TSTP Solution File: SEU252+1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU252+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n016.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 16:23:49 EDT 2023
% Result : Theorem 192.84s 193.18s
% Output : CNFRefutation 192.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 35
% Syntax : Number of formulae : 69 ( 10 unt; 27 typ; 0 def)
% Number of atoms : 135 ( 6 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 160 ( 67 ~; 68 |; 12 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 19 >; 8 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 8 con; 0-2 aty)
% Number of variables : 89 ( 3 sgn; 40 !; 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,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_28,type,
set_union2: ( $i * $i ) > $i ).
tff(decl_29,type,
set_intersection2: ( $i * $i ) > $i ).
tff(decl_30,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_31,type,
singleton: $i > $i ).
tff(decl_32,type,
relation_field: $i > $i ).
tff(decl_33,type,
relation_dom: $i > $i ).
tff(decl_34,type,
relation_rng: $i > $i ).
tff(decl_35,type,
relation_restriction: ( $i * $i ) > $i ).
tff(decl_36,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_37,type,
element: ( $i * $i ) > $o ).
tff(decl_38,type,
empty_set: $i ).
tff(decl_39,type,
reflexive: $i > $o ).
tff(decl_40,type,
esk1_1: $i > $i ).
tff(decl_41,type,
esk2_1: $i > $i ).
tff(decl_42,type,
esk3_0: $i ).
tff(decl_43,type,
esk4_0: $i ).
tff(decl_44,type,
esk5_0: $i ).
tff(decl_45,type,
esk6_0: $i ).
tff(decl_46,type,
esk7_0: $i ).
tff(decl_47,type,
esk8_0: $i ).
tff(decl_48,type,
esk9_0: $i ).
fof(t106_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(l1_wellord1,axiom,
! [X1] :
( relation(X1)
=> ( reflexive(X1)
<=> ! [X2] :
( in(X2,relation_field(X1))
=> in(ordered_pair(X2,X2),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_wellord1) ).
fof(t16_wellord1,axiom,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_restriction(X3,X2))
<=> ( in(X1,X3)
& in(X1,cartesian_product2(X2,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_wellord1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(t19_wellord1,axiom,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_field(relation_restriction(X3,X2)))
=> ( in(X1,relation_field(X3))
& in(X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_wellord1) ).
fof(dt_k2_wellord1,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_restriction(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(t22_wellord1,conjecture,
! [X1,X2] :
( relation(X2)
=> ( reflexive(X2)
=> reflexive(relation_restriction(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_wellord1) ).
fof(c_0_8,plain,
! [X40,X41,X42,X43] :
( ( in(X40,X42)
| ~ in(ordered_pair(X40,X41),cartesian_product2(X42,X43)) )
& ( in(X41,X43)
| ~ in(ordered_pair(X40,X41),cartesian_product2(X42,X43)) )
& ( ~ in(X40,X42)
| ~ in(X41,X43)
| in(ordered_pair(X40,X41),cartesian_product2(X42,X43)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t106_zfmisc_1])])]) ).
fof(c_0_9,plain,
! [X15,X16] : ordered_pair(X15,X16) = unordered_pair(unordered_pair(X15,X16),singleton(X15)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_10,plain,
! [X32,X33] :
( ( ~ reflexive(X32)
| ~ in(X33,relation_field(X32))
| in(ordered_pair(X33,X33),X32)
| ~ relation(X32) )
& ( in(esk2_1(X32),relation_field(X32))
| reflexive(X32)
| ~ relation(X32) )
& ( ~ in(ordered_pair(esk2_1(X32),esk2_1(X32)),X32)
| reflexive(X32)
| ~ relation(X32) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l1_wellord1])])])])]) ).
fof(c_0_11,plain,
! [X44,X45,X46] :
( ( in(X44,X46)
| ~ in(X44,relation_restriction(X46,X45))
| ~ relation(X46) )
& ( in(X44,cartesian_product2(X45,X45))
| ~ in(X44,relation_restriction(X46,X45))
| ~ relation(X46) )
& ( ~ in(X44,X46)
| ~ in(X44,cartesian_product2(X45,X45))
| in(X44,relation_restriction(X46,X45))
| ~ relation(X46) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t16_wellord1])])]) ).
cnf(c_0_12,plain,
( in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
| ~ in(X1,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( reflexive(X1)
| ~ in(ordered_pair(esk2_1(X1),esk2_1(X1)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,plain,
! [X9,X10] : unordered_pair(X9,X10) = unordered_pair(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_16,plain,
( in(X1,relation_restriction(X2,X3))
| ~ in(X1,X2)
| ~ in(X1,cartesian_product2(X3,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X4))
| ~ in(X3,X4)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_18,plain,
! [X47,X48,X49] :
( ( in(X47,relation_field(X49))
| ~ in(X47,relation_field(relation_restriction(X49,X48)))
| ~ relation(X49) )
& ( in(X47,X48)
| ~ in(X47,relation_field(relation_restriction(X49,X48)))
| ~ relation(X49) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t19_wellord1])])]) ).
fof(c_0_19,plain,
! [X20,X21] :
( ~ relation(X20)
| relation(relation_restriction(X20,X21)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_wellord1])]) ).
cnf(c_0_20,plain,
( reflexive(X1)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(esk2_1(X1),esk2_1(X1)),singleton(esk2_1(X1))),X1) ),
inference(rw,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_21,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),relation_restriction(X3,X4))
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
| ~ in(X2,X4)
| ~ in(X1,X4) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,plain,
( in(X1,X2)
| ~ in(X1,relation_field(relation_restriction(X3,X2)))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
( in(esk2_1(X1),relation_field(X1))
| reflexive(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_25,plain,
( relation(relation_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( in(ordered_pair(X2,X2),X1)
| ~ reflexive(X1)
| ~ in(X2,relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_27,negated_conjecture,
~ ! [X1,X2] :
( relation(X2)
=> ( reflexive(X2)
=> reflexive(relation_restriction(X2,X1)) ) ),
inference(assume_negation,[status(cth)],[t22_wellord1]) ).
cnf(c_0_28,plain,
( reflexive(X1)
| ~ relation(X1)
| ~ in(unordered_pair(singleton(esk2_1(X1)),unordered_pair(esk2_1(X1),esk2_1(X1))),X1) ),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_29,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),relation_restriction(X3,X4))
| ~ relation(X3)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X3)
| ~ in(X2,X4)
| ~ in(X1,X4) ),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_30,plain,
( reflexive(relation_restriction(X1,X2))
| in(esk2_1(relation_restriction(X1,X2)),X2)
| ~ relation(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_31,plain,
( in(unordered_pair(unordered_pair(X2,X2),singleton(X2)),X1)
| ~ relation(X1)
| ~ reflexive(X1)
| ~ in(X2,relation_field(X1)) ),
inference(rw,[status(thm)],[c_0_26,c_0_13]) ).
cnf(c_0_32,plain,
( in(X1,relation_field(X2))
| ~ in(X1,relation_field(relation_restriction(X2,X3)))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_33,negated_conjecture,
( relation(esk9_0)
& reflexive(esk9_0)
& ~ reflexive(relation_restriction(esk9_0,esk8_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])]) ).
cnf(c_0_34,plain,
( reflexive(relation_restriction(X1,X2))
| ~ relation(X1)
| ~ in(unordered_pair(singleton(esk2_1(relation_restriction(X1,X2))),unordered_pair(esk2_1(relation_restriction(X1,X2)),esk2_1(relation_restriction(X1,X2)))),X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_25]) ).
cnf(c_0_35,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X1)),X2)
| ~ reflexive(X2)
| ~ relation(X2)
| ~ in(X1,relation_field(X2)) ),
inference(spm,[status(thm)],[c_0_31,c_0_21]) ).
cnf(c_0_36,plain,
( reflexive(relation_restriction(X1,X2))
| in(esk2_1(relation_restriction(X1,X2)),relation_field(X1))
| ~ relation(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_24]),c_0_25]) ).
cnf(c_0_37,negated_conjecture,
~ reflexive(relation_restriction(esk9_0,esk8_0)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,plain,
( reflexive(relation_restriction(X1,X2))
| ~ reflexive(X1)
| ~ relation(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_39,negated_conjecture,
reflexive(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,negated_conjecture,
relation(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_40])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU252+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n016.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % 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 : Wed Aug 23 13:26:52 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 192.84/193.18 % Version : CSE_E---1.5
% 192.84/193.18 % Problem : theBenchmark.p
% 192.84/193.18 % Proof found
% 192.84/193.18 % SZS status Theorem for theBenchmark.p
% 192.84/193.18 % SZS output start Proof
% See solution above
% 192.84/193.18 % Total time : 192.402000 s
% 192.84/193.18 % SZS output end Proof
% 192.84/193.18 % Total time : 192.413000 s
%------------------------------------------------------------------------------