TSTP Solution File: SEU304+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU304+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n012.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 : 300s
% DateTime : Thu Aug 31 16:24:17 EDT 2023
% Result : Theorem 0.21s 0.60s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 51
% Syntax : Number of formulae : 85 ( 11 unt; 44 typ; 0 def)
% Number of atoms : 187 ( 21 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 222 ( 76 ~; 73 |; 44 &)
% ( 4 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 62 ( 35 >; 27 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 9 con; 0-6 aty)
% Number of variables : 73 ( 0 sgn; 53 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
preboolean: $i > $o ).
tff(decl_24,type,
cup_closed: $i > $o ).
tff(decl_25,type,
diff_closed: $i > $o ).
tff(decl_26,type,
empty_carrier: $i > $o ).
tff(decl_27,type,
meet_commutative: $i > $o ).
tff(decl_28,type,
meet_semilatt_str: $i > $o ).
tff(decl_29,type,
the_carrier: $i > $i ).
tff(decl_30,type,
element: ( $i * $i ) > $o ).
tff(decl_31,type,
meet_commut: ( $i * $i * $i ) > $i ).
tff(decl_32,type,
join_semilatt_str: $i > $o ).
tff(decl_33,type,
join: ( $i * $i * $i ) > $i ).
tff(decl_34,type,
the_L_join: $i > $i ).
tff(decl_35,type,
apply_binary_as_element: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_36,type,
meet: ( $i * $i * $i ) > $i ).
tff(decl_37,type,
the_L_meet: $i > $i ).
tff(decl_38,type,
below: ( $i * $i * $i ) > $o ).
tff(decl_39,type,
latt_str: $i > $o ).
tff(decl_40,type,
meet_absorbing: $i > $o ).
tff(decl_41,type,
empty: $i > $o ).
tff(decl_42,type,
function: $i > $o ).
tff(decl_43,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_44,type,
quasi_total: ( $i * $i * $i ) > $o ).
tff(decl_45,type,
relation_of2: ( $i * $i * $i ) > $o ).
tff(decl_46,type,
one_sorted_str: $i > $o ).
tff(decl_47,type,
relation_of2_as_subset: ( $i * $i * $i ) > $o ).
tff(decl_48,type,
powerset: $i > $i ).
tff(decl_49,type,
apply_binary: ( $i * $i * $i ) > $i ).
tff(decl_50,type,
subset: ( $i * $i ) > $o ).
tff(decl_51,type,
empty_set: $i ).
tff(decl_52,type,
esk1_1: $i > $i ).
tff(decl_53,type,
esk2_1: $i > $i ).
tff(decl_54,type,
esk3_0: $i ).
tff(decl_55,type,
esk4_0: $i ).
tff(decl_56,type,
esk5_0: $i ).
tff(decl_57,type,
esk6_0: $i ).
tff(decl_58,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_59,type,
esk8_1: $i > $i ).
tff(decl_60,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_61,type,
esk10_0: $i ).
tff(decl_62,type,
esk11_1: $i > $i ).
tff(decl_63,type,
esk12_0: $i ).
tff(decl_64,type,
esk13_0: $i ).
tff(decl_65,type,
esk14_0: $i ).
fof(t23_lattices,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_absorbing(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> below(X1,meet_commut(X1,X2,X3),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_lattices) ).
fof(d3_lattices,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& join_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( below(X1,X2,X3)
<=> join(X1,X2,X3) = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_lattices) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( latt_str(X1)
=> ( meet_semilatt_str(X1)
& join_semilatt_str(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(redefinition_k4_lattices,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> meet_commut(X1,X2,X3) = meet(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_lattices) ).
fof(commutativity_k4_lattices,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> meet_commut(X1,X2,X3) = meet_commut(X1,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k4_lattices) ).
fof(d8_lattices,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> ( meet_absorbing(X1)
<=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> join(X1,meet(X1,X2,X3),X3) = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_lattices) ).
fof(dt_k2_lattices,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> element(meet(X1,X2,X3),the_carrier(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_lattices) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_absorbing(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> below(X1,meet_commut(X1,X2,X3),X2) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t23_lattices])]) ).
fof(c_0_8,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& join_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( below(X1,X2,X3)
<=> join(X1,X2,X3) = X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[d3_lattices]) ).
fof(c_0_9,plain,
! [X45] :
( ( meet_semilatt_str(X45)
| ~ latt_str(X45) )
& ( join_semilatt_str(X45)
| ~ latt_str(X45) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
fof(c_0_10,negated_conjecture,
( ~ empty_carrier(esk12_0)
& meet_commutative(esk12_0)
& meet_absorbing(esk12_0)
& latt_str(esk12_0)
& element(esk13_0,the_carrier(esk12_0))
& element(esk14_0,the_carrier(esk12_0))
& ~ below(esk12_0,meet_commut(esk12_0,esk13_0,esk14_0),esk13_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_11,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> meet_commut(X1,X2,X3) = meet(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[redefinition_k4_lattices]) ).
fof(c_0_12,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> meet_commut(X1,X2,X3) = meet_commut(X1,X3,X2) ),
inference(fof_simplification,[status(thm)],[commutativity_k4_lattices]) ).
fof(c_0_13,plain,
! [X20,X21,X22] :
( ( ~ below(X20,X21,X22)
| join(X20,X21,X22) = X22
| ~ element(X22,the_carrier(X20))
| ~ element(X21,the_carrier(X20))
| empty_carrier(X20)
| ~ join_semilatt_str(X20) )
& ( join(X20,X21,X22) != X22
| below(X20,X21,X22)
| ~ element(X22,the_carrier(X20))
| ~ element(X21,the_carrier(X20))
| empty_carrier(X20)
| ~ join_semilatt_str(X20) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
cnf(c_0_14,plain,
( join_semilatt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
latt_str(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,plain,
! [X74,X75,X76] :
( empty_carrier(X74)
| ~ meet_commutative(X74)
| ~ meet_semilatt_str(X74)
| ~ element(X75,the_carrier(X74))
| ~ element(X76,the_carrier(X74))
| meet_commut(X74,X75,X76) = meet(X74,X75,X76) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).
fof(c_0_17,plain,
! [X11,X12,X13] :
( empty_carrier(X11)
| ~ meet_commutative(X11)
| ~ meet_semilatt_str(X11)
| ~ element(X12,the_carrier(X11))
| ~ element(X13,the_carrier(X11))
| meet_commut(X11,X12,X13) = meet_commut(X11,X13,X12) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])]) ).
cnf(c_0_18,negated_conjecture,
~ below(esk12_0,meet_commut(esk12_0,esk13_0,esk14_0),esk13_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,plain,
( below(X1,X2,X3)
| empty_carrier(X1)
| join(X1,X2,X3) != X3
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
element(esk13_0,the_carrier(esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_21,negated_conjecture,
~ empty_carrier(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_22,negated_conjecture,
join_semilatt_str(esk12_0),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_23,plain,
( empty_carrier(X1)
| meet_commut(X1,X2,X3) = meet(X1,X2,X3)
| ~ meet_commutative(X1)
| ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
( empty_carrier(X1)
| meet_commut(X1,X2,X3) = meet_commut(X1,X3,X2)
| ~ meet_commutative(X1)
| ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
( meet_semilatt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_26,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> ( meet_absorbing(X1)
<=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> join(X1,meet(X1,X2,X3),X3) = X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[d8_lattices]) ).
cnf(c_0_27,negated_conjecture,
( join(esk12_0,meet_commut(esk12_0,esk13_0,esk14_0),esk13_0) != esk13_0
| ~ element(meet_commut(esk12_0,esk13_0,esk14_0),the_carrier(esk12_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[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_28,plain,
( meet_commut(X1,X2,X3) = meet(X1,X3,X2)
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ meet_semilatt_str(X1)
| ~ meet_commutative(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,negated_conjecture,
element(esk14_0,the_carrier(esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_30,negated_conjecture,
meet_semilatt_str(esk12_0),
inference(spm,[status(thm)],[c_0_25,c_0_15]) ).
cnf(c_0_31,negated_conjecture,
meet_commutative(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_32,plain,
! [X23,X24,X25] :
( ( ~ meet_absorbing(X23)
| ~ element(X24,the_carrier(X23))
| ~ element(X25,the_carrier(X23))
| join(X23,meet(X23,X24,X25),X25) = X25
| empty_carrier(X23)
| ~ latt_str(X23) )
& ( element(esk1_1(X23),the_carrier(X23))
| meet_absorbing(X23)
| empty_carrier(X23)
| ~ latt_str(X23) )
& ( element(esk2_1(X23),the_carrier(X23))
| meet_absorbing(X23)
| empty_carrier(X23)
| ~ latt_str(X23) )
& ( join(X23,meet(X23,esk1_1(X23),esk2_1(X23)),esk2_1(X23)) != esk2_1(X23)
| meet_absorbing(X23)
| empty_carrier(X23)
| ~ latt_str(X23) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])])])]) ).
fof(c_0_33,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> element(meet(X1,X2,X3),the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k2_lattices]) ).
cnf(c_0_34,negated_conjecture,
( join(esk12_0,meet(esk12_0,esk14_0,esk13_0),esk13_0) != esk13_0
| ~ element(meet(esk12_0,esk14_0,esk13_0),the_carrier(esk12_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)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_20]),c_0_29]),c_0_30]),c_0_31])]),c_0_21]) ).
cnf(c_0_35,plain,
( join(X1,meet(X1,X2,X3),X3) = X3
| empty_carrier(X1)
| ~ meet_absorbing(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_36,negated_conjecture,
meet_absorbing(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_37,plain,
! [X37,X38,X39] :
( empty_carrier(X37)
| ~ meet_semilatt_str(X37)
| ~ element(X38,the_carrier(X37))
| ~ element(X39,the_carrier(X37))
| element(meet(X37,X38,X39),the_carrier(X37)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])]) ).
cnf(c_0_38,negated_conjecture,
~ element(meet(esk12_0,esk14_0,esk13_0),the_carrier(esk12_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)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_15]),c_0_20]),c_0_29])]),c_0_21]) ).
cnf(c_0_39,plain,
( empty_carrier(X1)
| element(meet(X1,X2,X3),the_carrier(X1))
| ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_40,negated_conjecture,
$false,
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_38,c_0_39]),c_0_20]),c_0_29]),c_0_30])]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU304+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.15/0.35 % Computer : n012.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Wed Aug 23 17:52:42 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.21/0.57 start to proof: theBenchmark
% 0.21/0.60 % Version : CSE_E---1.5
% 0.21/0.60 % Problem : theBenchmark.p
% 0.21/0.60 % Proof found
% 0.21/0.60 % SZS status Theorem for theBenchmark.p
% 0.21/0.61 % SZS output start Proof
% See solution above
% 0.21/0.61 % Total time : 0.021000 s
% 0.21/0.61 % SZS output end Proof
% 0.21/0.61 % Total time : 0.025000 s
%------------------------------------------------------------------------------