TSTP Solution File: SEU369+1 by ET---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SEU369+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n021.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 09:19:26 EDT 2022
% Result : Theorem 0.24s 1.42s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 83 ( 14 unt; 0 def)
% Number of atoms : 398 ( 32 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 503 ( 188 ~; 207 |; 80 &)
% ( 6 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 32 ( 30 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-2 aty)
% Number of variables : 156 ( 26 sgn 80 !; 0 ?)
% 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_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(t7_lattice3,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('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t7_lattice3) ).
fof(redefinition_r3_lattices,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('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',redefinition_r3_lattices) ).
fof(cc1_lattices,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('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',cc1_lattices) ).
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(t2_lattice3,axiom,
! [X1,X2] :
( element(X2,the_carrier(boole_lattice(X1)))
=> ! [X3] :
( element(X3,the_carrier(boole_lattice(X1)))
=> ( below(boole_lattice(X1),X2,X3)
<=> subset(X2,X3) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t2_lattice3) ).
fof(fc1_knaster,axiom,
! [X1] :
( ~ empty_carrier(boole_lattice(X1))
& strict_latt_str(boole_lattice(X1))
& join_commutative(boole_lattice(X1))
& join_associative(boole_lattice(X1))
& meet_commutative(boole_lattice(X1))
& meet_associative(boole_lattice(X1))
& meet_absorbing(boole_lattice(X1))
& join_absorbing(boole_lattice(X1))
& lattice(boole_lattice(X1))
& distributive_lattstr(boole_lattice(X1))
& modular_lattstr(boole_lattice(X1))
& lower_bounded_semilattstr(boole_lattice(X1))
& upper_bounded_semilattstr(boole_lattice(X1))
& bounded_lattstr(boole_lattice(X1))
& complemented_lattstr(boole_lattice(X1))
& boolean_lattstr(boole_lattice(X1))
& complete_latt_str(boole_lattice(X1)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fc1_knaster) ).
fof(dt_k1_lattice3,axiom,
! [X1] :
( strict_latt_str(boole_lattice(X1))
& latt_str(boole_lattice(X1)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_k1_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(t2_yellow_1,conjecture,
! [X1,X2] :
( element(X2,the_carrier(boole_POSet(X1)))
=> ! [X3] :
( element(X3,the_carrier(boole_POSet(X1)))
=> ( related_reflexive(boole_POSet(X1),X2,X3)
<=> subset(X2,X3) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t2_yellow_1) ).
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(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(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(d2_yellow_1,axiom,
! [X1] : boole_POSet(X1) = poset_of_lattice(boole_lattice(X1)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d2_yellow_1) ).
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(c_0_16,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_17,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])]) ).
fof(c_0_18,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)],[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)],[t7_lattice3])])])])])])]) ).
fof(c_0_19,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)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_r3_lattices])])])]) ).
fof(c_0_20,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)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[cc1_lattices])])])]) ).
fof(c_0_21,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_22,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
( relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,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)],[c_0_18]) ).
cnf(c_0_25,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)],[c_0_19]) ).
cnf(c_0_26,plain,
( empty_carrier(X1)
| meet_commutative(X1)
| ~ latt_str(X1)
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
( empty_carrier(X1)
| meet_absorbing(X1)
| ~ latt_str(X1)
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,plain,
( empty_carrier(X1)
| join_absorbing(X1)
| ~ latt_str(X1)
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_29,plain,
! [X4,X5,X6] :
( ( ~ below(boole_lattice(X4),X5,X6)
| subset(X5,X6)
| ~ element(X6,the_carrier(boole_lattice(X4)))
| ~ element(X5,the_carrier(boole_lattice(X4))) )
& ( ~ subset(X5,X6)
| below(boole_lattice(X4),X5,X6)
| ~ element(X6,the_carrier(boole_lattice(X4)))
| ~ element(X5,the_carrier(boole_lattice(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)],[t2_lattice3])])])])])]) ).
fof(c_0_30,plain,
! [X2,X2,X2,X2,X2,X2,X2,X2,X2,X2,X2,X2,X2,X2,X2,X2,X2] :
( ~ empty_carrier(boole_lattice(X2))
& strict_latt_str(boole_lattice(X2))
& join_commutative(boole_lattice(X2))
& join_associative(boole_lattice(X2))
& meet_commutative(boole_lattice(X2))
& meet_associative(boole_lattice(X2))
& meet_absorbing(boole_lattice(X2))
& join_absorbing(boole_lattice(X2))
& lattice(boole_lattice(X2))
& distributive_lattstr(boole_lattice(X2))
& modular_lattstr(boole_lattice(X2))
& lower_bounded_semilattstr(boole_lattice(X2))
& upper_bounded_semilattstr(boole_lattice(X2))
& bounded_lattstr(boole_lattice(X2))
& complemented_lattstr(boole_lattice(X2))
& boolean_lattstr(boole_lattice(X2))
& complete_latt_str(boole_lattice(X2)) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fc1_knaster])])])]) ).
fof(c_0_31,plain,
! [X2,X2] :
( strict_latt_str(boole_lattice(X2))
& latt_str(boole_lattice(X2)) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[dt_k1_lattice3])])]) ).
cnf(c_0_32,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_21]) ).
cnf(c_0_33,plain,
( relation_of2(the_InternalRel(X1),the_carrier(X1),the_carrier(X1))
| ~ rel_str(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_34,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])]) ).
cnf(c_0_35,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)],[c_0_19]) ).
cnf(c_0_36,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)],[c_0_18]) ).
fof(c_0_37,negated_conjecture,
~ ! [X1,X2] :
( element(X2,the_carrier(boole_POSet(X1)))
=> ! [X3] :
( element(X3,the_carrier(boole_POSet(X1)))
=> ( related_reflexive(boole_POSet(X1),X2,X3)
<=> subset(X2,X3) ) ) ),
inference(assume_negation,[status(cth)],[t2_yellow_1]) ).
cnf(c_0_38,plain,
( related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3))
| empty_carrier(X1)
| ~ below(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27]),c_0_28]) ).
cnf(c_0_39,plain,
( below(boole_lattice(X2),X1,X3)
| ~ element(X1,the_carrier(boole_lattice(X2)))
| ~ element(X3,the_carrier(boole_lattice(X2)))
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_40,plain,
lattice(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_41,plain,
latt_str(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_42,plain,
~ empty_carrier(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_43,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_44,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)],[c_0_32,c_0_33]) ).
cnf(c_0_45,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_34]) ).
fof(c_0_46,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])])]) ).
fof(c_0_47,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])])]) ).
cnf(c_0_48,plain,
( subset(X1,X3)
| ~ element(X1,the_carrier(boole_lattice(X2)))
| ~ element(X3,the_carrier(boole_lattice(X2)))
| ~ below(boole_lattice(X2),X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_49,plain,
( below(X1,X2,X3)
| empty_carrier(X1)
| ~ related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3))
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_26]),c_0_27]),c_0_28]) ).
fof(c_0_50,negated_conjecture,
( element(esk30_0,the_carrier(boole_POSet(esk29_0)))
& element(esk31_0,the_carrier(boole_POSet(esk29_0)))
& ( ~ related_reflexive(boole_POSet(esk29_0),esk30_0,esk31_0)
| ~ subset(esk30_0,esk31_0) )
& ( related_reflexive(boole_POSet(esk29_0),esk30_0,esk31_0)
| subset(esk30_0,esk31_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)],[c_0_37])])])])]) ).
fof(c_0_51,plain,
! [X2] : boole_POSet(X2) = poset_of_lattice(boole_lattice(X2)),
inference(variable_rename,[status(thm)],[d2_yellow_1]) ).
cnf(c_0_52,plain,
( related_reflexive(poset_of_lattice(boole_lattice(X1)),cast_to_el_of_LattPOSet(boole_lattice(X1),X2),cast_to_el_of_LattPOSet(boole_lattice(X1),X3))
| ~ subset(X2,X3)
| ~ element(X3,the_carrier(boole_lattice(X1)))
| ~ element(X2,the_carrier(boole_lattice(X1))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_41])]),c_0_42]) ).
cnf(c_0_53,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_43]) ).
cnf(c_0_54,plain,
( the_carrier(X1) = X2
| X1 != rel_str_of(X2,X3)
| ~ strict_rel_str(X1)
| ~ rel_str(X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_55,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_46]) ).
cnf(c_0_56,plain,
( k2_lattice3(X1) = relation_of_lattice(X1)
| empty_carrier(X1)
| ~ latt_str(X1)
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
fof(c_0_57,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])])])]) ).
cnf(c_0_58,plain,
( subset(X1,X2)
| ~ related_reflexive(poset_of_lattice(boole_lattice(X3)),cast_to_el_of_LattPOSet(boole_lattice(X3),X1),cast_to_el_of_LattPOSet(boole_lattice(X3),X2))
| ~ element(X2,the_carrier(boole_lattice(X3)))
| ~ element(X1,the_carrier(boole_lattice(X3))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_40]),c_0_41])]),c_0_42]) ).
cnf(c_0_59,negated_conjecture,
( ~ subset(esk30_0,esk31_0)
| ~ related_reflexive(boole_POSet(esk29_0),esk30_0,esk31_0) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_60,plain,
boole_POSet(X1) = poset_of_lattice(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_61,plain,
( related_reflexive(poset_of_lattice(boole_lattice(X1)),cast_to_el_of_LattPOSet(boole_lattice(X1),X2),X3)
| ~ subset(X2,X3)
| ~ element(X3,the_carrier(boole_lattice(X1)))
| ~ element(X2,the_carrier(boole_lattice(X1))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_40]),c_0_41])]),c_0_42]) ).
cnf(c_0_62,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)],[c_0_54]) ).
cnf(c_0_63,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_55,c_0_56]) ).
cnf(c_0_64,plain,
( empty_carrier(X1)
| rel_str(poset_of_lattice(X1))
| ~ latt_str(X1)
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_65,plain,
( empty_carrier(X1)
| strict_rel_str(poset_of_lattice(X1))
| ~ latt_str(X1)
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_66,plain,
( subset(X1,X2)
| ~ related_reflexive(poset_of_lattice(boole_lattice(X3)),cast_to_el_of_LattPOSet(boole_lattice(X3),X1),X2)
| ~ element(X2,the_carrier(boole_lattice(X3)))
| ~ element(X1,the_carrier(boole_lattice(X3))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_53]),c_0_40]),c_0_41])]),c_0_42]) ).
cnf(c_0_67,negated_conjecture,
( subset(esk30_0,esk31_0)
| related_reflexive(boole_POSet(esk29_0),esk30_0,esk31_0) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_68,negated_conjecture,
( ~ subset(esk30_0,esk31_0)
| ~ related_reflexive(poset_of_lattice(boole_lattice(esk29_0)),esk30_0,esk31_0) ),
inference(rw,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_69,plain,
( related_reflexive(poset_of_lattice(boole_lattice(X1)),X2,X3)
| ~ subset(X2,X3)
| ~ element(X3,the_carrier(boole_lattice(X1)))
| ~ element(X2,the_carrier(boole_lattice(X1))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_53]),c_0_40]),c_0_41])]),c_0_42]) ).
cnf(c_0_70,negated_conjecture,
element(esk31_0,the_carrier(boole_POSet(esk29_0))),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_71,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(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]),c_0_65]) ).
cnf(c_0_72,plain,
( subset(X1,X2)
| ~ related_reflexive(poset_of_lattice(boole_lattice(X3)),X1,X2)
| ~ element(X2,the_carrier(boole_lattice(X3)))
| ~ element(X1,the_carrier(boole_lattice(X3))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_53]),c_0_40]),c_0_41])]),c_0_42]) ).
cnf(c_0_73,negated_conjecture,
( subset(esk30_0,esk31_0)
| related_reflexive(poset_of_lattice(boole_lattice(esk29_0)),esk30_0,esk31_0) ),
inference(rw,[status(thm)],[c_0_67,c_0_60]) ).
cnf(c_0_74,negated_conjecture,
( ~ subset(esk30_0,esk31_0)
| ~ element(esk31_0,the_carrier(boole_lattice(esk29_0)))
| ~ element(esk30_0,the_carrier(boole_lattice(esk29_0))) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_75,negated_conjecture,
element(esk31_0,the_carrier(poset_of_lattice(boole_lattice(esk29_0)))),
inference(rw,[status(thm)],[c_0_70,c_0_60]) ).
cnf(c_0_76,plain,
the_carrier(poset_of_lattice(boole_lattice(X1))) = the_carrier(boole_lattice(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_71]),c_0_40]),c_0_41])]) ).
cnf(c_0_77,negated_conjecture,
element(esk30_0,the_carrier(boole_POSet(esk29_0))),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_78,negated_conjecture,
( ~ element(esk31_0,the_carrier(boole_lattice(esk29_0)))
| ~ element(esk30_0,the_carrier(boole_lattice(esk29_0))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]) ).
cnf(c_0_79,negated_conjecture,
element(esk31_0,the_carrier(boole_lattice(esk29_0))),
inference(rw,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_80,negated_conjecture,
element(esk30_0,the_carrier(poset_of_lattice(boole_lattice(esk29_0)))),
inference(rw,[status(thm)],[c_0_77,c_0_60]) ).
cnf(c_0_81,negated_conjecture,
~ element(esk30_0,the_carrier(boole_lattice(esk29_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_79])]) ).
cnf(c_0_82,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_76]),c_0_81]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU369+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.12 % Command : run_ET %s %d
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 19 19:46:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.24/1.42 # Running protocol protocol_eprover_29fa5c60d0ee03ec4f64b055553dc135fbe4ee3a for 23 seconds:
% 0.24/1.42 # Preprocessing time : 0.027 s
% 0.24/1.42
% 0.24/1.42 # Proof found!
% 0.24/1.42 # SZS status Theorem
% 0.24/1.42 # SZS output start CNFRefutation
% See solution above
% 0.24/1.42 # Proof object total steps : 83
% 0.24/1.42 # Proof object clause steps : 50
% 0.24/1.42 # Proof object formula steps : 33
% 0.24/1.42 # Proof object conjectures : 16
% 0.24/1.42 # Proof object clause conjectures : 13
% 0.24/1.42 # Proof object formula conjectures : 3
% 0.24/1.42 # Proof object initial clauses used : 26
% 0.24/1.42 # Proof object initial formulas used : 16
% 0.24/1.42 # Proof object generating inferences : 17
% 0.24/1.42 # Proof object simplifying inferences : 45
% 0.24/1.42 # Training examples: 0 positive, 0 negative
% 0.24/1.42 # Parsed axioms : 121
% 0.24/1.42 # Removed by relevancy pruning/SinE : 0
% 0.24/1.42 # Initial clauses : 402
% 0.24/1.42 # Removed in clause preprocessing : 26
% 0.24/1.42 # Initial clauses in saturation : 376
% 0.24/1.42 # Processed clauses : 1386
% 0.24/1.42 # ...of these trivial : 50
% 0.24/1.42 # ...subsumed : 183
% 0.24/1.42 # ...remaining for further processing : 1152
% 0.24/1.42 # Other redundant clauses eliminated : 5
% 0.24/1.42 # Clauses deleted for lack of memory : 0
% 0.24/1.42 # Backward-subsumed : 13
% 0.24/1.42 # Backward-rewritten : 23
% 0.24/1.42 # Generated clauses : 3904
% 0.24/1.42 # ...of the previous two non-trivial : 3686
% 0.24/1.42 # Contextual simplify-reflections : 161
% 0.24/1.42 # Paramodulations : 3877
% 0.24/1.42 # Factorizations : 0
% 0.24/1.42 # Equation resolutions : 24
% 0.24/1.42 # Current number of processed clauses : 1115
% 0.24/1.42 # Positive orientable unit clauses : 242
% 0.24/1.42 # Positive unorientable unit clauses: 1
% 0.24/1.42 # Negative unit clauses : 26
% 0.24/1.42 # Non-unit-clauses : 846
% 0.24/1.42 # Current number of unprocessed clauses: 2586
% 0.24/1.42 # ...number of literals in the above : 14925
% 0.24/1.42 # Current number of archived formulas : 0
% 0.24/1.42 # Current number of archived clauses : 38
% 0.24/1.42 # Clause-clause subsumption calls (NU) : 241645
% 0.24/1.42 # Rec. Clause-clause subsumption calls : 60770
% 0.24/1.42 # Non-unit clause-clause subsumptions : 316
% 0.24/1.42 # Unit Clause-clause subsumption calls : 5275
% 0.24/1.42 # Rewrite failures with RHS unbound : 0
% 0.24/1.42 # BW rewrite match attempts : 41
% 0.24/1.42 # BW rewrite match successes : 8
% 0.24/1.42 # Condensation attempts : 0
% 0.24/1.42 # Condensation successes : 0
% 0.24/1.42 # Termbank termtop insertions : 97186
% 0.24/1.42
% 0.24/1.42 # -------------------------------------------------
% 0.24/1.42 # User time : 0.181 s
% 0.24/1.42 # System time : 0.005 s
% 0.24/1.42 # Total time : 0.186 s
% 0.24/1.42 # Maximum resident set size: 9116 pages
% 0.24/23.41 eprover: CPU time limit exceeded, terminating
% 0.24/23.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.43 eprover: No such file or directory
% 0.24/23.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.43 eprover: No such file or directory
% 0.24/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.44 eprover: No such file or directory
% 0.24/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.44 eprover: No such file or directory
% 0.24/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.45 eprover: No such file or directory
% 0.24/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.46 eprover: No such file or directory
% 0.24/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.46 eprover: No such file or directory
% 0.24/23.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.47 eprover: No such file or directory
% 0.24/23.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.47 eprover: No such file or directory
% 0.24/23.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.48 eprover: No such file or directory
% 0.24/23.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.48 eprover: No such file or directory
%------------------------------------------------------------------------------