TSTP Solution File: SET605+3 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET605+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n022.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 14:34:46 EDT 2023
% Result : Theorem 0.20s 0.59s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 14
% Syntax : Number of formulae : 22 ( 8 unt; 11 typ; 0 def)
% Number of atoms : 16 ( 8 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 11 ( 6 ~; 3 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 8 >; 6 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 1 sgn; 12 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
union: ( $i * $i ) > $i ).
tff(decl_23,type,
subset: ( $i * $i ) > $o ).
tff(decl_24,type,
difference: ( $i * $i ) > $i ).
tff(decl_25,type,
empty_set: $i ).
tff(decl_26,type,
member: ( $i * $i ) > $o ).
tff(decl_27,type,
empty: $i > $o ).
tff(decl_28,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_29,type,
esk2_1: $i > $i ).
tff(decl_30,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_31,type,
esk4_0: $i ).
tff(decl_32,type,
esk5_0: $i ).
fof(prove_th76,conjecture,
! [X1,X2] : difference(X1,union(X1,X2)) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th76) ).
fof(difference_empty_set,axiom,
! [X1,X2] :
( difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_empty_set) ).
fof(subset_of_union,axiom,
! [X1,X2] : subset(X1,union(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_of_union) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2] : difference(X1,union(X1,X2)) = empty_set,
inference(assume_negation,[status(cth)],[prove_th76]) ).
fof(c_0_4,negated_conjecture,
difference(esk4_0,union(esk4_0,esk5_0)) != empty_set,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
fof(c_0_5,plain,
! [X6,X7] :
( ( difference(X6,X7) != empty_set
| subset(X6,X7) )
& ( ~ subset(X6,X7)
| difference(X6,X7) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[difference_empty_set])]) ).
fof(c_0_6,plain,
! [X4,X5] : subset(X4,union(X4,X5)),
inference(variable_rename,[status(thm)],[subset_of_union]) ).
cnf(c_0_7,negated_conjecture,
difference(esk4_0,union(esk4_0,esk5_0)) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
( difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
subset(X1,union(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET605+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.16/0.35 % Computer : n022.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Sat Aug 26 14:52:10 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.20/0.59 % Version : CSE_E---1.5
% 0.20/0.59 % Problem : theBenchmark.p
% 0.20/0.59 % Proof found
% 0.20/0.59 % SZS status Theorem for theBenchmark.p
% 0.20/0.59 % SZS output start Proof
% See solution above
% 0.20/0.60 % Total time : 0.008000 s
% 0.20/0.60 % SZS output end Proof
% 0.20/0.60 % Total time : 0.011000 s
%------------------------------------------------------------------------------