TSTP Solution File: SET994+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET994+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n018.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 14:36:33 EDT 2023
% Result : Theorem 0.21s 0.60s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 34
% Syntax : Number of formulae : 69 ( 20 unt; 25 typ; 0 def)
% Number of atoms : 109 ( 41 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 95 ( 30 ~; 32 |; 21 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 15 >; 4 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 10 con; 0-2 aty)
% Number of variables : 49 ( 4 sgn; 24 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
empty: $i > $o ).
tff(decl_24,type,
function: $i > $o ).
tff(decl_25,type,
relation: $i > $o ).
tff(decl_26,type,
element: ( $i * $i ) > $o ).
tff(decl_27,type,
empty_set: $i ).
tff(decl_28,type,
relation_empty_yielding: $i > $o ).
tff(decl_29,type,
powerset: $i > $i ).
tff(decl_30,type,
relation_dom: $i > $i ).
tff(decl_31,type,
subset: ( $i * $i ) > $o ).
tff(decl_32,type,
apply: ( $i * $i ) > $i ).
tff(decl_33,type,
n0: $i ).
tff(decl_34,type,
n1: $i ).
tff(decl_35,type,
esk1_1: $i > $i ).
tff(decl_36,type,
esk2_0: $i ).
tff(decl_37,type,
esk3_0: $i ).
tff(decl_38,type,
esk4_1: $i > $i ).
tff(decl_39,type,
esk5_0: $i ).
tff(decl_40,type,
esk6_0: $i ).
tff(decl_41,type,
esk7_1: $i > $i ).
tff(decl_42,type,
esk8_0: $i ).
tff(decl_43,type,
esk9_0: $i ).
tff(decl_44,type,
esk10_1: $i > $i ).
tff(decl_45,type,
esk11_1: $i > $i ).
tff(decl_46,type,
esk12_0: $i ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(t16_funct_1,conjecture,
! [X1] :
( ! [X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( ( relation_dom(X2) = X1
& relation_dom(X3) = X1 )
=> X2 = X3 ) ) )
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_funct_1) ).
fof(s3_funct_1__e4_14__funct_1,axiom,
! [X1] :
? [X2] :
( relation(X2)
& function(X2)
& relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = n0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_funct_1__e4_14__funct_1) ).
fof(spc0_boole,axiom,
empty(n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',spc0_boole) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(s3_funct_1__e7_14__funct_1,axiom,
! [X1] :
? [X2] :
( relation(X2)
& function(X2)
& relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = n1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_funct_1__e7_14__funct_1) ).
fof(spc1_boole,axiom,
~ empty(n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',spc1_boole) ).
fof(fc12_relat_1,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(c_0_9,plain,
! [X45] :
( ~ empty(X45)
| X45 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] :
( ! [X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( ( relation_dom(X2) = X1
& relation_dom(X3) = X1 )
=> X2 = X3 ) ) )
=> X1 = empty_set ),
inference(assume_negation,[status(cth)],[t16_funct_1]) ).
fof(c_0_11,plain,
! [X24,X26] :
( relation(esk10_1(X24))
& function(esk10_1(X24))
& relation_dom(esk10_1(X24)) = X24
& ( ~ in(X26,X24)
| apply(esk10_1(X24),X26) = n0 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[s3_funct_1__e4_14__funct_1])])])]) ).
cnf(c_0_12,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
empty(n0),
inference(split_conjunct,[status(thm)],[spc0_boole]) ).
fof(c_0_14,plain,
! [X35,X36] :
( ~ element(X35,X36)
| empty(X36)
| in(X35,X36) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(c_0_15,plain,
! [X8] : element(esk1_1(X8),X8),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(c_0_16,negated_conjecture,
! [X31,X32] :
( ( ~ relation(X31)
| ~ function(X31)
| ~ relation(X32)
| ~ function(X32)
| relation_dom(X31) != esk12_0
| relation_dom(X32) != esk12_0
| X31 = X32 )
& esk12_0 != empty_set ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).
fof(c_0_17,plain,
! [X27,X29] :
( relation(esk11_1(X27))
& function(esk11_1(X27))
& relation_dom(esk11_1(X27)) = X27
& ( ~ in(X29,X27)
| apply(esk11_1(X27),X29) = n1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[s3_funct_1__e7_14__funct_1])])])]) ).
cnf(c_0_18,plain,
( apply(esk10_1(X2),X1) = n0
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
n0 = empty_set,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_20,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
element(esk1_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,negated_conjecture,
( X1 = X2
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2)
| relation_dom(X1) != esk12_0
| relation_dom(X2) != esk12_0 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
relation_dom(esk11_1(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
relation(esk11_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
function(esk11_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,plain,
( apply(esk10_1(X1),X2) = empty_set
| ~ in(X2,X1) ),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_27,plain,
( empty(X1)
| in(esk1_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,negated_conjecture,
( X1 = esk11_1(esk12_0)
| relation_dom(X1) != esk12_0
| ~ relation(X1)
| ~ function(X1) ),
inference(er,[status(thm)],[inference(cn,[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_25])])]) ).
cnf(c_0_29,plain,
relation_dom(esk10_1(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_30,plain,
relation(esk10_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_31,plain,
function(esk10_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_32,plain,
( apply(esk11_1(X2),X1) = n1
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_33,plain,
( apply(esk10_1(X1),esk1_1(X1)) = empty_set
| empty(X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,negated_conjecture,
esk10_1(esk12_0) = esk11_1(esk12_0),
inference(er,[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_31])])]) ).
cnf(c_0_35,plain,
( apply(esk11_1(X1),esk1_1(X1)) = n1
| empty(X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_27]) ).
cnf(c_0_36,negated_conjecture,
( apply(esk11_1(esk12_0),esk1_1(esk12_0)) = empty_set
| empty(esk12_0) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
fof(c_0_37,plain,
~ empty(n1),
inference(fof_simplification,[status(thm)],[spc1_boole]) ).
cnf(c_0_38,negated_conjecture,
( n1 = empty_set
| empty(esk12_0) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,negated_conjecture,
esk12_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_40,plain,
~ empty(n1),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_41,negated_conjecture,
n1 = empty_set,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_38]),c_0_39]) ).
cnf(c_0_42,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]) ).
cnf(c_0_43,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41]),c_0_42])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET994+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 09:51:59 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.58 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
% 0.21/0.60 % SZS output start Proof
% See solution above
% 0.21/0.60 % Total time : 0.010000 s
% 0.21/0.60 % SZS output end Proof
% 0.21/0.60 % Total time : 0.013000 s
%------------------------------------------------------------------------------