TSTP Solution File: SEU102+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU102+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 : n004.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 16:22:26 EDT 2023
% Result : Theorem 0.19s 0.60s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 38
% Syntax : Number of formulae : 61 ( 10 unt; 34 typ; 0 def)
% Number of atoms : 80 ( 9 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 86 ( 33 ~; 25 |; 20 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 33 ( 26 >; 7 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-3 aty)
% Number of variables : 45 ( 0 sgn; 28 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
empty: $i > $o ).
tff(decl_24,type,
finite: $i > $o ).
tff(decl_25,type,
preboolean: $i > $o ).
tff(decl_26,type,
cup_closed: $i > $o ).
tff(decl_27,type,
diff_closed: $i > $o ).
tff(decl_28,type,
powerset: $i > $i ).
tff(decl_29,type,
element: ( $i * $i ) > $o ).
tff(decl_30,type,
set_intersection2: ( $i * $i ) > $i ).
tff(decl_31,type,
prebool_difference: ( $i * $i * $i ) > $i ).
tff(decl_32,type,
set_difference: ( $i * $i ) > $i ).
tff(decl_33,type,
empty_set: $i ).
tff(decl_34,type,
cap_closed: $i > $o ).
tff(decl_35,type,
relation: $i > $o ).
tff(decl_36,type,
function: $i > $o ).
tff(decl_37,type,
one_to_one: $i > $o ).
tff(decl_38,type,
epsilon_transitive: $i > $o ).
tff(decl_39,type,
epsilon_connected: $i > $o ).
tff(decl_40,type,
ordinal: $i > $o ).
tff(decl_41,type,
natural: $i > $o ).
tff(decl_42,type,
subset: ( $i * $i ) > $o ).
tff(decl_43,type,
esk1_1: $i > $i ).
tff(decl_44,type,
esk2_0: $i ).
tff(decl_45,type,
esk3_0: $i ).
tff(decl_46,type,
esk4_1: $i > $i ).
tff(decl_47,type,
esk5_0: $i ).
tff(decl_48,type,
esk6_1: $i > $i ).
tff(decl_49,type,
esk7_1: $i > $i ).
tff(decl_50,type,
esk8_0: $i ).
tff(decl_51,type,
esk9_1: $i > $i ).
tff(decl_52,type,
esk10_1: $i > $i ).
tff(decl_53,type,
esk11_0: $i ).
tff(decl_54,type,
esk12_0: $i ).
tff(decl_55,type,
esk13_0: $i ).
fof(dt_k2_finsub_1,axiom,
! [X1,X2,X3] :
( ( ~ empty(X1)
& preboolean(X1)
& element(X2,X1)
& element(X3,X1) )
=> element(prebool_difference(X1,X2,X3),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_finsub_1) ).
fof(t13_finsub_1,conjecture,
! [X1,X2,X3] :
( ( ~ empty(X3)
& preboolean(X3) )
=> ( ( element(X1,X3)
& element(X2,X3) )
=> element(set_intersection2(X1,X2),X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_finsub_1) ).
fof(redefinition_k2_finsub_1,axiom,
! [X1,X2,X3] :
( ( ~ empty(X1)
& preboolean(X1)
& element(X2,X1)
& element(X3,X1) )
=> prebool_difference(X1,X2,X3) = set_difference(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_finsub_1) ).
fof(t48_xboole_1,axiom,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(c_0_4,plain,
! [X1,X2,X3] :
( ( ~ empty(X1)
& preboolean(X1)
& element(X2,X1)
& element(X3,X1) )
=> element(prebool_difference(X1,X2,X3),X1) ),
inference(fof_simplification,[status(thm)],[dt_k2_finsub_1]) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3] :
( ( ~ empty(X3)
& preboolean(X3) )
=> ( ( element(X1,X3)
& element(X2,X3) )
=> element(set_intersection2(X1,X2),X3) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t13_finsub_1])]) ).
fof(c_0_6,plain,
! [X1,X2,X3] :
( ( ~ empty(X1)
& preboolean(X1)
& element(X2,X1)
& element(X3,X1) )
=> prebool_difference(X1,X2,X3) = set_difference(X2,X3) ),
inference(fof_simplification,[status(thm)],[redefinition_k2_finsub_1]) ).
fof(c_0_7,plain,
! [X13,X14,X15] :
( empty(X13)
| ~ preboolean(X13)
| ~ element(X14,X13)
| ~ element(X15,X13)
| element(prebool_difference(X13,X14,X15),X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])]) ).
fof(c_0_8,negated_conjecture,
( ~ empty(esk13_0)
& preboolean(esk13_0)
& element(esk11_0,esk13_0)
& element(esk12_0,esk13_0)
& ~ element(set_intersection2(esk11_0,esk12_0),esk13_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_9,plain,
! [X40,X41,X42] :
( empty(X40)
| ~ preboolean(X40)
| ~ element(X41,X40)
| ~ element(X42,X40)
| prebool_difference(X40,X41,X42) = set_difference(X41,X42) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])]) ).
cnf(c_0_10,plain,
( empty(X1)
| element(prebool_difference(X1,X2,X3),X1)
| ~ preboolean(X1)
| ~ element(X2,X1)
| ~ element(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
element(esk12_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
preboolean(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
~ empty(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( empty(X1)
| prebool_difference(X1,X2,X3) = set_difference(X2,X3)
| ~ preboolean(X1)
| ~ element(X2,X1)
| ~ element(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
( element(prebool_difference(esk13_0,X1,esk12_0),esk13_0)
| ~ element(X1,esk13_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]),c_0_13]) ).
cnf(c_0_16,negated_conjecture,
( prebool_difference(esk13_0,X1,esk12_0) = set_difference(X1,esk12_0)
| ~ element(X1,esk13_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_11]),c_0_12])]),c_0_13]) ).
fof(c_0_17,plain,
! [X55,X56] : set_difference(X55,set_difference(X55,X56)) = set_intersection2(X55,X56),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
cnf(c_0_18,negated_conjecture,
( element(set_difference(X1,esk12_0),esk13_0)
| ~ element(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
~ element(set_intersection2(esk11_0,esk12_0),esk13_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,plain,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,negated_conjecture,
( element(prebool_difference(esk13_0,X1,set_difference(X2,esk12_0)),esk13_0)
| ~ element(X1,esk13_0)
| ~ element(X2,esk13_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_18]),c_0_12])]),c_0_13]) ).
cnf(c_0_22,negated_conjecture,
( prebool_difference(esk13_0,X1,set_difference(X2,esk12_0)) = set_difference(X1,set_difference(X2,esk12_0))
| ~ element(X1,esk13_0)
| ~ element(X2,esk13_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_18]),c_0_12])]),c_0_13]) ).
cnf(c_0_23,negated_conjecture,
~ element(set_difference(esk11_0,set_difference(esk11_0,esk12_0)),esk13_0),
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,negated_conjecture,
( element(set_difference(X1,set_difference(X2,esk12_0)),esk13_0)
| ~ element(X1,esk13_0)
| ~ element(X2,esk13_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
element(esk11_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU102+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
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 23 12:13:08 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 0.19/0.60 % Version : CSE_E---1.5
% 0.19/0.60 % Problem : theBenchmark.p
% 0.19/0.60 % Proof found
% 0.19/0.60 % SZS status Theorem for theBenchmark.p
% 0.19/0.60 % SZS output start Proof
% See solution above
% 0.19/0.60 % Total time : 0.033000 s
% 0.19/0.60 % SZS output end Proof
% 0.19/0.60 % Total time : 0.036000 s
%------------------------------------------------------------------------------