TSTP Solution File: SET890+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET890+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n029.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 14:36:09 EDT 2023
% Result : Theorem 0.21s 0.73s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of formulae : 35 ( 7 unt; 13 typ; 0 def)
% Number of atoms : 75 ( 36 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 82 ( 29 ~; 40 |; 9 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 10 >; 8 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 47 ( 0 sgn; 22 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
subset: ( $i * $i ) > $o ).
tff(decl_24,type,
singleton: $i > $i ).
tff(decl_25,type,
union: $i > $i ).
tff(decl_26,type,
empty: $i > $o ).
tff(decl_27,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_28,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_29,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_30,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_31,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_32,type,
esk6_0: $i ).
tff(decl_33,type,
esk7_0: $i ).
tff(decl_34,type,
esk8_0: $i ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(d4_tarski,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
fof(t31_zfmisc_1,conjecture,
! [X1] : union(singleton(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_zfmisc_1) ).
fof(c_0_3,plain,
! [X9,X10,X11,X12,X13,X14] :
( ( ~ in(X11,X10)
| X11 = X9
| X10 != singleton(X9) )
& ( X12 != X9
| in(X12,X10)
| X10 != singleton(X9) )
& ( ~ in(esk1_2(X13,X14),X14)
| esk1_2(X13,X14) != X13
| X14 = singleton(X13) )
& ( in(esk1_2(X13,X14),X14)
| esk1_2(X13,X14) = X13
| X14 = singleton(X13) ) ),
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_tarski])])])])])]) ).
fof(c_0_4,plain,
! [X22,X23,X24,X26,X27,X28,X29,X31] :
( ( in(X24,esk3_3(X22,X23,X24))
| ~ in(X24,X23)
| X23 != union(X22) )
& ( in(esk3_3(X22,X23,X24),X22)
| ~ in(X24,X23)
| X23 != union(X22) )
& ( ~ in(X26,X27)
| ~ in(X27,X22)
| in(X26,X23)
| X23 != union(X22) )
& ( ~ in(esk4_2(X28,X29),X29)
| ~ in(esk4_2(X28,X29),X31)
| ~ in(X31,X28)
| X29 = union(X28) )
& ( in(esk4_2(X28,X29),esk5_2(X28,X29))
| in(esk4_2(X28,X29),X29)
| X29 = union(X28) )
& ( in(esk5_2(X28,X29),X28)
| in(esk4_2(X28,X29),X29)
| X29 = union(X28) ) ),
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_tarski])])])])])]) ).
cnf(c_0_5,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_6,plain,
( X2 = union(X1)
| ~ in(esk4_2(X1,X2),X2)
| ~ in(esk4_2(X1,X2),X3)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
( in(esk5_2(X1,X2),X1)
| in(esk4_2(X1,X2),X2)
| X2 = union(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
( in(X1,X2)
| X2 != singleton(X1) ),
inference(er,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_10,plain,
( X1 = union(X2)
| in(esk5_2(X2,X1),X2)
| ~ in(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_7]) ).
cnf(c_0_11,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( union(singleton(X1)) = X1
| in(esk5_2(singleton(X1),X1),singleton(X1)) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
fof(c_0_14,negated_conjecture,
~ ! [X1] : union(singleton(X1)) = X1,
inference(assume_negation,[status(cth)],[t31_zfmisc_1]) ).
cnf(c_0_15,plain,
( in(esk4_2(X1,X2),esk5_2(X1,X2))
| in(esk4_2(X1,X2),X2)
| X2 = union(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_16,plain,
( esk5_2(singleton(X1),X1) = X1
| union(singleton(X1)) = X1 ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_17,negated_conjecture,
union(singleton(esk8_0)) != esk8_0,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
cnf(c_0_18,plain,
( union(singleton(X1)) = X1
| in(esk4_2(singleton(X1),X1),X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
union(singleton(esk8_0)) != esk8_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_20,plain,
union(singleton(X1)) = X1,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_18]),c_0_11])]),c_0_18]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET890+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n029.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 : Sat Aug 26 16:39:40 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 0.21/0.73 % Version : CSE_E---1.5
% 0.21/0.73 % Problem : theBenchmark.p
% 0.21/0.73 % Proof found
% 0.21/0.73 % SZS status Theorem for theBenchmark.p
% 0.21/0.73 % SZS output start Proof
% See solution above
% 0.21/0.74 % Total time : 0.137000 s
% 0.21/0.74 % SZS output end Proof
% 0.21/0.74 % Total time : 0.141000 s
%------------------------------------------------------------------------------