TSTP Solution File: SEU284+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU284+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 : n009.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 16:24:06 EDT 2023
% Result : Theorem 0.20s 0.60s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 26
% Syntax : Number of formulae : 68 ( 8 unt; 24 typ; 0 def)
% Number of atoms : 225 ( 131 equ)
% Maximal formula atoms : 104 ( 5 avg)
% Number of connectives : 257 ( 76 ~; 131 |; 45 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 39 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 16 >; 3 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-2 aty)
% Number of variables : 63 ( 12 sgn; 15 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
relation: $i > $o ).
tff(decl_23,type,
function: $i > $o ).
tff(decl_24,type,
relation_dom: $i > $i ).
tff(decl_25,type,
in: ( $i * $i ) > $o ).
tff(decl_26,type,
apply: ( $i * $i ) > $i ).
tff(decl_27,type,
singleton: $i > $i ).
tff(decl_28,type,
empty: $i > $o ).
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,
esk1_0: $i ).
tff(decl_33,type,
esk2_1: $i > $i ).
tff(decl_34,type,
esk3_0: $i ).
tff(decl_35,type,
esk4_1: $i > $i ).
tff(decl_36,type,
esk5_1: $i > $i ).
tff(decl_37,type,
esk6_1: $i > $i ).
tff(decl_38,type,
esk7_1: $i > $i ).
tff(decl_39,type,
esk8_1: $i > $i ).
tff(decl_40,type,
esk9_1: $i > $i ).
tff(decl_41,type,
esk10_0: $i ).
tff(decl_42,type,
esk11_0: $i ).
tff(decl_43,type,
esk12_0: $i ).
tff(decl_44,type,
esk13_0: $i ).
tff(decl_45,type,
esk14_0: $i ).
fof(s3_funct_1__e16_22__wellord2,conjecture,
! [X1] :
? [X2] :
( relation(X2)
& function(X2)
& relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = singleton(X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_funct_1__e16_22__wellord2) ).
fof(s2_funct_1__e16_22__wellord2__1,axiom,
! [X1] :
( ( ! [X2,X3,X4] :
( ( in(X2,X1)
& X3 = singleton(X2)
& X4 = singleton(X2) )
=> X3 = X4 )
& ! [X2] :
~ ( in(X2,X1)
& ! [X3] : X3 != singleton(X2) ) )
=> ? [X2] :
( relation(X2)
& function(X2)
& relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = singleton(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_funct_1__e16_22__wellord2__1) ).
fof(c_0_2,negated_conjecture,
~ ! [X1] :
? [X2] :
( relation(X2)
& function(X2)
& relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = singleton(X3) ) ),
inference(assume_negation,[status(cth)],[s3_funct_1__e16_22__wellord2]) ).
fof(c_0_3,plain,
! [X11,X16,X18] :
( ( relation(esk8_1(X11))
| in(esk7_1(X11),X11)
| in(esk4_1(X11),X11) )
& ( function(esk8_1(X11))
| in(esk7_1(X11),X11)
| in(esk4_1(X11),X11) )
& ( relation_dom(esk8_1(X11)) = X11
| in(esk7_1(X11),X11)
| in(esk4_1(X11),X11) )
& ( ~ in(X18,X11)
| apply(esk8_1(X11),X18) = singleton(X18)
| in(esk7_1(X11),X11)
| in(esk4_1(X11),X11) )
& ( relation(esk8_1(X11))
| X16 != singleton(esk7_1(X11))
| in(esk4_1(X11),X11) )
& ( function(esk8_1(X11))
| X16 != singleton(esk7_1(X11))
| in(esk4_1(X11),X11) )
& ( relation_dom(esk8_1(X11)) = X11
| X16 != singleton(esk7_1(X11))
| in(esk4_1(X11),X11) )
& ( ~ in(X18,X11)
| apply(esk8_1(X11),X18) = singleton(X18)
| X16 != singleton(esk7_1(X11))
| in(esk4_1(X11),X11) )
& ( relation(esk8_1(X11))
| in(esk7_1(X11),X11)
| esk5_1(X11) = singleton(esk4_1(X11)) )
& ( function(esk8_1(X11))
| in(esk7_1(X11),X11)
| esk5_1(X11) = singleton(esk4_1(X11)) )
& ( relation_dom(esk8_1(X11)) = X11
| in(esk7_1(X11),X11)
| esk5_1(X11) = singleton(esk4_1(X11)) )
& ( ~ in(X18,X11)
| apply(esk8_1(X11),X18) = singleton(X18)
| in(esk7_1(X11),X11)
| esk5_1(X11) = singleton(esk4_1(X11)) )
& ( relation(esk8_1(X11))
| X16 != singleton(esk7_1(X11))
| esk5_1(X11) = singleton(esk4_1(X11)) )
& ( function(esk8_1(X11))
| X16 != singleton(esk7_1(X11))
| esk5_1(X11) = singleton(esk4_1(X11)) )
& ( relation_dom(esk8_1(X11)) = X11
| X16 != singleton(esk7_1(X11))
| esk5_1(X11) = singleton(esk4_1(X11)) )
& ( ~ in(X18,X11)
| apply(esk8_1(X11),X18) = singleton(X18)
| X16 != singleton(esk7_1(X11))
| esk5_1(X11) = singleton(esk4_1(X11)) )
& ( relation(esk8_1(X11))
| in(esk7_1(X11),X11)
| esk6_1(X11) = singleton(esk4_1(X11)) )
& ( function(esk8_1(X11))
| in(esk7_1(X11),X11)
| esk6_1(X11) = singleton(esk4_1(X11)) )
& ( relation_dom(esk8_1(X11)) = X11
| in(esk7_1(X11),X11)
| esk6_1(X11) = singleton(esk4_1(X11)) )
& ( ~ in(X18,X11)
| apply(esk8_1(X11),X18) = singleton(X18)
| in(esk7_1(X11),X11)
| esk6_1(X11) = singleton(esk4_1(X11)) )
& ( relation(esk8_1(X11))
| X16 != singleton(esk7_1(X11))
| esk6_1(X11) = singleton(esk4_1(X11)) )
& ( function(esk8_1(X11))
| X16 != singleton(esk7_1(X11))
| esk6_1(X11) = singleton(esk4_1(X11)) )
& ( relation_dom(esk8_1(X11)) = X11
| X16 != singleton(esk7_1(X11))
| esk6_1(X11) = singleton(esk4_1(X11)) )
& ( ~ in(X18,X11)
| apply(esk8_1(X11),X18) = singleton(X18)
| X16 != singleton(esk7_1(X11))
| esk6_1(X11) = singleton(esk4_1(X11)) )
& ( relation(esk8_1(X11))
| in(esk7_1(X11),X11)
| esk5_1(X11) != esk6_1(X11) )
& ( function(esk8_1(X11))
| in(esk7_1(X11),X11)
| esk5_1(X11) != esk6_1(X11) )
& ( relation_dom(esk8_1(X11)) = X11
| in(esk7_1(X11),X11)
| esk5_1(X11) != esk6_1(X11) )
& ( ~ in(X18,X11)
| apply(esk8_1(X11),X18) = singleton(X18)
| in(esk7_1(X11),X11)
| esk5_1(X11) != esk6_1(X11) )
& ( relation(esk8_1(X11))
| X16 != singleton(esk7_1(X11))
| esk5_1(X11) != esk6_1(X11) )
& ( function(esk8_1(X11))
| X16 != singleton(esk7_1(X11))
| esk5_1(X11) != esk6_1(X11) )
& ( relation_dom(esk8_1(X11)) = X11
| X16 != singleton(esk7_1(X11))
| esk5_1(X11) != esk6_1(X11) )
& ( ~ in(X18,X11)
| apply(esk8_1(X11),X18) = singleton(X18)
| X16 != singleton(esk7_1(X11))
| esk5_1(X11) != esk6_1(X11) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[s2_funct_1__e16_22__wellord2__1])])])])]) ).
fof(c_0_4,negated_conjecture,
! [X6] :
( ( in(esk2_1(X6),esk1_0)
| ~ relation(X6)
| ~ function(X6)
| relation_dom(X6) != esk1_0 )
& ( apply(X6,esk2_1(X6)) != singleton(esk2_1(X6))
| ~ relation(X6)
| ~ function(X6)
| relation_dom(X6) != esk1_0 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])]) ).
cnf(c_0_5,plain,
( relation_dom(esk8_1(X1)) = X1
| esk6_1(X1) = singleton(esk4_1(X1))
| X2 != singleton(esk7_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_6,plain,
( relation(esk8_1(X1))
| esk6_1(X1) = singleton(esk4_1(X1))
| X2 != singleton(esk7_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_7,plain,
( function(esk8_1(X1))
| esk6_1(X1) = singleton(esk4_1(X1))
| X2 != singleton(esk7_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_8,plain,
( relation_dom(esk8_1(X1)) = X1
| esk5_1(X1) = singleton(esk4_1(X1))
| X2 != singleton(esk7_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_9,plain,
( relation(esk8_1(X1))
| esk5_1(X1) = singleton(esk4_1(X1))
| X2 != singleton(esk7_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_10,plain,
( function(esk8_1(X1))
| esk5_1(X1) = singleton(esk4_1(X1))
| X2 != singleton(esk7_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_11,plain,
( apply(esk8_1(X2),X1) = singleton(X1)
| esk6_1(X2) = singleton(esk4_1(X2))
| ~ in(X1,X2)
| X3 != singleton(esk7_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_12,negated_conjecture,
( in(esk2_1(X1),esk1_0)
| ~ relation(X1)
| ~ function(X1)
| relation_dom(X1) != esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_13,plain,
( esk6_1(X1) = singleton(esk4_1(X1))
| relation_dom(esk8_1(X1)) = X1 ),
inference(er,[status(thm)],[c_0_5]) ).
cnf(c_0_14,plain,
( esk6_1(X1) = singleton(esk4_1(X1))
| relation(esk8_1(X1)) ),
inference(er,[status(thm)],[c_0_6]) ).
cnf(c_0_15,plain,
( esk6_1(X1) = singleton(esk4_1(X1))
| function(esk8_1(X1)) ),
inference(er,[status(thm)],[c_0_7]) ).
cnf(c_0_16,plain,
( apply(esk8_1(X2),X1) = singleton(X1)
| esk5_1(X2) = singleton(esk4_1(X2))
| ~ in(X1,X2)
| X3 != singleton(esk7_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_17,plain,
( esk5_1(X1) = singleton(esk4_1(X1))
| relation_dom(esk8_1(X1)) = X1 ),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_18,plain,
( esk5_1(X1) = singleton(esk4_1(X1))
| relation(esk8_1(X1)) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_19,plain,
( esk5_1(X1) = singleton(esk4_1(X1))
| function(esk8_1(X1)) ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_20,plain,
( apply(esk8_1(X1),X2) = singleton(X2)
| esk6_1(X1) = singleton(esk4_1(X1))
| ~ in(X2,X1) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_21,negated_conjecture,
( esk6_1(esk1_0) = singleton(esk4_1(esk1_0))
| in(esk2_1(esk8_1(esk1_0)),esk1_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13])]),c_0_14]),c_0_15]) ).
cnf(c_0_22,plain,
( apply(esk8_1(X1),X2) = singleton(X2)
| esk5_1(X1) = singleton(esk4_1(X1))
| ~ in(X2,X1) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_23,negated_conjecture,
( esk5_1(esk1_0) = singleton(esk4_1(esk1_0))
| in(esk2_1(esk8_1(esk1_0)),esk1_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_17])]),c_0_18]),c_0_19]) ).
cnf(c_0_24,plain,
( relation_dom(esk8_1(X1)) = X1
| X2 != singleton(esk7_1(X1))
| esk5_1(X1) != esk6_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_25,negated_conjecture,
( apply(X1,esk2_1(X1)) != singleton(esk2_1(X1))
| ~ relation(X1)
| ~ function(X1)
| relation_dom(X1) != esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_26,negated_conjecture,
( apply(esk8_1(esk1_0),esk2_1(esk8_1(esk1_0))) = singleton(esk2_1(esk8_1(esk1_0)))
| esk6_1(esk1_0) = singleton(esk4_1(esk1_0)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,negated_conjecture,
( apply(esk8_1(esk1_0),esk2_1(esk8_1(esk1_0))) = singleton(esk2_1(esk8_1(esk1_0)))
| esk5_1(esk1_0) = singleton(esk4_1(esk1_0)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
( function(esk8_1(X1))
| X2 != singleton(esk7_1(X1))
| esk5_1(X1) != esk6_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_29,plain,
( relation(esk8_1(X1))
| X2 != singleton(esk7_1(X1))
| esk5_1(X1) != esk6_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_30,plain,
( apply(esk8_1(X2),X1) = singleton(X1)
| ~ in(X1,X2)
| X3 != singleton(esk7_1(X2))
| esk5_1(X2) != esk6_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_31,plain,
( relation_dom(esk8_1(X1)) = X1
| esk6_1(X1) != esk5_1(X1) ),
inference(er,[status(thm)],[c_0_24]) ).
cnf(c_0_32,negated_conjecture,
esk6_1(esk1_0) = singleton(esk4_1(esk1_0)),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_14]),c_0_15]),c_0_13]) ).
cnf(c_0_33,negated_conjecture,
esk5_1(esk1_0) = singleton(esk4_1(esk1_0)),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_27]),c_0_18]),c_0_19]),c_0_17]) ).
cnf(c_0_34,plain,
( function(esk8_1(X1))
| esk6_1(X1) != esk5_1(X1) ),
inference(er,[status(thm)],[c_0_28]) ).
cnf(c_0_35,plain,
( relation(esk8_1(X1))
| esk6_1(X1) != esk5_1(X1) ),
inference(er,[status(thm)],[c_0_29]) ).
cnf(c_0_36,plain,
( apply(esk8_1(X1),X2) = singleton(X2)
| esk6_1(X1) != esk5_1(X1)
| ~ in(X2,X1) ),
inference(er,[status(thm)],[c_0_30]) ).
cnf(c_0_37,negated_conjecture,
relation_dom(esk8_1(esk1_0)) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_38,negated_conjecture,
function(esk8_1(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_32]),c_0_33])]) ).
cnf(c_0_39,negated_conjecture,
relation(esk8_1(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_32]),c_0_33])]) ).
cnf(c_0_40,negated_conjecture,
( apply(esk8_1(esk1_0),X1) = singleton(X1)
| ~ in(X1,esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_32]),c_0_33])]) ).
cnf(c_0_41,negated_conjecture,
in(esk2_1(esk8_1(esk1_0)),esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_37]),c_0_38]),c_0_39])]) ).
cnf(c_0_42,negated_conjecture,
apply(esk8_1(esk1_0),esk2_1(esk8_1(esk1_0))) = singleton(esk2_1(esk8_1(esk1_0))),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_42]),c_0_37]),c_0_38]),c_0_39])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU284+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n009.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % 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 20:09:36 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.20/0.60 % Version : CSE_E---1.5
% 0.20/0.60 % Problem : theBenchmark.p
% 0.20/0.60 % Proof found
% 0.20/0.60 % SZS status Theorem for theBenchmark.p
% 0.20/0.60 % SZS output start Proof
% See solution above
% 0.20/0.61 % Total time : 0.027000 s
% 0.20/0.61 % SZS output end Proof
% 0.20/0.61 % Total time : 0.030000 s
%------------------------------------------------------------------------------