TSTP Solution File: SET578+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET578+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 : 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 14:34:35 EDT 2023
% Result : Theorem 0.15s 0.57s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 57 ( 15 unt; 8 typ; 0 def)
% Number of atoms : 117 ( 13 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 109 ( 41 ~; 47 |; 13 &)
% ( 5 <=>; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 91 ( 10 sgn; 31 !; 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_th19,conjecture,
! [X1,X2,X3] :
( ! [X4] :
( member(X4,X1)
<=> ( member(X4,X2)
& member(X4,X3) ) )
=> X1 = intersection(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th19) ).
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(intersection_defn,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3] :
( ! [X4] :
( member(X4,X1)
<=> ( member(X4,X2)
& member(X4,X3) ) )
=> X1 = intersection(X2,X3) ),
inference(assume_negation,[status(cth)],[prove_th19]) ).
fof(c_0_6,plain,
! [X12,X13,X14,X15,X16] :
( ( ~ subset(X12,X13)
| ~ member(X14,X12)
| member(X14,X13) )
& ( member(esk1_2(X15,X16),X15)
| subset(X15,X16) )
& ( ~ member(esk1_2(X15,X16),X16)
| subset(X15,X16) ) ),
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,
! [X29] :
( ( member(X29,esk4_0)
| ~ member(X29,esk3_0) )
& ( member(X29,esk5_0)
| ~ member(X29,esk3_0) )
& ( ~ member(X29,esk4_0)
| ~ member(X29,esk5_0)
| member(X29,esk3_0) )
& esk3_0 != intersection(esk4_0,esk5_0) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])]) ).
fof(c_0_8,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_9,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
( member(X1,esk5_0)
| ~ member(X1,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,negated_conjecture,
( subset(X1,esk5_0)
| ~ member(esk1_2(X1,esk5_0),esk3_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
( subset(intersection(X1,X2),X3)
| member(esk1_2(intersection(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_15,plain,
! [X10,X11] : intersection(X10,X11) = intersection(X11,X10),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_16,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,negated_conjecture,
( member(X1,esk4_0)
| ~ member(X1,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_18,negated_conjecture,
subset(intersection(X1,esk3_0),esk5_0),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,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_9,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
( subset(X1,esk4_0)
| ~ member(esk1_2(X1,esk4_0),esk3_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_17]) ).
cnf(c_0_22,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_23,negated_conjecture,
subset(intersection(esk3_0,X1),esk5_0),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_24,plain,
! [X8,X9] :
( ( subset(X8,X9)
| X8 != X9 )
& ( subset(X9,X8)
| X8 != X9 )
& ( ~ subset(X8,X9)
| ~ subset(X9,X8)
| X8 = X9 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).
cnf(c_0_25,plain,
( subset(X1,intersection(X2,X1))
| ~ member(esk1_2(X1,intersection(X2,X1)),X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_12]) ).
cnf(c_0_26,plain,
subset(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_9,c_0_14]) ).
cnf(c_0_27,negated_conjecture,
subset(intersection(X1,esk3_0),esk4_0),
inference(spm,[status(thm)],[c_0_21,c_0_14]) ).
cnf(c_0_28,negated_conjecture,
( member(X1,esk5_0)
| ~ member(X1,intersection(esk3_0,X2)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
subset(X1,intersection(X1,X1)),
inference(spm,[status(thm)],[c_0_25,c_0_12]) ).
cnf(c_0_31,plain,
subset(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_26,c_0_19]) ).
cnf(c_0_32,negated_conjecture,
subset(intersection(esk3_0,X1),esk4_0),
inference(spm,[status(thm)],[c_0_27,c_0_19]) ).
cnf(c_0_33,negated_conjecture,
( subset(intersection(esk3_0,X1),X2)
| member(esk1_2(intersection(esk3_0,X1),X2),esk5_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_12]) ).
cnf(c_0_34,plain,
intersection(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
cnf(c_0_35,negated_conjecture,
( member(X1,esk4_0)
| ~ member(X1,intersection(esk3_0,X2)) ),
inference(spm,[status(thm)],[c_0_22,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
( subset(esk3_0,X1)
| member(esk1_2(esk3_0,X1),esk5_0) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
( subset(intersection(esk3_0,X1),X2)
| member(esk1_2(intersection(esk3_0,X1),X2),esk4_0) ),
inference(spm,[status(thm)],[c_0_35,c_0_12]) ).
cnf(c_0_38,negated_conjecture,
( member(X1,esk3_0)
| ~ member(X1,esk4_0)
| ~ member(X1,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_39,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_40,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_20,c_0_36]) ).
cnf(c_0_41,negated_conjecture,
( subset(esk3_0,X1)
| member(esk1_2(esk3_0,X1),esk4_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_34]) ).
cnf(c_0_42,negated_conjecture,
( subset(intersection(X1,esk5_0),X2)
| member(esk1_2(intersection(X1,esk5_0),X2),esk3_0)
| ~ member(esk1_2(intersection(X1,esk5_0),X2),esk4_0) ),
inference(spm,[status(thm)],[c_0_38,c_0_14]) ).
cnf(c_0_43,plain,
( subset(intersection(X1,X2),X3)
| member(esk1_2(intersection(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_12]) ).
cnf(c_0_44,negated_conjecture,
subset(esk3_0,intersection(esk4_0,esk5_0)),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,negated_conjecture,
esk3_0 != intersection(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_46,negated_conjecture,
( subset(intersection(esk4_0,esk5_0),X1)
| member(esk1_2(intersection(esk4_0,esk5_0),X1),esk3_0) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,negated_conjecture,
~ subset(intersection(esk4_0,esk5_0),esk3_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_44]),c_0_45]) ).
cnf(c_0_48,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_46]),c_0_47]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET578+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
% 0.13/0.29 % Computer : n032.cluster.edu
% 0.13/0.29 % Model : x86_64 x86_64
% 0.13/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.29 % Memory : 8042.1875MB
% 0.13/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.29 % CPULimit : 300
% 0.13/0.29 % WCLimit : 300
% 0.13/0.29 % DateTime : Sat Aug 26 10:51:43 EDT 2023
% 0.13/0.29 % CPUTime :
% 0.15/0.47 start to proof: theBenchmark
% 0.15/0.57 % Version : CSE_E---1.5
% 0.15/0.57 % Problem : theBenchmark.p
% 0.15/0.57 % Proof found
% 0.15/0.57 % SZS status Theorem for theBenchmark.p
% 0.15/0.57 % SZS output start Proof
% See solution above
% 0.15/0.57 % Total time : 0.086000 s
% 0.15/0.57 % SZS output end Proof
% 0.15/0.57 % Total time : 0.088000 s
%------------------------------------------------------------------------------