TSTP Solution File: SET707+4 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET707+4 : 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 : n012.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 14:35:18 EDT 2023
% Result : Theorem 0.20s 0.60s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 24
% Syntax : Number of formulae : 67 ( 16 unt; 19 typ; 0 def)
% Number of atoms : 105 ( 45 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 88 ( 31 ~; 39 |; 11 &)
% ( 4 <=>; 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 : 24 ( 14 >; 10 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-2 aty)
% Number of variables : 58 ( 4 sgn; 30 !; 0 ?; 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,
esk1_2: ( $i * $i ) > $i ).
tff(decl_35,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_36,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_37,type,
esk4_0: $i ).
tff(decl_38,type,
esk5_0: $i ).
tff(decl_39,type,
esk6_0: $i ).
tff(decl_40,type,
esk7_0: $i ).
fof(thI50,conjecture,
! [X1,X2,X6,X7] :
( equal_set(unordered_pair(singleton(X1),unordered_pair(X1,X2)),unordered_pair(singleton(X6),unordered_pair(X6,X7)))
=> ( X1 = X6
& X2 = X7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI50) ).
fof(equal_set,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(unordered_pair,axiom,
! [X3,X1,X2] :
( member(X3,unordered_pair(X1,X2))
<=> ( X3 = X1
| X3 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',unordered_pair) ).
fof(singleton,axiom,
! [X3,X1] :
( member(X3,singleton(X1))
<=> X3 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',singleton) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X6,X7] :
( equal_set(unordered_pair(singleton(X1),unordered_pair(X1,X2)),unordered_pair(singleton(X6),unordered_pair(X6,X7)))
=> ( X1 = X6
& X2 = X7 ) ),
inference(assume_negation,[status(cth)],[thI50]) ).
fof(c_0_6,plain,
! [X14,X15] :
( ( subset(X14,X15)
| ~ equal_set(X14,X15) )
& ( subset(X15,X14)
| ~ equal_set(X14,X15) )
& ( ~ subset(X14,X15)
| ~ subset(X15,X14)
| equal_set(X14,X15) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])]) ).
fof(c_0_7,negated_conjecture,
( equal_set(unordered_pair(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)),unordered_pair(singleton(esk6_0),unordered_pair(esk6_0,esk7_0)))
& ( esk4_0 != esk6_0
| esk5_0 != esk7_0 ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_8,plain,
! [X8,X9,X10,X11,X12] :
( ( ~ subset(X8,X9)
| ~ member(X10,X8)
| member(X10,X9) )
& ( member(esk1_2(X11,X12),X11)
| subset(X11,X12) )
& ( ~ member(esk1_2(X11,X12),X12)
| subset(X11,X12) ) ),
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])])])])])]) ).
cnf(c_0_9,plain,
( subset(X1,X2)
| ~ equal_set(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
equal_set(unordered_pair(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)),unordered_pair(singleton(esk6_0),unordered_pair(esk6_0,esk7_0))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X30,X31,X32] :
( ( ~ member(X30,unordered_pair(X31,X32))
| X30 = X31
| X30 = X32 )
& ( X30 != X31
| member(X30,unordered_pair(X31,X32)) )
& ( X30 != X32
| member(X30,unordered_pair(X31,X32)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[unordered_pair])])]) ).
cnf(c_0_12,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
subset(unordered_pair(singleton(esk6_0),unordered_pair(esk6_0,esk7_0)),unordered_pair(singleton(esk4_0),unordered_pair(esk4_0,esk5_0))),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
( member(X1,unordered_pair(X2,X3))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
( member(X1,unordered_pair(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)))
| ~ member(X1,unordered_pair(singleton(esk6_0),unordered_pair(esk6_0,esk7_0))) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,plain,
member(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_17,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
member(singleton(esk6_0),unordered_pair(singleton(esk4_0),unordered_pair(esk4_0,esk5_0))),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
( member(X1,unordered_pair(X3,X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_20,plain,
! [X28,X29] :
( ( ~ member(X28,singleton(X29))
| X28 = X29 )
& ( X28 != X29
| member(X28,singleton(X29)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[singleton])]) ).
cnf(c_0_21,negated_conjecture,
( unordered_pair(esk4_0,esk5_0) = singleton(esk6_0)
| singleton(esk6_0) = singleton(esk4_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
member(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_23,plain,
( member(X1,singleton(X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,plain,
( X1 = X2
| ~ member(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
( singleton(esk6_0) = singleton(esk4_0)
| member(esk4_0,singleton(esk6_0)) ),
inference(spm,[status(thm)],[c_0_16,c_0_21]) ).
cnf(c_0_26,negated_conjecture,
member(unordered_pair(esk6_0,esk7_0),unordered_pair(singleton(esk4_0),unordered_pair(esk4_0,esk5_0))),
inference(spm,[status(thm)],[c_0_15,c_0_22]) ).
cnf(c_0_27,plain,
member(X1,singleton(X1)),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_28,negated_conjecture,
( singleton(esk6_0) = singleton(esk4_0)
| esk6_0 = esk4_0 ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
( unordered_pair(esk6_0,esk7_0) = unordered_pair(esk4_0,esk5_0)
| unordered_pair(esk6_0,esk7_0) = singleton(esk4_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_26]) ).
cnf(c_0_30,negated_conjecture,
esk6_0 = esk4_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_24]) ).
cnf(c_0_31,negated_conjecture,
( unordered_pair(esk4_0,esk7_0) = unordered_pair(esk4_0,esk5_0)
| unordered_pair(esk4_0,esk7_0) = singleton(esk4_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30]),c_0_30]) ).
cnf(c_0_32,negated_conjecture,
( esk4_0 != esk6_0
| esk5_0 != esk7_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_33,negated_conjecture,
( unordered_pair(esk4_0,esk7_0) = singleton(esk4_0)
| member(esk7_0,unordered_pair(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_22,c_0_31]) ).
cnf(c_0_34,negated_conjecture,
esk7_0 != esk5_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_30])]) ).
cnf(c_0_35,negated_conjecture,
( unordered_pair(esk4_0,esk7_0) = singleton(esk4_0)
| esk7_0 = esk4_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_33]),c_0_34]) ).
cnf(c_0_36,negated_conjecture,
esk7_0 = esk4_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_35]),c_0_24]) ).
cnf(c_0_37,plain,
( subset(X1,X2)
| ~ equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_38,negated_conjecture,
( unordered_pair(esk4_0,esk5_0) = unordered_pair(esk4_0,esk4_0)
| unordered_pair(esk4_0,esk4_0) = singleton(esk4_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_36]),c_0_36]) ).
cnf(c_0_39,negated_conjecture,
subset(unordered_pair(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)),unordered_pair(singleton(esk6_0),unordered_pair(esk6_0,esk7_0))),
inference(spm,[status(thm)],[c_0_37,c_0_10]) ).
cnf(c_0_40,negated_conjecture,
( unordered_pair(esk4_0,esk4_0) = singleton(esk4_0)
| member(esk5_0,unordered_pair(esk4_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_22,c_0_38]) ).
cnf(c_0_41,negated_conjecture,
esk5_0 != esk4_0,
inference(rw,[status(thm)],[c_0_34,c_0_36]) ).
cnf(c_0_42,negated_conjecture,
( member(X1,unordered_pair(singleton(esk6_0),unordered_pair(esk6_0,esk7_0)))
| ~ member(X1,unordered_pair(singleton(esk4_0),unordered_pair(esk4_0,esk5_0))) ),
inference(spm,[status(thm)],[c_0_12,c_0_39]) ).
cnf(c_0_43,negated_conjecture,
unordered_pair(esk4_0,esk4_0) = singleton(esk4_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_40]),c_0_41]) ).
cnf(c_0_44,negated_conjecture,
( X1 = singleton(esk4_0)
| ~ member(X1,unordered_pair(singleton(esk4_0),unordered_pair(esk4_0,esk5_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_42]),c_0_30]),c_0_36]),c_0_43]),c_0_30])]) ).
cnf(c_0_45,negated_conjecture,
unordered_pair(esk4_0,esk5_0) = singleton(esk4_0),
inference(spm,[status(thm)],[c_0_44,c_0_22]) ).
cnf(c_0_46,negated_conjecture,
member(esk5_0,singleton(esk4_0)),
inference(spm,[status(thm)],[c_0_22,c_0_45]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_46]),c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET707+4 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 10:00:41 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.20/0.60 % Version : CSE_E---1.5
% 0.20/0.60 % Problem : theBenchmark.p
% 0.20/0.60 % Proof found
% 0.20/0.60 % SZS status Theorem for theBenchmark.p
% 0.20/0.60 % SZS output start Proof
% See solution above
% 0.20/0.60 % Total time : 0.019000 s
% 0.20/0.60 % SZS output end Proof
% 0.20/0.60 % Total time : 0.022000 s
%------------------------------------------------------------------------------