TSTP Solution File: SET635+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET635+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 : n004.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 14:34:59 EDT 2023
% Result : Theorem 0.21s 0.64s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 20
% Syntax : Number of formulae : 42 ( 26 unt; 13 typ; 0 def)
% Number of atoms : 34 ( 26 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 3 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 9 >; 7 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn; 30 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
intersection: ( $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,
union: ( $i * $i ) > $i ).
tff(decl_27,type,
member: ( $i * $i ) > $o ).
tff(decl_28,type,
empty: $i > $o ).
tff(decl_29,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_30,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_31,type,
esk3_1: $i > $i ).
tff(decl_32,type,
esk4_0: $i ).
tff(decl_33,type,
esk5_0: $i ).
tff(decl_34,type,
esk6_0: $i ).
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(reflexivity_of_subset,axiom,
! [X1] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
fof(difference_and_intersection_and_union,axiom,
! [X1,X2,X3] : difference(X1,intersection(X2,X3)) = union(difference(X1,X2),difference(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_and_intersection_and_union) ).
fof(union_empty_set,axiom,
! [X1] : union(X1,empty_set) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_empty_set) ).
fof(prove_th117,conjecture,
! [X1,X2,X3] : intersection(X1,difference(X2,X3)) = difference(intersection(X1,X2),intersection(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th117) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(difference_and_intersection,axiom,
! [X1,X2,X3] : intersection(X1,difference(X2,X3)) = difference(intersection(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_and_intersection) ).
fof(c_0_7,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_8,plain,
! [X34] : subset(X34,X34),
inference(variable_rename,[status(thm)],[reflexivity_of_subset]) ).
fof(c_0_9,plain,
! [X9,X10,X11] : difference(X9,intersection(X10,X11)) = union(difference(X9,X10),difference(X9,X11)),
inference(variable_rename,[status(thm)],[difference_and_intersection_and_union]) ).
cnf(c_0_10,plain,
( difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X8] : union(X8,empty_set) = X8,
inference(variable_rename,[status(thm)],[union_empty_set]) ).
fof(c_0_13,negated_conjecture,
~ ! [X1,X2,X3] : intersection(X1,difference(X2,X3)) = difference(intersection(X1,X2),intersection(X1,X3)),
inference(assume_negation,[status(cth)],[prove_th117]) ).
cnf(c_0_14,plain,
difference(X1,intersection(X2,X3)) = union(difference(X1,X2),difference(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
difference(X1,X1) = empty_set,
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
union(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,plain,
! [X26,X27] : intersection(X26,X27) = intersection(X27,X26),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
fof(c_0_18,negated_conjecture,
intersection(esk4_0,difference(esk5_0,esk6_0)) != difference(intersection(esk4_0,esk5_0),intersection(esk4_0,esk6_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_19,plain,
! [X12,X13,X14] : intersection(X12,difference(X13,X14)) = difference(intersection(X12,X13),X14),
inference(variable_rename,[status(thm)],[difference_and_intersection]) ).
cnf(c_0_20,plain,
difference(X1,intersection(X2,X1)) = difference(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_21,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
intersection(esk4_0,difference(esk5_0,esk6_0)) != difference(intersection(esk4_0,esk5_0),intersection(esk4_0,esk6_0)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
intersection(X1,difference(X2,X3)) = difference(intersection(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
difference(X1,intersection(X1,X2)) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
difference(X1,intersection(intersection(X2,X1),X3)) = difference(X1,intersection(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_20]),c_0_14]) ).
cnf(c_0_26,negated_conjecture,
intersection(esk4_0,difference(esk5_0,intersection(esk4_0,esk6_0))) != intersection(esk4_0,difference(esk5_0,esk6_0)),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
intersection(X1,difference(X2,intersection(X1,X3))) = intersection(X1,difference(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_23]),c_0_25]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET635+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
% 0.14/0.34 % Computer : n004.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 12:22:08 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.61 start to proof: theBenchmark
% 0.21/0.64 % Version : CSE_E---1.5
% 0.21/0.64 % Problem : theBenchmark.p
% 0.21/0.64 % Proof found
% 0.21/0.64 % SZS status Theorem for theBenchmark.p
% 0.21/0.64 % SZS output start Proof
% See solution above
% 0.21/0.65 % Total time : 0.020000 s
% 0.21/0.65 % SZS output end Proof
% 0.21/0.65 % Total time : 0.023000 s
%------------------------------------------------------------------------------