TSTP Solution File: SET201+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET201+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 : n025.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 14:33:36 EDT 2023
% Result : Theorem 0.19s 0.75s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 42 ( 10 unt; 9 typ; 0 def)
% Number of atoms : 74 ( 3 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 66 ( 25 ~; 27 |; 9 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 64 ( 6 sgn; 26 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
intersection: ( $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_2: ( $i * $i ) > $i ).
tff(decl_27,type,
esk3_0: $i ).
tff(decl_28,type,
esk4_0: $i ).
tff(decl_29,type,
esk5_0: $i ).
tff(decl_30,type,
esk6_0: $i ).
fof(prove_th41,conjecture,
! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(intersection(X1,X3),intersection(X2,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th41) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(intersection_defn,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(intersection(X1,X3),intersection(X2,X4)) ),
inference(assume_negation,[status(cth)],[prove_th41]) ).
fof(c_0_5,plain,
! [X8,X9,X10,X11,X12] :
( ( ~ subset(X8,X9)
| ~ member(X10,X8)
| member(X10,X9) )
& ( member(esk1_2(X11,X12),X11)
| subset(X11,X12) )
& ( ~ member(esk1_2(X11,X12),X12)
| subset(X11,X12) ) ),
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_6,negated_conjecture,
( subset(esk3_0,esk4_0)
& subset(esk5_0,esk6_0)
& ~ subset(intersection(esk3_0,esk5_0),intersection(esk4_0,esk6_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
cnf(c_0_7,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
subset(esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X5,X6,X7] :
( ( member(X7,X5)
| ~ member(X7,intersection(X5,X6)) )
& ( member(X7,X6)
| ~ member(X7,intersection(X5,X6)) )
& ( ~ member(X7,X5)
| ~ member(X7,X6)
| member(X7,intersection(X5,X6)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])]) ).
cnf(c_0_10,negated_conjecture,
subset(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,negated_conjecture,
( member(X1,esk6_0)
| ~ member(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_13,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_15,negated_conjecture,
( member(X1,esk4_0)
| ~ member(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_7,c_0_10]) ).
cnf(c_0_16,negated_conjecture,
( subset(X1,esk6_0)
| ~ member(esk1_2(X1,esk6_0),esk5_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
( subset(intersection(X1,X2),X3)
| member(esk1_2(intersection(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( subset(X1,esk4_0)
| ~ member(esk1_2(X1,esk4_0),esk3_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_15]) ).
fof(c_0_19,plain,
! [X14,X15] : intersection(X14,X15) = intersection(X15,X14),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_20,negated_conjecture,
subset(intersection(X1,esk5_0),esk6_0),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
subset(intersection(X1,esk3_0),esk4_0),
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_22,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_24,negated_conjecture,
( member(X1,esk6_0)
| ~ member(X1,intersection(X2,esk5_0)) ),
inference(spm,[status(thm)],[c_0_7,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
subset(intersection(esk3_0,X1),esk4_0),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
( subset(X1,intersection(X2,X3))
| ~ member(esk1_2(X1,intersection(X2,X3)),X3)
| ~ member(esk1_2(X1,intersection(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_23]) ).
cnf(c_0_27,negated_conjecture,
( subset(intersection(X1,esk5_0),X2)
| member(esk1_2(intersection(X1,esk5_0),X2),esk6_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_14]) ).
cnf(c_0_28,negated_conjecture,
( member(X1,esk4_0)
| ~ member(X1,intersection(esk3_0,X2)) ),
inference(spm,[status(thm)],[c_0_7,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
( subset(intersection(X1,esk5_0),intersection(X2,esk6_0))
| ~ member(esk1_2(intersection(X1,esk5_0),intersection(X2,esk6_0)),X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
( subset(intersection(esk3_0,X1),X2)
| member(esk1_2(intersection(esk3_0,X1),X2),esk4_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_14]) ).
cnf(c_0_31,negated_conjecture,
~ subset(intersection(esk3_0,esk5_0),intersection(esk4_0,esk6_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET201+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 08:58:37 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.59 start to proof: theBenchmark
% 0.19/0.75 % Version : CSE_E---1.5
% 0.19/0.75 % Problem : theBenchmark.p
% 0.19/0.75 % Proof found
% 0.19/0.75 % SZS status Theorem for theBenchmark.p
% 0.19/0.75 % SZS output start Proof
% See solution above
% 0.19/0.75 % Total time : 0.153000 s
% 0.19/0.75 % SZS output end Proof
% 0.19/0.75 % Total time : 0.156000 s
%------------------------------------------------------------------------------