(X2))|relation_of2_as_subset(the_InternalRel(X2),the_carrier(X2),the_carrier(X2))),inference(variable_rename,[status(thm)],[315])).
% cnf(317,plain,(relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1))|~rel_str(X1)),inference(split_conjunct,[status(thm)],[316])).
% fof(362, 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)],[63])).
% fof(363, 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)],[362])).
% cnf(365,plain,(relation_of2(X1,X2,X3)|~relation_of2_as_subset(X1,X2,X3)),inference(split_conjunct,[status(thm)],[363])).
% fof(373, negated_conjecture,?[X1]:?[X2]:(((~(empty_carrier(X2))&lattice(X2))&latt_str(X2))&?[X3]:(element(X3,the_carrier(X2))&((~(latt_element_smaller(X2,X3,X1))|~(relstr_set_smaller(poset_of_lattice(X2),X1,cast_to_el_of_LattPOSet(X2,X3))))&(latt_element_smaller(X2,X3,X1)|relstr_set_smaller(poset_of_lattice(X2),X1,cast_to_el_of_LattPOSet(X2,X3)))))),inference(fof_nnf,[status(thm)],[101])).
% fof(374, negated_conjecture,?[X4]:?[X5]:(((~(empty_carrier(X5))&lattice(X5))&latt_str(X5))&?[X6]:(element(X6,the_carrier(X5))&((~(latt_element_smaller(X5,X6,X4))|~(relstr_set_smaller(poset_of_lattice(X5),X4,cast_to_el_of_LattPOSet(X5,X6))))&(latt_element_smaller(X5,X6,X4)|relstr_set_smaller(poset_of_lattice(X5),X4,cast_to_el_of_LattPOSet(X5,X6)))))),inference(variable_rename,[status(thm)],[373])).
% fof(375, negated_conjecture,(((~(empty_carrier(esk20_0))&lattice(esk20_0))&latt_str(esk20_0))&(element(esk21_0,the_carrier(esk20_0))&((~(latt_element_smaller(esk20_0,esk21_0,esk19_0))|~(relstr_set_smaller(poset_of_lattice(esk20_0),esk19_0,cast_to_el_of_LattPOSet(esk20_0,esk21_0))))&(latt_element_smaller(esk20_0,esk21_0,esk19_0)|relstr_set_smaller(poset_of_lattice(esk20_0),esk19_0,cast_to_el_of_LattPOSet(esk20_0,esk21_0)))))),inference(skolemize,[status(esa)],[374])).
% cnf(376,negated_conjecture,(relstr_set_smaller(poset_of_lattice(esk20_0),esk19_0,cast_to_el_of_LattPOSet(esk20_0,esk21_0))|latt_element_smaller(esk20_0,esk21_0,esk19_0)),inference(split_conjunct,[status(thm)],[375])).
% cnf(377,negated_conjecture,(~relstr_set_smaller(poset_of_lattice(esk20_0),esk19_0,cast_to_el_of_LattPOSet(esk20_0,esk21_0))|~latt_element_smaller(esk20_0,esk21_0,esk19_0)),inference(split_conjunct,[status(thm)],[375])).
% cnf(378,negated_conjecture,(element(esk21_0,the_carrier(esk20_0))),inference(split_conjunct,[status(thm)],[375])).
% cnf(379,negated_conjecture,(latt_str(esk20_0)),inference(split_conjunct,[status(thm)],[375])).
% cnf(380,negated_conjecture,(lattice(esk20_0)),inference(split_conjunct,[status(thm)],[375])).
% cnf(381,negated_conjecture,(~empty_carrier(esk20_0)),inference(split_conjunct,[status(thm)],[375])).
% cnf(416,negated_conjecture,(empty_carrier(esk20_0)|~relstr_set_smaller(poset_of_lattice(esk20_0),esk19_0,esk21_0)|~latt_element_smaller(esk20_0,esk21_0,esk19_0)|~element(esk21_0,the_carrier(esk20_0))|~latt_str(esk20_0)|~lattice(esk20_0)),inference(spm,[status(thm)],[377,114,theory(equality)])).
% cnf(422,negated_conjecture,(empty_carrier(esk20_0)|~relstr_set_smaller(poset_of_lattice(esk20_0),esk19_0,esk21_0)|~latt_element_smaller(esk20_0,esk21_0,esk19_0)|$false|~latt_str(esk20_0)|~lattice(esk20_0)),inference(rw,[status(thm)],[416,378,theory(equality)])).
% cnf(423,negated_conjecture,(empty_carrier(esk20_0)|~relstr_set_smaller(poset_of_lattice(esk20_0),esk19_0,esk21_0)|~latt_element_smaller(esk20_0,esk21_0,esk19_0)|$false|$false|~lattice(esk20_0)),inference(rw,[status(thm)],[422,379,theory(equality)])).
% cnf(424,negated_conjecture,(empty_carrier(esk20_0)|~relstr_set_smaller(poset_of_lattice(esk20_0),esk19_0,esk21_0)|~latt_element_smaller(esk20_0,esk21_0,esk19_0)|$false|$false|$false),inference(rw,[status(thm)],[423,380,theory(equality)])).
% cnf(425,negated_conjecture,(empty_carrier(esk20_0)|~relstr_set_smaller(poset_of_lattice(esk20_0),esk19_0,esk21_0)|~latt_element_smaller(esk20_0,esk21_0,esk19_0)),inference(cn,[status(thm)],[424,theory(equality)])).
% cnf(426,negated_conjecture,(~relstr_set_smaller(poset_of_lattice(esk20_0),esk19_0,esk21_0)|~latt_element_smaller(esk20_0,esk21_0,esk19_0)),inference(sr,[status(thm)],[425,381,theory(equality)])).
% cnf(429,plain,(relation_of2(the_InternalRel(X1),the_carrier(X1),the_carrier(X1))|~rel_str(X1)),inference(spm,[status(thm)],[365,317,theory(equality)])).
% cnf(441,plain,(element(X2,the_carrier(X1))|empty_carrier(X1)|~element(X2,the_carrier(poset_of_lattice(X1)))|~latt_str(X1)|~lattice(X1)),inference(spm,[status(thm)],[117,127,theory(equality)])).
% cnf(452,plain,(relstr_set_smaller(X2,X1,X3)|~empty(X1)|~rel_str(X2)|~element(X3,the_carrier(X2))),inference(spm,[status(thm)],[280,164,theory(equality)])).
% cnf(453,plain,(element(esk7_3(X1,X2,X3),X2)|relstr_set_smaller(X1,X2,X3)|~rel_str(X1)|~element(X3,the_carrier(X1))),inference(spm,[status(thm)],[157,164,theory(equality)])).
% cnf(455,plain,(latt_element_smaller(X2,X3,X1)|empty_carrier(X2)|~empty(X1)|~element(X3,the_carrier(X2))|~latt_str(X2)),inference(spm,[status(thm)],[280,134,theory(equality)])).
% cnf(456,plain,(element(esk3_3(X1,X2,X3),X3)|latt_element_smaller(X1,X2,X3)|empty_carrier(X1)|~element(X2,the_carrier(X1))|~latt_str(X1)),inference(spm,[status(thm)],[157,134,theory(equality)])).
% cnf(458,negated_conjecture,(related(poset_of_lattice(esk20_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk21_0))|latt_element_smaller(esk20_0,esk21_0,esk19_0)|~rel_str(poset_of_lattice(esk20_0))|~in(X1,esk19_0)|~element(X1,the_carrier(poset_of_lattice(esk20_0)))|~element(cast_to_el_of_LattPOSet(esk20_0,esk21_0),the_carrier(poset_of_lattice(esk20_0)))),inference(spm,[status(thm)],[166,376,theory(equality)])).
% cnf(459,plain,(relstr_set_smaller(X1,X2,X3)|empty_carrier(X1)|~rel_str(X1)|~element(X3,the_carrier(X1))|~reflexive_relstr(X1)|~related_reflexive(X1,esk7_3(X1,X2,X3),X3)|~element(esk7_3(X1,X2,X3),the_carrier(X1))),inference(spm,[status(thm)],[163,222,theory(equality)])).
% cnf(478,plain,(latt_element_smaller(X1,X2,X3)|empty_carrier(X1)|~element(X2,the_carrier(X1))|~latt_str(X1)|~join_absorbing(X1)|~meet_absorbing(X1)|~meet_commutative(X1)|~below_refl(X1,esk3_3(X1,X2,X3),X2)|~element(esk3_3(X1,X2,X3),the_carrier(X1))),inference(spm,[status(thm)],[133,217,theory(equality)])).
% cnf(482,plain,(related_reflexive(poset_of_lattice(X1),X2,cast_to_el_of_LattPOSet(X1,X3))|empty_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)],[123,114,theory(equality)])).
% cnf(532,plain,(element(esk7_3(poset_of_lattice(X1),X2,X3),the_carrier(X1))|empty_carrier(X1)|relstr_set_smaller(poset_of_lattice(X1),X2,X3)|~latt_str(X1)|~lattice(X1)|~rel_str(poset_of_lattice(X1))|~element(X3,the_carrier(poset_of_lattice(X1)))),inference(spm,[status(thm)],[441,165,theory(equality)])).
% cnf(536,plain,(element(cast_to_el_of_LattPOSet(X1,X2),the_carrier(X1))|empty_carrier(X1)|~latt_str(X1)|~lattice(X1)|~element(X2,the_carrier(X1))),inference(spm,[status(thm)],[441,104,theory(equality)])).
% cnf(548,negated_conjecture,(related_reflexive(poset_of_lattice(esk20_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk21_0))|empty_carrier(poset_of_lattice(esk20_0))|latt_element_smaller(esk20_0,esk21_0,esk19_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(X1,the_carrier(poset_of_lattice(esk20_0)))|~element(cast_to_el_of_LattPOSet(esk20_0,esk21_0),the_carrier(poset_of_lattice(esk20_0)))|~in(X1,esk19_0)),inference(spm,[status(thm)],[221,458,theory(equality)])).
% cnf(582,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)],[245,429,theory(equality)])).
% cnf(675,negated_conjecture,(~latt_element_smaller(esk20_0,esk21_0,esk19_0)|~empty(esk19_0)|~rel_str(poset_of_lattice(esk20_0))|~element(cast_to_el_of_LattPOSet(esk20_0,esk21_0),the_carrier(poset_of_lattice(esk20_0)))),inference(spm,[status(thm)],[377,452,theory(equality)])).
% cnf(680,negated_conjecture,(empty_carrier(esk20_0)|~empty(esk19_0)|~rel_str(poset_of_lattice(esk20_0))|~latt_element_smaller(esk20_0,esk21_0,esk19_0)|~element(esk21_0,the_carrier(esk20_0))|~latt_str(esk20_0)|~lattice(esk20_0)),inference(spm,[status(thm)],[675,104,theory(equality)])).
% cnf(690,negated_conjecture,(empty_carrier(esk20_0)|~empty(esk19_0)|~rel_str(poset_of_lattice(esk20_0))|~latt_element_smaller(esk20_0,esk21_0,esk19_0)|$false|~latt_str(esk20_0)|~lattice(esk20_0)),inference(rw,[status(thm)],[680,378,theory(equality)])).
% cnf(691,negated_conjecture,(empty_carrier(esk20_0)|~empty(esk19_0)|~rel_str(poset_of_lattice(esk20_0))|~latt_element_smaller(esk20_0,esk21_0,esk19_0)|$false|$false|~lattice(esk20_0)),inference(rw,[status(thm)],[690,379,theory(equality)])).
% cnf(692,negated_conjecture,(empty_carrier(esk20_0)|~empty(esk19_0)|~rel_str(poset_of_lattice(esk20_0))|~latt_element_smaller(esk20_0,esk21_0,esk19_0)|$false|$false|$false),inference(rw,[status(thm)],[691,380,theory(equality)])).
% cnf(693,negated_conjecture,(empty_carrier(esk20_0)|~empty(esk19_0)|~rel_str(poset_of_lattice(esk20_0))|~latt_element_smaller(esk20_0,esk21_0,esk19_0)),inference(cn,[status(thm)],[692,theory(equality)])).
% cnf(694,negated_conjecture,(~empty(esk19_0)|~rel_str(poset_of_lattice(esk20_0))|~latt_element_smaller(esk20_0,esk21_0,esk19_0)),inference(sr,[status(thm)],[693,381,theory(equality)])).
% cnf(723,negated_conjecture,(below_refl(esk20_0,X1,esk21_0)|empty_carrier(esk20_0)|latt_element_smaller(esk20_0,esk21_0,esk19_0)|empty_carrier(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))|~latt_str(esk20_0)|~lattice(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~in(cast_to_el_of_LattPOSet(esk20_0,X1),esk19_0)|~element(cast_to_el_of_LattPOSet(esk20_0,esk21_0),the_carrier(poset_of_lattice(esk20_0)))|~element(cast_to_el_of_LattPOSet(esk20_0,X1),the_carrier(poset_of_lattice(esk20_0)))),inference(spm,[status(thm)],[122,548,theory(equality)])).
% cnf(725,negated_conjecture,(below_refl(esk20_0,X1,esk21_0)|empty_carrier(esk20_0)|latt_element_smaller(esk20_0,esk21_0,esk19_0)|empty_carrier(poset_of_lattice(esk20_0))|$false|~element(X1,the_carrier(esk20_0))|~latt_str(esk20_0)|~lattice(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~in(cast_to_el_of_LattPOSet(esk20_0,X1),esk19_0)|~element(cast_to_el_of_LattPOSet(esk20_0,esk21_0),the_carrier(poset_of_lattice(esk20_0)))|~element(cast_to_el_of_LattPOSet(esk20_0,X1),the_carrier(poset_of_lattice(esk20_0)))),inference(rw,[status(thm)],[723,378,theory(equality)])).
% cnf(726,negated_conjecture,(below_refl(esk20_0,X1,esk21_0)|empty_carrier(esk20_0)|latt_element_smaller(esk20_0,esk21_0,esk19_0)|empty_carrier(poset_of_lattice(esk20_0))|$false|~element(X1,the_carrier(esk20_0))|$false|~lattice(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~in(cast_to_el_of_LattPOSet(esk20_0,X1),esk19_0)|~element(cast_to_el_of_LattPOSet(esk20_0,esk21_0),the_carrier(poset_of_lattice(esk20_0)))|~element(cast_to_el_of_LattPOSet(esk20_0,X1),the_carrier(poset_of_lattice(esk20_0)))),inference(rw,[status(thm)],[725,379,theory(equality)])).
% cnf(727,negated_conjecture,(below_refl(esk20_0,X1,esk21_0)|empty_carrier(esk20_0)|latt_element_smaller(esk20_0,esk21_0,esk19_0)|empty_carrier(poset_of_lattice(esk20_0))|$false|~element(X1,the_carrier(esk20_0))|$false|$false|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~in(cast_to_el_of_LattPOSet(esk20_0,X1),esk19_0)|~element(cast_to_el_of_LattPOSet(esk20_0,esk21_0),the_carrier(poset_of_lattice(esk20_0)))|~element(cast_to_el_of_LattPOSet(esk20_0,X1),the_carrier(poset_of_lattice(esk20_0)))),inference(rw,[status(thm)],[726,380,theory(equality)])).
% cnf(728,negated_conjecture,(below_refl(esk20_0,X1,esk21_0)|empty_carrier(esk20_0)|latt_element_smaller(esk20_0,esk21_0,esk19_0)|empty_carrier(poset_of_lattice(esk20_0))|~element(X1,the_carrier(esk20_0))|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~in(cast_to_el_of_LattPOSet(esk20_0,X1),esk19_0)|~element(cast_to_el_of_LattPOSet(esk20_0,esk21_0),the_carrier(poset_of_lattice(esk20_0)))|~element(cast_to_el_of_LattPOSet(esk20_0,X1),the_carrier(poset_of_lattice(esk20_0)))),inference(cn,[status(thm)],[727,theory(equality)])).
% cnf(729,negated_conjecture,(below_refl(esk20_0,X1,esk21_0)|latt_element_smaller(esk20_0,esk21_0,esk19_0)|empty_carrier(poset_of_lattice(esk20_0))|~element(X1,the_carrier(esk20_0))|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~in(cast_to_el_of_LattPOSet(esk20_0,X1),esk19_0)|~element(cast_to_el_of_LattPOSet(esk20_0,esk21_0),the_carrier(poset_of_lattice(esk20_0)))|~element(cast_to_el_of_LattPOSet(esk20_0,X1),the_carrier(poset_of_lattice(esk20_0)))),inference(sr,[status(thm)],[728,381,theory(equality)])).
% cnf(735,negated_conjecture,(empty_carrier(esk20_0)|~empty(esk19_0)|~rel_str(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(esk20_0))|~latt_str(esk20_0)),inference(spm,[status(thm)],[694,455,theory(equality)])).
% cnf(737,negated_conjecture,(empty_carrier(esk20_0)|~empty(esk19_0)|~rel_str(poset_of_lattice(esk20_0))|$false|~latt_str(esk20_0)),inference(rw,[status(thm)],[735,378,theory(equality)])).
% cnf(738,negated_conjecture,(empty_carrier(esk20_0)|~empty(esk19_0)|~rel_str(poset_of_lattice(esk20_0))|$false|$false),inference(rw,[status(thm)],[737,379,theory(equality)])).
% cnf(739,negated_conjecture,(empty_carrier(esk20_0)|~empty(esk19_0)|~rel_str(poset_of_lattice(esk20_0))),inference(cn,[status(thm)],[738,theory(equality)])).
% cnf(740,negated_conjecture,(~empty(esk19_0)|~rel_str(poset_of_lattice(esk20_0))),inference(sr,[status(thm)],[739,381,theory(equality)])).
% cnf(741,negated_conjecture,(empty_carrier(esk20_0)|~empty(esk19_0)|~latt_str(esk20_0)|~lattice(esk20_0)),inference(spm,[status(thm)],[740,208,theory(equality)])).
% cnf(742,negated_conjecture,(empty_carrier(esk20_0)|~empty(esk19_0)|$false|~lattice(esk20_0)),inference(rw,[status(thm)],[741,379,theory(equality)])).
% cnf(743,negated_conjecture,(empty_carrier(esk20_0)|~empty(esk19_0)|$false|$false),inference(rw,[status(thm)],[742,380,theory(equality)])).
% cnf(744,negated_conjecture,(empty_carrier(esk20_0)|~empty(esk19_0)),inference(cn,[status(thm)],[743,theory(equality)])).
% cnf(745,negated_conjecture,(~empty(esk19_0)),inference(sr,[status(thm)],[744,381,theory(equality)])).
% cnf(748,negated_conjecture,(latt_element_smaller(esk20_0,esk21_0,esk19_0)|below_refl(esk20_0,X1,esk21_0)|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~in(cast_to_el_of_LattPOSet(esk20_0,X1),esk19_0)|~element(cast_to_el_of_LattPOSet(esk20_0,X1),the_carrier(poset_of_lattice(esk20_0)))|~element(X1,the_carrier(esk20_0))|~element(esk21_0,the_carrier(esk20_0))|~latt_str(esk20_0)|~lattice(esk20_0)),inference(spm,[status(thm)],[729,104,theory(equality)])).
% cnf(758,negated_conjecture,(latt_element_smaller(esk20_0,esk21_0,esk19_0)|below_refl(esk20_0,X1,esk21_0)|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~in(cast_to_el_of_LattPOSet(esk20_0,X1),esk19_0)|~element(cast_to_el_of_LattPOSet(esk20_0,X1),the_carrier(poset_of_lattice(esk20_0)))|~element(X1,the_carrier(esk20_0))|$false|~latt_str(esk20_0)|~lattice(esk20_0)),inference(rw,[status(thm)],[748,378,theory(equality)])).
% cnf(759,negated_conjecture,(latt_element_smaller(esk20_0,esk21_0,esk19_0)|below_refl(esk20_0,X1,esk21_0)|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~in(cast_to_el_of_LattPOSet(esk20_0,X1),esk19_0)|~element(cast_to_el_of_LattPOSet(esk20_0,X1),the_carrier(poset_of_lattice(esk20_0)))|~element(X1,the_carrier(esk20_0))|$false|$false|~lattice(esk20_0)),inference(rw,[status(thm)],[758,379,theory(equality)])).
% cnf(760,negated_conjecture,(latt_element_smaller(esk20_0,esk21_0,esk19_0)|below_refl(esk20_0,X1,esk21_0)|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~in(cast_to_el_of_LattPOSet(esk20_0,X1),esk19_0)|~element(cast_to_el_of_LattPOSet(esk20_0,X1),the_carrier(poset_of_lattice(esk20_0)))|~element(X1,the_carrier(esk20_0))|$false|$false|$false),inference(rw,[status(thm)],[759,380,theory(equality)])).
% cnf(761,negated_conjecture,(latt_element_smaller(esk20_0,esk21_0,esk19_0)|below_refl(esk20_0,X1,esk21_0)|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~in(cast_to_el_of_LattPOSet(esk20_0,X1),esk19_0)|~element(cast_to_el_of_LattPOSet(esk20_0,X1),the_carrier(poset_of_lattice(esk20_0)))|~element(X1,the_carrier(esk20_0))),inference(cn,[status(thm)],[760,theory(equality)])).
% cnf(762,negated_conjecture,(latt_element_smaller(esk20_0,esk21_0,esk19_0)|below_refl(esk20_0,X1,esk21_0)|empty_carrier(poset_of_lattice(esk20_0))|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~in(cast_to_el_of_LattPOSet(esk20_0,X1),esk19_0)|~element(cast_to_el_of_LattPOSet(esk20_0,X1),the_carrier(poset_of_lattice(esk20_0)))|~element(X1,the_carrier(esk20_0))),inference(sr,[status(thm)],[761,381,theory(equality)])).
% cnf(768,negated_conjecture,(latt_element_smaller(esk20_0,esk21_0,esk19_0)|below_refl(esk20_0,X1,esk21_0)|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~in(cast_to_el_of_LattPOSet(esk20_0,X1),esk19_0)|~element(X1,the_carrier(esk20_0))|~latt_str(esk20_0)|~lattice(esk20_0)),inference(spm,[status(thm)],[762,104,theory(equality)])).
% cnf(777,negated_conjecture,(latt_element_smaller(esk20_0,esk21_0,esk19_0)|below_refl(esk20_0,X1,esk21_0)|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~in(cast_to_el_of_LattPOSet(esk20_0,X1),esk19_0)|~element(X1,the_carrier(esk20_0))|$false|~lattice(esk20_0)),inference(rw,[status(thm)],[768,379,theory(equality)])).
% cnf(778,negated_conjecture,(latt_element_smaller(esk20_0,esk21_0,esk19_0)|below_refl(esk20_0,X1,esk21_0)|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~in(cast_to_el_of_LattPOSet(esk20_0,X1),esk19_0)|~element(X1,the_carrier(esk20_0))|$false|$false),inference(rw,[status(thm)],[777,380,theory(equality)])).
% cnf(779,negated_conjecture,(latt_element_smaller(esk20_0,esk21_0,esk19_0)|below_refl(esk20_0,X1,esk21_0)|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~in(cast_to_el_of_LattPOSet(esk20_0,X1),esk19_0)|~element(X1,the_carrier(esk20_0))),inference(cn,[status(thm)],[778,theory(equality)])).
% cnf(780,negated_conjecture,(latt_element_smaller(esk20_0,esk21_0,esk19_0)|below_refl(esk20_0,X1,esk21_0)|empty_carrier(poset_of_lattice(esk20_0))|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~in(cast_to_el_of_LattPOSet(esk20_0,X1),esk19_0)|~element(X1,the_carrier(esk20_0))),inference(sr,[status(thm)],[779,381,theory(equality)])).
% cnf(782,negated_conjecture,(latt_element_smaller(esk20_0,esk21_0,esk19_0)|below_refl(esk20_0,X1,esk21_0)|empty_carrier(poset_of_lattice(esk20_0))|empty(esk19_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(X1,the_carrier(esk20_0))|~element(cast_to_el_of_LattPOSet(esk20_0,X1),esk19_0)),inference(spm,[status(thm)],[780,254,theory(equality)])).
% cnf(787,negated_conjecture,(latt_element_smaller(esk20_0,esk21_0,esk19_0)|below_refl(esk20_0,X1,esk21_0)|empty_carrier(poset_of_lattice(esk20_0))|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(X1,the_carrier(esk20_0))|~element(cast_to_el_of_LattPOSet(esk20_0,X1),esk19_0)),inference(sr,[status(thm)],[782,745,theory(equality)])).
% cnf(990,plain,(the_carrier(X1)=X2|X1!=rel_str_of(X2,X3)|~rel_str(X1)|~strict_rel_str(X1)),inference(spm,[status(thm)],[582,288,theory(equality)])).
% cnf(993,plain,(the_carrier(rel_str_of(X1,X2))=X1|~strict_rel_str(rel_str_of(X1,X2))|~rel_str(rel_str_of(X1,X2))),inference(er,[status(thm)],[990,theory(equality)])).
% cnf(999,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(spm,[status(thm)],[993,139,theory(equality)])).
% cnf(1106,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)],[999,208])).
% cnf(1107,plain,(the_carrier(poset_of_lattice(X1))=the_carrier(X1)|empty_carrier(X1)|~latt_str(X1)|~lattice(X1)),inference(csr,[status(thm)],[1106,176])).
% cnf(1118,plain,(relstr_set_smaller(poset_of_lattice(X1),X2,X3)|element(esk7_3(poset_of_lattice(X1),X2,X3),the_carrier(X1))|empty_carrier(X1)|~rel_str(poset_of_lattice(X1))|~element(X3,the_carrier(X1))|~latt_str(X1)|~lattice(X1)),inference(spm,[status(thm)],[165,1107,theory(equality)])).
% cnf(1250,plain,(relstr_set_smaller(X1,X2,X3)|empty_carrier(X1)|~reflexive_relstr(X1)|~rel_str(X1)|~related_reflexive(X1,esk7_3(X1,X2,X3),X3)|~element(X3,the_carrier(X1))),inference(csr,[status(thm)],[459,165])).
% cnf(1926,plain,(latt_element_smaller(X1,X2,X3)|empty_carrier(X1)|~join_absorbing(X1)|~meet_absorbing(X1)|~meet_commutative(X1)|~below_refl(X1,esk3_3(X1,X2,X3),X2)|~element(X2,the_carrier(X1))|~latt_str(X1)),inference(csr,[status(thm)],[478,135])).
% cnf(1928,negated_conjecture,(latt_element_smaller(esk20_0,esk21_0,X1)|empty_carrier(esk20_0)|latt_element_smaller(esk20_0,esk21_0,esk19_0)|empty_carrier(poset_of_lattice(esk20_0))|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~element(esk21_0,the_carrier(esk20_0))|~latt_str(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(cast_to_el_of_LattPOSet(esk20_0,esk3_3(esk20_0,esk21_0,X1)),esk19_0)|~element(esk3_3(esk20_0,esk21_0,X1),the_carrier(esk20_0))),inference(spm,[status(thm)],[1926,787,theory(equality)])).
% cnf(1933,negated_conjecture,(latt_element_smaller(esk20_0,esk21_0,X1)|empty_carrier(esk20_0)|latt_element_smaller(esk20_0,esk21_0,esk19_0)|empty_carrier(poset_of_lattice(esk20_0))|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|$false|~latt_str(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(cast_to_el_of_LattPOSet(esk20_0,esk3_3(esk20_0,esk21_0,X1)),esk19_0)|~element(esk3_3(esk20_0,esk21_0,X1),the_carrier(esk20_0))),inference(rw,[status(thm)],[1928,378,theory(equality)])).
% cnf(1934,negated_conjecture,(latt_element_smaller(esk20_0,esk21_0,X1)|empty_carrier(esk20_0)|latt_element_smaller(esk20_0,esk21_0,esk19_0)|empty_carrier(poset_of_lattice(esk20_0))|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|$false|$false|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(cast_to_el_of_LattPOSet(esk20_0,esk3_3(esk20_0,esk21_0,X1)),esk19_0)|~element(esk3_3(esk20_0,esk21_0,X1),the_carrier(esk20_0))),inference(rw,[status(thm)],[1933,379,theory(equality)])).
% cnf(1935,negated_conjecture,(latt_element_smaller(esk20_0,esk21_0,X1)|empty_carrier(esk20_0)|latt_element_smaller(esk20_0,esk21_0,esk19_0)|empty_carrier(poset_of_lattice(esk20_0))|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(cast_to_el_of_LattPOSet(esk20_0,esk3_3(esk20_0,esk21_0,X1)),esk19_0)|~element(esk3_3(esk20_0,esk21_0,X1),the_carrier(esk20_0))),inference(cn,[status(thm)],[1934,theory(equality)])).
% cnf(1936,negated_conjecture,(latt_element_smaller(esk20_0,esk21_0,X1)|latt_element_smaller(esk20_0,esk21_0,esk19_0)|empty_carrier(poset_of_lattice(esk20_0))|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(cast_to_el_of_LattPOSet(esk20_0,esk3_3(esk20_0,esk21_0,X1)),esk19_0)|~element(esk3_3(esk20_0,esk21_0,X1),the_carrier(esk20_0))),inference(sr,[status(thm)],[1935,381,theory(equality)])).
% cnf(1984,plain,(relstr_set_smaller(poset_of_lattice(X1),X2,cast_to_el_of_LattPOSet(X1,X3))|empty_carrier(poset_of_lattice(X1))|empty_carrier(X1)|~reflexive_relstr(poset_of_lattice(X1))|~rel_str(poset_of_lattice(X1))|~element(cast_to_el_of_LattPOSet(X1,X3),the_carrier(poset_of_lattice(X1)))|~below_refl(X1,esk7_3(poset_of_lattice(X1),X2,cast_to_el_of_LattPOSet(X1,X3)),X3)|~element(X3,the_carrier(X1))|~element(esk7_3(poset_of_lattice(X1),X2,cast_to_el_of_LattPOSet(X1,X3)),the_carrier(X1))|~latt_str(X1)|~lattice(X1)),inference(spm,[status(thm)],[1250,482,theory(equality)])).
% cnf(1985,plain,(below_refl(X1,X2,X3)|empty_carrier(X1)|~element(X3,the_carrier(X1))|~element(X2,the_carrier(X1))|~latt_str(X1)|~lattice(X1)|~below_refl(X1,cast_to_el_of_LattPOSet(X1,X2),X3)|~element(cast_to_el_of_LattPOSet(X1,X2),the_carrier(X1))),inference(spm,[status(thm)],[122,482,theory(equality)])).
% cnf(2598,plain,(relstr_set_smaller(poset_of_lattice(X1),X2,X3)|element(esk7_3(poset_of_lattice(X1),X2,X3),the_carrier(X1))|empty_carrier(X1)|~element(X3,the_carrier(poset_of_lattice(X1)))|~latt_str(X1)|~lattice(X1)),inference(csr,[status(thm)],[532,208])).
% cnf(9128,plain,(relstr_set_smaller(poset_of_lattice(X1),X2,X3)|element(esk7_3(poset_of_lattice(X1),X2,X3),the_carrier(X1))|empty_carrier(X1)|~element(X3,the_carrier(X1))|~latt_str(X1)|~lattice(X1)),inference(csr,[status(thm)],[1118,208])).
% cnf(10279,negated_conjecture,(latt_element_smaller(esk20_0,esk21_0,esk19_0)|latt_element_smaller(esk20_0,esk21_0,X1)|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(esk3_3(esk20_0,esk21_0,X1),esk19_0)|~element(esk3_3(esk20_0,esk21_0,X1),the_carrier(esk20_0))|~latt_str(esk20_0)|~lattice(esk20_0)),inference(spm,[status(thm)],[1936,114,theory(equality)])).
% cnf(10280,negated_conjecture,(latt_element_smaller(esk20_0,esk21_0,esk19_0)|latt_element_smaller(esk20_0,esk21_0,X1)|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(esk3_3(esk20_0,esk21_0,X1),esk19_0)|~element(esk3_3(esk20_0,esk21_0,X1),the_carrier(esk20_0))|$false|~lattice(esk20_0)),inference(rw,[status(thm)],[10279,379,theory(equality)])).
% cnf(10281,negated_conjecture,(latt_element_smaller(esk20_0,esk21_0,esk19_0)|latt_element_smaller(esk20_0,esk21_0,X1)|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(esk3_3(esk20_0,esk21_0,X1),esk19_0)|~element(esk3_3(esk20_0,esk21_0,X1),the_carrier(esk20_0))|$false|$false),inference(rw,[status(thm)],[10280,380,theory(equality)])).
% cnf(10282,negated_conjecture,(latt_element_smaller(esk20_0,esk21_0,esk19_0)|latt_element_smaller(esk20_0,esk21_0,X1)|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(esk3_3(esk20_0,esk21_0,X1),esk19_0)|~element(esk3_3(esk20_0,esk21_0,X1),the_carrier(esk20_0))),inference(cn,[status(thm)],[10281,theory(equality)])).
% cnf(10283,negated_conjecture,(latt_element_smaller(esk20_0,esk21_0,esk19_0)|latt_element_smaller(esk20_0,esk21_0,X1)|empty_carrier(poset_of_lattice(esk20_0))|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(esk3_3(esk20_0,esk21_0,X1),esk19_0)|~element(esk3_3(esk20_0,esk21_0,X1),the_carrier(esk20_0))),inference(sr,[status(thm)],[10282,381,theory(equality)])).
% cnf(10333,negated_conjecture,(latt_element_smaller(esk20_0,esk21_0,esk19_0)|latt_element_smaller(esk20_0,esk21_0,X1)|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(esk3_3(esk20_0,esk21_0,X1),esk19_0)|~element(esk21_0,the_carrier(esk20_0))|~latt_str(esk20_0)),inference(spm,[status(thm)],[10283,135,theory(equality)])).
% cnf(10348,negated_conjecture,(latt_element_smaller(esk20_0,esk21_0,esk19_0)|latt_element_smaller(esk20_0,esk21_0,X1)|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(esk3_3(esk20_0,esk21_0,X1),esk19_0)|$false|~latt_str(esk20_0)),inference(rw,[status(thm)],[10333,378,theory(equality)])).
% cnf(10349,negated_conjecture,(latt_element_smaller(esk20_0,esk21_0,esk19_0)|latt_element_smaller(esk20_0,esk21_0,X1)|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(esk3_3(esk20_0,esk21_0,X1),esk19_0)|$false|$false),inference(rw,[status(thm)],[10348,379,theory(equality)])).
% cnf(10350,negated_conjecture,(latt_element_smaller(esk20_0,esk21_0,esk19_0)|latt_element_smaller(esk20_0,esk21_0,X1)|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(esk3_3(esk20_0,esk21_0,X1),esk19_0)),inference(cn,[status(thm)],[10349,theory(equality)])).
% cnf(10351,negated_conjecture,(latt_element_smaller(esk20_0,esk21_0,esk19_0)|latt_element_smaller(esk20_0,esk21_0,X1)|empty_carrier(poset_of_lattice(esk20_0))|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(esk3_3(esk20_0,esk21_0,X1),esk19_0)),inference(sr,[status(thm)],[10350,381,theory(equality)])).
% cnf(10366,negated_conjecture,(latt_element_smaller(esk20_0,esk21_0,esk19_0)|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(esk20_0))|~latt_str(esk20_0)),inference(spm,[status(thm)],[10351,456,theory(equality)])).
% cnf(10369,negated_conjecture,(latt_element_smaller(esk20_0,esk21_0,esk19_0)|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|$false|~latt_str(esk20_0)),inference(rw,[status(thm)],[10366,378,theory(equality)])).
% cnf(10370,negated_conjecture,(latt_element_smaller(esk20_0,esk21_0,esk19_0)|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|$false|$false),inference(rw,[status(thm)],[10369,379,theory(equality)])).
% cnf(10371,negated_conjecture,(latt_element_smaller(esk20_0,esk21_0,esk19_0)|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))),inference(cn,[status(thm)],[10370,theory(equality)])).
% cnf(10372,negated_conjecture,(latt_element_smaller(esk20_0,esk21_0,esk19_0)|empty_carrier(poset_of_lattice(esk20_0))|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))),inference(sr,[status(thm)],[10371,381,theory(equality)])).
% cnf(10382,negated_conjecture,(below(esk20_0,X1,esk21_0)|empty_carrier(esk20_0)|empty_carrier(poset_of_lattice(esk20_0))|~in(X1,esk19_0)|~element(X1,the_carrier(esk20_0))|~element(esk21_0,the_carrier(esk20_0))|~latt_str(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))),inference(spm,[status(thm)],[136,10372,theory(equality)])).
% cnf(10383,negated_conjecture,(below(esk20_0,X1,esk21_0)|empty_carrier(esk20_0)|empty_carrier(poset_of_lattice(esk20_0))|~in(X1,esk19_0)|~element(X1,the_carrier(esk20_0))|$false|~latt_str(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))),inference(rw,[status(thm)],[10382,378,theory(equality)])).
% cnf(10384,negated_conjecture,(below(esk20_0,X1,esk21_0)|empty_carrier(esk20_0)|empty_carrier(poset_of_lattice(esk20_0))|~in(X1,esk19_0)|~element(X1,the_carrier(esk20_0))|$false|$false|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))),inference(rw,[status(thm)],[10383,379,theory(equality)])).
% cnf(10385,negated_conjecture,(below(esk20_0,X1,esk21_0)|empty_carrier(esk20_0)|empty_carrier(poset_of_lattice(esk20_0))|~in(X1,esk19_0)|~element(X1,the_carrier(esk20_0))|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))),inference(cn,[status(thm)],[10384,theory(equality)])).
% cnf(10386,negated_conjecture,(below(esk20_0,X1,esk21_0)|empty_carrier(poset_of_lattice(esk20_0))|~in(X1,esk19_0)|~element(X1,the_carrier(esk20_0))|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))),inference(sr,[status(thm)],[10385,381,theory(equality)])).
% cnf(10388,negated_conjecture,(below_refl(esk20_0,X1,esk21_0)|empty_carrier(esk20_0)|empty_carrier(poset_of_lattice(esk20_0))|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~element(X1,the_carrier(esk20_0))|~element(esk21_0,the_carrier(esk20_0))|~latt_str(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~in(X1,esk19_0)),inference(spm,[status(thm)],[216,10386,theory(equality)])).
% cnf(10393,negated_conjecture,(below_refl(esk20_0,X1,esk21_0)|empty_carrier(esk20_0)|empty_carrier(poset_of_lattice(esk20_0))|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~element(X1,the_carrier(esk20_0))|$false|~latt_str(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~in(X1,esk19_0)),inference(rw,[status(thm)],[10388,378,theory(equality)])).
% cnf(10394,negated_conjecture,(below_refl(esk20_0,X1,esk21_0)|empty_carrier(esk20_0)|empty_carrier(poset_of_lattice(esk20_0))|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~element(X1,the_carrier(esk20_0))|$false|$false|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~in(X1,esk19_0)),inference(rw,[status(thm)],[10393,379,theory(equality)])).
% cnf(10395,negated_conjecture,(below_refl(esk20_0,X1,esk21_0)|empty_carrier(esk20_0)|empty_carrier(poset_of_lattice(esk20_0))|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~element(X1,the_carrier(esk20_0))|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~in(X1,esk19_0)),inference(cn,[status(thm)],[10394,theory(equality)])).
% cnf(10396,negated_conjecture,(below_refl(esk20_0,X1,esk21_0)|empty_carrier(poset_of_lattice(esk20_0))|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~element(X1,the_carrier(esk20_0))|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~in(X1,esk19_0)),inference(sr,[status(thm)],[10395,381,theory(equality)])).
% cnf(30989,plain,(relstr_set_smaller(poset_of_lattice(X1),X2,cast_to_el_of_LattPOSet(X1,X3))|empty_carrier(poset_of_lattice(X1))|empty_carrier(X1)|~reflexive_relstr(poset_of_lattice(X1))|~rel_str(poset_of_lattice(X1))|~below_refl(X1,esk7_3(poset_of_lattice(X1),X2,cast_to_el_of_LattPOSet(X1,X3)),X3)|~element(cast_to_el_of_LattPOSet(X1,X3),the_carrier(poset_of_lattice(X1)))|~element(X3,the_carrier(X1))|~latt_str(X1)|~lattice(X1)),inference(csr,[status(thm)],[1984,2598])).
% cnf(30990,plain,(relstr_set_smaller(poset_of_lattice(X1),X2,cast_to_el_of_LattPOSet(X1,X3))|empty_carrier(poset_of_lattice(X1))|empty_carrier(X1)|~reflexive_relstr(poset_of_lattice(X1))|~rel_str(poset_of_lattice(X1))|~below_refl(X1,esk7_3(poset_of_lattice(X1),X2,cast_to_el_of_LattPOSet(X1,X3)),X3)|~element(X3,the_carrier(X1))|~latt_str(X1)|~lattice(X1)),inference(csr,[status(thm)],[30989,104])).
% cnf(30991,plain,(relstr_set_smaller(poset_of_lattice(X1),X2,cast_to_el_of_LattPOSet(X1,X3))|empty_carrier(poset_of_lattice(X1))|empty_carrier(X1)|~reflexive_relstr(poset_of_lattice(X1))|~below_refl(X1,esk7_3(poset_of_lattice(X1),X2,cast_to_el_of_LattPOSet(X1,X3)),X3)|~element(X3,the_carrier(X1))|~latt_str(X1)|~lattice(X1)),inference(csr,[status(thm)],[30990,208])).
% cnf(30992,plain,(relstr_set_smaller(poset_of_lattice(X1),X2,cast_to_el_of_LattPOSet(X1,X3))|empty_carrier(poset_of_lattice(X1))|empty_carrier(X1)|~below_refl(X1,esk7_3(poset_of_lattice(X1),X2,cast_to_el_of_LattPOSet(X1,X3)),X3)|~element(X3,the_carrier(X1))|~latt_str(X1)|~lattice(X1)),inference(csr,[status(thm)],[30991,175])).
% cnf(30993,plain,(relstr_set_smaller(poset_of_lattice(X1),X2,cast_to_el_of_LattPOSet(X1,X3))|empty_carrier(X1)|~below_refl(X1,esk7_3(poset_of_lattice(X1),X2,cast_to_el_of_LattPOSet(X1,X3)),X3)|~element(X3,the_carrier(X1))|~latt_str(X1)|~lattice(X1)),inference(csr,[status(thm)],[30992,177])).
% cnf(31100,plain,(below_refl(X1,X2,X3)|empty_carrier(X1)|~below_refl(X1,cast_to_el_of_LattPOSet(X1,X2),X3)|~element(X3,the_carrier(X1))|~element(X2,the_carrier(X1))|~latt_str(X1)|~lattice(X1)),inference(csr,[status(thm)],[1985,536])).
% cnf(31105,negated_conjecture,(below_refl(esk20_0,X1,esk21_0)|empty_carrier(esk20_0)|empty_carrier(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))|~latt_str(esk20_0)|~lattice(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~in(cast_to_el_of_LattPOSet(esk20_0,X1),esk19_0)|~element(cast_to_el_of_LattPOSet(esk20_0,X1),the_carrier(esk20_0))),inference(spm,[status(thm)],[31100,10396,theory(equality)])).
% cnf(31132,negated_conjecture,(below_refl(esk20_0,X1,esk21_0)|empty_carrier(esk20_0)|empty_carrier(poset_of_lattice(esk20_0))|$false|~element(X1,the_carrier(esk20_0))|~latt_str(esk20_0)|~lattice(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~in(cast_to_el_of_LattPOSet(esk20_0,X1),esk19_0)|~element(cast_to_el_of_LattPOSet(esk20_0,X1),the_carrier(esk20_0))),inference(rw,[status(thm)],[31105,378,theory(equality)])).
% cnf(31133,negated_conjecture,(below_refl(esk20_0,X1,esk21_0)|empty_carrier(esk20_0)|empty_carrier(poset_of_lattice(esk20_0))|$false|~element(X1,the_carrier(esk20_0))|$false|~lattice(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~in(cast_to_el_of_LattPOSet(esk20_0,X1),esk19_0)|~element(cast_to_el_of_LattPOSet(esk20_0,X1),the_carrier(esk20_0))),inference(rw,[status(thm)],[31132,379,theory(equality)])).
% cnf(31134,negated_conjecture,(below_refl(esk20_0,X1,esk21_0)|empty_carrier(esk20_0)|empty_carrier(poset_of_lattice(esk20_0))|$false|~element(X1,the_carrier(esk20_0))|$false|$false|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~in(cast_to_el_of_LattPOSet(esk20_0,X1),esk19_0)|~element(cast_to_el_of_LattPOSet(esk20_0,X1),the_carrier(esk20_0))),inference(rw,[status(thm)],[31133,380,theory(equality)])).
% cnf(31135,negated_conjecture,(below_refl(esk20_0,X1,esk21_0)|empty_carrier(esk20_0)|empty_carrier(poset_of_lattice(esk20_0))|~element(X1,the_carrier(esk20_0))|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~in(cast_to_el_of_LattPOSet(esk20_0,X1),esk19_0)|~element(cast_to_el_of_LattPOSet(esk20_0,X1),the_carrier(esk20_0))),inference(cn,[status(thm)],[31134,theory(equality)])).
% cnf(31136,negated_conjecture,(below_refl(esk20_0,X1,esk21_0)|empty_carrier(poset_of_lattice(esk20_0))|~element(X1,the_carrier(esk20_0))|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~in(cast_to_el_of_LattPOSet(esk20_0,X1),esk19_0)|~element(cast_to_el_of_LattPOSet(esk20_0,X1),the_carrier(esk20_0))),inference(sr,[status(thm)],[31135,381,theory(equality)])).
% cnf(31527,negated_conjecture,(below_refl(esk20_0,X1,esk21_0)|empty_carrier(poset_of_lattice(esk20_0))|empty(esk19_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(cast_to_el_of_LattPOSet(esk20_0,X1),the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))|~element(cast_to_el_of_LattPOSet(esk20_0,X1),esk19_0)),inference(spm,[status(thm)],[31136,254,theory(equality)])).
% cnf(31532,negated_conjecture,(below_refl(esk20_0,X1,esk21_0)|empty_carrier(poset_of_lattice(esk20_0))|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(cast_to_el_of_LattPOSet(esk20_0,X1),the_carrier(esk20_0))|~element(X1,the_carrier(esk20_0))|~element(cast_to_el_of_LattPOSet(esk20_0,X1),esk19_0)),inference(sr,[status(thm)],[31527,745,theory(equality)])).
% cnf(31533,negated_conjecture,(below_refl(esk20_0,X1,esk21_0)|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(X1,the_carrier(esk20_0))|~element(X1,esk19_0)|~latt_str(esk20_0)|~lattice(esk20_0)),inference(spm,[status(thm)],[31532,114,theory(equality)])).
% cnf(31535,negated_conjecture,(below_refl(esk20_0,X1,esk21_0)|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(X1,the_carrier(esk20_0))|~element(X1,esk19_0)|$false|~lattice(esk20_0)),inference(rw,[status(thm)],[31533,379,theory(equality)])).
% cnf(31536,negated_conjecture,(below_refl(esk20_0,X1,esk21_0)|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(X1,the_carrier(esk20_0))|~element(X1,esk19_0)|$false|$false),inference(rw,[status(thm)],[31535,380,theory(equality)])).
% cnf(31537,negated_conjecture,(below_refl(esk20_0,X1,esk21_0)|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(X1,the_carrier(esk20_0))|~element(X1,esk19_0)),inference(cn,[status(thm)],[31536,theory(equality)])).
% cnf(31538,negated_conjecture,(below_refl(esk20_0,X1,esk21_0)|empty_carrier(poset_of_lattice(esk20_0))|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(X1,the_carrier(esk20_0))|~element(X1,esk19_0)),inference(sr,[status(thm)],[31537,381,theory(equality)])).
% cnf(31543,negated_conjecture,(relstr_set_smaller(poset_of_lattice(esk20_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk21_0))|empty_carrier(esk20_0)|empty_carrier(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(esk20_0))|~latt_str(esk20_0)|~lattice(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(esk7_3(poset_of_lattice(esk20_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk21_0)),the_carrier(esk20_0))|~element(esk7_3(poset_of_lattice(esk20_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk21_0)),esk19_0)),inference(spm,[status(thm)],[30993,31538,theory(equality)])).
% cnf(31547,negated_conjecture,(relstr_set_smaller(poset_of_lattice(esk20_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk21_0))|empty_carrier(esk20_0)|empty_carrier(poset_of_lattice(esk20_0))|$false|~latt_str(esk20_0)|~lattice(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(esk7_3(poset_of_lattice(esk20_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk21_0)),the_carrier(esk20_0))|~element(esk7_3(poset_of_lattice(esk20_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk21_0)),esk19_0)),inference(rw,[status(thm)],[31543,378,theory(equality)])).
% cnf(31548,negated_conjecture,(relstr_set_smaller(poset_of_lattice(esk20_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk21_0))|empty_carrier(esk20_0)|empty_carrier(poset_of_lattice(esk20_0))|$false|$false|~lattice(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(esk7_3(poset_of_lattice(esk20_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk21_0)),the_carrier(esk20_0))|~element(esk7_3(poset_of_lattice(esk20_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk21_0)),esk19_0)),inference(rw,[status(thm)],[31547,379,theory(equality)])).
% cnf(31549,negated_conjecture,(relstr_set_smaller(poset_of_lattice(esk20_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk21_0))|empty_carrier(esk20_0)|empty_carrier(poset_of_lattice(esk20_0))|$false|$false|$false|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(esk7_3(poset_of_lattice(esk20_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk21_0)),the_carrier(esk20_0))|~element(esk7_3(poset_of_lattice(esk20_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk21_0)),esk19_0)),inference(rw,[status(thm)],[31548,380,theory(equality)])).
% cnf(31550,negated_conjecture,(relstr_set_smaller(poset_of_lattice(esk20_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk21_0))|empty_carrier(esk20_0)|empty_carrier(poset_of_lattice(esk20_0))|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(esk7_3(poset_of_lattice(esk20_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk21_0)),the_carrier(esk20_0))|~element(esk7_3(poset_of_lattice(esk20_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk21_0)),esk19_0)),inference(cn,[status(thm)],[31549,theory(equality)])).
% cnf(31551,negated_conjecture,(relstr_set_smaller(poset_of_lattice(esk20_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk21_0))|empty_carrier(poset_of_lattice(esk20_0))|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(esk7_3(poset_of_lattice(esk20_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk21_0)),the_carrier(esk20_0))|~element(esk7_3(poset_of_lattice(esk20_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk21_0)),esk19_0)),inference(sr,[status(thm)],[31550,381,theory(equality)])).
% cnf(31622,negated_conjecture,(relstr_set_smaller(poset_of_lattice(esk20_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk21_0))|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(esk7_3(poset_of_lattice(esk20_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk21_0)),esk19_0)|~element(cast_to_el_of_LattPOSet(esk20_0,esk21_0),the_carrier(esk20_0))|~latt_str(esk20_0)|~lattice(esk20_0)),inference(spm,[status(thm)],[31551,9128,theory(equality)])).
% cnf(31637,negated_conjecture,(relstr_set_smaller(poset_of_lattice(esk20_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk21_0))|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(esk7_3(poset_of_lattice(esk20_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk21_0)),esk19_0)|~element(cast_to_el_of_LattPOSet(esk20_0,esk21_0),the_carrier(esk20_0))|$false|~lattice(esk20_0)),inference(rw,[status(thm)],[31622,379,theory(equality)])).
% cnf(31638,negated_conjecture,(relstr_set_smaller(poset_of_lattice(esk20_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk21_0))|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(esk7_3(poset_of_lattice(esk20_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk21_0)),esk19_0)|~element(cast_to_el_of_LattPOSet(esk20_0,esk21_0),the_carrier(esk20_0))|$false|$false),inference(rw,[status(thm)],[31637,380,theory(equality)])).
% cnf(31639,negated_conjecture,(relstr_set_smaller(poset_of_lattice(esk20_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk21_0))|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(esk7_3(poset_of_lattice(esk20_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk21_0)),esk19_0)|~element(cast_to_el_of_LattPOSet(esk20_0,esk21_0),the_carrier(esk20_0))),inference(cn,[status(thm)],[31638,theory(equality)])).
% cnf(31640,negated_conjecture,(relstr_set_smaller(poset_of_lattice(esk20_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk21_0))|empty_carrier(poset_of_lattice(esk20_0))|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(esk7_3(poset_of_lattice(esk20_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk21_0)),esk19_0)|~element(cast_to_el_of_LattPOSet(esk20_0,esk21_0),the_carrier(esk20_0))),inference(sr,[status(thm)],[31639,381,theory(equality)])).
% cnf(31677,negated_conjecture,(relstr_set_smaller(poset_of_lattice(esk20_0),esk19_0,cast_to_el_of_LattPOSet(esk20_0,esk21_0))|empty_carrier(poset_of_lattice(esk20_0))|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(cast_to_el_of_LattPOSet(esk20_0,esk21_0),the_carrier(esk20_0))|~element(cast_to_el_of_LattPOSet(esk20_0,esk21_0),the_carrier(poset_of_lattice(esk20_0)))),inference(spm,[status(thm)],[31640,453,theory(equality)])).
% cnf(31686,negated_conjecture,(relstr_set_smaller(poset_of_lattice(esk20_0),esk19_0,esk21_0)|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))|~element(esk21_0,the_carrier(esk20_0))|~latt_str(esk20_0)|~lattice(esk20_0)),inference(spm,[status(thm)],[31677,114,theory(equality)])).
% cnf(31687,negated_conjecture,(relstr_set_smaller(poset_of_lattice(esk20_0),esk19_0,esk21_0)|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))|$false|~latt_str(esk20_0)|~lattice(esk20_0)),inference(rw,[status(thm)],[31686,378,theory(equality)])).
% cnf(31688,negated_conjecture,(relstr_set_smaller(poset_of_lattice(esk20_0),esk19_0,esk21_0)|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))|$false|$false|~lattice(esk20_0)),inference(rw,[status(thm)],[31687,379,theory(equality)])).
% cnf(31689,negated_conjecture,(relstr_set_smaller(poset_of_lattice(esk20_0),esk19_0,esk21_0)|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))|$false|$false|$false),inference(rw,[status(thm)],[31688,380,theory(equality)])).
% cnf(31690,negated_conjecture,(relstr_set_smaller(poset_of_lattice(esk20_0),esk19_0,esk21_0)|empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))),inference(cn,[status(thm)],[31689,theory(equality)])).
% cnf(31691,negated_conjecture,(relstr_set_smaller(poset_of_lattice(esk20_0),esk19_0,esk21_0)|empty_carrier(poset_of_lattice(esk20_0))|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))),inference(sr,[status(thm)],[31690,381,theory(equality)])).
% cnf(31693,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|~latt_element_smaller(esk20_0,esk21_0,esk19_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))),inference(spm,[status(thm)],[426,31691,theory(equality)])).
% cnf(31694,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~reflexive_relstr(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))),inference(csr,[status(thm)],[31693,10372])).
% cnf(31695,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~rel_str(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))|~latt_str(esk20_0)|~lattice(esk20_0)),inference(spm,[status(thm)],[31694,175,theory(equality)])).
% cnf(31696,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~rel_str(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))|$false|~lattice(esk20_0)),inference(rw,[status(thm)],[31695,379,theory(equality)])).
% cnf(31697,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~rel_str(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))|$false|$false),inference(rw,[status(thm)],[31696,380,theory(equality)])).
% cnf(31698,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~rel_str(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))),inference(cn,[status(thm)],[31697,theory(equality)])).
% cnf(31699,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|~join_absorbing(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~rel_str(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))),inference(sr,[status(thm)],[31698,381,theory(equality)])).
% cnf(31700,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~rel_str(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))|~latt_str(esk20_0)|~lattice(esk20_0)),inference(spm,[status(thm)],[31699,266,theory(equality)])).
% cnf(31701,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~rel_str(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))|$false|~lattice(esk20_0)),inference(rw,[status(thm)],[31700,379,theory(equality)])).
% cnf(31702,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~rel_str(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))|$false|$false),inference(rw,[status(thm)],[31701,380,theory(equality)])).
% cnf(31703,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~rel_str(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))),inference(cn,[status(thm)],[31702,theory(equality)])).
% cnf(31704,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|~meet_absorbing(esk20_0)|~meet_commutative(esk20_0)|~rel_str(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))),inference(sr,[status(thm)],[31703,381,theory(equality)])).
% cnf(31705,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~meet_commutative(esk20_0)|~rel_str(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))|~latt_str(esk20_0)|~lattice(esk20_0)),inference(spm,[status(thm)],[31704,267,theory(equality)])).
% cnf(31706,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~meet_commutative(esk20_0)|~rel_str(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))|$false|~lattice(esk20_0)),inference(rw,[status(thm)],[31705,379,theory(equality)])).
% cnf(31707,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~meet_commutative(esk20_0)|~rel_str(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))|$false|$false),inference(rw,[status(thm)],[31706,380,theory(equality)])).
% cnf(31708,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~meet_commutative(esk20_0)|~rel_str(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))),inference(cn,[status(thm)],[31707,theory(equality)])).
% cnf(31709,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|~meet_commutative(esk20_0)|~rel_str(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))),inference(sr,[status(thm)],[31708,381,theory(equality)])).
% cnf(31710,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~rel_str(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))|~latt_str(esk20_0)|~lattice(esk20_0)),inference(spm,[status(thm)],[31709,269,theory(equality)])).
% cnf(31711,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~rel_str(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))|$false|~lattice(esk20_0)),inference(rw,[status(thm)],[31710,379,theory(equality)])).
% cnf(31712,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~rel_str(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))|$false|$false),inference(rw,[status(thm)],[31711,380,theory(equality)])).
% cnf(31713,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~rel_str(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))),inference(cn,[status(thm)],[31712,theory(equality)])).
% cnf(31714,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|~rel_str(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))),inference(sr,[status(thm)],[31713,381,theory(equality)])).
% cnf(31715,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))|~latt_str(esk20_0)|~lattice(esk20_0)),inference(spm,[status(thm)],[31714,208,theory(equality)])).
% cnf(31716,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))|$false|~lattice(esk20_0)),inference(rw,[status(thm)],[31715,379,theory(equality)])).
% cnf(31717,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))|$false|$false),inference(rw,[status(thm)],[31716,380,theory(equality)])).
% cnf(31718,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))),inference(cn,[status(thm)],[31717,theory(equality)])).
% cnf(31719,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|~element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))),inference(sr,[status(thm)],[31718,381,theory(equality)])).
% cnf(31724,negated_conjecture,(empty_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)],[31719,1107,theory(equality)])).
% cnf(31726,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|$false|~latt_str(esk20_0)|~lattice(esk20_0)),inference(rw,[status(thm)],[31724,378,theory(equality)])).
% cnf(31727,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|$false|$false|~lattice(esk20_0)),inference(rw,[status(thm)],[31726,379,theory(equality)])).
% cnf(31728,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)|$false|$false|$false),inference(rw,[status(thm)],[31727,380,theory(equality)])).
% cnf(31729,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))|empty_carrier(esk20_0)),inference(cn,[status(thm)],[31728,theory(equality)])).
% cnf(31730,negated_conjecture,(empty_carrier(poset_of_lattice(esk20_0))),inference(sr,[status(thm)],[31729,381,theory(equality)])).
% cnf(31736,negated_conjecture,(empty_carrier(esk20_0)|~latt_str(esk20_0)|~lattice(esk20_0)),inference(spm,[status(thm)],[177,31730,theory(equality)])).
% cnf(31780,negated_conjecture,(empty_carrier(esk20_0)|$false|~lattice(esk20_0)),inference(rw,[status(thm)],[31736,379,theory(equality)])).
% cnf(31781,negated_conjecture,(empty_carrier(esk20_0)|$false|$false),inference(rw,[status(thm)],[31780,380,theory(equality)])).
% cnf(31782,negated_conjecture,(empty_carrier(esk20_0)),inference(cn,[status(thm)],[31781,theory(equality)])).
% cnf(31783,negated_conjecture,($false),inference(sr,[status(thm)],[31782,381,theory(equality)])).
% cnf(31784,negated_conjecture,($false),31783,['proof']).
% # SZS output end CNFRefutation
% # Processed clauses                  : 4831
% # ...of these trivial                : 23
% # ...subsumed                        : 3620
% # ...remaining for further processing: 1188
% # Other redundant clauses eliminated : 2
% # Clauses deleted for lack of memory : 0
% # Backward-subsumed                  : 116
% # Backward-rewritten                 : 64
% # Generated clauses                  : 18809
% # ...of the previous two non-trivial : 17803
% # Contextual simplify-reflections    : 7097
% # Paramodulations                    : 18749
% # Factorizations                     : 0
% # Equation resolutions               : 45
% # Current number of processed clauses: 890
% #    Positive orientable unit clauses: 47
% #    Positive unorientable unit clauses: 0
% #    Negative unit clauses           : 11
% #    Non-unit-clauses                : 832
% # Current number of unprocessed clauses: 12228
% # ...number of literals in the above : 81174
% # Clause-clause subsumption calls (NU) : 432922
% # Rec. Clause-clause subsumption calls : 116414
% # Unit Clause-clause subsumption calls : 531
% # Rewrite failures with RHS unbound  : 0
% # Indexed BW rewrite attempts        : 24
% # Indexed BW rewrite successes       : 10
% # Backwards rewriting index:   572 leaves,   1.58+/-1.352 terms/leaf
% # Paramod-from index:          257 leaves,   1.35+/-0.761 terms/leaf
% # Paramod-into index:          472 leaves,   1.55+/-1.201 terms/leaf
% # -------------------------------------------------
% # User time              : 1.213 s
% # System time            : 0.033 s
% # Total time             : 1.246 s
% # Maximum resident set size: 0 pages
% PrfWatch: 1.76 CPU 1.87 WC
% FINAL PrfWatch: 1.76 CPU 1.87 WC
% SZS output end Solution for /tmp/SystemOnTPTP5776/SEU349+1.tptp
% 
%------------------------------------------------------------------------------