%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SEU343+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 09:19:10 EDT 2022
% Result : Theorem 0.23s 1.41s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 76 ( 13 unt; 0 def)
% Number of atoms : 278 ( 67 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 360 ( 158 ~; 144 |; 37 &)
% ( 2 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 3 con; 0-6 aty)
% Number of variables : 130 ( 9 sgn 73 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t1_lattice3,conjecture,
! [X1,X2] :
( element(X2,the_carrier(boole_lattice(X1)))
=> ! [X3] :
( element(X3,the_carrier(boole_lattice(X1)))
=> ( join(boole_lattice(X1),X2,X3) = set_union2(X2,X3)
& meet(boole_lattice(X1),X2,X3) = set_intersection2(X2,X3) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t1_lattice3) ).
fof(d2_lattices,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> meet(X1,X2,X3) = apply_binary_as_element(the_carrier(X1),the_carrier(X1),the_carrier(X1),the_L_meet(X1),X2,X3) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d2_lattices) ).
fof(fc1_lattice3,axiom,
! [X1] :
( ~ empty_carrier(boole_lattice(X1))
& strict_latt_str(boole_lattice(X1)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fc1_lattice3) ).
fof(d1_lattices,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& join_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> join(X1,X2,X3) = apply_binary_as_element(the_carrier(X1),the_carrier(X1),the_carrier(X1),the_L_join(X1),X2,X3) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d1_lattices) ).
fof(d1_lattice3,axiom,
! [X1,X2] :
( ( strict_latt_str(X2)
& latt_str(X2) )
=> ( X2 = boole_lattice(X1)
<=> ( the_carrier(X2) = powerset(X1)
& ! [X3] :
( element(X3,powerset(X1))
=> ! [X4] :
( element(X4,powerset(X1))
=> ( apply_binary(the_L_join(X2),X3,X4) = subset_union2(X1,X3,X4)
& apply_binary(the_L_meet(X2),X3,X4) = subset_intersection2(X1,X3,X4) ) ) ) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d1_lattice3) ).
fof(dt_k1_lattice3,axiom,
! [X1] :
( strict_latt_str(boole_lattice(X1))
& latt_str(boole_lattice(X1)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_k1_lattice3) ).
fof(redefinition_k2_binop_1,axiom,
! [X1,X2,X3,X4,X5,X6] :
( ( ~ empty(X1)
& ~ empty(X2)
& function(X4)
& quasi_total(X4,cartesian_product2(X1,X2),X3)
& relation_of2(X4,cartesian_product2(X1,X2),X3)
& element(X5,X1)
& element(X6,X2) )
=> apply_binary_as_element(X1,X2,X3,X4,X5,X6) = apply_binary(X4,X5,X6) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',redefinition_k2_binop_1) ).
fof(fc1_subset_1,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fc1_subset_1) ).
fof(dt_u1_lattices,axiom,
! [X1] :
( meet_semilatt_str(X1)
=> ( function(the_L_meet(X1))
& quasi_total(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
& relation_of2_as_subset(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_u1_lattices) ).
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',redefinition_m2_relset_1) ).
fof(dt_u2_lattices,axiom,
! [X1] :
( join_semilatt_str(X1)
=> ( function(the_L_join(X1))
& quasi_total(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
& relation_of2_as_subset(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_u2_lattices) ).
fof(redefinition_k5_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_intersection2(X1,X2,X3) = set_intersection2(X2,X3) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',redefinition_k5_subset_1) ).
fof(redefinition_k4_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_union2(X1,X2,X3) = set_union2(X2,X3) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',redefinition_k4_subset_1) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( latt_str(X1)
=> ( meet_semilatt_str(X1)
& join_semilatt_str(X1) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_l3_lattices) ).
fof(c_0_14,negated_conjecture,
~ ! [X1,X2] :
( element(X2,the_carrier(boole_lattice(X1)))
=> ! [X3] :
( element(X3,the_carrier(boole_lattice(X1)))
=> ( join(boole_lattice(X1),X2,X3) = set_union2(X2,X3)
& meet(boole_lattice(X1),X2,X3) = set_intersection2(X2,X3) ) ) ),
inference(assume_negation,[status(cth)],[t1_lattice3]) ).
fof(c_0_15,negated_conjecture,
( element(esk2_0,the_carrier(boole_lattice(esk1_0)))
& element(esk3_0,the_carrier(boole_lattice(esk1_0)))
& ( join(boole_lattice(esk1_0),esk2_0,esk3_0) != set_union2(esk2_0,esk3_0)
| meet(boole_lattice(esk1_0),esk2_0,esk3_0) != set_intersection2(esk2_0,esk3_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_14])])])])]) ).
fof(c_0_16,plain,
! [X4,X5,X6] :
( empty_carrier(X4)
| ~ meet_semilatt_str(X4)
| ~ element(X5,the_carrier(X4))
| ~ element(X6,the_carrier(X4))
| meet(X4,X5,X6) = apply_binary_as_element(the_carrier(X4),the_carrier(X4),the_carrier(X4),the_L_meet(X4),X5,X6) ),
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)],[d2_lattices])])])])])]) ).
fof(c_0_17,plain,
! [X2,X2] :
( ~ empty_carrier(boole_lattice(X2))
& strict_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_lattice3])])])]) ).
cnf(c_0_18,negated_conjecture,
( meet(boole_lattice(esk1_0),esk2_0,esk3_0) != set_intersection2(esk2_0,esk3_0)
| join(boole_lattice(esk1_0),esk2_0,esk3_0) != set_union2(esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
( meet(X1,X2,X3) = apply_binary_as_element(the_carrier(X1),the_carrier(X1),the_carrier(X1),the_L_meet(X1),X2,X3)
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,negated_conjecture,
element(esk3_0,the_carrier(boole_lattice(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
element(esk2_0,the_carrier(boole_lattice(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
~ empty_carrier(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_23,plain,
! [X4,X5,X6] :
( empty_carrier(X4)
| ~ join_semilatt_str(X4)
| ~ element(X5,the_carrier(X4))
| ~ element(X6,the_carrier(X4))
| join(X4,X5,X6) = apply_binary_as_element(the_carrier(X4),the_carrier(X4),the_carrier(X4),the_L_join(X4),X5,X6) ),
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)],[d1_lattices])])])])])]) ).
fof(c_0_24,plain,
! [X5,X6,X7,X8] :
( ( the_carrier(X6) = powerset(X5)
| X6 != boole_lattice(X5)
| ~ strict_latt_str(X6)
| ~ latt_str(X6) )
& ( apply_binary(the_L_join(X6),X7,X8) = subset_union2(X5,X7,X8)
| ~ element(X8,powerset(X5))
| ~ element(X7,powerset(X5))
| X6 != boole_lattice(X5)
| ~ strict_latt_str(X6)
| ~ latt_str(X6) )
& ( apply_binary(the_L_meet(X6),X7,X8) = subset_intersection2(X5,X7,X8)
| ~ element(X8,powerset(X5))
| ~ element(X7,powerset(X5))
| X6 != boole_lattice(X5)
| ~ strict_latt_str(X6)
| ~ latt_str(X6) )
& ( element(esk4_2(X5,X6),powerset(X5))
| the_carrier(X6) != powerset(X5)
| X6 = boole_lattice(X5)
| ~ strict_latt_str(X6)
| ~ latt_str(X6) )
& ( element(esk5_2(X5,X6),powerset(X5))
| the_carrier(X6) != powerset(X5)
| X6 = boole_lattice(X5)
| ~ strict_latt_str(X6)
| ~ latt_str(X6) )
& ( apply_binary(the_L_join(X6),esk4_2(X5,X6),esk5_2(X5,X6)) != subset_union2(X5,esk4_2(X5,X6),esk5_2(X5,X6))
| apply_binary(the_L_meet(X6),esk4_2(X5,X6),esk5_2(X5,X6)) != subset_intersection2(X5,esk4_2(X5,X6),esk5_2(X5,X6))
| the_carrier(X6) != powerset(X5)
| X6 = boole_lattice(X5)
| ~ strict_latt_str(X6)
| ~ latt_str(X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_lattice3])])])])])])]) ).
fof(c_0_25,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_26,negated_conjecture,
( apply_binary_as_element(the_carrier(boole_lattice(esk1_0)),the_carrier(boole_lattice(esk1_0)),the_carrier(boole_lattice(esk1_0)),the_L_meet(boole_lattice(esk1_0)),esk2_0,esk3_0) != set_intersection2(esk2_0,esk3_0)
| join(boole_lattice(esk1_0),esk2_0,esk3_0) != set_union2(esk2_0,esk3_0)
| ~ meet_semilatt_str(boole_lattice(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])]),c_0_22]) ).
cnf(c_0_27,plain,
( join(X1,X2,X3) = apply_binary_as_element(the_carrier(X1),the_carrier(X1),the_carrier(X1),the_L_join(X1),X2,X3)
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
( the_carrier(X1) = powerset(X2)
| ~ latt_str(X1)
| ~ strict_latt_str(X1)
| X1 != boole_lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
strict_latt_str(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,plain,
latt_str(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,negated_conjecture,
( apply_binary_as_element(the_carrier(boole_lattice(esk1_0)),the_carrier(boole_lattice(esk1_0)),the_carrier(boole_lattice(esk1_0)),the_L_meet(boole_lattice(esk1_0)),esk2_0,esk3_0) != set_intersection2(esk2_0,esk3_0)
| apply_binary_as_element(the_carrier(boole_lattice(esk1_0)),the_carrier(boole_lattice(esk1_0)),the_carrier(boole_lattice(esk1_0)),the_L_join(boole_lattice(esk1_0)),esk2_0,esk3_0) != set_union2(esk2_0,esk3_0)
| ~ meet_semilatt_str(boole_lattice(esk1_0))
| ~ join_semilatt_str(boole_lattice(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_20]),c_0_21])]),c_0_22]) ).
cnf(c_0_32,plain,
the_carrier(boole_lattice(X1)) = powerset(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_28]),c_0_29]),c_0_30])]) ).
fof(c_0_33,plain,
! [X7,X8,X9,X10,X11,X12] :
( empty(X7)
| empty(X8)
| ~ function(X10)
| ~ quasi_total(X10,cartesian_product2(X7,X8),X9)
| ~ relation_of2(X10,cartesian_product2(X7,X8),X9)
| ~ element(X11,X7)
| ~ element(X12,X8)
| apply_binary_as_element(X7,X8,X9,X10,X11,X12) = apply_binary(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_k2_binop_1])])]) ).
fof(c_0_34,plain,
! [X2] : ~ empty(powerset(X2)),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fc1_subset_1])]) ).
fof(c_0_35,plain,
! [X2] :
( ( function(the_L_meet(X2))
| ~ meet_semilatt_str(X2) )
& ( quasi_total(the_L_meet(X2),cartesian_product2(the_carrier(X2),the_carrier(X2)),the_carrier(X2))
| ~ meet_semilatt_str(X2) )
& ( relation_of2_as_subset(the_L_meet(X2),cartesian_product2(the_carrier(X2),the_carrier(X2)),the_carrier(X2))
| ~ meet_semilatt_str(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_lattices])])]) ).
fof(c_0_36,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_37,plain,
! [X2] :
( ( function(the_L_join(X2))
| ~ join_semilatt_str(X2) )
& ( quasi_total(the_L_join(X2),cartesian_product2(the_carrier(X2),the_carrier(X2)),the_carrier(X2))
| ~ join_semilatt_str(X2) )
& ( relation_of2_as_subset(the_L_join(X2),cartesian_product2(the_carrier(X2),the_carrier(X2)),the_carrier(X2))
| ~ join_semilatt_str(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u2_lattices])])]) ).
cnf(c_0_38,negated_conjecture,
( apply_binary_as_element(powerset(esk1_0),powerset(esk1_0),powerset(esk1_0),the_L_meet(boole_lattice(esk1_0)),esk2_0,esk3_0) != set_intersection2(esk2_0,esk3_0)
| apply_binary_as_element(powerset(esk1_0),powerset(esk1_0),powerset(esk1_0),the_L_join(boole_lattice(esk1_0)),esk2_0,esk3_0) != set_union2(esk2_0,esk3_0)
| ~ meet_semilatt_str(boole_lattice(esk1_0))
| ~ join_semilatt_str(boole_lattice(esk1_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]) ).
cnf(c_0_39,plain,
( apply_binary_as_element(X1,X2,X3,X4,X5,X6) = apply_binary(X4,X5,X6)
| empty(X2)
| empty(X1)
| ~ element(X6,X2)
| ~ element(X5,X1)
| ~ relation_of2(X4,cartesian_product2(X1,X2),X3)
| ~ quasi_total(X4,cartesian_product2(X1,X2),X3)
| ~ function(X4) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,negated_conjecture,
element(esk3_0,powerset(esk1_0)),
inference(rw,[status(thm)],[c_0_20,c_0_32]) ).
cnf(c_0_41,negated_conjecture,
element(esk2_0,powerset(esk1_0)),
inference(rw,[status(thm)],[c_0_21,c_0_32]) ).
cnf(c_0_42,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_43,plain,
( function(the_L_meet(X1))
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_44,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_45,plain,
( relation_of2_as_subset(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_46,negated_conjecture,
( apply_binary_as_element(powerset(esk1_0),powerset(esk1_0),powerset(esk1_0),the_L_join(boole_lattice(esk1_0)),esk2_0,esk3_0) != set_union2(esk2_0,esk3_0)
| apply_binary(the_L_meet(boole_lattice(esk1_0)),esk2_0,esk3_0) != set_intersection2(esk2_0,esk3_0)
| ~ relation_of2(the_L_meet(boole_lattice(esk1_0)),cartesian_product2(powerset(esk1_0),powerset(esk1_0)),powerset(esk1_0))
| ~ quasi_total(the_L_meet(boole_lattice(esk1_0)),cartesian_product2(powerset(esk1_0),powerset(esk1_0)),powerset(esk1_0))
| ~ meet_semilatt_str(boole_lattice(esk1_0))
| ~ join_semilatt_str(boole_lattice(esk1_0)) ),
inference(csr,[status(thm)],[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]),c_0_43]) ).
cnf(c_0_47,plain,
( function(the_L_join(X1))
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_48,plain,
( apply_binary(the_L_meet(X1),X3,X4) = subset_intersection2(X2,X3,X4)
| ~ latt_str(X1)
| ~ strict_latt_str(X1)
| X1 != boole_lattice(X2)
| ~ element(X3,powerset(X2))
| ~ element(X4,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_49,plain,
( quasi_total(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_50,plain,
( quasi_total(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_51,plain,
( relation_of2(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| ~ join_semilatt_str(X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_52,negated_conjecture,
( apply_binary(the_L_join(boole_lattice(esk1_0)),esk2_0,esk3_0) != set_union2(esk2_0,esk3_0)
| apply_binary(the_L_meet(boole_lattice(esk1_0)),esk2_0,esk3_0) != set_intersection2(esk2_0,esk3_0)
| ~ relation_of2(the_L_meet(boole_lattice(esk1_0)),cartesian_product2(powerset(esk1_0),powerset(esk1_0)),powerset(esk1_0))
| ~ relation_of2(the_L_join(boole_lattice(esk1_0)),cartesian_product2(powerset(esk1_0),powerset(esk1_0)),powerset(esk1_0))
| ~ quasi_total(the_L_meet(boole_lattice(esk1_0)),cartesian_product2(powerset(esk1_0),powerset(esk1_0)),powerset(esk1_0))
| ~ quasi_total(the_L_join(boole_lattice(esk1_0)),cartesian_product2(powerset(esk1_0),powerset(esk1_0)),powerset(esk1_0))
| ~ meet_semilatt_str(boole_lattice(esk1_0))
| ~ join_semilatt_str(boole_lattice(esk1_0)) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_39]),c_0_40]),c_0_41])]),c_0_42]),c_0_47]) ).
cnf(c_0_53,plain,
( apply_binary(the_L_meet(boole_lattice(X1)),X2,X3) = subset_intersection2(X1,X2,X3)
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_48]),c_0_29]),c_0_30])]) ).
cnf(c_0_54,plain,
( quasi_total(the_L_join(boole_lattice(X1)),cartesian_product2(powerset(X1),powerset(X1)),powerset(X1))
| ~ join_semilatt_str(boole_lattice(X1)) ),
inference(spm,[status(thm)],[c_0_49,c_0_32]) ).
cnf(c_0_55,plain,
( quasi_total(the_L_meet(boole_lattice(X1)),cartesian_product2(powerset(X1),powerset(X1)),powerset(X1))
| ~ meet_semilatt_str(boole_lattice(X1)) ),
inference(spm,[status(thm)],[c_0_50,c_0_32]) ).
cnf(c_0_56,plain,
( relation_of2(the_L_join(boole_lattice(X1)),cartesian_product2(powerset(X1),powerset(X1)),powerset(X1))
| ~ join_semilatt_str(boole_lattice(X1)) ),
inference(spm,[status(thm)],[c_0_51,c_0_32]) ).
cnf(c_0_57,plain,
( apply_binary(the_L_join(X1),X3,X4) = subset_union2(X2,X3,X4)
| ~ latt_str(X1)
| ~ strict_latt_str(X1)
| X1 != boole_lattice(X2)
| ~ element(X3,powerset(X2))
| ~ element(X4,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_58,plain,
( relation_of2_as_subset(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_59,negated_conjecture,
( apply_binary(the_L_join(boole_lattice(esk1_0)),esk2_0,esk3_0) != set_union2(esk2_0,esk3_0)
| set_intersection2(esk2_0,esk3_0) != subset_intersection2(esk1_0,esk2_0,esk3_0)
| ~ relation_of2(the_L_meet(boole_lattice(esk1_0)),cartesian_product2(powerset(esk1_0),powerset(esk1_0)),powerset(esk1_0))
| ~ meet_semilatt_str(boole_lattice(esk1_0))
| ~ join_semilatt_str(boole_lattice(esk1_0)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[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_54]),c_0_55]),c_0_56]) ).
cnf(c_0_60,plain,
( apply_binary(the_L_join(boole_lattice(X1)),X2,X3) = subset_union2(X1,X2,X3)
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_57]),c_0_29]),c_0_30])]) ).
fof(c_0_61,plain,
! [X4,X5,X6] :
( ~ element(X5,powerset(X4))
| ~ element(X6,powerset(X4))
| subset_intersection2(X4,X5,X6) = set_intersection2(X5,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_subset_1])]) ).
cnf(c_0_62,plain,
( relation_of2(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_58]) ).
cnf(c_0_63,negated_conjecture,
( subset_union2(esk1_0,esk2_0,esk3_0) != set_union2(esk2_0,esk3_0)
| set_intersection2(esk2_0,esk3_0) != subset_intersection2(esk1_0,esk2_0,esk3_0)
| ~ relation_of2(the_L_meet(boole_lattice(esk1_0)),cartesian_product2(powerset(esk1_0),powerset(esk1_0)),powerset(esk1_0))
| ~ meet_semilatt_str(boole_lattice(esk1_0))
| ~ join_semilatt_str(boole_lattice(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_40]),c_0_41])]) ).
cnf(c_0_64,plain,
( subset_intersection2(X1,X2,X3) = set_intersection2(X2,X3)
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_65,plain,
( relation_of2(the_L_meet(boole_lattice(X1)),cartesian_product2(powerset(X1),powerset(X1)),powerset(X1))
| ~ meet_semilatt_str(boole_lattice(X1)) ),
inference(spm,[status(thm)],[c_0_62,c_0_32]) ).
cnf(c_0_66,negated_conjecture,
( subset_intersection2(X1,esk2_0,esk3_0) != subset_intersection2(esk1_0,esk2_0,esk3_0)
| subset_union2(esk1_0,esk2_0,esk3_0) != set_union2(esk2_0,esk3_0)
| ~ meet_semilatt_str(boole_lattice(esk1_0))
| ~ join_semilatt_str(boole_lattice(esk1_0))
| ~ element(esk3_0,powerset(X1))
| ~ element(esk2_0,powerset(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]) ).
fof(c_0_67,plain,
! [X4,X5,X6] :
( ~ element(X5,powerset(X4))
| ~ element(X6,powerset(X4))
| subset_union2(X4,X5,X6) = set_union2(X5,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_subset_1])]) ).
cnf(c_0_68,negated_conjecture,
( subset_union2(esk1_0,esk2_0,esk3_0) != set_union2(esk2_0,esk3_0)
| ~ meet_semilatt_str(boole_lattice(esk1_0))
| ~ join_semilatt_str(boole_lattice(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_66]),c_0_40]),c_0_41])]) ).
cnf(c_0_69,plain,
( subset_union2(X1,X2,X3) = set_union2(X2,X3)
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
fof(c_0_70,plain,
! [X2] :
( ( meet_semilatt_str(X2)
| ~ latt_str(X2) )
& ( join_semilatt_str(X2)
| ~ latt_str(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
cnf(c_0_71,negated_conjecture,
( ~ meet_semilatt_str(boole_lattice(esk1_0))
| ~ join_semilatt_str(boole_lattice(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_40]),c_0_41])]) ).
cnf(c_0_72,plain,
( meet_semilatt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_73,negated_conjecture,
~ join_semilatt_str(boole_lattice(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_30])]) ).
cnf(c_0_74,plain,
( join_semilatt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_75,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU343+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : run_ET %s %d
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 20 04:10:14 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.23/1.41 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.23/1.41 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.23/1.41 # Preprocessing time : 0.019 s
% 0.23/1.41
% 0.23/1.41 # Proof found!
% 0.23/1.41 # SZS status Theorem
% 0.23/1.41 # SZS output start CNFRefutation
% See solution above
% 0.23/1.41 # Proof object total steps : 76
% 0.23/1.41 # Proof object clause steps : 47
% 0.23/1.41 # Proof object formula steps : 29
% 0.23/1.41 # Proof object conjectures : 20
% 0.23/1.41 # Proof object clause conjectures : 17
% 0.23/1.41 # Proof object formula conjectures : 3
% 0.23/1.41 # Proof object initial clauses used : 24
% 0.23/1.41 # Proof object initial formulas used : 14
% 0.23/1.41 # Proof object generating inferences : 20
% 0.23/1.41 # Proof object simplifying inferences : 55
% 0.23/1.41 # Training examples: 0 positive, 0 negative
% 0.23/1.41 # Parsed axioms : 86
% 0.23/1.41 # Removed by relevancy pruning/SinE : 28
% 0.23/1.41 # Initial clauses : 84
% 0.23/1.41 # Removed in clause preprocessing : 0
% 0.23/1.41 # Initial clauses in saturation : 84
% 0.23/1.41 # Processed clauses : 215
% 0.23/1.41 # ...of these trivial : 5
% 0.23/1.41 # ...subsumed : 63
% 0.23/1.41 # ...remaining for further processing : 147
% 0.23/1.41 # Other redundant clauses eliminated : 0
% 0.23/1.41 # Clauses deleted for lack of memory : 0
% 0.23/1.41 # Backward-subsumed : 12
% 0.23/1.41 # Backward-rewritten : 10
% 0.23/1.41 # Generated clauses : 266
% 0.23/1.41 # ...of the previous two non-trivial : 225
% 0.23/1.41 # Contextual simplify-reflections : 15
% 0.23/1.41 # Paramodulations : 259
% 0.23/1.41 # Factorizations : 0
% 0.23/1.41 # Equation resolutions : 7
% 0.23/1.41 # Current number of processed clauses : 125
% 0.23/1.41 # Positive orientable unit clauses : 31
% 0.23/1.41 # Positive unorientable unit clauses: 2
% 0.23/1.41 # Negative unit clauses : 8
% 0.23/1.41 # Non-unit-clauses : 84
% 0.23/1.41 # Current number of unprocessed clauses: 56
% 0.23/1.41 # ...number of literals in the above : 314
% 0.23/1.41 # Current number of archived formulas : 0
% 0.23/1.41 # Current number of archived clauses : 22
% 0.23/1.41 # Clause-clause subsumption calls (NU) : 3551
% 0.23/1.41 # Rec. Clause-clause subsumption calls : 1476
% 0.23/1.41 # Non-unit clause-clause subsumptions : 87
% 0.23/1.41 # Unit Clause-clause subsumption calls : 179
% 0.23/1.41 # Rewrite failures with RHS unbound : 0
% 0.23/1.41 # BW rewrite match attempts : 16
% 0.23/1.41 # BW rewrite match successes : 15
% 0.23/1.41 # Condensation attempts : 0
% 0.23/1.41 # Condensation successes : 0
% 0.23/1.41 # Termbank termtop insertions : 11033
% 0.23/1.41
% 0.23/1.41 # -------------------------------------------------
% 0.23/1.41 # User time : 0.034 s
% 0.23/1.41 # System time : 0.001 s
% 0.23/1.41 # Total time : 0.035 s
% 0.23/1.41 # Maximum resident set size: 3748 pages
% 0.23/23.41 eprover: CPU time limit exceeded, terminating
% 0.23/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.23/23.43 eprover: No such file or directory
% 0.23/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.23/23.44 eprover: No such file or directory
% 0.23/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.23/23.44 eprover: No such file or directory
% 0.23/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.23/23.45 eprover: No such file or directory
% 0.23/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.23/23.45 eprover: No such file or directory
% 0.23/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.23/23.46 eprover: No such file or directory
% 0.23/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.23/23.47 eprover: No such file or directory
% 0.23/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.23/23.47 eprover: No such file or directory
% 0.23/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.23/23.48 eprover: No such file or directory
% 0.23/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.23/23.48 eprover: No such file or directory
% 0.23/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.23/23.49 eprover: No such file or directory
%------------------------------------------------------------------------------