TSTP Solution File: SEU039+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU039+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n011.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 16:22:13 EDT 2023
% Result : Theorem 0.19s 0.63s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 42
% Syntax : Number of formulae : 70 ( 11 unt; 34 typ; 0 def)
% Number of atoms : 185 ( 43 equ)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 246 ( 97 ~; 101 |; 31 &)
% ( 5 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 36 ( 22 >; 14 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 12 con; 0-3 aty)
% Number of variables : 85 ( 2 sgn; 54 !; 1 ?; 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,
one_to_one: $i > $o ).
tff(decl_27,type,
set_intersection2: ( $i * $i ) > $i ).
tff(decl_28,type,
relation_rng: $i > $i ).
tff(decl_29,type,
relation_dom: $i > $i ).
tff(decl_30,type,
apply: ( $i * $i ) > $i ).
tff(decl_31,type,
relation_dom_restriction: ( $i * $i ) > $i ).
tff(decl_32,type,
element: ( $i * $i ) > $o ).
tff(decl_33,type,
empty_set: $i ).
tff(decl_34,type,
relation_empty_yielding: $i > $o ).
tff(decl_35,type,
powerset: $i > $i ).
tff(decl_36,type,
subset: ( $i * $i ) > $o ).
tff(decl_37,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_38,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_39,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_40,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_41,type,
esk5_1: $i > $i ).
tff(decl_42,type,
esk6_0: $i ).
tff(decl_43,type,
esk7_0: $i ).
tff(decl_44,type,
esk8_1: $i > $i ).
tff(decl_45,type,
esk9_0: $i ).
tff(decl_46,type,
esk10_0: $i ).
tff(decl_47,type,
esk11_0: $i ).
tff(decl_48,type,
esk12_1: $i > $i ).
tff(decl_49,type,
esk13_0: $i ).
tff(decl_50,type,
esk14_0: $i ).
tff(decl_51,type,
esk15_0: $i ).
tff(decl_52,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_53,type,
esk17_0: $i ).
tff(decl_54,type,
esk18_0: $i ).
tff(decl_55,type,
esk19_0: $i ).
fof(d5_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
fof(t73_funct_1,conjecture,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( ( in(X2,relation_dom(X3))
& in(X2,X1) )
=> in(apply(X3,X2),relation_rng(relation_dom_restriction(X3,X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_funct_1) ).
fof(t72_funct_1,axiom,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,X1)
=> apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_funct_1) ).
fof(fc4_funct_1,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1) )
=> ( relation(relation_dom_restriction(X1,X2))
& function(relation_dom_restriction(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_funct_1) ).
fof(dt_k7_relat_1,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_dom_restriction(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(t68_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( X2 = relation_dom_restriction(X3,X1)
<=> ( relation_dom(X2) = set_intersection2(relation_dom(X3),X1)
& ! [X4] :
( in(X4,relation_dom(X2))
=> apply(X2,X4) = apply(X3,X4) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_funct_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(c_0_8,plain,
! [X21,X22,X23,X25,X26,X27,X29] :
( ( in(esk2_3(X21,X22,X23),relation_dom(X21))
| ~ in(X23,X22)
| X22 != relation_rng(X21)
| ~ relation(X21)
| ~ function(X21) )
& ( X23 = apply(X21,esk2_3(X21,X22,X23))
| ~ in(X23,X22)
| X22 != relation_rng(X21)
| ~ relation(X21)
| ~ function(X21) )
& ( ~ in(X26,relation_dom(X21))
| X25 != apply(X21,X26)
| in(X25,X22)
| X22 != relation_rng(X21)
| ~ relation(X21)
| ~ function(X21) )
& ( ~ in(esk3_2(X21,X27),X27)
| ~ in(X29,relation_dom(X21))
| esk3_2(X21,X27) != apply(X21,X29)
| X27 = relation_rng(X21)
| ~ relation(X21)
| ~ function(X21) )
& ( in(esk4_2(X21,X27),relation_dom(X21))
| in(esk3_2(X21,X27),X27)
| X27 = relation_rng(X21)
| ~ relation(X21)
| ~ function(X21) )
& ( esk3_2(X21,X27) = apply(X21,esk4_2(X21,X27))
| in(esk3_2(X21,X27),X27)
| X27 = relation_rng(X21)
| ~ relation(X21)
| ~ function(X21) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_funct_1])])])])])]) ).
fof(c_0_9,negated_conjecture,
~ ! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( ( in(X2,relation_dom(X3))
& in(X2,X1) )
=> in(apply(X3,X2),relation_rng(relation_dom_restriction(X3,X1))) ) ),
inference(assume_negation,[status(cth)],[t73_funct_1]) ).
cnf(c_0_10,plain,
( in(X3,X4)
| ~ in(X1,relation_dom(X2))
| X3 != apply(X2,X1)
| X4 != relation_rng(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,plain,
! [X79,X80,X81] :
( ~ relation(X81)
| ~ function(X81)
| ~ in(X80,X79)
| apply(relation_dom_restriction(X81,X79),X80) = apply(X81,X80) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t72_funct_1])]) ).
fof(c_0_12,plain,
! [X40,X41] :
( ( relation(relation_dom_restriction(X40,X41))
| ~ relation(X40)
| ~ function(X40) )
& ( function(relation_dom_restriction(X40,X41))
| ~ relation(X40)
| ~ function(X40) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc4_funct_1])])]) ).
fof(c_0_13,plain,
! [X31,X32] :
( ~ relation(X31)
| relation(relation_dom_restriction(X31,X32)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_relat_1])]) ).
fof(c_0_14,negated_conjecture,
( relation(esk19_0)
& function(esk19_0)
& in(esk18_0,relation_dom(esk19_0))
& in(esk18_0,esk17_0)
& ~ in(apply(esk19_0,esk18_0),relation_rng(relation_dom_restriction(esk19_0,esk17_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
cnf(c_0_15,plain,
( in(apply(X1,X2),relation_rng(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(X1)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_10])]) ).
cnf(c_0_16,plain,
( apply(relation_dom_restriction(X1,X3),X2) = apply(X1,X2)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( function(relation_dom_restriction(X1,X2))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_19,plain,
! [X73,X74,X75,X76] :
( ( relation_dom(X74) = set_intersection2(relation_dom(X75),X73)
| X74 != relation_dom_restriction(X75,X73)
| ~ relation(X75)
| ~ function(X75)
| ~ relation(X74)
| ~ function(X74) )
& ( ~ in(X76,relation_dom(X74))
| apply(X74,X76) = apply(X75,X76)
| X74 != relation_dom_restriction(X75,X73)
| ~ relation(X75)
| ~ function(X75)
| ~ relation(X74)
| ~ function(X74) )
& ( in(esk16_3(X73,X74,X75),relation_dom(X74))
| relation_dom(X74) != set_intersection2(relation_dom(X75),X73)
| X74 = relation_dom_restriction(X75,X73)
| ~ relation(X75)
| ~ function(X75)
| ~ relation(X74)
| ~ function(X74) )
& ( apply(X74,esk16_3(X73,X74,X75)) != apply(X75,esk16_3(X73,X74,X75))
| relation_dom(X74) != set_intersection2(relation_dom(X75),X73)
| X74 = relation_dom_restriction(X75,X73)
| ~ relation(X75)
| ~ function(X75)
| ~ relation(X74)
| ~ function(X74) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t68_funct_1])])])])]) ).
cnf(c_0_20,negated_conjecture,
~ in(apply(esk19_0,esk18_0),relation_rng(relation_dom_restriction(esk19_0,esk17_0))),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
( in(apply(X1,X2),relation_rng(relation_dom_restriction(X1,X3)))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3)))
| ~ in(X2,X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18]) ).
cnf(c_0_22,negated_conjecture,
relation(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,negated_conjecture,
function(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,negated_conjecture,
in(esk18_0,esk17_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_25,plain,
( relation_dom(X1) = set_intersection2(relation_dom(X2),X3)
| X1 != relation_dom_restriction(X2,X3)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_26,plain,
! [X10,X11] : set_intersection2(X10,X11) = set_intersection2(X11,X10),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(c_0_27,plain,
! [X12,X13,X14,X15,X16,X17,X18,X19] :
( ( in(X15,X12)
| ~ in(X15,X14)
| X14 != set_intersection2(X12,X13) )
& ( in(X15,X13)
| ~ in(X15,X14)
| X14 != set_intersection2(X12,X13) )
& ( ~ in(X16,X12)
| ~ in(X16,X13)
| in(X16,X14)
| X14 != set_intersection2(X12,X13) )
& ( ~ in(esk1_3(X17,X18,X19),X19)
| ~ in(esk1_3(X17,X18,X19),X17)
| ~ in(esk1_3(X17,X18,X19),X18)
| X19 = set_intersection2(X17,X18) )
& ( in(esk1_3(X17,X18,X19),X17)
| in(esk1_3(X17,X18,X19),X19)
| X19 = set_intersection2(X17,X18) )
& ( in(esk1_3(X17,X18,X19),X18)
| in(esk1_3(X17,X18,X19),X19)
| X19 = set_intersection2(X17,X18) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_xboole_0])])])])])]) ).
cnf(c_0_28,negated_conjecture,
~ in(esk18_0,relation_dom(relation_dom_restriction(esk19_0,esk17_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23]),c_0_24])]) ).
cnf(c_0_29,plain,
( relation_dom(relation_dom_restriction(X1,X2)) = set_intersection2(relation_dom(X1),X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_25]),c_0_17]),c_0_18]) ).
cnf(c_0_30,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,negated_conjecture,
~ in(esk18_0,set_intersection2(esk17_0,relation_dom(esk19_0))),
inference(rw,[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_22]),c_0_23])]),c_0_30]) ).
cnf(c_0_33,plain,
( in(X1,set_intersection2(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_31]) ).
cnf(c_0_34,negated_conjecture,
in(esk18_0,relation_dom(esk19_0)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU039+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 01:34:07 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.58 start to proof: theBenchmark
% 0.19/0.63 % Version : CSE_E---1.5
% 0.19/0.63 % Problem : theBenchmark.p
% 0.19/0.63 % Proof found
% 0.19/0.63 % SZS status Theorem for theBenchmark.p
% 0.19/0.63 % SZS output start Proof
% See solution above
% 0.19/0.63 % Total time : 0.040000 s
% 0.19/0.63 % SZS output end Proof
% 0.19/0.63 % Total time : 0.044000 s
%------------------------------------------------------------------------------