TSTP Solution File: SET600+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET600+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 : n021.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 14:34:44 EDT 2023
% Result : Theorem 0.22s 0.59s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 17
% Syntax : Number of formulae : 51 ( 12 unt; 10 typ; 0 def)
% Number of atoms : 111 ( 47 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 108 ( 38 ~; 48 |; 14 &)
% ( 7 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 7 >; 5 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 66 ( 8 sgn; 38 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
union: ( $i * $i ) > $i ).
tff(decl_23,type,
member: ( $i * $i ) > $o ).
tff(decl_24,type,
empty_set: $i ).
tff(decl_25,type,
subset: ( $i * $i ) > $o ).
tff(decl_26,type,
empty: $i > $o ).
tff(decl_27,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_28,type,
esk2_1: $i > $i ).
tff(decl_29,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_30,type,
esk4_0: $i ).
tff(decl_31,type,
esk5_0: $i ).
fof(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(prove_th59,conjecture,
! [X1,X2] :
( union(X1,X2) = empty_set
<=> ( X1 = empty_set
& X2 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th59) ).
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(union_defn,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(equal_member_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(c_0_7,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2] :
( union(X1,X2) = empty_set
<=> ( X1 = empty_set
& X2 = empty_set ) ),
inference(assume_negation,[status(cth)],[prove_th59]) ).
fof(c_0_9,plain,
! [X7] : ~ member(X7,empty_set),
inference(variable_rename,[status(thm)],[c_0_7]) ).
fof(c_0_10,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_11,plain,
! [X4,X5,X6] :
( ( ~ member(X6,union(X4,X5))
| member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X4)
| member(X6,union(X4,X5)) )
& ( ~ member(X6,X5)
| member(X6,union(X4,X5)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])]) ).
fof(c_0_12,negated_conjecture,
( ( union(esk4_0,esk5_0) != empty_set
| esk4_0 != empty_set
| esk5_0 != empty_set )
& ( esk4_0 = empty_set
| union(esk4_0,esk5_0) = empty_set )
& ( esk5_0 = empty_set
| union(esk4_0,esk5_0) = empty_set ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
fof(c_0_13,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_14,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
( esk5_0 = empty_set
| union(esk4_0,esk5_0) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_18,plain,
! [X23,X24,X25,X26,X27,X28] :
( ( ~ member(X25,X23)
| member(X25,X24)
| X23 != X24 )
& ( ~ member(X26,X24)
| member(X26,X23)
| X23 != X24 )
& ( ~ member(esk3_2(X27,X28),X27)
| ~ member(esk3_2(X27,X28),X28)
| X27 = X28 )
& ( member(esk3_2(X27,X28),X27)
| member(esk3_2(X27,X28),X28)
| X27 = X28 ) ),
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_19,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,negated_conjecture,
( esk5_0 = empty_set
| ~ member(X1,esk5_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_14]) ).
cnf(c_0_22,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_23,negated_conjecture,
( esk4_0 = empty_set
| union(esk4_0,esk5_0) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_24,plain,
( member(esk3_2(X1,X2),X1)
| member(esk3_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,negated_conjecture,
( esk5_0 = empty_set
| subset(esk5_0,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_15]) ).
fof(c_0_27,plain,
! [X10,X11] : union(X10,X11) = union(X11,X10),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_28,negated_conjecture,
( esk4_0 = empty_set
| ~ member(X1,esk4_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_14]) ).
cnf(c_0_29,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_30,plain,
( empty_set = X1
| member(esk3_2(empty_set,X1),X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_24]) ).
cnf(c_0_31,negated_conjecture,
( union(esk4_0,esk5_0) != empty_set
| esk4_0 != empty_set
| esk5_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_32,negated_conjecture,
esk5_0 = empty_set,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,negated_conjecture,
( esk4_0 = empty_set
| subset(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_15]) ).
cnf(c_0_35,plain,
( union(X1,X2) = empty_set
| member(esk3_2(empty_set,union(X1,X2)),X1)
| member(esk3_2(empty_set,union(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,negated_conjecture,
( union(empty_set,esk4_0) != empty_set
| esk4_0 != empty_set ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_32])]) ).
cnf(c_0_37,negated_conjecture,
esk4_0 = empty_set,
inference(spm,[status(thm)],[c_0_25,c_0_34]) ).
cnf(c_0_38,plain,
( union(X1,X1) = empty_set
| member(esk3_2(empty_set,union(X1,X1)),X1) ),
inference(ef,[status(thm)],[c_0_35]) ).
cnf(c_0_39,negated_conjecture,
union(empty_set,empty_set) != empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_37])]) ).
cnf(c_0_40,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_38]),c_0_39]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET600+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.36 % Computer : n021.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat Aug 26 09:40:26 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.57 start to proof: theBenchmark
% 0.22/0.59 % Version : CSE_E---1.5
% 0.22/0.59 % Problem : theBenchmark.p
% 0.22/0.59 % Proof found
% 0.22/0.59 % SZS status Theorem for theBenchmark.p
% 0.22/0.59 % SZS output start Proof
% See solution above
% 0.22/0.60 % Total time : 0.010000 s
% 0.22/0.60 % SZS output end Proof
% 0.22/0.60 % Total time : 0.012000 s
%------------------------------------------------------------------------------