TSTP Solution File: SEU344+1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU344+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 : n031.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 16:24:37 EDT 2023
% Result : Theorem 0.20s 0.66s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 60
% Syntax : Number of formulae : 92 ( 13 unt; 52 typ; 0 def)
% Number of atoms : 112 ( 19 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 114 ( 42 ~; 39 |; 15 &)
% ( 4 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 71 ( 39 >; 32 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-3 aty)
% Number of functors : 36 ( 36 usr; 13 con; 0-6 aty)
% Number of variables : 55 ( 4 sgn; 36 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
latt_str: $i > $o ).
tff(decl_23,type,
strict_latt_str: $i > $o ).
tff(decl_24,type,
the_carrier: $i > $i ).
tff(decl_25,type,
the_L_join: $i > $i ).
tff(decl_26,type,
the_L_meet: $i > $i ).
tff(decl_27,type,
latt_str_of: ( $i * $i * $i ) > $i ).
tff(decl_28,type,
in: ( $i * $i ) > $o ).
tff(decl_29,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_30,type,
powerset: $i > $i ).
tff(decl_31,type,
element: ( $i * $i ) > $o ).
tff(decl_32,type,
relation: $i > $o ).
tff(decl_33,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_34,type,
set_union2: ( $i * $i ) > $i ).
tff(decl_35,type,
set_intersection2: ( $i * $i ) > $i ).
tff(decl_36,type,
function: $i > $o ).
tff(decl_37,type,
apply_binary: ( $i * $i * $i ) > $i ).
tff(decl_38,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_39,type,
apply: ( $i * $i ) > $i ).
tff(decl_40,type,
empty_carrier: $i > $o ).
tff(decl_41,type,
join_semilatt_str: $i > $o ).
tff(decl_42,type,
join: ( $i * $i * $i ) > $i ).
tff(decl_43,type,
apply_binary_as_element: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_44,type,
meet_semilatt_str: $i > $o ).
tff(decl_45,type,
meet: ( $i * $i * $i ) > $i ).
tff(decl_46,type,
below: ( $i * $i * $i ) > $o ).
tff(decl_47,type,
singleton: $i > $i ).
tff(decl_48,type,
quasi_total: ( $i * $i * $i ) > $o ).
tff(decl_49,type,
relation_of2: ( $i * $i * $i ) > $o ).
tff(decl_50,type,
boole_lattice: $i > $i ).
tff(decl_51,type,
empty: $i > $o ).
tff(decl_52,type,
one_sorted_str: $i > $o ).
tff(decl_53,type,
relation_of2_as_subset: ( $i * $i * $i ) > $o ).
tff(decl_54,type,
empty_set: $i ).
tff(decl_55,type,
subset: ( $i * $i ) > $o ).
tff(decl_56,type,
esk1_0: $i ).
tff(decl_57,type,
esk2_0: $i ).
tff(decl_58,type,
esk3_0: $i ).
tff(decl_59,type,
esk4_0: $i ).
tff(decl_60,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_61,type,
esk6_1: $i > $i ).
tff(decl_62,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_63,type,
esk8_1: $i > $i ).
tff(decl_64,type,
esk9_0: $i ).
tff(decl_65,type,
esk10_1: $i > $i ).
tff(decl_66,type,
esk11_0: $i ).
tff(decl_67,type,
esk12_0: $i ).
tff(decl_68,type,
esk13_0: $i ).
tff(decl_69,type,
esk14_1: $i > $i ).
tff(decl_70,type,
esk15_0: $i ).
tff(decl_71,type,
esk16_0: $i ).
tff(decl_72,type,
esk17_0: $i ).
tff(decl_73,type,
esk18_0: $i ).
fof(t2_lattice3,conjecture,
! [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/benchmark/theBenchmark.p',t2_lattice3) ).
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(fc1_lattice3,axiom,
! [X1] :
( ~ empty_carrier(boole_lattice(X1))
& strict_latt_str(boole_lattice(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_lattice3) ).
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(dt_k1_lattice3,axiom,
! [X1] :
( strict_latt_str(boole_lattice(X1))
& latt_str(boole_lattice(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattice3) ).
fof(t1_lattice3,axiom,
! [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/sandbox/benchmark/theBenchmark.p',t1_lattice3) ).
fof(t12_xboole_1,axiom,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(t7_xboole_1,axiom,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(c_0_8,negated_conjecture,
~ ! [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) ) ) ),
inference(assume_negation,[status(cth)],[t2_lattice3]) ).
fof(c_0_9,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_10,plain,
! [X1] :
( ~ empty_carrier(boole_lattice(X1))
& strict_latt_str(boole_lattice(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_lattice3]) ).
fof(c_0_11,plain,
! [X51] :
( ( meet_semilatt_str(X51)
| ~ latt_str(X51) )
& ( join_semilatt_str(X51)
| ~ latt_str(X51) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
fof(c_0_12,plain,
! [X36] :
( strict_latt_str(boole_lattice(X36))
& latt_str(boole_lattice(X36)) ),
inference(variable_rename,[status(thm)],[dt_k1_lattice3]) ).
fof(c_0_13,plain,
! [X116,X117,X118] :
( ( join(boole_lattice(X116),X117,X118) = set_union2(X117,X118)
| ~ element(X118,the_carrier(boole_lattice(X116)))
| ~ element(X117,the_carrier(boole_lattice(X116))) )
& ( meet(boole_lattice(X116),X117,X118) = set_intersection2(X117,X118)
| ~ element(X118,the_carrier(boole_lattice(X116)))
| ~ element(X117,the_carrier(boole_lattice(X116))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_lattice3])])])]) ).
fof(c_0_14,negated_conjecture,
( element(esk17_0,the_carrier(boole_lattice(esk16_0)))
& element(esk18_0,the_carrier(boole_lattice(esk16_0)))
& ( ~ below(boole_lattice(esk16_0),esk17_0,esk18_0)
| ~ subset(esk17_0,esk18_0) )
& ( below(boole_lattice(esk16_0),esk17_0,esk18_0)
| subset(esk17_0,esk18_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_15,plain,
! [X28,X29,X30] :
( ( ~ below(X28,X29,X30)
| join(X28,X29,X30) = X30
| ~ element(X30,the_carrier(X28))
| ~ element(X29,the_carrier(X28))
| empty_carrier(X28)
| ~ join_semilatt_str(X28) )
& ( join(X28,X29,X30) != X30
| below(X28,X29,X30)
| ~ element(X30,the_carrier(X28))
| ~ element(X29,the_carrier(X28))
| empty_carrier(X28)
| ~ join_semilatt_str(X28) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
fof(c_0_16,plain,
! [X69] :
( ~ empty_carrier(boole_lattice(X69))
& strict_latt_str(boole_lattice(X69)) ),
inference(variable_rename,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( join_semilatt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
latt_str(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
( join(boole_lattice(X1),X2,X3) = set_union2(X2,X3)
| ~ element(X3,the_carrier(boole_lattice(X1)))
| ~ element(X2,the_carrier(boole_lattice(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
element(esk18_0,the_carrier(boole_lattice(esk16_0))),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,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_15]) ).
cnf(c_0_22,plain,
~ empty_carrier(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
join_semilatt_str(boole_lattice(X1)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,negated_conjecture,
( join(boole_lattice(esk16_0),X1,esk18_0) = set_union2(X1,esk18_0)
| ~ element(X1,the_carrier(boole_lattice(esk16_0))) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
element(esk17_0,the_carrier(boole_lattice(esk16_0))),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_26,plain,
! [X113,X114] :
( ~ subset(X113,X114)
| set_union2(X113,X114) = X114 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])]) ).
fof(c_0_27,plain,
! [X138,X139] : subset(X138,set_union2(X138,X139)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
cnf(c_0_28,negated_conjecture,
( join(boole_lattice(esk16_0),X1,esk18_0) = esk18_0
| ~ below(boole_lattice(esk16_0),X1,esk18_0)
| ~ element(X1,the_carrier(boole_lattice(esk16_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_20]),c_0_22]),c_0_23])]) ).
cnf(c_0_29,negated_conjecture,
( below(boole_lattice(esk16_0),esk17_0,esk18_0)
| subset(esk17_0,esk18_0) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_30,negated_conjecture,
join(boole_lattice(esk16_0),esk17_0,esk18_0) = set_union2(esk17_0,esk18_0),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,plain,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,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_15]) ).
cnf(c_0_33,plain,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,negated_conjecture,
set_union2(esk17_0,esk18_0) = esk18_0,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_25])]),c_0_31]) ).
cnf(c_0_35,negated_conjecture,
( below(boole_lattice(esk16_0),esk17_0,esk18_0)
| set_union2(esk17_0,esk18_0) != esk18_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_32,c_0_30]),c_0_23]),c_0_20]),c_0_25])]),c_0_22]) ).
cnf(c_0_36,negated_conjecture,
( ~ below(boole_lattice(esk16_0),esk17_0,esk18_0)
| ~ subset(esk17_0,esk18_0) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_37,negated_conjecture,
subset(esk17_0,esk18_0),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,negated_conjecture,
below(boole_lattice(esk16_0),esk17_0,esk18_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_34])]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]),c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU344+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n031.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 01:11:50 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 0.20/0.66 % Version : CSE_E---1.5
% 0.20/0.66 % Problem : theBenchmark.p
% 0.20/0.66 % Proof found
% 0.20/0.66 % SZS status Theorem for theBenchmark.p
% 0.20/0.66 % SZS output start Proof
% See solution above
% 0.20/0.67 % Total time : 0.071000 s
% 0.20/0.67 % SZS output end Proof
% 0.20/0.67 % Total time : 0.073000 s
%------------------------------------------------------------------------------