TSTP Solution File: SET881+1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET881+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n007.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 14:36:07 EDT 2023
% Result : Theorem 0.21s 0.59s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 14
% Syntax : Number of formulae : 24 ( 7 unt; 11 typ; 0 def)
% Number of atoms : 42 ( 28 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 47 ( 18 ~; 20 |; 6 &)
% ( 3 <=>; 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 : 11 ( 6 >; 5 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 30 ( 3 sgn; 20 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_24,type,
empty_set: $i ).
tff(decl_25,type,
empty: $i > $o ).
tff(decl_26,type,
singleton: $i > $i ).
tff(decl_27,type,
set_difference: ( $i * $i ) > $i ).
tff(decl_28,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_29,type,
esk2_0: $i ).
tff(decl_30,type,
esk3_0: $i ).
tff(decl_31,type,
esk4_0: $i ).
tff(decl_32,type,
esk5_0: $i ).
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(t22_zfmisc_1,conjecture,
! [X1,X2] : set_difference(singleton(X1),unordered_pair(X1,X2)) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_zfmisc_1) ).
fof(l36_zfmisc_1,axiom,
! [X1,X2] :
( set_difference(singleton(X1),X2) = empty_set
<=> in(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l36_zfmisc_1) ).
fof(c_0_3,plain,
! [X9,X10,X11,X12,X13,X14,X15,X16] :
( ( ~ in(X12,X11)
| X12 = X9
| X12 = X10
| X11 != unordered_pair(X9,X10) )
& ( X13 != X9
| in(X13,X11)
| X11 != unordered_pair(X9,X10) )
& ( X13 != X10
| in(X13,X11)
| X11 != unordered_pair(X9,X10) )
& ( esk1_3(X14,X15,X16) != X14
| ~ in(esk1_3(X14,X15,X16),X16)
| X16 = unordered_pair(X14,X15) )
& ( esk1_3(X14,X15,X16) != X15
| ~ in(esk1_3(X14,X15,X16),X16)
| X16 = unordered_pair(X14,X15) )
& ( in(esk1_3(X14,X15,X16),X16)
| esk1_3(X14,X15,X16) = X14
| esk1_3(X14,X15,X16) = X15
| X16 = unordered_pair(X14,X15) ) ),
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)],[d2_tarski])])])])])]) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2] : set_difference(singleton(X1),unordered_pair(X1,X2)) = empty_set,
inference(assume_negation,[status(cth)],[t22_zfmisc_1]) ).
fof(c_0_5,plain,
! [X18,X19] :
( ( set_difference(singleton(X18),X19) != empty_set
| in(X18,X19) )
& ( ~ in(X18,X19)
| set_difference(singleton(X18),X19) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l36_zfmisc_1])]) ).
cnf(c_0_6,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
fof(c_0_7,negated_conjecture,
set_difference(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)) != empty_set,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
cnf(c_0_8,plain,
( set_difference(singleton(X1),X2) = empty_set
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
in(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_6])]) ).
cnf(c_0_10,negated_conjecture,
set_difference(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
set_difference(singleton(X1),unordered_pair(X1,X2)) = empty_set,
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET881+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n007.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 11:57:11 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 0.21/0.59 % Version : CSE_E---1.5
% 0.21/0.59 % Problem : theBenchmark.p
% 0.21/0.59 % Proof found
% 0.21/0.59 % SZS status Theorem for theBenchmark.p
% 0.21/0.59 % SZS output start Proof
% See solution above
% 0.21/0.59 % Total time : 0.004000 s
% 0.21/0.59 % SZS output end Proof
% 0.21/0.59 % Total time : 0.006000 s
%------------------------------------------------------------------------------