TSTP Solution File: SEU346+1 by ET---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SEU346+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 09:19:12 EDT 2022
% Result : Theorem 0.27s 6.45s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 25
% Syntax : Number of formulae : 140 ( 28 unt; 0 def)
% Number of atoms : 576 ( 50 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 732 ( 296 ~; 328 |; 70 &)
% ( 6 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 3 con; 0-4 aty)
% Number of variables : 230 ( 13 sgn 103 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',redefinition_m2_relset_1) ).
fof(dt_k2_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ( reflexive(k2_lattice3(X1))
& antisymmetric(k2_lattice3(X1))
& transitive(k2_lattice3(X1))
& v1_partfun1(k2_lattice3(X1),the_carrier(X1),the_carrier(X1))
& relation_of2_as_subset(k2_lattice3(X1),the_carrier(X1),the_carrier(X1)) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_k2_lattice3) ).
fof(free_g1_orders_2,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('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',free_g1_orders_2) ).
fof(d2_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> poset_of_lattice(X1) = rel_str_of(the_carrier(X1),k2_lattice3(X1)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d2_lattice3) ).
fof(abstractness_v1_orders_2,axiom,
! [X1] :
( rel_str(X1)
=> ( strict_rel_str(X1)
=> X1 = rel_str_of(the_carrier(X1),the_InternalRel(X1)) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',abstractness_v1_orders_2) ).
fof(t7_lattice3,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( below_refl(X1,X2,X3)
<=> related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3)) ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t7_lattice3) ).
fof(fc4_lattice3,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('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fc4_lattice3) ).
fof(fc1_struct_0,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fc1_struct_0) ).
fof(dt_k3_lattice3,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('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_k3_lattice3) ).
fof(d9_orders_2,axiom,
! [X1] :
( rel_str(X1)
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( related(X1,X2,X3)
<=> in(ordered_pair(X2,X3),the_InternalRel(X1)) ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d9_orders_2) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d5_tarski) ).
fof(d3_lattice3,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('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d3_lattice3) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',commutativity_k2_tarski) ).
fof(dt_u1_orders_2,axiom,
! [X1] :
( rel_str(X1)
=> relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_u1_orders_2) ).
fof(redefinition_r3_orders_2,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('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',redefinition_r3_orders_2) ).
fof(dt_l1_orders_2,axiom,
! [X1] :
( rel_str(X1)
=> one_sorted_str(X1) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_l1_orders_2) ).
fof(redefinition_k1_domain_1,axiom,
! [X1,X2,X3,X4] :
( ( ~ empty(X1)
& ~ empty(X2)
& element(X3,X1)
& element(X4,X2) )
=> ordered_pair_as_product_element(X1,X2,X3,X4) = ordered_pair(X3,X4) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',redefinition_k1_domain_1) ).
fof(fc1_orders_2,axiom,
! [X1,X2] :
( ( ~ empty(X1)
& relation_of2(X2,X1,X1) )
=> ( ~ empty_carrier(rel_str_of(X1,X2))
& strict_rel_str(rel_str_of(X1,X2)) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fc1_orders_2) ).
fof(t32_filter_1,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))
<=> below_refl(X1,X2,X3) ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t32_filter_1) ).
fof(redefinition_k2_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> k2_lattice3(X1) = relation_of_lattice(X1) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',redefinition_k2_lattice3) ).
fof(reflexivity_r3_orders_2,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,X2) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',reflexivity_r3_orders_2) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',existence_m1_subset_1) ).
fof(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t1_subset) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t7_boole) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t2_subset) ).
fof(c_0_25,plain,
! [X4,X5,X6,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(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])])])]) ).
fof(c_0_26,plain,
! [X2] :
( ( reflexive(k2_lattice3(X2))
| empty_carrier(X2)
| ~ lattice(X2)
| ~ latt_str(X2) )
& ( antisymmetric(k2_lattice3(X2))
| empty_carrier(X2)
| ~ lattice(X2)
| ~ latt_str(X2) )
& ( transitive(k2_lattice3(X2))
| empty_carrier(X2)
| ~ lattice(X2)
| ~ latt_str(X2) )
& ( v1_partfun1(k2_lattice3(X2),the_carrier(X2),the_carrier(X2))
| empty_carrier(X2)
| ~ lattice(X2)
| ~ latt_str(X2) )
& ( relation_of2_as_subset(k2_lattice3(X2),the_carrier(X2),the_carrier(X2))
| empty_carrier(X2)
| ~ lattice(X2)
| ~ latt_str(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k2_lattice3])])])]) ).
fof(c_0_27,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)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[free_g1_orders_2])])])])])]) ).
cnf(c_0_28,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,plain,
( empty_carrier(X1)
| relation_of2_as_subset(k2_lattice3(X1),the_carrier(X1),the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_30,plain,
( X2 = X3
| ~ relation_of2(X1,X2,X2)
| rel_str_of(X2,X1) != rel_str_of(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_31,plain,
( relation_of2(k2_lattice3(X1),the_carrier(X1),the_carrier(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_32,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)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d2_lattice3])])]) ).
cnf(c_0_33,plain,
( the_carrier(X1) = X2
| empty_carrier(X1)
| rel_str_of(the_carrier(X1),k2_lattice3(X1)) != rel_str_of(X2,X3)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,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)],[c_0_32]) ).
fof(c_0_35,plain,
! [X2] :
( ~ rel_str(X2)
| ~ strict_rel_str(X2)
| X2 = rel_str_of(the_carrier(X2),the_InternalRel(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[abstractness_v1_orders_2])]) ).
fof(c_0_36,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( below_refl(X1,X2,X3)
<=> related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3)) ) ) ) ),
inference(assume_negation,[status(cth)],[t7_lattice3]) ).
fof(c_0_37,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)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc4_lattice3])])])]) ).
fof(c_0_38,plain,
! [X2] :
( empty_carrier(X2)
| ~ one_sorted_str(X2)
| ~ empty(the_carrier(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc1_struct_0])])]) ).
cnf(c_0_39,plain,
( the_carrier(X1) = X2
| empty_carrier(X1)
| poset_of_lattice(X1) != rel_str_of(X2,X3)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,plain,
( X1 = rel_str_of(the_carrier(X1),the_InternalRel(X1))
| ~ strict_rel_str(X1)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_41,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)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k3_lattice3])])])]) ).
fof(c_0_42,plain,
! [X4,X5,X6] :
( ( ~ related(X4,X5,X6)
| in(ordered_pair(X5,X6),the_InternalRel(X4))
| ~ element(X6,the_carrier(X4))
| ~ element(X5,the_carrier(X4))
| ~ rel_str(X4) )
& ( ~ in(ordered_pair(X5,X6),the_InternalRel(X4))
| related(X4,X5,X6)
| ~ element(X6,the_carrier(X4))
| ~ element(X5,the_carrier(X4))
| ~ rel_str(X4) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_orders_2])])])])])]) ).
fof(c_0_43,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_44,negated_conjecture,
( ~ empty_carrier(esk20_0)
& lattice(esk20_0)
& latt_str(esk20_0)
& element(esk21_0,the_carrier(esk20_0))
& element(esk22_0,the_carrier(esk20_0))
& ( ~ below_refl(esk20_0,esk21_0,esk22_0)
| ~ related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),cast_to_el_of_LattPOSet(esk20_0,esk22_0)) )
& ( below_refl(esk20_0,esk21_0,esk22_0)
| related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),cast_to_el_of_LattPOSet(esk20_0,esk22_0)) ) ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_36])])])])])]) ).
cnf(c_0_45,plain,
( empty_carrier(X1)
| ~ latt_str(X1)
| ~ lattice(X1)
| ~ empty_carrier(poset_of_lattice(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_46,plain,
( empty_carrier(X1)
| ~ empty(the_carrier(X1))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_47,plain,
( the_carrier(X1) = the_carrier(X2)
| empty_carrier(X1)
| poset_of_lattice(X1) != X2
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ strict_rel_str(X2)
| ~ rel_str(X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_48,plain,
( empty_carrier(X1)
| rel_str(poset_of_lattice(X1))
| ~ latt_str(X1)
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_49,plain,
( empty_carrier(X1)
| strict_rel_str(poset_of_lattice(X1))
| ~ latt_str(X1)
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_50,plain,
! [X3,X4] :
( empty_carrier(X3)
| ~ lattice(X3)
| ~ latt_str(X3)
| ~ element(X4,the_carrier(X3))
| cast_to_el_of_LattPOSet(X3,X4) = X4 ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d3_lattice3])])])])])]) ).
cnf(c_0_51,plain,
( related(X1,X2,X3)
| ~ rel_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ in(ordered_pair(X2,X3),the_InternalRel(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_52,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
fof(c_0_53,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(c_0_54,plain,
! [X2] :
( ~ rel_str(X2)
| relation_of2_as_subset(the_InternalRel(X2),the_carrier(X2),the_carrier(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_orders_2])]) ).
cnf(c_0_55,negated_conjecture,
~ empty_carrier(esk20_0),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_56,plain,
( empty_carrier(X1)
| ~ one_sorted_str(poset_of_lattice(X1))
| ~ empty(the_carrier(poset_of_lattice(X1)))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_57,negated_conjecture,
lattice(esk20_0),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_58,negated_conjecture,
latt_str(esk20_0),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_59,plain,
( the_carrier(poset_of_lattice(X1)) = the_carrier(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_47]),c_0_48]),c_0_49]) ).
cnf(c_0_60,negated_conjecture,
( ~ related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),cast_to_el_of_LattPOSet(esk20_0,esk22_0))
| ~ below_refl(esk20_0,esk21_0,esk22_0) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_61,plain,
( cast_to_el_of_LattPOSet(X1,X2) = X2
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_62,negated_conjecture,
element(esk22_0,the_carrier(esk20_0)),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_63,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)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_r3_orders_2])])])]) ).
cnf(c_0_64,plain,
( related(X1,X2,X3)
| ~ rel_str(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),the_InternalRel(X1)) ),
inference(rw,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_65,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_66,plain,
( relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_67,negated_conjecture,
( ~ one_sorted_str(poset_of_lattice(esk20_0))
| ~ empty(the_carrier(poset_of_lattice(esk20_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]),c_0_58])]) ).
cnf(c_0_68,negated_conjecture,
the_carrier(poset_of_lattice(esk20_0)) = the_carrier(esk20_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_59]),c_0_57]),c_0_58])]) ).
fof(c_0_69,plain,
! [X2] :
( ~ rel_str(X2)
| one_sorted_str(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_orders_2])]) ).
fof(c_0_70,plain,
! [X5,X6,X7,X8] :
( empty(X5)
| empty(X6)
| ~ element(X7,X5)
| ~ element(X8,X6)
| ordered_pair_as_product_element(X5,X6,X7,X8) = ordered_pair(X7,X8) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_k1_domain_1])])]) ).
cnf(c_0_71,plain,
( in(ordered_pair(X2,X3),the_InternalRel(X1))
| ~ rel_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ related(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_72,negated_conjecture,
( ~ related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),esk22_0)
| ~ below_refl(esk20_0,esk21_0,esk22_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]),c_0_57]),c_0_58])]),c_0_55]) ).
cnf(c_0_73,negated_conjecture,
element(esk21_0,the_carrier(esk20_0)),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_74,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)],[c_0_63]) ).
cnf(c_0_75,plain,
( related(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),the_InternalRel(X1))
| ~ rel_str(X1) ),
inference(rw,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_76,plain,
( empty_carrier(X1)
| reflexive_relstr(poset_of_lattice(X1))
| ~ latt_str(X1)
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_77,plain,
! [X3,X4] :
( ( ~ empty_carrier(rel_str_of(X3,X4))
| empty(X3)
| ~ relation_of2(X4,X3,X3) )
& ( strict_rel_str(rel_str_of(X3,X4))
| empty(X3)
| ~ relation_of2(X4,X3,X3) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc1_orders_2])])])]) ).
cnf(c_0_78,plain,
( relation_of2(the_InternalRel(X1),the_carrier(X1),the_carrier(X1))
| ~ rel_str(X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_66]) ).
cnf(c_0_79,negated_conjecture,
rel_str(poset_of_lattice(esk20_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_48]),c_0_57]),c_0_58])]) ).
cnf(c_0_80,negated_conjecture,
strict_rel_str(poset_of_lattice(esk20_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_49]),c_0_57]),c_0_58])]) ).
cnf(c_0_81,negated_conjecture,
( ~ one_sorted_str(poset_of_lattice(esk20_0))
| ~ empty(the_carrier(esk20_0)) ),
inference(rw,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_82,plain,
( one_sorted_str(X1)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_83,plain,
( ordered_pair_as_product_element(X1,X2,X3,X4) = ordered_pair(X3,X4)
| empty(X2)
| empty(X1)
| ~ element(X4,X2)
| ~ element(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_84,plain,
( X1 = X4
| ~ relation_of2(X1,X2,X2)
| rel_str_of(X2,X1) != rel_str_of(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_85,plain,
( in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),the_InternalRel(X1))
| ~ rel_str(X1)
| ~ related(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1)) ),
inference(rw,[status(thm)],[c_0_71,c_0_52]) ).
cnf(c_0_86,negated_conjecture,
( related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),cast_to_el_of_LattPOSet(esk20_0,esk22_0))
| below_refl(esk20_0,esk21_0,esk22_0) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_87,negated_conjecture,
( ~ related_reflexive(poset_of_lattice(esk20_0),esk21_0,esk22_0)
| ~ below_refl(esk20_0,esk21_0,esk22_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_61]),c_0_73]),c_0_57]),c_0_58])]),c_0_55]) ).
cnf(c_0_88,plain,
( related_reflexive(X1,X2,X3)
| empty_carrier(X1)
| ~ reflexive_relstr(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),the_InternalRel(X1))
| ~ rel_str(X1) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_89,negated_conjecture,
reflexive_relstr(poset_of_lattice(esk20_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_76]),c_0_57]),c_0_58])]) ).
cnf(c_0_90,plain,
( empty(X2)
| ~ relation_of2(X1,X2,X2)
| ~ empty_carrier(rel_str_of(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_91,negated_conjecture,
relation_of2(the_InternalRel(poset_of_lattice(esk20_0)),the_carrier(esk20_0),the_carrier(esk20_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_68]),c_0_79])]) ).
cnf(c_0_92,negated_conjecture,
rel_str_of(the_carrier(esk20_0),the_InternalRel(poset_of_lattice(esk20_0))) = poset_of_lattice(esk20_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_68]),c_0_80]),c_0_79])]) ).
cnf(c_0_93,negated_conjecture,
~ empty(the_carrier(esk20_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_79])]) ).
fof(c_0_94,plain,
! [X4,X5,X6] :
( ( ~ in(ordered_pair_as_product_element(the_carrier(X4),the_carrier(X4),X5,X6),relation_of_lattice(X4))
| below_refl(X4,X5,X6)
| ~ element(X6,the_carrier(X4))
| ~ element(X5,the_carrier(X4))
| empty_carrier(X4)
| ~ lattice(X4)
| ~ latt_str(X4) )
& ( ~ below_refl(X4,X5,X6)
| in(ordered_pair_as_product_element(the_carrier(X4),the_carrier(X4),X5,X6),relation_of_lattice(X4))
| ~ element(X6,the_carrier(X4))
| ~ element(X5,the_carrier(X4))
| empty_carrier(X4)
| ~ lattice(X4)
| ~ latt_str(X4) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t32_filter_1])])])])])])]) ).
cnf(c_0_95,plain,
( ordered_pair_as_product_element(X1,X2,X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3))
| empty(X2)
| empty(X1)
| ~ element(X4,X2)
| ~ element(X3,X1) ),
inference(rw,[status(thm)],[c_0_83,c_0_52]) ).
cnf(c_0_96,plain,
( the_InternalRel(X1) = X2
| rel_str_of(the_carrier(X1),the_InternalRel(X1)) != rel_str_of(X3,X2)
| ~ rel_str(X1) ),
inference(spm,[status(thm)],[c_0_84,c_0_78]) ).
fof(c_0_97,plain,
! [X2] :
( empty_carrier(X2)
| ~ lattice(X2)
| ~ latt_str(X2)
| k2_lattice3(X2) = relation_of_lattice(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_k2_lattice3])])]) ).
fof(c_0_98,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,X5) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r3_orders_2])])])])]) ).
fof(c_0_99,plain,
! [X3] : element(esk7_1(X3),X3),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
cnf(c_0_100,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),the_InternalRel(X3))
| ~ related(X3,X1,X2)
| ~ element(X2,the_carrier(X3))
| ~ element(X1,the_carrier(X3))
| ~ rel_str(X3) ),
inference(rw,[status(thm)],[c_0_85,c_0_65]) ).
cnf(c_0_101,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)],[c_0_63]) ).
cnf(c_0_102,negated_conjecture,
( related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),esk22_0)
| below_refl(esk20_0,esk21_0,esk22_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_61]),c_0_62]),c_0_57]),c_0_58])]),c_0_55]) ).
cnf(c_0_103,negated_conjecture,
( empty_carrier(poset_of_lattice(esk20_0))
| ~ below_refl(esk20_0,esk21_0,esk22_0)
| ~ element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))
| ~ element(esk22_0,the_carrier(poset_of_lattice(esk20_0)))
| ~ in(unordered_pair(singleton(esk21_0),unordered_pair(esk21_0,esk22_0)),the_InternalRel(poset_of_lattice(esk20_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89]),c_0_79])]) ).
cnf(c_0_104,negated_conjecture,
~ empty_carrier(poset_of_lattice(esk20_0)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92]),c_0_93]) ).
cnf(c_0_105,plain,
( empty_carrier(X1)
| below_refl(X1,X2,X3)
| ~ latt_str(X1)
| ~ lattice(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_106,plain,
( ordered_pair_as_product_element(X1,X2,X3,X4) = unordered_pair(singleton(X3),unordered_pair(X3,X4))
| empty(X1)
| empty(X2)
| ~ element(X4,X2)
| ~ element(X3,X1) ),
inference(rw,[status(thm)],[c_0_95,c_0_65]) ).
cnf(c_0_107,plain,
( the_InternalRel(X1) = X2
| X1 != rel_str_of(X3,X2)
| ~ strict_rel_str(X1)
| ~ rel_str(X1) ),
inference(spm,[status(thm)],[c_0_96,c_0_40]) ).
cnf(c_0_108,plain,
( k2_lattice3(X1) = relation_of_lattice(X1)
| empty_carrier(X1)
| ~ latt_str(X1)
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_109,plain,
( related_reflexive(X1,X2,X2)
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ rel_str(X1)
| ~ reflexive_relstr(X1) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_110,plain,
element(esk7_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
fof(c_0_111,plain,
! [X3,X4] :
( ~ in(X3,X4)
| element(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
cnf(c_0_112,plain,
( empty_carrier(X1)
| in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),the_InternalRel(X1))
| ~ related_reflexive(X1,X2,X3)
| ~ reflexive_relstr(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ rel_str(X1) ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_113,negated_conjecture,
( related_reflexive(poset_of_lattice(esk20_0),esk21_0,esk22_0)
| below_refl(esk20_0,esk21_0,esk22_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_61]),c_0_73]),c_0_57]),c_0_58])]),c_0_55]) ).
cnf(c_0_114,negated_conjecture,
( ~ below_refl(esk20_0,esk21_0,esk22_0)
| ~ in(unordered_pair(singleton(esk21_0),unordered_pair(esk21_0,esk22_0)),the_InternalRel(poset_of_lattice(esk20_0))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_68]),c_0_73]),c_0_68]),c_0_62])]),c_0_104]) ).
cnf(c_0_115,plain,
( below_refl(X1,X2,X3)
| empty(the_carrier(X1))
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),relation_of_lattice(X1))
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_116,plain,
( the_InternalRel(rel_str_of(X1,X2)) = X2
| ~ strict_rel_str(rel_str_of(X1,X2))
| ~ rel_str(rel_str_of(X1,X2)) ),
inference(er,[status(thm)],[c_0_107]) ).
cnf(c_0_117,plain,
( rel_str_of(the_carrier(X1),relation_of_lattice(X1)) = poset_of_lattice(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_108]) ).
fof(c_0_118,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ empty(X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
cnf(c_0_119,plain,
( related_reflexive(X1,X2,X2)
| empty_carrier(X1)
| ~ reflexive_relstr(X1)
| ~ element(X2,the_carrier(X1))
| ~ rel_str(X1) ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_120,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_121,plain,
( empty_carrier(X1)
| in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))
| ~ latt_str(X1)
| ~ lattice(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ below_refl(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_122,negated_conjecture,
( below_refl(esk20_0,esk21_0,esk22_0)
| empty_carrier(poset_of_lattice(esk20_0))
| in(unordered_pair(singleton(esk21_0),unordered_pair(esk21_0,esk22_0)),the_InternalRel(poset_of_lattice(esk20_0)))
| ~ element(esk22_0,the_carrier(poset_of_lattice(esk20_0)))
| ~ element(esk21_0,the_carrier(poset_of_lattice(esk20_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_89]),c_0_79])]) ).
cnf(c_0_123,negated_conjecture,
( ~ in(unordered_pair(singleton(esk21_0),unordered_pair(esk21_0,esk22_0)),the_InternalRel(poset_of_lattice(esk20_0)))
| ~ in(unordered_pair(singleton(esk21_0),unordered_pair(esk21_0,esk22_0)),relation_of_lattice(esk20_0)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_62]),c_0_73]),c_0_57]),c_0_58])]),c_0_93]),c_0_55]) ).
cnf(c_0_124,plain,
( relation_of_lattice(X1) = the_InternalRel(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_48]),c_0_49]) ).
cnf(c_0_125,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_126,plain,
( empty_carrier(X1)
| in(unordered_pair(singleton(X2),unordered_pair(X2,X2)),the_InternalRel(X1))
| ~ reflexive_relstr(X1)
| ~ element(X2,the_carrier(X1))
| ~ rel_str(X1) ),
inference(spm,[status(thm)],[c_0_112,c_0_119]) ).
cnf(c_0_127,plain,
( element(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))
| empty_carrier(X1)
| ~ below_refl(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_128,negated_conjecture,
( below_refl(esk20_0,esk21_0,esk22_0)
| in(unordered_pair(singleton(esk21_0),unordered_pair(esk21_0,esk22_0)),the_InternalRel(poset_of_lattice(esk20_0))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_68]),c_0_62]),c_0_68]),c_0_73])]),c_0_104]) ).
cnf(c_0_129,negated_conjecture,
~ in(unordered_pair(singleton(esk21_0),unordered_pair(esk21_0,esk22_0)),the_InternalRel(poset_of_lattice(esk20_0))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_57]),c_0_58])]),c_0_55]) ).
cnf(c_0_130,plain,
( empty_carrier(X1)
| ~ reflexive_relstr(X1)
| ~ empty(the_InternalRel(X1))
| ~ element(X2,the_carrier(X1))
| ~ rel_str(X1) ),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_131,plain,
( empty(the_carrier(X1))
| element(unordered_pair(singleton(X2),unordered_pair(X2,X3)),relation_of_lattice(X1))
| empty_carrier(X1)
| ~ below_refl(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[c_0_127,c_0_106]) ).
cnf(c_0_132,negated_conjecture,
below_refl(esk20_0,esk21_0,esk22_0),
inference(sr,[status(thm)],[c_0_128,c_0_129]) ).
fof(c_0_133,plain,
! [X3,X4] :
( ~ element(X3,X4)
| empty(X4)
| in(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
cnf(c_0_134,negated_conjecture,
( ~ empty(the_InternalRel(poset_of_lattice(esk20_0)))
| ~ element(X1,the_carrier(esk20_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_68]),c_0_89]),c_0_79])]),c_0_104]) ).
cnf(c_0_135,negated_conjecture,
element(unordered_pair(singleton(esk21_0),unordered_pair(esk21_0,esk22_0)),relation_of_lattice(esk20_0)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_62]),c_0_73]),c_0_57]),c_0_58])]),c_0_93]),c_0_55]) ).
cnf(c_0_136,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_133]) ).
cnf(c_0_137,negated_conjecture,
~ empty(the_InternalRel(poset_of_lattice(esk20_0))),
inference(spm,[status(thm)],[c_0_134,c_0_62]) ).
cnf(c_0_138,negated_conjecture,
element(unordered_pair(singleton(esk21_0),unordered_pair(esk21_0,esk22_0)),the_InternalRel(poset_of_lattice(esk20_0))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_124]),c_0_57]),c_0_58])]),c_0_55]) ).
cnf(c_0_139,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_136]),c_0_137]),c_0_138])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU346+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 19 18:11:03 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.27/6.45 # Running protocol protocol_eprover_29fa5c60d0ee03ec4f64b055553dc135fbe4ee3a for 23 seconds:
% 0.27/6.45 # Preprocessing time : 0.023 s
% 0.27/6.45
% 0.27/6.45 # Proof found!
% 0.27/6.45 # SZS status Theorem
% 0.27/6.45 # SZS output start CNFRefutation
% See solution above
% 0.27/6.45 # Proof object total steps : 140
% 0.27/6.45 # Proof object clause steps : 89
% 0.27/6.45 # Proof object formula steps : 51
% 0.27/6.45 # Proof object conjectures : 36
% 0.27/6.45 # Proof object clause conjectures : 33
% 0.27/6.45 # Proof object formula conjectures : 3
% 0.27/6.45 # Proof object initial clauses used : 37
% 0.27/6.45 # Proof object initial formulas used : 25
% 0.27/6.45 # Proof object generating inferences : 42
% 0.27/6.45 # Proof object simplifying inferences : 103
% 0.27/6.45 # Training examples: 0 positive, 0 negative
% 0.27/6.45 # Parsed axioms : 93
% 0.27/6.45 # Removed by relevancy pruning/SinE : 0
% 0.27/6.45 # Initial clauses : 182
% 0.27/6.45 # Removed in clause preprocessing : 13
% 0.27/6.45 # Initial clauses in saturation : 169
% 0.27/6.45 # Processed clauses : 12867
% 0.27/6.45 # ...of these trivial : 300
% 0.27/6.45 # ...subsumed : 9053
% 0.27/6.45 # ...remaining for further processing : 3513
% 0.27/6.45 # Other redundant clauses eliminated : 7
% 0.27/6.45 # Clauses deleted for lack of memory : 53638
% 0.27/6.45 # Backward-subsumed : 256
% 0.27/6.45 # Backward-rewritten : 30
% 0.27/6.45 # Generated clauses : 140962
% 0.27/6.45 # ...of the previous two non-trivial : 129897
% 0.27/6.45 # Contextual simplify-reflections : 16383
% 0.27/6.45 # Paramodulations : 140817
% 0.27/6.45 # Factorizations : 0
% 0.27/6.45 # Equation resolutions : 141
% 0.27/6.45 # Current number of processed clauses : 3225
% 0.27/6.45 # Positive orientable unit clauses : 107
% 0.27/6.45 # Positive unorientable unit clauses: 1
% 0.27/6.45 # Negative unit clauses : 27
% 0.27/6.45 # Non-unit-clauses : 3090
% 0.27/6.45 # Current number of unprocessed clauses: 57596
% 0.27/6.45 # ...number of literals in the above : 604749
% 0.27/6.45 # Current number of archived formulas : 0
% 0.27/6.45 # Current number of archived clauses : 288
% 0.27/6.45 # Clause-clause subsumption calls (NU) : 10412402
% 0.27/6.45 # Rec. Clause-clause subsumption calls : 288826
% 0.27/6.45 # Non-unit clause-clause subsumptions : 25341
% 0.27/6.45 # Unit Clause-clause subsumption calls : 18141
% 0.27/6.45 # Rewrite failures with RHS unbound : 0
% 0.27/6.45 # BW rewrite match attempts : 81
% 0.27/6.45 # BW rewrite match successes : 18
% 0.27/6.45 # Condensation attempts : 0
% 0.27/6.45 # Condensation successes : 0
% 0.27/6.45 # Termbank termtop insertions : 8155800
% 0.27/6.45
% 0.27/6.45 # -------------------------------------------------
% 0.27/6.45 # User time : 5.656 s
% 0.27/6.45 # System time : 0.098 s
% 0.27/6.45 # Total time : 5.754 s
% 0.27/6.45 # Maximum resident set size: 133072 pages
% 0.27/23.42 eprover: CPU time limit exceeded, terminating
% 0.27/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.44 eprover: No such file or directory
% 0.27/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.45 eprover: No such file or directory
% 0.27/23.45 eprover: CPU time limit exceeded, terminating
% 0.27/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.45 eprover: No such file or directory
% 0.27/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.ineprover: No such file or directory
% 0.27/23.46
% 0.27/23.46 eprover: No such file or directory
% 0.27/23.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.peprover:
% 0.27/23.47 Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.47 eprover: No such file or directory
% 0.27/23.47 eprover: No such file or directory
% 0.27/23.47 eprover: eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.pCannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.47
% 0.27/23.47 eprover: No such file or directory
% 0.27/23.47 eprover: No such file or directory
% 0.27/23.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.48 eprover: No such file or directory
% 0.27/23.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.48 eprover: No such file or directory
% 0.27/23.49 eprover: eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.inCannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.49
% 0.27/23.49 eprover: No such file or directory
% 0.27/23.49 eprover: No such file or directory
% 0.27/23.49 eprover: eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.inCannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.49
% 0.27/23.49 eprover: No such file or directory
% 0.27/23.49 eprover: No such file or directory
% 0.27/23.50 eprover: eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.pCannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.50
% 0.27/23.50 eprover: No such file or directory
% 0.27/23.50 eprover: No such file or directory
% 0.27/23.51 eprover: eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.51 Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.51 eprover: No such file or directory
% 0.27/23.51 eprover: No such file or directory
% 0.27/23.51 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.51 eprover: No such file or directory
% 0.27/23.52 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.52 eprover: No such file or directory
%------------------------------------------------------------------------------