TSTP Solution File: SEU056+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU056+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 : n014.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 16:22:17 EDT 2023
% Result : Theorem 0.20s 0.63s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 31
% Syntax : Number of formulae : 50 ( 10 unt; 27 typ; 0 def)
% Number of atoms : 53 ( 15 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 45 ( 15 ~; 12 |; 10 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 15 >; 6 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 12 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn; 18 !; 0 ?; 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,
disjoint: ( $i * $i ) > $o ).
tff(decl_29,type,
empty_set: $i ).
tff(decl_30,type,
element: ( $i * $i ) > $o ).
tff(decl_31,type,
relation_empty_yielding: $i > $o ).
tff(decl_32,type,
powerset: $i > $i ).
tff(decl_33,type,
subset: ( $i * $i ) > $o ).
tff(decl_34,type,
relation_image: ( $i * $i ) > $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_0: $i ).
tff(decl_42,type,
esk8_1: $i > $i ).
tff(decl_43,type,
esk9_0: $i ).
tff(decl_44,type,
esk10_0: $i ).
tff(decl_45,type,
esk11_0: $i ).
tff(decl_46,type,
esk12_0: $i ).
tff(decl_47,type,
esk13_0: $i ).
tff(decl_48,type,
esk14_0: $i ).
fof(t125_funct_1,conjecture,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( ( disjoint(X1,X2)
& one_to_one(X3) )
=> disjoint(relation_image(X3,X1),relation_image(X3,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t125_funct_1) ).
fof(t121_funct_1,axiom,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( one_to_one(X3)
=> relation_image(X3,set_intersection2(X1,X2)) = set_intersection2(relation_image(X3,X1),relation_image(X3,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_funct_1) ).
fof(d7_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(t149_relat_1,axiom,
! [X1] :
( relation(X1)
=> relation_image(X1,empty_set) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_relat_1) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( ( disjoint(X1,X2)
& one_to_one(X3) )
=> disjoint(relation_image(X3,X1),relation_image(X3,X2)) ) ),
inference(assume_negation,[status(cth)],[t125_funct_1]) ).
fof(c_0_5,plain,
! [X34,X35,X36] :
( ~ relation(X36)
| ~ function(X36)
| ~ one_to_one(X36)
| relation_image(X36,set_intersection2(X34,X35)) = set_intersection2(relation_image(X36,X34),relation_image(X36,X35)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t121_funct_1])]) ).
fof(c_0_6,negated_conjecture,
( relation(esk14_0)
& function(esk14_0)
& disjoint(esk12_0,esk13_0)
& one_to_one(esk14_0)
& ~ disjoint(relation_image(esk14_0,esk12_0),relation_image(esk14_0,esk13_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_7,plain,
! [X11,X12] :
( ( ~ disjoint(X11,X12)
| set_intersection2(X11,X12) = empty_set )
& ( set_intersection2(X11,X12) != empty_set
| disjoint(X11,X12) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])]) ).
fof(c_0_8,plain,
! [X40] :
( ~ relation(X40)
| relation_image(X40,empty_set) = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t149_relat_1])]) ).
cnf(c_0_9,plain,
( relation_image(X1,set_intersection2(X2,X3)) = set_intersection2(relation_image(X1,X2),relation_image(X1,X3))
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
one_to_one(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
relation(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,negated_conjecture,
function(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,negated_conjecture,
disjoint(esk12_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,plain,
( relation_image(X1,empty_set) = empty_set
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,negated_conjecture,
relation_image(esk14_0,set_intersection2(X1,X2)) = set_intersection2(relation_image(esk14_0,X1),relation_image(esk14_0,X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_12])]) ).
cnf(c_0_17,negated_conjecture,
set_intersection2(esk12_0,esk13_0) = empty_set,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
relation_image(esk14_0,empty_set) = empty_set,
inference(spm,[status(thm)],[c_0_15,c_0_11]) ).
cnf(c_0_19,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_20,negated_conjecture,
set_intersection2(relation_image(esk14_0,esk12_0),relation_image(esk14_0,esk13_0)) = empty_set,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_21,negated_conjecture,
~ disjoint(relation_image(esk14_0,esk12_0),relation_image(esk14_0,esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU056+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 : n014.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 : Wed Aug 23 18:25:19 EDT 2023
% 0.20/0.35 % CPUTime :
% 0.20/0.61 start to proof: theBenchmark
% 0.20/0.63 % Version : CSE_E---1.5
% 0.20/0.63 % Problem : theBenchmark.p
% 0.20/0.63 % Proof found
% 0.20/0.63 % SZS status Theorem for theBenchmark.p
% 0.20/0.63 % SZS output start Proof
% See solution above
% 0.20/0.63 % Total time : 0.009000 s
% 0.20/0.63 % SZS output end Proof
% 0.20/0.63 % Total time : 0.011000 s
%------------------------------------------------------------------------------