TSTP Solution File: SEU008+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU008+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 16:22:07 EDT 2023
% Result : Theorem 0.20s 0.69s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 35
% Syntax : Number of formulae : 63 ( 16 unt; 28 typ; 0 def)
% Number of atoms : 122 ( 39 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 140 ( 53 ~; 55 |; 20 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 18 >; 9 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 10 con; 0-3 aty)
% Number of variables : 64 ( 4 sgn; 38 !; 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,
set_intersection2: ( $i * $i ) > $i ).
tff(decl_27,type,
relation_composition: ( $i * $i ) > $i ).
tff(decl_28,type,
identity_relation: $i > $i ).
tff(decl_29,type,
element: ( $i * $i ) > $o ).
tff(decl_30,type,
empty_set: $i ).
tff(decl_31,type,
relation_empty_yielding: $i > $o ).
tff(decl_32,type,
powerset: $i > $i ).
tff(decl_33,type,
relation_dom: $i > $i ).
tff(decl_34,type,
subset: ( $i * $i ) > $o ).
tff(decl_35,type,
apply: ( $i * $i ) > $i ).
tff(decl_36,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_37,type,
esk2_1: $i > $i ).
tff(decl_38,type,
esk3_0: $i ).
tff(decl_39,type,
esk4_0: $i ).
tff(decl_40,type,
esk5_1: $i > $i ).
tff(decl_41,type,
esk6_0: $i ).
tff(decl_42,type,
esk7_0: $i ).
tff(decl_43,type,
esk8_1: $i > $i ).
tff(decl_44,type,
esk9_0: $i ).
tff(decl_45,type,
esk10_0: $i ).
tff(decl_46,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_47,type,
esk12_0: $i ).
tff(decl_48,type,
esk13_0: $i ).
tff(decl_49,type,
esk14_0: $i ).
fof(t38_funct_1,conjecture,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,set_intersection2(relation_dom(X3),X1))
=> apply(X3,X2) = apply(relation_composition(identity_relation(X1),X3),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_funct_1) ).
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(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(t34_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( X2 = identity_relation(X1)
<=> ( relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).
fof(dt_k6_relat_1,axiom,
! [X1] : relation(identity_relation(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(fc2_funct_1,axiom,
! [X1] :
( relation(identity_relation(X1))
& function(identity_relation(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(t23_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(X2))
=> apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,set_intersection2(relation_dom(X3),X1))
=> apply(X3,X2) = apply(relation_composition(identity_relation(X1),X3),X2) ) ),
inference(assume_negation,[status(cth)],[t38_funct_1]) ).
fof(c_0_8,plain,
! [X11,X12,X13,X14,X15,X16,X17,X18] :
( ( in(X14,X11)
| ~ in(X14,X13)
| X13 != set_intersection2(X11,X12) )
& ( in(X14,X12)
| ~ in(X14,X13)
| X13 != set_intersection2(X11,X12) )
& ( ~ in(X15,X11)
| ~ in(X15,X12)
| in(X15,X13)
| X13 != set_intersection2(X11,X12) )
& ( ~ in(esk1_3(X16,X17,X18),X18)
| ~ in(esk1_3(X16,X17,X18),X16)
| ~ in(esk1_3(X16,X17,X18),X17)
| X18 = set_intersection2(X16,X17) )
& ( in(esk1_3(X16,X17,X18),X16)
| in(esk1_3(X16,X17,X18),X18)
| X18 = set_intersection2(X16,X17) )
& ( in(esk1_3(X16,X17,X18),X17)
| in(esk1_3(X16,X17,X18),X18)
| X18 = set_intersection2(X16,X17) ) ),
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])])])])])]) ).
fof(c_0_9,negated_conjecture,
( relation(esk14_0)
& function(esk14_0)
& in(esk13_0,set_intersection2(relation_dom(esk14_0),esk12_0))
& apply(esk14_0,esk13_0) != apply(relation_composition(identity_relation(esk12_0),esk14_0),esk13_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_10,plain,
! [X9,X10] : set_intersection2(X9,X10) = set_intersection2(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(c_0_11,plain,
! [X57,X58,X59] :
( ( relation_dom(X58) = X57
| X58 != identity_relation(X57)
| ~ relation(X58)
| ~ function(X58) )
& ( ~ in(X59,X57)
| apply(X58,X59) = X59
| X58 != identity_relation(X57)
| ~ relation(X58)
| ~ function(X58) )
& ( in(esk11_2(X57,X58),X57)
| relation_dom(X58) != X57
| X58 = identity_relation(X57)
| ~ relation(X58)
| ~ function(X58) )
& ( apply(X58,esk11_2(X57,X58)) != esk11_2(X57,X58)
| relation_dom(X58) != X57
| X58 = identity_relation(X57)
| ~ relation(X58)
| ~ function(X58) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t34_funct_1])])])])]) ).
fof(c_0_12,plain,
! [X22] : relation(identity_relation(X22)),
inference(variable_rename,[status(thm)],[dt_k6_relat_1]) ).
fof(c_0_13,plain,
! [X32] :
( relation(identity_relation(X32))
& function(identity_relation(X32)) ),
inference(variable_rename,[status(thm)],[fc2_funct_1]) ).
cnf(c_0_14,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,negated_conjecture,
in(esk13_0,set_intersection2(relation_dom(esk14_0),esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_17,plain,
! [X51,X52,X53] :
( ~ relation(X52)
| ~ function(X52)
| ~ relation(X53)
| ~ function(X53)
| ~ in(X51,relation_dom(X52))
| apply(relation_composition(X52,X53),X51) = apply(X53,apply(X52,X51)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_funct_1])])]) ).
cnf(c_0_18,plain,
( relation_dom(X1) = X2
| X1 != identity_relation(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
function(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( apply(X3,X1) = X1
| ~ in(X1,X2)
| X3 != identity_relation(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_22,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_23,negated_conjecture,
in(esk13_0,set_intersection2(esk12_0,relation_dom(esk14_0))),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_24,plain,
( apply(relation_composition(X1,X2),X3) = apply(X2,apply(X1,X3))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ in(X3,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
relation_dom(identity_relation(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_18]),c_0_19]),c_0_20])]) ).
cnf(c_0_26,plain,
( apply(identity_relation(X1),X2) = X2
| ~ in(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_21]),c_0_19]),c_0_20])]) ).
cnf(c_0_27,negated_conjecture,
in(esk13_0,esk12_0),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
( apply(X1,apply(identity_relation(X2),X3)) = apply(relation_composition(identity_relation(X2),X1),X3)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X3,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_19]),c_0_20])]) ).
cnf(c_0_29,negated_conjecture,
apply(identity_relation(esk12_0),esk13_0) = esk13_0,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
apply(esk14_0,esk13_0) != apply(relation_composition(identity_relation(esk12_0),esk14_0),esk13_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_31,negated_conjecture,
( apply(relation_composition(identity_relation(esk12_0),X1),esk13_0) = apply(X1,esk13_0)
| ~ relation(X1)
| ~ function(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_27]),c_0_29]) ).
cnf(c_0_32,negated_conjecture,
relation(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_33,negated_conjecture,
function(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU008+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 20:18:04 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.20/0.69 % Version : CSE_E---1.5
% 0.20/0.69 % Problem : theBenchmark.p
% 0.20/0.69 % Proof found
% 0.20/0.69 % SZS status Theorem for theBenchmark.p
% 0.20/0.69 % SZS output start Proof
% See solution above
% 0.20/0.70 % Total time : 0.116000 s
% 0.20/0.70 % SZS output end Proof
% 0.20/0.70 % Total time : 0.120000 s
%------------------------------------------------------------------------------