TSTP Solution File: SET636+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET636+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 : n026.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 0.66s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 20
% Syntax : Number of formulae : 61 ( 8 unt; 13 typ; 0 def)
% Number of atoms : 122 ( 18 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 128 ( 54 ~; 52 |; 12 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 10 >; 8 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 87 ( 4 sgn; 42 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
intersection: ( $i * $i ) > $i ).
tff(decl_23,type,
member: ( $i * $i ) > $o ).
tff(decl_24,type,
intersect: ( $i * $i ) > $o ).
tff(decl_25,type,
empty_set: $i ).
tff(decl_26,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_27,type,
subset: ( $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_2: ( $i * $i ) > $i ).
tff(decl_33,type,
esk5_0: $i ).
tff(decl_34,type,
esk6_0: $i ).
fof(empty_defn,axiom,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_defn) ).
fof(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_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(intersect_defn,axiom,
! [X1,X2] :
( intersect(X1,X2)
<=> ? [X3] :
( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).
fof(disjoint_defn,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> ~ intersect(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint_defn) ).
fof(prove_th118,conjecture,
! [X1,X2] :
( disjoint(X1,X2)
<=> intersection(X1,X2) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th118) ).
fof(c_0_7,plain,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
inference(fof_simplification,[status(thm)],[empty_defn]) ).
fof(c_0_8,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
fof(c_0_9,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])])]) ).
fof(c_0_10,plain,
! [X29,X30,X31] :
( ( ~ empty(X29)
| ~ member(X30,X29) )
& ( member(esk3_1(X31),X31)
| empty(X31) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])]) ).
fof(c_0_11,plain,
! [X13] : ~ member(X13,empty_set),
inference(variable_rename,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X33,X34,X35,X36,X37,X38] :
( ( ~ member(X35,X33)
| member(X35,X34)
| X33 != X34 )
& ( ~ member(X36,X34)
| member(X36,X33)
| X33 != X34 )
& ( ~ member(esk4_2(X37,X38),X37)
| ~ member(esk4_2(X37,X38),X38)
| X37 = X38 )
& ( member(esk4_2(X37,X38),X37)
| member(esk4_2(X37,X38),X38)
| X37 = X38 ) ),
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])])])])])]) ).
fof(c_0_13,plain,
! [X7,X8,X10,X11,X12] :
( ( member(esk1_2(X7,X8),X7)
| ~ intersect(X7,X8) )
& ( member(esk1_2(X7,X8),X8)
| ~ intersect(X7,X8) )
& ( ~ member(X12,X10)
| ~ member(X12,X11)
| intersect(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)],[intersect_defn])])])])])]) ).
cnf(c_0_14,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( member(esk3_1(X1),X1)
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,plain,
! [X1,X2] :
( disjoint(X1,X2)
<=> ~ intersect(X1,X2) ),
inference(fof_simplification,[status(thm)],[disjoint_defn]) ).
fof(c_0_17,negated_conjecture,
~ ! [X1,X2] :
( disjoint(X1,X2)
<=> intersection(X1,X2) = empty_set ),
inference(assume_negation,[status(cth)],[prove_th118]) ).
cnf(c_0_18,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
( member(esk4_2(X1,X2),X1)
| member(esk4_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
( intersect(X2,X3)
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( empty(intersection(X1,X2))
| member(esk3_1(intersection(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_23,plain,
! [X14,X15] :
( ( ~ disjoint(X14,X15)
| ~ intersect(X14,X15) )
& ( intersect(X14,X15)
| disjoint(X14,X15) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])]) ).
fof(c_0_24,negated_conjecture,
( ( ~ disjoint(esk5_0,esk6_0)
| intersection(esk5_0,esk6_0) != empty_set )
& ( disjoint(esk5_0,esk6_0)
| intersection(esk5_0,esk6_0) = empty_set ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).
cnf(c_0_25,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_26,plain,
( empty_set = X1
| member(esk4_2(empty_set,X1),X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_27,plain,
( empty(intersection(X1,X2))
| intersect(X3,X2)
| ~ member(esk3_1(intersection(X1,X2)),X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,plain,
( empty(intersection(X1,X2))
| member(esk3_1(intersection(X1,X2)),X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_15]) ).
cnf(c_0_29,plain,
( ~ disjoint(X1,X2)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,negated_conjecture,
( disjoint(esk5_0,esk6_0)
| intersection(esk5_0,esk6_0) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
( empty_set = X1
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
( empty(intersection(X1,X2))
| intersect(X1,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_34,negated_conjecture,
( intersection(esk5_0,esk6_0) = empty_set
| ~ intersect(esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
( intersection(X1,X2) = empty_set
| intersect(X1,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
( ~ empty(intersection(X1,X2))
| ~ member(X3,X2)
| ~ member(X3,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
intersection(esk5_0,esk6_0) = empty_set,
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,plain,
empty(empty_set),
inference(spm,[status(thm)],[c_0_18,c_0_15]) ).
cnf(c_0_39,negated_conjecture,
( ~ disjoint(esk5_0,esk6_0)
| intersection(esk5_0,esk6_0) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_40,plain,
( intersect(X1,X2)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_41,negated_conjecture,
( ~ member(X1,esk6_0)
| ~ member(X1,esk5_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]) ).
cnf(c_0_42,plain,
( member(esk1_2(X1,X2),X2)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_43,negated_conjecture,
( intersect(esk5_0,esk6_0)
| intersection(esk5_0,esk6_0) != empty_set ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,negated_conjecture,
( ~ intersect(X1,esk6_0)
| ~ member(esk1_2(X1,esk6_0),esk5_0) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_45,plain,
( member(esk1_2(X1,X2),X1)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_46,negated_conjecture,
intersect(esk5_0,esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_37])]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET636+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 15:37:03 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.62 start to proof: theBenchmark
% 0.21/0.66 % Version : CSE_E---1.5
% 0.21/0.66 % Problem : theBenchmark.p
% 0.21/0.66 % Proof found
% 0.21/0.66 % SZS status Theorem for theBenchmark.p
% 0.21/0.66 % SZS output start Proof
% See solution above
% 0.21/0.67 % Total time : 0.030000 s
% 0.21/0.67 % SZS output end Proof
% 0.21/0.67 % Total time : 0.033000 s
%------------------------------------------------------------------------------