TSTP Solution File: SET199+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET199+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 : n006.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 14:33:35 EDT 2023
% Result : Theorem 0.24s 0.73s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 57 ( 13 unt; 8 typ; 0 def)
% Number of atoms : 117 ( 15 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 105 ( 37 ~; 49 |; 12 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 95 ( 8 sgn; 33 !; 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 ).
fof(prove_intersection_of_subsets,conjecture,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3) )
=> subset(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_intersection_of_subsets) ).
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(equal_member_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_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_5,negated_conjecture,
~ ! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3) )
=> subset(X1,intersection(X2,X3)) ),
inference(assume_negation,[status(cth)],[prove_intersection_of_subsets]) ).
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(esk3_0,esk4_0)
& subset(esk3_0,esk5_0)
& ~ subset(esk3_0,intersection(esk4_0,esk5_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_8,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
subset(esk3_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X4,X5,X6] :
( ( member(X6,X4)
| ~ member(X6,intersection(X4,X5)) )
& ( member(X6,X5)
| ~ member(X6,intersection(X4,X5)) )
& ( ~ member(X6,X4)
| ~ member(X6,X5)
| member(X6,intersection(X4,X5)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])]) ).
cnf(c_0_11,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,negated_conjecture,
( member(X1,esk5_0)
| ~ member(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_15,plain,
! [X16,X17,X18,X19,X20,X21] :
( ( ~ member(X18,X16)
| member(X18,X17)
| X16 != X17 )
& ( ~ member(X19,X17)
| member(X19,X16)
| X16 != X17 )
& ( ~ member(esk2_2(X20,X21),X20)
| ~ member(esk2_2(X20,X21),X21)
| X20 = X21 )
& ( member(esk2_2(X20,X21),X20)
| member(esk2_2(X20,X21),X21)
| X20 = X21 ) ),
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)],[equal_member_defn])])])])])]) ).
cnf(c_0_16,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
subset(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_18,negated_conjecture,
( subset(X1,esk5_0)
| ~ member(esk1_2(X1,esk5_0),esk3_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_19,plain,
( subset(intersection(X1,X2),X3)
| member(esk1_2(intersection(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_20,plain,
! [X13,X14] : intersection(X13,X14) = intersection(X14,X13),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_21,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_22,plain,
( member(esk2_2(X1,X2),X1)
| member(esk2_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,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_16]) ).
cnf(c_0_24,negated_conjecture,
( member(X1,esk4_0)
| ~ member(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_8,c_0_17]) ).
cnf(c_0_25,negated_conjecture,
subset(intersection(X1,esk3_0),esk5_0),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
( intersection(X1,X2) = X3
| member(esk2_2(intersection(X1,X2),X3),X3)
| member(esk2_2(intersection(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,plain,
( subset(X1,intersection(X2,X1))
| ~ member(esk1_2(X1,intersection(X2,X1)),X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_14]) ).
cnf(c_0_29,negated_conjecture,
( subset(X1,esk4_0)
| ~ member(esk1_2(X1,esk4_0),esk3_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_24]) ).
cnf(c_0_30,negated_conjecture,
subset(intersection(esk3_0,X1),esk5_0),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,plain,
( X1 = X2
| ~ member(esk2_2(X1,X2),X1)
| ~ member(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_32,plain,
( intersection(X1,X2) = X1
| member(esk2_2(intersection(X1,X2),X1),X1) ),
inference(ef,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
subset(X1,intersection(X1,X1)),
inference(spm,[status(thm)],[c_0_28,c_0_14]) ).
cnf(c_0_34,negated_conjecture,
subset(intersection(X1,esk3_0),esk4_0),
inference(spm,[status(thm)],[c_0_29,c_0_19]) ).
cnf(c_0_35,negated_conjecture,
( member(X1,esk5_0)
| ~ member(X1,intersection(esk3_0,X2)) ),
inference(spm,[status(thm)],[c_0_8,c_0_30]) ).
cnf(c_0_36,plain,
( intersection(X1,X2) = X1
| ~ member(esk2_2(intersection(X1,X2),X1),intersection(X1,X2)) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,plain,
( member(X1,intersection(X2,X2))
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_8,c_0_33]) ).
cnf(c_0_38,plain,
( intersection(X1,X2) = X2
| member(esk2_2(intersection(X1,X2),X2),X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_26]) ).
cnf(c_0_39,negated_conjecture,
subset(intersection(esk3_0,X1),esk4_0),
inference(spm,[status(thm)],[c_0_34,c_0_26]) ).
cnf(c_0_40,negated_conjecture,
( subset(intersection(esk3_0,X1),X2)
| member(esk1_2(intersection(esk3_0,X1),X2),esk5_0) ),
inference(spm,[status(thm)],[c_0_35,c_0_14]) ).
cnf(c_0_41,plain,
intersection(X1,X1) = X1,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_42,negated_conjecture,
( member(X1,esk4_0)
| ~ member(X1,intersection(esk3_0,X2)) ),
inference(spm,[status(thm)],[c_0_8,c_0_39]) ).
cnf(c_0_43,negated_conjecture,
( subset(esk3_0,X1)
| member(esk1_2(esk3_0,X1),esk5_0) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_44,negated_conjecture,
( subset(intersection(esk3_0,X1),X2)
| member(esk1_2(intersection(esk3_0,X1),X2),esk4_0) ),
inference(spm,[status(thm)],[c_0_42,c_0_14]) ).
cnf(c_0_45,negated_conjecture,
( subset(esk3_0,intersection(X1,esk5_0))
| ~ member(esk1_2(esk3_0,intersection(X1,esk5_0)),X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_43]) ).
cnf(c_0_46,negated_conjecture,
( subset(esk3_0,X1)
| member(esk1_2(esk3_0,X1),esk4_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_41]) ).
cnf(c_0_47,negated_conjecture,
~ subset(esk3_0,intersection(esk4_0,esk5_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_48,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET199+3 : TPTP v8.1.2. Released v2.2.0.
% 0.14/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.38 % Computer : n006.cluster.edu
% 0.14/0.38 % Model : x86_64 x86_64
% 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38 % Memory : 8042.1875MB
% 0.14/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.38 % CPULimit : 300
% 0.14/0.38 % WCLimit : 300
% 0.14/0.38 % DateTime : Sat Aug 26 10:08:23 EDT 2023
% 0.14/0.39 % CPUTime :
% 0.24/0.66 start to proof: theBenchmark
% 0.24/0.72 % Version : CSE_E---1.5
% 0.24/0.72 % Problem : theBenchmark.p
% 0.24/0.73 % Proof found
% 0.24/0.73 % SZS status Theorem for theBenchmark.p
% 0.24/0.73 % SZS output start Proof
% See solution above
% 0.24/0.73 % Total time : 0.053000 s
% 0.24/0.73 % SZS output end Proof
% 0.24/0.73 % Total time : 0.057000 s
%------------------------------------------------------------------------------