TSTP Solution File: SEU239+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU239+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 : n017.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 16:23:42 EDT 2023
% Result : Theorem 0.21s 0.61s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 30
% Syntax : Number of formulae : 61 ( 10 unt; 25 typ; 0 def)
% Number of atoms : 102 ( 6 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 113 ( 47 ~; 49 |; 6 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 17 >; 7 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn; 22 !; 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,
is_reflexive_in: ( $i * $i ) > $o ).
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,
reflexive: $i > $o ).
tff(decl_36,type,
element: ( $i * $i ) > $o ).
tff(decl_37,type,
empty_set: $i ).
tff(decl_38,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_39,type,
esk2_1: $i > $i ).
tff(decl_40,type,
esk3_0: $i ).
tff(decl_41,type,
esk4_0: $i ).
tff(decl_42,type,
esk5_0: $i ).
tff(decl_43,type,
esk6_0: $i ).
tff(decl_44,type,
esk7_0: $i ).
tff(decl_45,type,
esk8_0: $i ).
tff(decl_46,type,
esk9_0: $i ).
fof(l1_wellord1,conjecture,
! [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(d1_relat_2,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( is_reflexive_in(X1,X2)
<=> ! [X3] :
( in(X3,X2)
=> in(ordered_pair(X3,X3),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_2) ).
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(d9_relat_2,axiom,
! [X1] :
( relation(X1)
=> ( reflexive(X1)
<=> is_reflexive_in(X1,relation_field(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_relat_2) ).
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(c_0_5,negated_conjecture,
~ ! [X1] :
( relation(X1)
=> ( reflexive(X1)
<=> ! [X2] :
( in(X2,relation_field(X1))
=> in(ordered_pair(X2,X2),X1) ) ) ),
inference(assume_negation,[status(cth)],[l1_wellord1]) ).
fof(c_0_6,plain,
! [X12,X13,X14,X15] :
( ( ~ is_reflexive_in(X12,X13)
| ~ in(X14,X13)
| in(ordered_pair(X14,X14),X12)
| ~ relation(X12) )
& ( in(esk1_2(X12,X15),X15)
| is_reflexive_in(X12,X15)
| ~ relation(X12) )
& ( ~ in(ordered_pair(esk1_2(X12,X15),esk1_2(X12,X15)),X12)
| is_reflexive_in(X12,X15)
| ~ relation(X12) ) ),
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)],[d1_relat_2])])])])])]) ).
fof(c_0_7,plain,
! [X17,X18] : ordered_pair(X17,X18) = unordered_pair(unordered_pair(X17,X18),singleton(X17)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_8,negated_conjecture,
! [X32] :
( relation(esk3_0)
& ( in(esk4_0,relation_field(esk3_0))
| ~ reflexive(esk3_0) )
& ( ~ in(ordered_pair(esk4_0,esk4_0),esk3_0)
| ~ reflexive(esk3_0) )
& ( reflexive(esk3_0)
| ~ in(X32,relation_field(esk3_0))
| in(ordered_pair(X32,X32),esk3_0) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])]) ).
cnf(c_0_9,plain,
( in(ordered_pair(X3,X3),X1)
| ~ is_reflexive_in(X1,X2)
| ~ in(X3,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X20] :
( ( ~ reflexive(X20)
| is_reflexive_in(X20,relation_field(X20))
| ~ relation(X20) )
& ( ~ is_reflexive_in(X20,relation_field(X20))
| reflexive(X20)
| ~ relation(X20) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_relat_2])])]) ).
cnf(c_0_12,negated_conjecture,
( reflexive(esk3_0)
| in(ordered_pair(X1,X1),esk3_0)
| ~ in(X1,relation_field(esk3_0)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,plain,
! [X8,X9] : unordered_pair(X8,X9) = unordered_pair(X9,X8),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_14,negated_conjecture,
( ~ in(ordered_pair(esk4_0,esk4_0),esk3_0)
| ~ reflexive(esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
( in(unordered_pair(unordered_pair(X3,X3),singleton(X3)),X1)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ is_reflexive_in(X1,X2) ),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_16,plain,
( is_reflexive_in(X1,relation_field(X1))
| ~ reflexive(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
( reflexive(esk3_0)
| in(unordered_pair(unordered_pair(X1,X1),singleton(X1)),esk3_0)
| ~ in(X1,relation_field(esk3_0)) ),
inference(rw,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_18,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,negated_conjecture,
( ~ reflexive(esk3_0)
| ~ in(unordered_pair(unordered_pair(esk4_0,esk4_0),singleton(esk4_0)),esk3_0) ),
inference(rw,[status(thm)],[c_0_14,c_0_10]) ).
cnf(c_0_20,plain,
( in(unordered_pair(unordered_pair(X1,X1),singleton(X1)),X2)
| ~ reflexive(X2)
| ~ relation(X2)
| ~ in(X1,relation_field(X2)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
relation(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_22,negated_conjecture,
( in(esk4_0,relation_field(esk3_0))
| ~ reflexive(esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_23,plain,
( is_reflexive_in(X1,X2)
| ~ in(ordered_pair(esk1_2(X1,X2),esk1_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_24,negated_conjecture,
( reflexive(esk3_0)
| in(unordered_pair(singleton(X1),unordered_pair(X1,X1)),esk3_0)
| ~ in(X1,relation_field(esk3_0)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_25,negated_conjecture,
~ reflexive(esk3_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]),c_0_22]) ).
cnf(c_0_26,plain,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(esk1_2(X1,X2),esk1_2(X1,X2)),singleton(esk1_2(X1,X2))),X1) ),
inference(rw,[status(thm)],[c_0_23,c_0_10]) ).
cnf(c_0_27,negated_conjecture,
( in(unordered_pair(unordered_pair(X1,X1),singleton(X1)),esk3_0)
| ~ in(X1,relation_field(esk3_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_18]),c_0_25]) ).
cnf(c_0_28,plain,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| ~ in(unordered_pair(singleton(esk1_2(X1,X2)),unordered_pair(esk1_2(X1,X2),esk1_2(X1,X2))),X1) ),
inference(rw,[status(thm)],[c_0_26,c_0_18]) ).
cnf(c_0_29,negated_conjecture,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X1)),esk3_0)
| ~ in(X1,relation_field(esk3_0)) ),
inference(spm,[status(thm)],[c_0_27,c_0_18]) ).
cnf(c_0_30,plain,
( in(esk1_2(X1,X2),X2)
| is_reflexive_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_31,negated_conjecture,
( is_reflexive_in(esk3_0,X1)
| ~ in(esk1_2(esk3_0,X1),relation_field(esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_21])]) ).
cnf(c_0_32,negated_conjecture,
( is_reflexive_in(esk3_0,X1)
| in(esk1_2(esk3_0,X1),X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_21]) ).
cnf(c_0_33,plain,
( reflexive(X1)
| ~ is_reflexive_in(X1,relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_34,negated_conjecture,
is_reflexive_in(esk3_0,relation_field(esk3_0)),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_21])]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU239+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 : n017.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 18:54:38 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 0.21/0.61 % Version : CSE_E---1.5
% 0.21/0.61 % Problem : theBenchmark.p
% 0.21/0.61 % Proof found
% 0.21/0.61 % SZS status Theorem for theBenchmark.p
% 0.21/0.61 % SZS output start Proof
% See solution above
% 0.21/0.62 % Total time : 0.029000 s
% 0.21/0.62 % SZS output end Proof
% 0.21/0.62 % Total time : 0.032000 s
%------------------------------------------------------------------------------