TSTP Solution File: SEU305+1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU305+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n009.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 0.20s 0.61s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 39
% Syntax : Number of formulae : 63 ( 11 unt; 35 typ; 0 def)
% Number of atoms : 125 ( 21 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 146 ( 49 ~; 45 |; 32 &)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 53 ( 28 >; 25 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 7 con; 0-6 aty)
% Number of variables : 48 ( 0 sgn; 33 !; 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,
join_commutative: $i > $o ).
tff(decl_28,type,
join_semilatt_str: $i > $o ).
tff(decl_29,type,
the_carrier: $i > $i ).
tff(decl_30,type,
element: ( $i * $i ) > $o ).
tff(decl_31,type,
join_commut: ( $i * $i * $i ) > $i ).
tff(decl_32,type,
join: ( $i * $i * $i ) > $i ).
tff(decl_33,type,
the_L_join: $i > $i ).
tff(decl_34,type,
apply_binary_as_element: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_35,type,
below: ( $i * $i * $i ) > $o ).
tff(decl_36,type,
empty: $i > $o ).
tff(decl_37,type,
function: $i > $o ).
tff(decl_38,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_39,type,
quasi_total: ( $i * $i * $i ) > $o ).
tff(decl_40,type,
relation_of2: ( $i * $i * $i ) > $o ).
tff(decl_41,type,
one_sorted_str: $i > $o ).
tff(decl_42,type,
relation_of2_as_subset: ( $i * $i * $i ) > $o ).
tff(decl_43,type,
powerset: $i > $i ).
tff(decl_44,type,
apply_binary: ( $i * $i * $i ) > $i ).
tff(decl_45,type,
subset: ( $i * $i ) > $o ).
tff(decl_46,type,
empty_set: $i ).
tff(decl_47,type,
esk1_0: $i ).
tff(decl_48,type,
esk2_0: $i ).
tff(decl_49,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_50,type,
esk4_1: $i > $i ).
tff(decl_51,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_52,type,
esk6_0: $i ).
tff(decl_53,type,
esk7_1: $i > $i ).
tff(decl_54,type,
esk8_0: $i ).
tff(decl_55,type,
esk9_0: $i ).
tff(decl_56,type,
esk10_0: $i ).
fof(redefinition_k3_lattices,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> join_commut(X1,X2,X3) = join(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_lattices) ).
fof(commutativity_k3_lattices,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> join_commut(X1,X2,X3) = join_commut(X1,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_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/sandbox2/benchmark/theBenchmark.p',d3_lattices) ).
fof(t26_lattices,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( below(X1,X2,X3)
& below(X1,X3,X2) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_lattices) ).
fof(c_0_4,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> join_commut(X1,X2,X3) = join(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[redefinition_k3_lattices]) ).
fof(c_0_5,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> join_commut(X1,X2,X3) = join_commut(X1,X3,X2) ),
inference(fof_simplification,[status(thm)],[commutativity_k3_lattices]) ).
fof(c_0_6,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_7,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( below(X1,X2,X3)
& below(X1,X3,X2) )
=> X2 = X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t26_lattices])]) ).
fof(c_0_8,plain,
! [X58,X59,X60] :
( empty_carrier(X58)
| ~ join_commutative(X58)
| ~ join_semilatt_str(X58)
| ~ element(X59,the_carrier(X58))
| ~ element(X60,the_carrier(X58))
| join_commut(X58,X59,X60) = join(X58,X59,X60) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])]) ).
fof(c_0_9,plain,
! [X11,X12,X13] :
( empty_carrier(X11)
| ~ join_commutative(X11)
| ~ join_semilatt_str(X11)
| ~ element(X12,the_carrier(X11))
| ~ element(X13,the_carrier(X11))
| join_commut(X11,X12,X13) = join_commut(X11,X13,X12) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])]) ).
fof(c_0_10,plain,
! [X17,X18,X19] :
( ( ~ below(X17,X18,X19)
| join(X17,X18,X19) = X19
| ~ element(X19,the_carrier(X17))
| ~ element(X18,the_carrier(X17))
| empty_carrier(X17)
| ~ join_semilatt_str(X17) )
& ( join(X17,X18,X19) != X19
| below(X17,X18,X19)
| ~ element(X19,the_carrier(X17))
| ~ element(X18,the_carrier(X17))
| empty_carrier(X17)
| ~ join_semilatt_str(X17) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_11,negated_conjecture,
( ~ empty_carrier(esk8_0)
& join_commutative(esk8_0)
& join_semilatt_str(esk8_0)
& element(esk9_0,the_carrier(esk8_0))
& element(esk10_0,the_carrier(esk8_0))
& below(esk8_0,esk9_0,esk10_0)
& below(esk8_0,esk10_0,esk9_0)
& esk9_0 != esk10_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_12,plain,
( empty_carrier(X1)
| join_commut(X1,X2,X3) = join(X1,X2,X3)
| ~ join_commutative(X1)
| ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( empty_carrier(X1)
| join_commut(X1,X2,X3) = join_commut(X1,X3,X2)
| ~ join_commutative(X1)
| ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( join(X1,X2,X3) = X3
| empty_carrier(X1)
| ~ below(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
below(esk8_0,esk10_0,esk9_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
element(esk9_0,the_carrier(esk8_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
element(esk10_0,the_carrier(esk8_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
join_semilatt_str(esk8_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,negated_conjecture,
~ empty_carrier(esk8_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,plain,
( join_commut(X1,X2,X3) = join(X1,X3,X2)
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ join_semilatt_str(X1)
| ~ join_commutative(X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_21,negated_conjecture,
below(esk8_0,esk9_0,esk10_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_22,negated_conjecture,
join(esk8_0,esk10_0,esk9_0) = esk9_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_14,c_0_15]),c_0_16]),c_0_17]),c_0_18])]),c_0_19]) ).
cnf(c_0_23,plain,
( join(X1,X2,X3) = join(X1,X3,X2)
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ join_semilatt_str(X1)
| ~ join_commutative(X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_20]) ).
cnf(c_0_24,negated_conjecture,
join(esk8_0,esk9_0,esk10_0) = esk10_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_14,c_0_21]),c_0_17]),c_0_16]),c_0_18])]),c_0_19]) ).
cnf(c_0_25,negated_conjecture,
join_commutative(esk8_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_26,negated_conjecture,
esk9_0 != esk10_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_27,negated_conjecture,
$false,
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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_16]),c_0_17]),c_0_18]),c_0_25])]),c_0_26]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU305+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 23 12:09:52 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 0.20/0.61 % Version : CSE_E---1.5
% 0.20/0.61 % Problem : theBenchmark.p
% 0.20/0.61 % Proof found
% 0.20/0.61 % SZS status Theorem for theBenchmark.p
% 0.20/0.61 % SZS output start Proof
% See solution above
% 0.20/0.61 % Total time : 0.017000 s
% 0.20/0.61 % SZS output end Proof
% 0.20/0.61 % Total time : 0.021000 s
%------------------------------------------------------------------------------