TSTP Solution File: SET009+3 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET009+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 : n012.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 14:31:59 EDT 2023
% Result : Theorem 0.14s 0.50s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 31 ( 4 unt; 7 typ; 0 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 59 ( 23 ~; 23 |; 7 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 55 ( 2 sgn; 23 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
difference: ( $i * $i ) > $i ).
tff(decl_23,type,
member: ( $i * $i ) > $o ).
tff(decl_24,type,
subset: ( $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 ).
fof(difference_defn,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(prove_subset_difference,conjecture,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(difference(X3,X2),difference(X3,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_subset_difference) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(c_0_3,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[difference_defn]) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3] :
( subset(X1,X2)
=> subset(difference(X3,X2),difference(X3,X1)) ),
inference(assume_negation,[status(cth)],[prove_subset_difference]) ).
fof(c_0_5,plain,
! [X4,X5,X6] :
( ( member(X6,X4)
| ~ member(X6,difference(X4,X5)) )
& ( ~ member(X6,X5)
| ~ member(X6,difference(X4,X5)) )
& ( ~ member(X6,X4)
| member(X6,X5)
| member(X6,difference(X4,X5)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
fof(c_0_6,plain,
! [X7,X8,X9,X10,X11] :
( ( ~ subset(X7,X8)
| ~ member(X9,X7)
| member(X9,X8) )
& ( member(esk1_2(X10,X11),X10)
| subset(X10,X11) )
& ( ~ member(esk1_2(X10,X11),X11)
| subset(X10,X11) ) ),
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)],[subset_defn])])])])])]) ).
fof(c_0_7,negated_conjecture,
( subset(esk2_0,esk3_0)
& ~ subset(difference(esk4_0,esk3_0),difference(esk4_0,esk2_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
cnf(c_0_8,plain,
( ~ member(X1,X2)
| ~ member(X1,difference(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
subset(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,plain,
( member(X1,X3)
| member(X1,difference(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_14,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_15,plain,
( subset(difference(X1,X2),X3)
| ~ member(esk1_2(difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_16,negated_conjecture,
( member(X1,esk3_0)
| ~ member(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_17,plain,
( subset(X1,difference(X2,X3))
| member(esk1_2(X1,difference(X2,X3)),X3)
| ~ member(esk1_2(X1,difference(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,plain,
( subset(difference(X1,X2),X3)
| member(esk1_2(difference(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_9]) ).
cnf(c_0_19,negated_conjecture,
( subset(difference(X1,esk3_0),X2)
| ~ member(esk1_2(difference(X1,esk3_0),X2),esk2_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
( subset(difference(X1,X2),difference(X1,X3))
| member(esk1_2(difference(X1,X2),difference(X1,X3)),X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
~ subset(difference(esk4_0,esk3_0),difference(esk4_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_22,negated_conjecture,
subset(difference(X1,esk3_0),difference(X1,esk2_0)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET009+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.10 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.09/0.30 % Computer : n012.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Sat Aug 26 16:22:25 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.14/0.48 start to proof: theBenchmark
% 0.14/0.50 % Version : CSE_E---1.5
% 0.14/0.50 % Problem : theBenchmark.p
% 0.14/0.50 % Proof found
% 0.14/0.50 % SZS status Theorem for theBenchmark.p
% 0.14/0.50 % SZS output start Proof
% See solution above
% 0.14/0.50 % Total time : 0.011000 s
% 0.14/0.50 % SZS output end Proof
% 0.14/0.50 % Total time : 0.012000 s
%------------------------------------------------------------------------------