TSTP Solution File: SET589+3 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET589+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n032.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 14:34:39 EDT 2023
% Result : Theorem 0.17s 0.54s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 12
% Syntax : Number of formulae : 26 ( 4 unt; 8 typ; 0 def)
% Number of atoms : 40 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 37 ( 15 ~; 12 |; 5 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 4 >; 4 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn; 26 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
subset: ( $i * $i ) > $o ).
tff(decl_23,type,
difference: ( $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_0: $i ).
tff(decl_27,type,
esk3_0: $i ).
tff(decl_28,type,
esk4_0: $i ).
tff(decl_29,type,
esk5_0: $i ).
fof(transitivity_of_subset,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_subset) ).
fof(difference_subset2,axiom,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(difference(X3,X2),difference(X3,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_subset2) ).
fof(prove_th48,conjecture,
! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(difference(X1,X4),difference(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th48) ).
fof(difference_subset1,axiom,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(difference(X1,X3),difference(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_subset1) ).
fof(c_0_4,plain,
! [X5,X6,X7] :
( ~ subset(X5,X6)
| ~ subset(X6,X7)
| subset(X5,X7) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[transitivity_of_subset])]) ).
fof(c_0_5,plain,
! [X11,X12,X13] :
( ~ subset(X11,X12)
| subset(difference(X13,X12),difference(X13,X11)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[difference_subset2])]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(difference(X1,X4),difference(X2,X3)) ),
inference(assume_negation,[status(cth)],[prove_th48]) ).
cnf(c_0_7,plain,
( subset(X1,X3)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
( subset(difference(X3,X2),difference(X3,X1))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_9,plain,
! [X8,X9,X10] :
( ~ subset(X8,X9)
| subset(difference(X8,X10),difference(X9,X10)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[difference_subset1])]) ).
fof(c_0_10,negated_conjecture,
( subset(esk2_0,esk3_0)
& subset(esk4_0,esk5_0)
& ~ subset(difference(esk2_0,esk5_0),difference(esk3_0,esk4_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
cnf(c_0_11,plain,
( subset(X1,difference(X2,X3))
| ~ subset(X1,difference(X2,X4))
| ~ subset(X3,X4) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,plain,
( subset(difference(X1,X3),difference(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,negated_conjecture,
~ subset(difference(esk2_0,esk5_0),difference(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( subset(difference(X1,X2),difference(X3,X4))
| ~ subset(X4,X2)
| ~ subset(X1,X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,negated_conjecture,
subset(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
subset(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET589+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.11 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Sat Aug 26 12:21:43 EDT 2023
% 0.11/0.31 % CPUTime :
% 0.17/0.49 start to proof: theBenchmark
% 0.17/0.54 % Version : CSE_E---1.5
% 0.17/0.54 % Problem : theBenchmark.p
% 0.17/0.54 % Proof found
% 0.17/0.54 % SZS status Theorem for theBenchmark.p
% 0.17/0.54 % SZS output start Proof
% See solution above
% 0.17/0.54 % Total time : 0.037000 s
% 0.17/0.54 % SZS output end Proof
% 0.17/0.54 % Total time : 0.038000 s
%------------------------------------------------------------------------------