TSTP Solution File: SET002+3 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET002+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 : n001.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 14:31:56 EDT 2023
% Result : Theorem 0.19s 0.58s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 9
% Syntax : Number of formulae : 17 ( 8 unt; 6 typ; 0 def)
% Number of atoms : 14 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 5 >; 5 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn; 8 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
subset: ( $i * $i ) > $o ).
tff(decl_23,type,
union: ( $i * $i ) > $i ).
tff(decl_24,type,
member: ( $i * $i ) > $o ).
tff(decl_25,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_26,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_27,type,
esk3_0: $i ).
fof(prove_idempotency_of_union,conjecture,
! [X1] : union(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_idempotency_of_union) ).
fof(subset_union,axiom,
! [X1,X2] :
( subset(X1,X2)
=> union(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_union) ).
fof(reflexivity_of_subset,axiom,
! [X1] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
fof(c_0_3,negated_conjecture,
~ ! [X1] : union(X1,X1) = X1,
inference(assume_negation,[status(cth)],[prove_idempotency_of_union]) ).
fof(c_0_4,negated_conjecture,
union(esk3_0,esk3_0) != esk3_0,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
fof(c_0_5,plain,
! [X4,X5] :
( ~ subset(X4,X5)
| union(X4,X5) = X5 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subset_union])]) ).
fof(c_0_6,plain,
! [X19] : subset(X19,X19),
inference(variable_rename,[status(thm)],[reflexivity_of_subset]) ).
cnf(c_0_7,negated_conjecture,
union(esk3_0,esk3_0) != esk3_0,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
( union(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
subset(X1,X1),
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
% 0.00/0.12 % Problem : SET002+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.34 % Computer : n001.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Sat Aug 26 09:30:30 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 0.19/0.58 % Version : CSE_E---1.5
% 0.19/0.58 % Problem : theBenchmark.p
% 0.19/0.58 % Proof found
% 0.19/0.58 % SZS status Theorem for theBenchmark.p
% 0.19/0.58 % SZS output start Proof
% See solution above
% 0.19/0.58 % Total time : 0.007000 s
% 0.19/0.58 % SZS output end Proof
% 0.19/0.58 % Total time : 0.009000 s
%------------------------------------------------------------------------------