TSTP Solution File: SET763+4 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET763+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n007.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 00:53:49 EDT 2022
% Result : Theorem 0.16s 1.35s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 14 unt; 0 def)
% Number of atoms : 148 ( 4 equ)
% Maximal formula atoms : 55 ( 4 avg)
% Number of connectives : 175 ( 62 ~; 69 |; 34 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-4 aty)
% Number of variables : 85 ( 16 sgn 52 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thIIa13,conjecture,
! [X6,X1,X2,X3] :
( ( maps(X6,X1,X2)
& subset(X3,X1)
& equal_set(image2(X6,X3),empty_set) )
=> equal_set(X3,empty_set) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',thIIa13) ).
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(empty_set,axiom,
! [X3] : ~ member(X3,empty_set),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',empty_set) ).
fof(image2,axiom,
! [X6,X1,X5] :
( member(X5,image2(X6,X1))
<=> ? [X3] :
( member(X3,X1)
& apply(X6,X3,X5) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',image2) ).
fof(maps,axiom,
! [X6,X1,X2] :
( maps(X6,X1,X2)
<=> ( ! [X3] :
( member(X3,X1)
=> ? [X5] :
( member(X5,X2)
& apply(X6,X3,X5) ) )
& ! [X3,X7,X8] :
( ( member(X3,X1)
& member(X7,X2)
& member(X8,X2) )
=> ( ( apply(X6,X3,X7)
& apply(X6,X3,X8) )
=> X7 = X8 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',maps) ).
fof(c_0_6,negated_conjecture,
~ ! [X6,X1,X2,X3] :
( ( maps(X6,X1,X2)
& subset(X3,X1)
& equal_set(image2(X6,X3),empty_set) )
=> equal_set(X3,empty_set) ),
inference(assume_negation,[status(cth)],[thIIa13]) ).
fof(c_0_7,plain,
! [X3,X4,X3,X4] :
( ( subset(X3,X4)
| ~ equal_set(X3,X4) )
& ( subset(X4,X3)
| ~ equal_set(X3,X4) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| equal_set(X3,X4) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])])])]) ).
fof(c_0_8,negated_conjecture,
( maps(esk1_0,esk2_0,esk3_0)
& subset(esk4_0,esk2_0)
& equal_set(image2(esk1_0,esk4_0),empty_set)
& ~ equal_set(esk4_0,empty_set) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_9,plain,
! [X4,X5,X6,X4,X5] :
( ( ~ subset(X4,X5)
| ~ member(X6,X4)
| member(X6,X5) )
& ( member(esk6_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ member(esk6_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subset])])])])])])]) ).
cnf(c_0_10,plain,
( subset(X1,X2)
| ~ equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
equal_set(image2(esk1_0,esk4_0),empty_set),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X4] : ~ member(X4,empty_set),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[empty_set])]) ).
fof(c_0_13,plain,
! [X7,X8,X9,X7,X8,X9,X11] :
( ( member(esk5_3(X7,X8,X9),X8)
| ~ member(X9,image2(X7,X8)) )
& ( apply(X7,esk5_3(X7,X8,X9),X9)
| ~ member(X9,image2(X7,X8)) )
& ( ~ member(X11,X8)
| ~ apply(X7,X11,X9)
| member(X9,image2(X7,X8)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[image2])])])])])])]) ).
fof(c_0_14,plain,
! [X9,X10,X11,X12,X14,X15,X16,X9,X10,X11,X18] :
( ( member(esk7_4(X9,X10,X11,X12),X11)
| ~ member(X12,X10)
| ~ maps(X9,X10,X11) )
& ( apply(X9,X12,esk7_4(X9,X10,X11,X12))
| ~ member(X12,X10)
| ~ maps(X9,X10,X11) )
& ( ~ member(X14,X10)
| ~ member(X15,X11)
| ~ member(X16,X11)
| ~ apply(X9,X14,X15)
| ~ apply(X9,X14,X16)
| X15 = X16
| ~ maps(X9,X10,X11) )
& ( member(esk9_3(X9,X10,X11),X10)
| member(esk8_3(X9,X10,X11),X10)
| maps(X9,X10,X11) )
& ( member(esk10_3(X9,X10,X11),X11)
| member(esk8_3(X9,X10,X11),X10)
| maps(X9,X10,X11) )
& ( member(esk11_3(X9,X10,X11),X11)
| member(esk8_3(X9,X10,X11),X10)
| maps(X9,X10,X11) )
& ( apply(X9,esk9_3(X9,X10,X11),esk10_3(X9,X10,X11))
| member(esk8_3(X9,X10,X11),X10)
| maps(X9,X10,X11) )
& ( apply(X9,esk9_3(X9,X10,X11),esk11_3(X9,X10,X11))
| member(esk8_3(X9,X10,X11),X10)
| maps(X9,X10,X11) )
& ( esk10_3(X9,X10,X11) != esk11_3(X9,X10,X11)
| member(esk8_3(X9,X10,X11),X10)
| maps(X9,X10,X11) )
& ( member(esk9_3(X9,X10,X11),X10)
| ~ member(X18,X11)
| ~ apply(X9,esk8_3(X9,X10,X11),X18)
| maps(X9,X10,X11) )
& ( member(esk10_3(X9,X10,X11),X11)
| ~ member(X18,X11)
| ~ apply(X9,esk8_3(X9,X10,X11),X18)
| maps(X9,X10,X11) )
& ( member(esk11_3(X9,X10,X11),X11)
| ~ member(X18,X11)
| ~ apply(X9,esk8_3(X9,X10,X11),X18)
| maps(X9,X10,X11) )
& ( apply(X9,esk9_3(X9,X10,X11),esk10_3(X9,X10,X11))
| ~ member(X18,X11)
| ~ apply(X9,esk8_3(X9,X10,X11),X18)
| maps(X9,X10,X11) )
& ( apply(X9,esk9_3(X9,X10,X11),esk11_3(X9,X10,X11))
| ~ member(X18,X11)
| ~ apply(X9,esk8_3(X9,X10,X11),X18)
| maps(X9,X10,X11) )
& ( esk10_3(X9,X10,X11) != esk11_3(X9,X10,X11)
| ~ member(X18,X11)
| ~ apply(X9,esk8_3(X9,X10,X11),X18)
| maps(X9,X10,X11) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[maps])])])])])])]) ).
cnf(c_0_15,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,negated_conjecture,
subset(image2(esk1_0,esk4_0),empty_set),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_17,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( member(X1,image2(X2,X3))
| ~ apply(X2,X4,X1)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( apply(X1,X4,esk7_4(X1,X2,X3,X4))
| ~ maps(X1,X2,X3)
| ~ member(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
~ member(X1,image2(esk1_0,esk4_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_21,plain,
( member(esk7_4(X1,X2,X3,X4),image2(X1,X5))
| ~ maps(X1,X2,X3)
| ~ member(X4,X5)
| ~ member(X4,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,negated_conjecture,
subset(esk4_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_23,negated_conjecture,
~ equal_set(esk4_0,empty_set),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_24,plain,
( equal_set(X1,X2)
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_25,plain,
( subset(X1,X2)
| member(esk6_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_26,negated_conjecture,
( ~ maps(esk1_0,X1,X2)
| ~ member(X3,esk4_0)
| ~ member(X3,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,negated_conjecture,
maps(esk1_0,esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_28,negated_conjecture,
( member(X1,esk2_0)
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_22]) ).
cnf(c_0_29,negated_conjecture,
( ~ subset(empty_set,esk4_0)
| ~ subset(esk4_0,empty_set) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[c_0_17,c_0_25]) ).
cnf(c_0_31,negated_conjecture,
~ member(X1,esk4_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_32,negated_conjecture,
~ subset(esk4_0,empty_set),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]) ).
cnf(c_0_33,negated_conjecture,
subset(esk4_0,X1),
inference(spm,[status(thm)],[c_0_31,c_0_25]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET763+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.09/0.09 % Command : run_ET %s %d
% 0.09/0.29 % Computer : n007.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Sun Jul 10 03:24:31 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.16/1.35 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.16/1.35 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.16/1.35 # Preprocessing time : 0.013 s
% 0.16/1.35
% 0.16/1.35 # Proof found!
% 0.16/1.35 # SZS status Theorem
% 0.16/1.35 # SZS output start CNFRefutation
% See solution above
% 0.16/1.35 # Proof object total steps : 35
% 0.16/1.35 # Proof object clause steps : 22
% 0.16/1.35 # Proof object formula steps : 13
% 0.16/1.35 # Proof object conjectures : 16
% 0.16/1.35 # Proof object clause conjectures : 13
% 0.16/1.35 # Proof object formula conjectures : 3
% 0.16/1.35 # Proof object initial clauses used : 11
% 0.16/1.35 # Proof object initial formulas used : 6
% 0.16/1.35 # Proof object generating inferences : 9
% 0.16/1.35 # Proof object simplifying inferences : 6
% 0.16/1.35 # Training examples: 0 positive, 0 negative
% 0.16/1.35 # Parsed axioms : 29
% 0.16/1.35 # Removed by relevancy pruning/SinE : 23
% 0.16/1.35 # Initial clauses : 29
% 0.16/1.35 # Removed in clause preprocessing : 0
% 0.16/1.35 # Initial clauses in saturation : 29
% 0.16/1.35 # Processed clauses : 72
% 0.16/1.35 # ...of these trivial : 0
% 0.16/1.35 # ...subsumed : 9
% 0.16/1.35 # ...remaining for further processing : 63
% 0.16/1.35 # Other redundant clauses eliminated : 0
% 0.16/1.35 # Clauses deleted for lack of memory : 0
% 0.16/1.35 # Backward-subsumed : 0
% 0.16/1.35 # Backward-rewritten : 9
% 0.16/1.35 # Generated clauses : 108
% 0.16/1.35 # ...of the previous two non-trivial : 98
% 0.16/1.35 # Contextual simplify-reflections : 1
% 0.16/1.35 # Paramodulations : 108
% 0.16/1.35 # Factorizations : 0
% 0.16/1.35 # Equation resolutions : 0
% 0.16/1.35 # Current number of processed clauses : 54
% 0.16/1.35 # Positive orientable unit clauses : 12
% 0.16/1.35 # Positive unorientable unit clauses: 0
% 0.16/1.35 # Negative unit clauses : 6
% 0.16/1.35 # Non-unit-clauses : 36
% 0.16/1.35 # Current number of unprocessed clauses: 50
% 0.16/1.35 # ...number of literals in the above : 156
% 0.16/1.35 # Current number of archived formulas : 0
% 0.16/1.35 # Current number of archived clauses : 9
% 0.16/1.35 # Clause-clause subsumption calls (NU) : 110
% 0.16/1.35 # Rec. Clause-clause subsumption calls : 54
% 0.16/1.35 # Non-unit clause-clause subsumptions : 2
% 0.16/1.35 # Unit Clause-clause subsumption calls : 49
% 0.16/1.35 # Rewrite failures with RHS unbound : 0
% 0.16/1.35 # BW rewrite match attempts : 16
% 0.16/1.35 # BW rewrite match successes : 9
% 0.16/1.35 # Condensation attempts : 0
% 0.16/1.35 # Condensation successes : 0
% 0.16/1.35 # Termbank termtop insertions : 3432
% 0.16/1.35
% 0.16/1.35 # -------------------------------------------------
% 0.16/1.35 # User time : 0.016 s
% 0.16/1.35 # System time : 0.001 s
% 0.16/1.35 # Total time : 0.017 s
% 0.16/1.35 # Maximum resident set size: 3052 pages
%------------------------------------------------------------------------------