TSTP Solution File: SET766+4 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET766+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% 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 : 600s
% DateTime : Tue Jul 19 00:53:50 EDT 2022
% Result : Theorem 0.22s 1.40s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 5 unt; 0 def)
% Number of atoms : 276 ( 0 equ)
% Maximal formula atoms : 207 ( 13 avg)
% Number of connectives : 329 ( 73 ~; 170 |; 70 &)
% ( 4 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 65 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 62 ( 8 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(equivalence,axiom,
! [X1,X7] :
( equivalence(X7,X1)
<=> ( ! [X3] :
( member(X3,X1)
=> apply(X7,X3,X3) )
& ! [X3,X5] :
( ( member(X3,X1)
& member(X5,X1) )
=> ( apply(X7,X3,X5)
=> apply(X7,X5,X3) ) )
& ! [X3,X5,X6] :
( ( member(X3,X1)
& member(X5,X1)
& member(X6,X1) )
=> ( ( apply(X7,X3,X5)
& apply(X7,X5,X6) )
=> apply(X7,X3,X6) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax',equivalence) ).
fof(thIII02,conjecture,
! [X4,X7,X1] :
( ( equivalence(X7,X4)
& member(X1,X4) )
=> member(X1,equivalence_class(X1,X4,X7)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',thIII02) ).
fof(equivalence_class,axiom,
! [X7,X4,X1,X3] :
( member(X3,equivalence_class(X1,X4,X7))
<=> ( member(X3,X4)
& apply(X7,X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax',equivalence_class) ).
fof(c_0_3,plain,
! [X1,X7] :
( epred1_2(X7,X1)
<=> ( ! [X3] :
( member(X3,X1)
=> apply(X7,X3,X3) )
& ! [X3,X5] :
( ( member(X3,X1)
& member(X5,X1) )
=> ( apply(X7,X3,X5)
=> apply(X7,X5,X3) ) )
& ! [X3,X5,X6] :
( ( member(X3,X1)
& member(X5,X1)
& member(X6,X1) )
=> ( ( apply(X7,X3,X5)
& apply(X7,X5,X6) )
=> apply(X7,X3,X6) ) ) ) ),
introduced(definition) ).
fof(c_0_4,axiom,
! [X1,X7] :
( equivalence(X7,X1)
<=> epred1_2(X7,X1) ),
inference(apply_def,[status(thm)],[equivalence,c_0_3]) ).
fof(c_0_5,negated_conjecture,
~ ! [X4,X7,X1] :
( ( equivalence(X7,X4)
& member(X1,X4) )
=> member(X1,equivalence_class(X1,X4,X7)) ),
inference(assume_negation,[status(cth)],[thIII02]) ).
fof(c_0_6,plain,
! [X8,X9,X8,X9] :
( ( ~ equivalence(X9,X8)
| epred1_2(X9,X8) )
& ( ~ epred1_2(X9,X8)
| equivalence(X9,X8) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_7,negated_conjecture,
( equivalence(esk2_0,esk1_0)
& member(esk3_0,esk1_0)
& ~ member(esk3_0,equivalence_class(esk3_0,esk1_0,esk2_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,X13,X14,X15,X8,X9] :
( ( ~ member(X10,X8)
| apply(X9,X10,X10)
| ~ epred1_2(X9,X8) )
& ( ~ member(X11,X8)
| ~ member(X12,X8)
| ~ apply(X9,X11,X12)
| apply(X9,X12,X11)
| ~ epred1_2(X9,X8) )
& ( ~ member(X13,X8)
| ~ member(X14,X8)
| ~ member(X15,X8)
| ~ apply(X9,X13,X14)
| ~ apply(X9,X14,X15)
| apply(X9,X13,X15)
| ~ epred1_2(X9,X8) )
& ( member(esk7_2(X8,X9),X8)
| member(esk5_2(X8,X9),X8)
| member(esk4_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk8_2(X8,X9),X8)
| member(esk5_2(X8,X9),X8)
| member(esk4_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk9_2(X8,X9),X8)
| member(esk5_2(X8,X9),X8)
| member(esk4_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( apply(X9,esk7_2(X8,X9),esk8_2(X8,X9))
| member(esk5_2(X8,X9),X8)
| member(esk4_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( apply(X9,esk8_2(X8,X9),esk9_2(X8,X9))
| member(esk5_2(X8,X9),X8)
| member(esk4_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( ~ apply(X9,esk7_2(X8,X9),esk9_2(X8,X9))
| member(esk5_2(X8,X9),X8)
| member(esk4_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk7_2(X8,X9),X8)
| member(esk6_2(X8,X9),X8)
| member(esk4_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk8_2(X8,X9),X8)
| member(esk6_2(X8,X9),X8)
| member(esk4_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk9_2(X8,X9),X8)
| member(esk6_2(X8,X9),X8)
| member(esk4_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( apply(X9,esk7_2(X8,X9),esk8_2(X8,X9))
| member(esk6_2(X8,X9),X8)
| member(esk4_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( apply(X9,esk8_2(X8,X9),esk9_2(X8,X9))
| member(esk6_2(X8,X9),X8)
| member(esk4_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( ~ apply(X9,esk7_2(X8,X9),esk9_2(X8,X9))
| member(esk6_2(X8,X9),X8)
| member(esk4_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk7_2(X8,X9),X8)
| apply(X9,esk5_2(X8,X9),esk6_2(X8,X9))
| member(esk4_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk8_2(X8,X9),X8)
| apply(X9,esk5_2(X8,X9),esk6_2(X8,X9))
| member(esk4_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk9_2(X8,X9),X8)
| apply(X9,esk5_2(X8,X9),esk6_2(X8,X9))
| member(esk4_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( apply(X9,esk7_2(X8,X9),esk8_2(X8,X9))
| apply(X9,esk5_2(X8,X9),esk6_2(X8,X9))
| member(esk4_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( apply(X9,esk8_2(X8,X9),esk9_2(X8,X9))
| apply(X9,esk5_2(X8,X9),esk6_2(X8,X9))
| member(esk4_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( ~ apply(X9,esk7_2(X8,X9),esk9_2(X8,X9))
| apply(X9,esk5_2(X8,X9),esk6_2(X8,X9))
| member(esk4_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk7_2(X8,X9),X8)
| ~ apply(X9,esk6_2(X8,X9),esk5_2(X8,X9))
| member(esk4_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk8_2(X8,X9),X8)
| ~ apply(X9,esk6_2(X8,X9),esk5_2(X8,X9))
| member(esk4_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk9_2(X8,X9),X8)
| ~ apply(X9,esk6_2(X8,X9),esk5_2(X8,X9))
| member(esk4_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( apply(X9,esk7_2(X8,X9),esk8_2(X8,X9))
| ~ apply(X9,esk6_2(X8,X9),esk5_2(X8,X9))
| member(esk4_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( apply(X9,esk8_2(X8,X9),esk9_2(X8,X9))
| ~ apply(X9,esk6_2(X8,X9),esk5_2(X8,X9))
| member(esk4_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( ~ apply(X9,esk7_2(X8,X9),esk9_2(X8,X9))
| ~ apply(X9,esk6_2(X8,X9),esk5_2(X8,X9))
| member(esk4_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk7_2(X8,X9),X8)
| member(esk5_2(X8,X9),X8)
| ~ apply(X9,esk4_2(X8,X9),esk4_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk8_2(X8,X9),X8)
| member(esk5_2(X8,X9),X8)
| ~ apply(X9,esk4_2(X8,X9),esk4_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk9_2(X8,X9),X8)
| member(esk5_2(X8,X9),X8)
| ~ apply(X9,esk4_2(X8,X9),esk4_2(X8,X9))
| epred1_2(X9,X8) )
& ( apply(X9,esk7_2(X8,X9),esk8_2(X8,X9))
| member(esk5_2(X8,X9),X8)
| ~ apply(X9,esk4_2(X8,X9),esk4_2(X8,X9))
| epred1_2(X9,X8) )
& ( apply(X9,esk8_2(X8,X9),esk9_2(X8,X9))
| member(esk5_2(X8,X9),X8)
| ~ apply(X9,esk4_2(X8,X9),esk4_2(X8,X9))
| epred1_2(X9,X8) )
& ( ~ apply(X9,esk7_2(X8,X9),esk9_2(X8,X9))
| member(esk5_2(X8,X9),X8)
| ~ apply(X9,esk4_2(X8,X9),esk4_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk7_2(X8,X9),X8)
| member(esk6_2(X8,X9),X8)
| ~ apply(X9,esk4_2(X8,X9),esk4_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk8_2(X8,X9),X8)
| member(esk6_2(X8,X9),X8)
| ~ apply(X9,esk4_2(X8,X9),esk4_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk9_2(X8,X9),X8)
| member(esk6_2(X8,X9),X8)
| ~ apply(X9,esk4_2(X8,X9),esk4_2(X8,X9))
| epred1_2(X9,X8) )
& ( apply(X9,esk7_2(X8,X9),esk8_2(X8,X9))
| member(esk6_2(X8,X9),X8)
| ~ apply(X9,esk4_2(X8,X9),esk4_2(X8,X9))
| epred1_2(X9,X8) )
& ( apply(X9,esk8_2(X8,X9),esk9_2(X8,X9))
| member(esk6_2(X8,X9),X8)
| ~ apply(X9,esk4_2(X8,X9),esk4_2(X8,X9))
| epred1_2(X9,X8) )
& ( ~ apply(X9,esk7_2(X8,X9),esk9_2(X8,X9))
| member(esk6_2(X8,X9),X8)
| ~ apply(X9,esk4_2(X8,X9),esk4_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk7_2(X8,X9),X8)
| apply(X9,esk5_2(X8,X9),esk6_2(X8,X9))
| ~ apply(X9,esk4_2(X8,X9),esk4_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk8_2(X8,X9),X8)
| apply(X9,esk5_2(X8,X9),esk6_2(X8,X9))
| ~ apply(X9,esk4_2(X8,X9),esk4_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk9_2(X8,X9),X8)
| apply(X9,esk5_2(X8,X9),esk6_2(X8,X9))
| ~ apply(X9,esk4_2(X8,X9),esk4_2(X8,X9))
| epred1_2(X9,X8) )
& ( apply(X9,esk7_2(X8,X9),esk8_2(X8,X9))
| apply(X9,esk5_2(X8,X9),esk6_2(X8,X9))
| ~ apply(X9,esk4_2(X8,X9),esk4_2(X8,X9))
| epred1_2(X9,X8) )
& ( apply(X9,esk8_2(X8,X9),esk9_2(X8,X9))
| apply(X9,esk5_2(X8,X9),esk6_2(X8,X9))
| ~ apply(X9,esk4_2(X8,X9),esk4_2(X8,X9))
| epred1_2(X9,X8) )
& ( ~ apply(X9,esk7_2(X8,X9),esk9_2(X8,X9))
| apply(X9,esk5_2(X8,X9),esk6_2(X8,X9))
| ~ apply(X9,esk4_2(X8,X9),esk4_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk7_2(X8,X9),X8)
| ~ apply(X9,esk6_2(X8,X9),esk5_2(X8,X9))
| ~ apply(X9,esk4_2(X8,X9),esk4_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk8_2(X8,X9),X8)
| ~ apply(X9,esk6_2(X8,X9),esk5_2(X8,X9))
| ~ apply(X9,esk4_2(X8,X9),esk4_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk9_2(X8,X9),X8)
| ~ apply(X9,esk6_2(X8,X9),esk5_2(X8,X9))
| ~ apply(X9,esk4_2(X8,X9),esk4_2(X8,X9))
| epred1_2(X9,X8) )
& ( apply(X9,esk7_2(X8,X9),esk8_2(X8,X9))
| ~ apply(X9,esk6_2(X8,X9),esk5_2(X8,X9))
| ~ apply(X9,esk4_2(X8,X9),esk4_2(X8,X9))
| epred1_2(X9,X8) )
& ( apply(X9,esk8_2(X8,X9),esk9_2(X8,X9))
| ~ apply(X9,esk6_2(X8,X9),esk5_2(X8,X9))
| ~ apply(X9,esk4_2(X8,X9),esk4_2(X8,X9))
| epred1_2(X9,X8) )
& ( ~ apply(X9,esk7_2(X8,X9),esk9_2(X8,X9))
| ~ apply(X9,esk6_2(X8,X9),esk5_2(X8,X9))
| ~ apply(X9,esk4_2(X8,X9),esk4_2(X8,X9))
| epred1_2(X9,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)],[c_0_3])])])])])])]) ).
cnf(c_0_9,plain,
( epred1_2(X1,X2)
| ~ equivalence(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
equivalence(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X8,X9,X10,X11,X8,X9,X10,X11] :
( ( member(X11,X9)
| ~ member(X11,equivalence_class(X10,X9,X8)) )
& ( apply(X8,X10,X11)
| ~ member(X11,equivalence_class(X10,X9,X8)) )
& ( ~ member(X11,X9)
| ~ apply(X8,X10,X11)
| member(X11,equivalence_class(X10,X9,X8)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equivalence_class])])])])]) ).
cnf(c_0_12,plain,
( apply(X1,X3,X3)
| ~ epred1_2(X1,X2)
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
epred1_2(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
( member(X1,equivalence_class(X2,X3,X4))
| ~ apply(X4,X2,X1)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( apply(esk2_0,X1,X1)
| ~ member(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,negated_conjecture,
~ member(esk3_0,equivalence_class(esk3_0,esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,plain,
( member(X1,equivalence_class(X1,X2,esk2_0))
| ~ member(X1,esk1_0)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,negated_conjecture,
member(esk3_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET766+4 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.12 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 07:54:58 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.22/1.40 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.22/1.40 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.22/1.40 # Preprocessing time : 0.016 s
% 0.22/1.40
% 0.22/1.40 # Proof found!
% 0.22/1.40 # SZS status Theorem
% 0.22/1.40 # SZS output start CNFRefutation
% See solution above
% 0.22/1.40 # Proof object total steps : 20
% 0.22/1.40 # Proof object clause steps : 10
% 0.22/1.40 # Proof object formula steps : 10
% 0.22/1.40 # Proof object conjectures : 8
% 0.22/1.40 # Proof object clause conjectures : 5
% 0.22/1.40 # Proof object formula conjectures : 3
% 0.22/1.40 # Proof object initial clauses used : 6
% 0.22/1.40 # Proof object initial formulas used : 3
% 0.22/1.40 # Proof object generating inferences : 4
% 0.22/1.40 # Proof object simplifying inferences : 2
% 0.22/1.40 # Training examples: 0 positive, 0 negative
% 0.22/1.40 # Parsed axioms : 17
% 0.22/1.40 # Removed by relevancy pruning/SinE : 14
% 0.22/1.40 # Initial clauses : 59
% 0.22/1.40 # Removed in clause preprocessing : 0
% 0.22/1.40 # Initial clauses in saturation : 59
% 0.22/1.40 # Processed clauses : 62
% 0.22/1.40 # ...of these trivial : 0
% 0.22/1.40 # ...subsumed : 0
% 0.22/1.40 # ...remaining for further processing : 62
% 0.22/1.40 # Other redundant clauses eliminated : 0
% 0.22/1.40 # Clauses deleted for lack of memory : 0
% 0.22/1.40 # Backward-subsumed : 0
% 0.22/1.40 # Backward-rewritten : 0
% 0.22/1.40 # Generated clauses : 105
% 0.22/1.40 # ...of the previous two non-trivial : 100
% 0.22/1.40 # Contextual simplify-reflections : 0
% 0.22/1.40 # Paramodulations : 105
% 0.22/1.40 # Factorizations : 0
% 0.22/1.40 # Equation resolutions : 0
% 0.22/1.40 # Current number of processed clauses : 62
% 0.22/1.40 # Positive orientable unit clauses : 3
% 0.22/1.40 # Positive unorientable unit clauses: 0
% 0.22/1.40 # Negative unit clauses : 1
% 0.22/1.40 # Non-unit-clauses : 58
% 0.22/1.40 # Current number of unprocessed clauses: 97
% 0.22/1.40 # ...number of literals in the above : 532
% 0.22/1.40 # Current number of archived formulas : 0
% 0.22/1.40 # Current number of archived clauses : 0
% 0.22/1.40 # Clause-clause subsumption calls (NU) : 749
% 0.22/1.40 # Rec. Clause-clause subsumption calls : 374
% 0.22/1.40 # Non-unit clause-clause subsumptions : 0
% 0.22/1.40 # Unit Clause-clause subsumption calls : 52
% 0.22/1.40 # Rewrite failures with RHS unbound : 0
% 0.22/1.40 # BW rewrite match attempts : 0
% 0.22/1.40 # BW rewrite match successes : 0
% 0.22/1.40 # Condensation attempts : 0
% 0.22/1.40 # Condensation successes : 0
% 0.22/1.40 # Termbank termtop insertions : 5766
% 0.22/1.40
% 0.22/1.40 # -------------------------------------------------
% 0.22/1.40 # User time : 0.022 s
% 0.22/1.40 # System time : 0.001 s
% 0.22/1.40 # Total time : 0.023 s
% 0.22/1.40 # Maximum resident set size: 3088 pages
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