TSTP Solution File: SET351+4 by Enigma---0.5.1
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%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : SET351+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n003.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 : 600s
% DateTime : Tue Jul 19 00:11:10 EDT 2022
% Result : Theorem 6.85s 2.91s
% Output : CNFRefutation 6.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 9 unt; 0 def)
% Number of atoms : 90 ( 9 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 91 ( 39 ~; 38 |; 9 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 25 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thI39,conjecture,
! [X1] : equal_set(sum(singleton(X1)),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI39) ).
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(sum,axiom,
! [X3,X1] :
( member(X3,sum(X1))
<=> ? [X5] :
( member(X5,X1)
& member(X3,X5) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',sum) ).
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] : equal_set(sum(singleton(X1)),X1),
inference(assume_negation,[status(cth)],[thI39]) ).
fof(c_0_6,negated_conjecture,
~ equal_set(sum(singleton(esk4_0)),esk4_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_7,plain,
! [X12,X13] :
( ( subset(X12,X13)
| ~ equal_set(X12,X13) )
& ( subset(X13,X12)
| ~ equal_set(X12,X13) )
& ( ~ subset(X12,X13)
| ~ subset(X13,X12)
| equal_set(X12,X13) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])]) ).
cnf(c_0_8,negated_conjecture,
~ equal_set(sum(singleton(esk4_0)),esk4_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( equal_set(X1,X2)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X6,X7,X8,X9,X10] :
( ( ~ subset(X6,X7)
| ~ member(X8,X6)
| member(X8,X7) )
& ( member(esk1_2(X9,X10),X9)
| subset(X9,X10) )
& ( ~ member(esk1_2(X9,X10),X10)
| subset(X9,X10) ) ),
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_11,negated_conjecture,
( ~ subset(esk4_0,sum(singleton(esk4_0)))
| ~ subset(sum(singleton(esk4_0)),esk4_0) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_13,plain,
! [X31,X32,X34,X35,X36] :
( ( member(esk2_2(X31,X32),X32)
| ~ member(X31,sum(X32)) )
& ( member(X31,esk2_2(X31,X32))
| ~ member(X31,sum(X32)) )
& ( ~ member(X36,X35)
| ~ member(X34,X36)
| member(X34,sum(X35)) ) ),
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)],[sum])])])])])]) ).
cnf(c_0_14,negated_conjecture,
( member(esk1_2(sum(singleton(esk4_0)),esk4_0),sum(singleton(esk4_0)))
| ~ subset(esk4_0,sum(singleton(esk4_0))) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,plain,
! [X26,X27] :
( ( ~ member(X26,singleton(X27))
| X26 = X27 )
& ( X26 != X27
| member(X26,singleton(X27)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[singleton])]) ).
cnf(c_0_17,plain,
( member(esk2_2(X1,X2),X2)
| ~ member(X1,sum(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
( member(esk1_2(sum(singleton(esk4_0)),esk4_0),sum(singleton(esk4_0)))
| member(esk1_2(esk4_0,sum(singleton(esk4_0))),esk4_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_12]) ).
cnf(c_0_19,negated_conjecture,
( member(esk1_2(sum(singleton(esk4_0)),esk4_0),sum(singleton(esk4_0)))
| ~ member(esk1_2(esk4_0,sum(singleton(esk4_0))),sum(singleton(esk4_0))) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
( X1 = X2
| ~ member(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
( member(esk2_2(esk1_2(sum(singleton(esk4_0)),esk4_0),singleton(esk4_0)),singleton(esk4_0))
| member(esk1_2(esk4_0,sum(singleton(esk4_0))),esk4_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
( member(esk2_2(esk1_2(sum(singleton(esk4_0)),esk4_0),singleton(esk4_0)),singleton(esk4_0))
| ~ member(esk1_2(esk4_0,sum(singleton(esk4_0))),sum(singleton(esk4_0))) ),
inference(spm,[status(thm)],[c_0_17,c_0_19]) ).
cnf(c_0_23,plain,
( member(X3,sum(X2))
| ~ member(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_24,negated_conjecture,
( esk2_2(esk1_2(sum(singleton(esk4_0)),esk4_0),singleton(esk4_0)) = esk4_0
| member(esk1_2(esk4_0,sum(singleton(esk4_0))),esk4_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
( member(X1,singleton(X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,negated_conjecture,
( esk2_2(esk1_2(sum(singleton(esk4_0)),esk4_0),singleton(esk4_0)) = esk4_0
| ~ member(esk1_2(esk4_0,sum(singleton(esk4_0))),sum(singleton(esk4_0))) ),
inference(spm,[status(thm)],[c_0_20,c_0_22]) ).
cnf(c_0_27,negated_conjecture,
( esk2_2(esk1_2(sum(singleton(esk4_0)),esk4_0),singleton(esk4_0)) = esk4_0
| member(esk1_2(esk4_0,sum(singleton(esk4_0))),sum(X1))
| ~ member(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
member(X1,singleton(X1)),
inference(er,[status(thm)],[c_0_25]) ).
cnf(c_0_29,negated_conjecture,
( ~ member(esk1_2(sum(singleton(esk4_0)),esk4_0),esk4_0)
| ~ subset(esk4_0,sum(singleton(esk4_0))) ),
inference(spm,[status(thm)],[c_0_11,c_0_15]) ).
cnf(c_0_30,plain,
( member(X1,esk2_2(X1,X2))
| ~ member(X1,sum(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_31,negated_conjecture,
esk2_2(esk1_2(sum(singleton(esk4_0)),esk4_0),singleton(esk4_0)) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).
cnf(c_0_32,negated_conjecture,
( member(esk1_2(esk4_0,sum(singleton(esk4_0))),esk4_0)
| ~ member(esk1_2(sum(singleton(esk4_0)),esk4_0),esk4_0) ),
inference(spm,[status(thm)],[c_0_29,c_0_12]) ).
cnf(c_0_33,negated_conjecture,
( ~ member(esk1_2(esk4_0,sum(singleton(esk4_0))),sum(singleton(esk4_0)))
| ~ member(esk1_2(sum(singleton(esk4_0)),esk4_0),esk4_0) ),
inference(spm,[status(thm)],[c_0_29,c_0_15]) ).
cnf(c_0_34,negated_conjecture,
member(esk1_2(esk4_0,sum(singleton(esk4_0))),esk4_0),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_18]),c_0_31]),c_0_32]) ).
cnf(c_0_35,negated_conjecture,
~ member(esk1_2(esk4_0,sum(singleton(esk4_0))),sum(singleton(esk4_0))),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_19]),c_0_31]),c_0_33]) ).
cnf(c_0_36,negated_conjecture,
( member(esk1_2(esk4_0,sum(singleton(esk4_0))),sum(X1))
| ~ member(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET351+4 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.14 % Command : enigmatic-eprover.py %s %d 1
% 0.14/0.35 % Computer : n003.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 : 600
% 0.14/0.35 % DateTime : Mon Jul 11 04:14:31 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.46 # ENIGMATIC: Selected SinE mode:
% 0.21/0.46 # Parsing /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.46 # Filter: axfilter_auto 0 goes into file theBenchmark_axfilter_auto 0.p
% 0.21/0.46 # Filter: axfilter_auto 1 goes into file theBenchmark_axfilter_auto 1.p
% 0.21/0.46 # Filter: axfilter_auto 2 goes into file theBenchmark_axfilter_auto 2.p
% 6.85/2.91 # ENIGMATIC: Solved by autoschedule:
% 6.85/2.91 # No SInE strategy applied
% 6.85/2.91 # Trying AutoSched0 for 150 seconds
% 6.85/2.91 # AutoSched0-Mode selected heuristic G_E___208_C09_12_F1_SE_CS_SP_PS_S070I
% 6.85/2.91 # and selection function SelectVGNonCR.
% 6.85/2.91 #
% 6.85/2.91 # Preprocessing time : 0.015 s
% 6.85/2.91 # Presaturation interreduction done
% 6.85/2.91
% 6.85/2.91 # Proof found!
% 6.85/2.91 # SZS status Theorem
% 6.85/2.91 # SZS output start CNFRefutation
% See solution above
% 6.85/2.91 # Training examples: 0 positive, 0 negative
% 6.85/2.91
% 6.85/2.91 # -------------------------------------------------
% 6.85/2.91 # User time : 0.022 s
% 6.85/2.91 # System time : 0.003 s
% 6.85/2.91 # Total time : 0.026 s
% 6.85/2.91 # Maximum resident set size: 7116 pages
% 6.85/2.91
%------------------------------------------------------------------------------