TSTP Solution File: SEV517+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEV517+1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n018.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 19:21:14 EDT 2023
% Result : Theorem 1.26s 1.47s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 54
% Syntax : Number of formulae : 80 ( 10 unt; 50 typ; 0 def)
% Number of atoms : 180 ( 11 equ)
% Maximal formula atoms : 105 ( 6 avg)
% Number of connectives : 221 ( 71 ~; 101 |; 39 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 39 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 88 ( 45 >; 43 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 40 ( 40 usr; 5 con; 0-3 aty)
% Number of variables : 63 ( 2 sgn; 38 !; 4 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
subset: ( $i * $i ) > $o ).
tff(decl_23,type,
member: ( $i * $i ) > $o ).
tff(decl_24,type,
equal_set: ( $i * $i ) > $o ).
tff(decl_25,type,
power_set: $i > $i ).
tff(decl_26,type,
intersection: ( $i * $i ) > $i ).
tff(decl_27,type,
union: ( $i * $i ) > $i ).
tff(decl_28,type,
empty_set: $i ).
tff(decl_29,type,
difference: ( $i * $i ) > $i ).
tff(decl_30,type,
singleton: $i > $i ).
tff(decl_31,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_32,type,
sum: $i > $i ).
tff(decl_33,type,
product: $i > $i ).
tff(decl_34,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_35,type,
partition: ( $i * $i ) > $o ).
tff(decl_36,type,
equivalence: ( $i * $i ) > $o ).
tff(decl_37,type,
apply: ( $i * $i * $i ) > $o ).
tff(decl_38,type,
equivalence_class: ( $i * $i * $i ) > $i ).
tff(decl_39,type,
pre_order: ( $i * $i ) > $o ).
tff(decl_40,type,
non_overlapping: $i > $o ).
tff(decl_41,type,
insertIntoMember: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
unaryUnion: $i > $i ).
tff(decl_43,type,
epred1_2: ( $i * $i ) > $o ).
tff(decl_44,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_45,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_46,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_47,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_48,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_49,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_50,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_51,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_52,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_53,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_54,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_56,type,
esk13_2: ( $i * $i ) > $i ).
tff(decl_57,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_58,type,
esk15_1: $i > $i ).
tff(decl_59,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_60,type,
esk17_2: ( $i * $i ) > $i ).
tff(decl_61,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_62,type,
esk19_0: $i ).
tff(decl_63,type,
esk20_0: $i ).
tff(decl_64,type,
esk21_0: $i ).
tff(decl_65,type,
esk22_0: $i ).
tff(decl_66,type,
esk23_2: ( $i * $i ) > $i ).
tff(decl_67,type,
esk24_2: ( $i * $i ) > $i ).
tff(decl_68,type,
esk25_2: ( $i * $i ) > $i ).
tff(decl_69,type,
esk26_2: ( $i * $i ) > $i ).
tff(decl_70,type,
esk27_2: ( $i * $i ) > $i ).
tff(decl_71,type,
esk28_2: ( $i * $i ) > $i ).
fof(diff_elem_in_partition,conjecture,
! [X3,X1,X2,X11] :
( ( member(X3,difference(X1,X2))
& partition(X11,X1) )
=> ? [X12] :
( member(X12,difference(X11,singleton(X2)))
& member(X3,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diff_elem_in_partition) ).
fof(difference,axiom,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( member(X2,X4)
& ~ member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',difference) ).
fof(partition,axiom,
! [X1,X4] :
( partition(X1,X4)
<=> ( ! [X3] :
( member(X3,X1)
=> subset(X3,X4) )
& ! [X3] :
( member(X3,X4)
=> ? [X5] :
( member(X5,X1)
& member(X3,X5) ) )
& ! [X3,X5] :
( ( member(X3,X1)
& member(X5,X1) )
=> ( ? [X6] :
( member(X6,X3)
& member(X6,X5) )
=> X3 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+2.ax',partition) ).
fof(singleton,axiom,
! [X3,X1] :
( member(X3,singleton(X1))
<=> X3 = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',singleton) ).
fof(c_0_4,negated_conjecture,
~ ! [X3,X1,X2,X11] :
( ( member(X3,difference(X1,X2))
& partition(X11,X1) )
=> ? [X12] :
( member(X12,difference(X11,singleton(X2)))
& member(X3,X12) ) ),
inference(assume_negation,[status(cth)],[diff_elem_in_partition]) ).
fof(c_0_5,plain,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( member(X2,X4)
& ~ member(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[difference]) ).
fof(c_0_6,plain,
! [X56,X57,X58,X59,X61,X62,X63,X64,X65,X68] :
( ( ~ member(X58,X56)
| subset(X58,X57)
| ~ partition(X56,X57) )
& ( member(esk5_3(X56,X57,X59),X56)
| ~ member(X59,X57)
| ~ partition(X56,X57) )
& ( member(X59,esk5_3(X56,X57,X59))
| ~ member(X59,X57)
| ~ partition(X56,X57) )
& ( ~ member(X61,X56)
| ~ member(X62,X56)
| ~ member(X63,X61)
| ~ member(X63,X62)
| X61 = X62
| ~ partition(X56,X57) )
& ( member(esk8_2(X64,X65),X64)
| member(esk7_2(X64,X65),X65)
| member(esk6_2(X64,X65),X64)
| partition(X64,X65) )
& ( member(esk9_2(X64,X65),X64)
| member(esk7_2(X64,X65),X65)
| member(esk6_2(X64,X65),X64)
| partition(X64,X65) )
& ( member(esk10_2(X64,X65),esk8_2(X64,X65))
| member(esk7_2(X64,X65),X65)
| member(esk6_2(X64,X65),X64)
| partition(X64,X65) )
& ( member(esk10_2(X64,X65),esk9_2(X64,X65))
| member(esk7_2(X64,X65),X65)
| member(esk6_2(X64,X65),X64)
| partition(X64,X65) )
& ( esk8_2(X64,X65) != esk9_2(X64,X65)
| member(esk7_2(X64,X65),X65)
| member(esk6_2(X64,X65),X64)
| partition(X64,X65) )
& ( member(esk8_2(X64,X65),X64)
| ~ member(X68,X64)
| ~ member(esk7_2(X64,X65),X68)
| member(esk6_2(X64,X65),X64)
| partition(X64,X65) )
& ( member(esk9_2(X64,X65),X64)
| ~ member(X68,X64)
| ~ member(esk7_2(X64,X65),X68)
| member(esk6_2(X64,X65),X64)
| partition(X64,X65) )
& ( member(esk10_2(X64,X65),esk8_2(X64,X65))
| ~ member(X68,X64)
| ~ member(esk7_2(X64,X65),X68)
| member(esk6_2(X64,X65),X64)
| partition(X64,X65) )
& ( member(esk10_2(X64,X65),esk9_2(X64,X65))
| ~ member(X68,X64)
| ~ member(esk7_2(X64,X65),X68)
| member(esk6_2(X64,X65),X64)
| partition(X64,X65) )
& ( esk8_2(X64,X65) != esk9_2(X64,X65)
| ~ member(X68,X64)
| ~ member(esk7_2(X64,X65),X68)
| member(esk6_2(X64,X65),X64)
| partition(X64,X65) )
& ( member(esk8_2(X64,X65),X64)
| member(esk7_2(X64,X65),X65)
| ~ subset(esk6_2(X64,X65),X65)
| partition(X64,X65) )
& ( member(esk9_2(X64,X65),X64)
| member(esk7_2(X64,X65),X65)
| ~ subset(esk6_2(X64,X65),X65)
| partition(X64,X65) )
& ( member(esk10_2(X64,X65),esk8_2(X64,X65))
| member(esk7_2(X64,X65),X65)
| ~ subset(esk6_2(X64,X65),X65)
| partition(X64,X65) )
& ( member(esk10_2(X64,X65),esk9_2(X64,X65))
| member(esk7_2(X64,X65),X65)
| ~ subset(esk6_2(X64,X65),X65)
| partition(X64,X65) )
& ( esk8_2(X64,X65) != esk9_2(X64,X65)
| member(esk7_2(X64,X65),X65)
| ~ subset(esk6_2(X64,X65),X65)
| partition(X64,X65) )
& ( member(esk8_2(X64,X65),X64)
| ~ member(X68,X64)
| ~ member(esk7_2(X64,X65),X68)
| ~ subset(esk6_2(X64,X65),X65)
| partition(X64,X65) )
& ( member(esk9_2(X64,X65),X64)
| ~ member(X68,X64)
| ~ member(esk7_2(X64,X65),X68)
| ~ subset(esk6_2(X64,X65),X65)
| partition(X64,X65) )
& ( member(esk10_2(X64,X65),esk8_2(X64,X65))
| ~ member(X68,X64)
| ~ member(esk7_2(X64,X65),X68)
| ~ subset(esk6_2(X64,X65),X65)
| partition(X64,X65) )
& ( member(esk10_2(X64,X65),esk9_2(X64,X65))
| ~ member(X68,X64)
| ~ member(esk7_2(X64,X65),X68)
| ~ subset(esk6_2(X64,X65),X65)
| partition(X64,X65) )
& ( esk8_2(X64,X65) != esk9_2(X64,X65)
| ~ member(X68,X64)
| ~ member(esk7_2(X64,X65),X68)
| ~ subset(esk6_2(X64,X65),X65)
| partition(X64,X65) ) ),
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)],[partition])])])])])]) ).
fof(c_0_7,negated_conjecture,
! [X112] :
( member(esk19_0,difference(esk20_0,esk21_0))
& partition(esk22_0,esk20_0)
& ( ~ member(X112,difference(esk22_0,singleton(esk21_0)))
| ~ member(esk19_0,X112) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_8,plain,
! [X30,X31,X32] :
( ( member(X30,X32)
| ~ member(X30,difference(X32,X31)) )
& ( ~ member(X30,X31)
| ~ member(X30,difference(X32,X31)) )
& ( ~ member(X30,X32)
| member(X30,X31)
| member(X30,difference(X32,X31)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_9,plain,
( member(X1,esk5_3(X2,X3,X1))
| ~ member(X1,X3)
| ~ partition(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
partition(esk22_0,esk20_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
member(esk19_0,difference(esk20_0,esk21_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( member(esk5_3(X1,X2,X3),X1)
| ~ member(X3,X2)
| ~ partition(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,negated_conjecture,
( member(X1,esk5_3(esk22_0,esk20_0,X1))
| ~ member(X1,esk20_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,negated_conjecture,
member(esk19_0,esk20_0),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,negated_conjecture,
( member(esk5_3(esk22_0,esk20_0,X1),esk22_0)
| ~ member(X1,esk20_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_10]) ).
cnf(c_0_17,negated_conjecture,
( ~ member(X1,difference(esk22_0,singleton(esk21_0)))
| ~ member(esk19_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_18,negated_conjecture,
member(esk19_0,esk5_3(esk22_0,esk20_0,esk19_0)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
( member(X1,X3)
| member(X1,difference(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,negated_conjecture,
member(esk5_3(esk22_0,esk20_0,esk19_0),esk22_0),
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
fof(c_0_21,plain,
! [X33,X34] :
( ( ~ member(X33,singleton(X34))
| X33 = X34 )
& ( X33 != X34
| member(X33,singleton(X34)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[singleton])]) ).
cnf(c_0_22,negated_conjecture,
~ member(esk5_3(esk22_0,esk20_0,esk19_0),difference(esk22_0,singleton(esk21_0))),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( member(esk5_3(esk22_0,esk20_0,esk19_0),difference(esk22_0,X1))
| member(esk5_3(esk22_0,esk20_0,esk19_0),X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
( X1 = X2
| ~ member(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,negated_conjecture,
member(esk5_3(esk22_0,esk20_0,esk19_0),singleton(esk21_0)),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,plain,
( ~ member(X1,X2)
| ~ member(X1,difference(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_27,negated_conjecture,
esk5_3(esk22_0,esk20_0,esk19_0) = esk21_0,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
~ member(esk19_0,esk21_0),
inference(spm,[status(thm)],[c_0_26,c_0_12]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_27]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV517+1 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.18/0.34 % Computer : n018.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Thu Aug 24 02:35:27 EDT 2023
% 0.18/0.35 % CPUTime :
% 0.21/0.57 start to proof: theBenchmark
% 1.26/1.47 % Version : CSE_E---1.5
% 1.26/1.47 % Problem : theBenchmark.p
% 1.26/1.47 % Proof found
% 1.26/1.47 % SZS status Theorem for theBenchmark.p
% 1.26/1.47 % SZS output start Proof
% See solution above
% 1.26/1.47 % Total time : 0.893000 s
% 1.26/1.47 % SZS output end Proof
% 1.26/1.47 % Total time : 0.897000 s
%------------------------------------------------------------------------------