TSTP Solution File: SWV157+1 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SWV157+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n019.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 : Wed Jul 20 18:15:24 EDT 2022
% Result : Theorem 0.22s 1.41s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 12 unt; 0 def)
% Number of atoms : 85 ( 28 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 86 ( 26 ~; 18 |; 30 &)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 17 con; 0-3 aty)
% Number of variables : 30 ( 2 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cl5_nebula_norm_0007,conjecture,
( ( pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))
& leq(n0,pv10)
& leq(n0,pv47)
& leq(pv10,n135299)
& leq(pv47,n4)
& ! [X14] :
( ( leq(n0,X14)
& leq(X14,pred(pv47)) )
=> a_select3(q,pv10,X14) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X14)),minus(a_select2(x,pv10),a_select2(mu,X14))),tptp_minus_2),times(a_select2(sigma,X14),a_select2(sigma,X14)))),a_select2(rho,X14)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X14))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) )
& ! [X18] :
( ( leq(n0,X18)
& leq(X18,pred(pv10)) )
=> sum(n0,n4,a_select3(q,X18,tptp_sum_index)) = n1 ) )
=> ! [X4] :
( ( leq(n0,X4)
& leq(X4,pv47) )
=> ( pv47 != X4
=> a_select3(q,pv10,X4) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X4)),minus(a_select2(x,pv10),a_select2(mu,X4))),tptp_minus_2),times(a_select2(sigma,X4),a_select2(sigma,X4)))),a_select2(rho,X4)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X4))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',cl5_nebula_norm_0007) ).
fof(pred_minus_1,axiom,
! [X1] : minus(X1,n1) = pred(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',pred_minus_1) ).
fof(leq_gt_pred,axiom,
! [X1,X2] :
( leq(X1,pred(X2))
<=> gt(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',leq_gt_pred) ).
fof(leq_gt2,axiom,
! [X1,X2] :
( ( leq(X1,X2)
& X1 != X2 )
=> gt(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',leq_gt2) ).
fof(c_0_4,negated_conjecture,
~ ( ( pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))
& leq(n0,pv10)
& leq(n0,pv47)
& leq(pv10,n135299)
& leq(pv47,n4)
& ! [X14] :
( ( leq(n0,X14)
& leq(X14,pred(pv47)) )
=> a_select3(q,pv10,X14) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X14)),minus(a_select2(x,pv10),a_select2(mu,X14))),tptp_minus_2),times(a_select2(sigma,X14),a_select2(sigma,X14)))),a_select2(rho,X14)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X14))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) )
& ! [X18] :
( ( leq(n0,X18)
& leq(X18,pred(pv10)) )
=> sum(n0,n4,a_select3(q,X18,tptp_sum_index)) = n1 ) )
=> ! [X4] :
( ( leq(n0,X4)
& leq(X4,pv47) )
=> ( pv47 != X4
=> a_select3(q,pv10,X4) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X4)),minus(a_select2(x,pv10),a_select2(mu,X4))),tptp_minus_2),times(a_select2(sigma,X4),a_select2(sigma,X4)))),a_select2(rho,X4)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X4))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) ) ) ),
inference(assume_negation,[status(cth)],[cl5_nebula_norm_0007]) ).
fof(c_0_5,negated_conjecture,
! [X19,X20] :
( pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))
& leq(n0,pv10)
& leq(n0,pv47)
& leq(pv10,n135299)
& leq(pv47,n4)
& ( ~ leq(n0,X19)
| ~ leq(X19,pred(pv47))
| a_select3(q,pv10,X19) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X19)),minus(a_select2(x,pv10),a_select2(mu,X19))),tptp_minus_2),times(a_select2(sigma,X19),a_select2(sigma,X19)))),a_select2(rho,X19)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X19))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) )
& ( ~ leq(n0,X20)
| ~ leq(X20,pred(pv10))
| sum(n0,n4,a_select3(q,X20,tptp_sum_index)) = n1 )
& leq(n0,esk1_0)
& leq(esk1_0,pv47)
& pv47 != esk1_0
& a_select3(q,pv10,esk1_0) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,esk1_0)),minus(a_select2(x,pv10),a_select2(mu,esk1_0))),tptp_minus_2),times(a_select2(sigma,esk1_0),a_select2(sigma,esk1_0)))),a_select2(rho,esk1_0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,esk1_0))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) ),
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_4])])])])])]) ).
fof(c_0_6,plain,
! [X2] : minus(X2,n1) = pred(X2),
inference(variable_rename,[status(thm)],[pred_minus_1]) ).
cnf(c_0_7,negated_conjecture,
( a_select3(q,pv10,X1) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X1)),minus(a_select2(x,pv10),a_select2(mu,X1))),tptp_minus_2),times(a_select2(sigma,X1),a_select2(sigma,X1)))),a_select2(rho,X1)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X1))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index)))))
| ~ leq(X1,pred(pv47))
| ~ leq(n0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
minus(X1,n1) = pred(X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
a_select3(q,pv10,esk1_0) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,esk1_0)),minus(a_select2(x,pv10),a_select2(mu,esk1_0))),tptp_minus_2),times(a_select2(sigma,esk1_0),a_select2(sigma,esk1_0)))),a_select2(rho,esk1_0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,esk1_0))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index)))),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,negated_conjecture,
( a_select3(q,pv10,X1) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X1)),minus(a_select2(x,pv10),a_select2(mu,X1))),tptp_minus_2),times(a_select2(sigma,X1),a_select2(sigma,X1)))),a_select2(rho,X1)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X1))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index)))))
| ~ leq(n0,X1)
| ~ leq(X1,minus(pv47,n1)) ),
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
fof(c_0_12,plain,
! [X3,X4,X3,X4] :
( ( ~ leq(X3,pred(X4))
| gt(X4,X3) )
& ( ~ gt(X4,X3)
| leq(X3,pred(X4)) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[leq_gt_pred])])])]) ).
fof(c_0_13,plain,
! [X3,X4] :
( ~ leq(X3,X4)
| X3 = X4
| gt(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[leq_gt2])]) ).
cnf(c_0_14,negated_conjecture,
a_select3(q,pv10,esk1_0) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,esk1_0)),minus(a_select2(x,pv10),a_select2(mu,esk1_0))),tptp_minus_2),times(a_select2(sigma,esk1_0),a_select2(sigma,esk1_0)))),a_select2(rho,esk1_0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,esk1_0))),pv84),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,negated_conjecture,
( a_select3(q,pv10,X1) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X1)),minus(a_select2(x,pv10),a_select2(mu,X1))),tptp_minus_2),times(a_select2(sigma,X1),a_select2(sigma,X1)))),a_select2(rho,X1)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X1))),pv84)
| ~ leq(X1,minus(pv47,n1))
| ~ leq(n0,X1) ),
inference(rw,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_16,negated_conjecture,
leq(n0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_17,plain,
( leq(X1,pred(X2))
| ~ gt(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( gt(X1,X2)
| X2 = X1
| ~ leq(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,negated_conjecture,
leq(esk1_0,pv47),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_20,negated_conjecture,
pv47 != esk1_0,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_21,negated_conjecture,
~ leq(esk1_0,minus(pv47,n1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]) ).
cnf(c_0_22,plain,
( leq(X1,minus(X2,n1))
| ~ gt(X2,X1) ),
inference(rw,[status(thm)],[c_0_17,c_0_8]) ).
cnf(c_0_23,negated_conjecture,
gt(pv47,esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SWV157+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.07/0.12 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n019.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 : Wed Jun 15 13:15:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.22/1.41 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.22/1.41 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.22/1.41 # Preprocessing time : 0.021 s
% 0.22/1.41
% 0.22/1.41 # Proof found!
% 0.22/1.41 # SZS status Theorem
% 0.22/1.41 # SZS output start CNFRefutation
% See solution above
% 0.22/1.41 # Proof object total steps : 25
% 0.22/1.41 # Proof object clause steps : 16
% 0.22/1.41 # Proof object formula steps : 9
% 0.22/1.41 # Proof object conjectures : 15
% 0.22/1.41 # Proof object clause conjectures : 12
% 0.22/1.41 # Proof object formula conjectures : 3
% 0.22/1.41 # Proof object initial clauses used : 9
% 0.22/1.41 # Proof object initial formulas used : 4
% 0.22/1.41 # Proof object generating inferences : 3
% 0.22/1.41 # Proof object simplifying inferences : 9
% 0.22/1.41 # Training examples: 0 positive, 0 negative
% 0.22/1.41 # Parsed axioms : 100
% 0.22/1.41 # Removed by relevancy pruning/SinE : 23
% 0.22/1.41 # Initial clauses : 90
% 0.22/1.41 # Removed in clause preprocessing : 2
% 0.22/1.41 # Initial clauses in saturation : 88
% 0.22/1.41 # Processed clauses : 93
% 0.22/1.41 # ...of these trivial : 0
% 0.22/1.41 # ...subsumed : 0
% 0.22/1.41 # ...remaining for further processing : 93
% 0.22/1.41 # Other redundant clauses eliminated : 0
% 0.22/1.41 # Clauses deleted for lack of memory : 0
% 0.22/1.41 # Backward-subsumed : 0
% 0.22/1.41 # Backward-rewritten : 4
% 0.22/1.41 # Generated clauses : 245
% 0.22/1.41 # ...of the previous two non-trivial : 224
% 0.22/1.41 # Contextual simplify-reflections : 0
% 0.22/1.41 # Paramodulations : 243
% 0.22/1.41 # Factorizations : 2
% 0.22/1.41 # Equation resolutions : 0
% 0.22/1.41 # Current number of processed clauses : 89
% 0.22/1.41 # Positive orientable unit clauses : 59
% 0.22/1.41 # Positive unorientable unit clauses: 3
% 0.22/1.41 # Negative unit clauses : 4
% 0.22/1.41 # Non-unit-clauses : 23
% 0.22/1.41 # Current number of unprocessed clauses: 210
% 0.22/1.41 # ...number of literals in the above : 541
% 0.22/1.41 # Current number of archived formulas : 0
% 0.22/1.41 # Current number of archived clauses : 6
% 0.22/1.41 # Clause-clause subsumption calls (NU) : 129
% 0.22/1.41 # Rec. Clause-clause subsumption calls : 25
% 0.22/1.41 # Non-unit clause-clause subsumptions : 0
% 0.22/1.41 # Unit Clause-clause subsumption calls : 98
% 0.22/1.41 # Rewrite failures with RHS unbound : 0
% 0.22/1.41 # BW rewrite match attempts : 16
% 0.22/1.41 # BW rewrite match successes : 15
% 0.22/1.41 # Condensation attempts : 0
% 0.22/1.41 # Condensation successes : 0
% 0.22/1.41 # Termbank termtop insertions : 7469
% 0.22/1.41
% 0.22/1.41 # -------------------------------------------------
% 0.22/1.41 # User time : 0.031 s
% 0.22/1.41 # System time : 0.002 s
% 0.22/1.41 # Total time : 0.033 s
% 0.22/1.41 # Maximum resident set size: 3504 pages
%------------------------------------------------------------------------------