TSTP Solution File: SEU271+1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU271+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 : n008.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 16:24:00 EDT 2023
% Result : Theorem 5.62s 5.66s
% Output : CNFRefutation 5.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 46
% Syntax : Number of formulae : 89 ( 15 unt; 38 typ; 0 def)
% Number of atoms : 192 ( 36 equ)
% Maximal formula atoms : 33 ( 3 avg)
% Number of connectives : 231 ( 90 ~; 111 |; 20 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 38 ( 27 >; 11 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 11 con; 0-2 aty)
% Number of variables : 101 ( 1 sgn; 35 !; 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,
ordinal: $i > $o ).
tff(decl_26,type,
epsilon_transitive: $i > $o ).
tff(decl_27,type,
epsilon_connected: $i > $o ).
tff(decl_28,type,
relation: $i > $o ).
tff(decl_29,type,
one_to_one: $i > $o ).
tff(decl_30,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_31,type,
set_union2: ( $i * $i ) > $i ).
tff(decl_32,type,
subset: ( $i * $i ) > $o ).
tff(decl_33,type,
antisymmetric: $i > $o ).
tff(decl_34,type,
relation_field: $i > $i ).
tff(decl_35,type,
is_antisymmetric_in: ( $i * $i ) > $o ).
tff(decl_36,type,
inclusion_relation: $i > $i ).
tff(decl_37,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_38,type,
singleton: $i > $i ).
tff(decl_39,type,
relation_dom: $i > $i ).
tff(decl_40,type,
relation_rng: $i > $i ).
tff(decl_41,type,
element: ( $i * $i ) > $o ).
tff(decl_42,type,
empty_set: $i ).
tff(decl_43,type,
relation_empty_yielding: $i > $o ).
tff(decl_44,type,
powerset: $i > $i ).
tff(decl_45,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_46,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_47,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_48,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk5_1: $i > $i ).
tff(decl_50,type,
esk6_0: $i ).
tff(decl_51,type,
esk7_0: $i ).
tff(decl_52,type,
esk8_0: $i ).
tff(decl_53,type,
esk9_0: $i ).
tff(decl_54,type,
esk10_0: $i ).
tff(decl_55,type,
esk11_0: $i ).
tff(decl_56,type,
esk12_0: $i ).
tff(decl_57,type,
esk13_0: $i ).
tff(decl_58,type,
esk14_0: $i ).
tff(decl_59,type,
esk15_0: $i ).
fof(d1_wellord2,axiom,
! [X1,X2] :
( relation(X2)
=> ( X2 = inclusion_relation(X1)
<=> ( relation_field(X2) = X1
& ! [X3,X4] :
( ( in(X3,X1)
& in(X4,X1) )
=> ( in(ordered_pair(X3,X4),X2)
<=> subset(X3,X4) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_wellord2) ).
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(d4_relat_2,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( is_antisymmetric_in(X1,X2)
<=> ! [X3,X4] :
( ( in(X3,X2)
& in(X4,X2)
& in(ordered_pair(X3,X4),X1)
& in(ordered_pair(X4,X3),X1) )
=> X3 = X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_2) ).
fof(dt_k1_wellord2,axiom,
! [X1] : relation(inclusion_relation(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_wellord2) ).
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(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(d12_relat_2,axiom,
! [X1] :
( relation(X1)
=> ( antisymmetric(X1)
<=> is_antisymmetric_in(X1,relation_field(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_relat_2) ).
fof(t5_wellord2,conjecture,
! [X1] : antisymmetric(inclusion_relation(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_wellord2) ).
fof(c_0_8,plain,
! [X19,X20,X21,X22] :
( ( relation_field(X20) = X19
| X20 != inclusion_relation(X19)
| ~ relation(X20) )
& ( ~ in(ordered_pair(X21,X22),X20)
| subset(X21,X22)
| ~ in(X21,X19)
| ~ in(X22,X19)
| X20 != inclusion_relation(X19)
| ~ relation(X20) )
& ( ~ subset(X21,X22)
| in(ordered_pair(X21,X22),X20)
| ~ in(X21,X19)
| ~ in(X22,X19)
| X20 != inclusion_relation(X19)
| ~ relation(X20) )
& ( in(esk1_2(X19,X20),X19)
| relation_field(X20) != X19
| X20 = inclusion_relation(X19)
| ~ relation(X20) )
& ( in(esk2_2(X19,X20),X19)
| relation_field(X20) != X19
| X20 = inclusion_relation(X19)
| ~ relation(X20) )
& ( ~ in(ordered_pair(esk1_2(X19,X20),esk2_2(X19,X20)),X20)
| ~ subset(esk1_2(X19,X20),esk2_2(X19,X20))
| relation_field(X20) != X19
| X20 = inclusion_relation(X19)
| ~ relation(X20) )
& ( in(ordered_pair(esk1_2(X19,X20),esk2_2(X19,X20)),X20)
| subset(esk1_2(X19,X20),esk2_2(X19,X20))
| relation_field(X20) != X19
| X20 = inclusion_relation(X19)
| ~ relation(X20) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_wellord2])])])])]) ).
fof(c_0_9,plain,
! [X32,X33] : ordered_pair(X32,X33) = unordered_pair(unordered_pair(X32,X33),singleton(X32)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_10,plain,
! [X25,X26,X27,X28,X29] :
( ( ~ is_antisymmetric_in(X25,X26)
| ~ in(X27,X26)
| ~ in(X28,X26)
| ~ in(ordered_pair(X27,X28),X25)
| ~ in(ordered_pair(X28,X27),X25)
| X27 = X28
| ~ relation(X25) )
& ( in(esk3_2(X25,X29),X29)
| is_antisymmetric_in(X25,X29)
| ~ relation(X25) )
& ( in(esk4_2(X25,X29),X29)
| is_antisymmetric_in(X25,X29)
| ~ relation(X25) )
& ( in(ordered_pair(esk3_2(X25,X29),esk4_2(X25,X29)),X25)
| is_antisymmetric_in(X25,X29)
| ~ relation(X25) )
& ( in(ordered_pair(esk4_2(X25,X29),esk3_2(X25,X29)),X25)
| is_antisymmetric_in(X25,X29)
| ~ relation(X25) )
& ( esk3_2(X25,X29) != esk4_2(X25,X29)
| is_antisymmetric_in(X25,X29)
| ~ relation(X25) ) ),
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)],[d4_relat_2])])])])])]) ).
cnf(c_0_11,plain,
( subset(X1,X2)
| ~ in(ordered_pair(X1,X2),X3)
| ~ in(X1,X4)
| ~ in(X2,X4)
| X3 != inclusion_relation(X4)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X35] : relation(inclusion_relation(X35)),
inference(variable_rename,[status(thm)],[dt_k1_wellord2]) ).
cnf(c_0_14,plain,
( in(ordered_pair(esk3_2(X1,X2),esk4_2(X1,X2)),X1)
| is_antisymmetric_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,plain,
! [X12,X13] : unordered_pair(X12,X13) = unordered_pair(X13,X12),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_16,plain,
( subset(X1,X2)
| X3 != inclusion_relation(X4)
| ~ relation(X3)
| ~ in(X2,X4)
| ~ in(X1,X4)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
relation(inclusion_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( is_antisymmetric_in(X1,X2)
| in(unordered_pair(unordered_pair(esk3_2(X1,X2),esk4_2(X1,X2)),singleton(esk3_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[c_0_14,c_0_12]) ).
cnf(c_0_19,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
( subset(X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),inclusion_relation(X3))
| ~ in(X2,X3)
| ~ in(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_16]),c_0_17])]) ).
cnf(c_0_21,plain,
( is_antisymmetric_in(X1,X2)
| in(unordered_pair(singleton(esk3_2(X1,X2)),unordered_pair(esk3_2(X1,X2),esk4_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
( in(ordered_pair(esk4_2(X1,X2),esk3_2(X1,X2)),X1)
| is_antisymmetric_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_23,plain,
( subset(X1,X2)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),inclusion_relation(X3))
| ~ in(X2,X3)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_24,plain,
( is_antisymmetric_in(inclusion_relation(X1),X2)
| in(unordered_pair(singleton(esk3_2(inclusion_relation(X1),X2)),unordered_pair(esk3_2(inclusion_relation(X1),X2),esk4_2(inclusion_relation(X1),X2))),inclusion_relation(X1)) ),
inference(spm,[status(thm)],[c_0_21,c_0_17]) ).
cnf(c_0_25,plain,
( in(esk4_2(X1,X2),X2)
| is_antisymmetric_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_26,plain,
( in(esk3_2(X1,X2),X2)
| is_antisymmetric_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_27,plain,
( is_antisymmetric_in(X1,X2)
| in(unordered_pair(unordered_pair(esk4_2(X1,X2),esk3_2(X1,X2)),singleton(esk4_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[c_0_22,c_0_12]) ).
fof(c_0_28,plain,
! [X16,X17] :
( ( subset(X16,X17)
| X16 != X17 )
& ( subset(X17,X16)
| X16 != X17 )
& ( ~ subset(X16,X17)
| ~ subset(X17,X16)
| X16 = X17 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
cnf(c_0_29,plain,
( is_antisymmetric_in(inclusion_relation(X1),X2)
| subset(esk3_2(inclusion_relation(X1),X2),esk4_2(inclusion_relation(X1),X2))
| ~ in(esk4_2(inclusion_relation(X1),X2),X1)
| ~ in(esk3_2(inclusion_relation(X1),X2),X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,plain,
( is_antisymmetric_in(inclusion_relation(X1),X2)
| in(esk4_2(inclusion_relation(X1),X2),X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_17]) ).
cnf(c_0_31,plain,
( is_antisymmetric_in(inclusion_relation(X1),X2)
| in(esk3_2(inclusion_relation(X1),X2),X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_17]) ).
cnf(c_0_32,plain,
( subset(X1,X2)
| ~ in(unordered_pair(unordered_pair(X2,X1),singleton(X1)),inclusion_relation(X3))
| ~ in(X2,X3)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_33,plain,
( is_antisymmetric_in(X1,X2)
| in(unordered_pair(singleton(esk4_2(X1,X2)),unordered_pair(esk3_2(X1,X2),esk4_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_19]),c_0_19]) ).
fof(c_0_34,plain,
! [X18] :
( ( ~ antisymmetric(X18)
| is_antisymmetric_in(X18,relation_field(X18))
| ~ relation(X18) )
& ( ~ is_antisymmetric_in(X18,relation_field(X18))
| antisymmetric(X18)
| ~ relation(X18) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d12_relat_2])])]) ).
cnf(c_0_35,plain,
( relation_field(X1) = X2
| X1 != inclusion_relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_36,negated_conjecture,
~ ! [X1] : antisymmetric(inclusion_relation(X1)),
inference(assume_negation,[status(cth)],[t5_wellord2]) ).
cnf(c_0_37,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,plain,
( is_antisymmetric_in(inclusion_relation(X1),X1)
| subset(esk3_2(inclusion_relation(X1),X1),esk4_2(inclusion_relation(X1),X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_39,plain,
( subset(X1,X2)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X2,X1)),inclusion_relation(X3))
| ~ in(X2,X3)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_32,c_0_19]) ).
cnf(c_0_40,plain,
( is_antisymmetric_in(inclusion_relation(X1),X2)
| in(unordered_pair(singleton(esk4_2(inclusion_relation(X1),X2)),unordered_pair(esk3_2(inclusion_relation(X1),X2),esk4_2(inclusion_relation(X1),X2))),inclusion_relation(X1)) ),
inference(spm,[status(thm)],[c_0_33,c_0_17]) ).
cnf(c_0_41,plain,
( is_antisymmetric_in(X1,X2)
| esk3_2(X1,X2) != esk4_2(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_42,plain,
( antisymmetric(X1)
| ~ is_antisymmetric_in(X1,relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_43,plain,
relation_field(inclusion_relation(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_35]),c_0_17])]) ).
fof(c_0_44,negated_conjecture,
~ antisymmetric(inclusion_relation(esk15_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])]) ).
cnf(c_0_45,plain,
( esk4_2(inclusion_relation(X1),X1) = esk3_2(inclusion_relation(X1),X1)
| is_antisymmetric_in(inclusion_relation(X1),X1)
| ~ subset(esk4_2(inclusion_relation(X1),X1),esk3_2(inclusion_relation(X1),X1)) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_46,plain,
( is_antisymmetric_in(inclusion_relation(X1),X2)
| subset(esk4_2(inclusion_relation(X1),X2),esk3_2(inclusion_relation(X1),X2))
| ~ in(esk3_2(inclusion_relation(X1),X2),X1)
| ~ in(esk4_2(inclusion_relation(X1),X2),X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_47,plain,
( is_antisymmetric_in(inclusion_relation(X1),X2)
| esk4_2(inclusion_relation(X1),X2) != esk3_2(inclusion_relation(X1),X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_17]) ).
cnf(c_0_48,plain,
( antisymmetric(inclusion_relation(X1))
| ~ is_antisymmetric_in(inclusion_relation(X1),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_17])]) ).
cnf(c_0_49,negated_conjecture,
~ antisymmetric(inclusion_relation(esk15_0)),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_50,plain,
$false,
inference(cdclpropres,[status(thm)],[c_0_45,c_0_46,c_0_30,c_0_31,c_0_47,c_0_48,c_0_49]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU271+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n008.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
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 23 17:03:17 EDT 2023
% 0.20/0.34 % CPUTime :
% 0.20/0.61 start to proof: theBenchmark
% 5.62/5.66 % Version : CSE_E---1.5
% 5.62/5.66 % Problem : theBenchmark.p
% 5.62/5.66 % Proof found
% 5.62/5.66 % SZS status Theorem for theBenchmark.p
% 5.62/5.66 % SZS output start Proof
% See solution above
% 5.62/5.67 % Total time : 5.043000 s
% 5.62/5.67 % SZS output end Proof
% 5.62/5.67 % Total time : 5.046000 s
%------------------------------------------------------------------------------