%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWV158+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:53:50 PM UTC 2026
% Result : Theorem 0.13s 0.44s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 1
% Syntax : Number of formulae : 7 ( 4 unt; 0 def)
% Number of atoms : 49 ( 18 equ)
% Maximal formula atoms : 15 ( 7 avg)
% Number of connectives : 49 ( 7 ~; 4 |; 28 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 17 con; 0-3 aty)
% Number of variables : 8 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cl5_nebula_norm_0008,conjecture,
( ( ! [X18] :
( ( leq(X18,pred(pv10))
& leq(n0,X18) )
=> sum(n0,n4,a_select3(q,X18,tptp_sum_index)) = n1 )
& ! [X14] :
( ( leq(X14,pred(pv47))
& leq(n0,X14) )
=> 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))))) )
& leq(pv47,n4)
& leq(pv10,n135299)
& leq(n0,pv47)
& leq(n0,pv10)
& 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)))) )
=> ! [X4] :
( ( leq(X4,pv47)
& leq(n0,X4) )
=> ( pv47 = X4
=> divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,pv47)),minus(a_select2(x,pv10),a_select2(mu,pv47))),tptp_minus_2),times(a_select2(sigma,pv47),a_select2(sigma,pv47)))),a_select2(rho,pv47)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,pv47))),pv84) = 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/benchmark/theBenchmark.p',cl5_nebula_norm_0008) ).
fof(c_0_1,negated_conjecture,
~ ( ( ! [X18] :
( ( leq(X18,pred(pv10))
& leq(n0,X18) )
=> sum(n0,n4,a_select3(q,X18,tptp_sum_index)) = n1 )
& ! [X14] :
( ( leq(X14,pred(pv47))
& leq(n0,X14) )
=> 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))))) )
& leq(pv47,n4)
& leq(pv10,n135299)
& leq(n0,pv47)
& leq(n0,pv10)
& 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)))) )
=> ! [X4] :
( ( leq(X4,pv47)
& leq(n0,X4) )
=> ( pv47 = X4
=> divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,pv47)),minus(a_select2(x,pv10),a_select2(mu,pv47))),tptp_minus_2),times(a_select2(sigma,pv47),a_select2(sigma,pv47)))),a_select2(rho,pv47)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,pv47))),pv84) = 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_0008]) ).
fof(c_0_2,negated_conjecture,
! [X28,X29] :
( divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,pv47)),minus(a_select2(x,pv10),a_select2(mu,pv47))),tptp_minus_2),times(a_select2(sigma,pv47),a_select2(sigma,pv47)))),a_select2(rho,pv47)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,pv47))),pv84) != 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)))))
& pv47 = esk1_0
& leq(esk1_0,pv47)
& leq(n0,esk1_0)
& ( sum(n0,n4,a_select3(q,X29,tptp_sum_index)) = n1
| ~ leq(X29,pred(pv10))
| ~ leq(n0,X29) )
& ( a_select3(q,pv10,X28) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X28)),minus(a_select2(x,pv10),a_select2(mu,X28))),tptp_minus_2),times(a_select2(sigma,X28),a_select2(sigma,X28)))),a_select2(rho,X28)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X28))),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(X28,pred(pv47))
| ~ leq(n0,X28) )
& leq(pv47,n4)
& leq(pv10,n135299)
& leq(n0,pv47)
& leq(n0,pv10)
& 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(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])])])]) ).
cnf(c_0_3,negated_conjecture,
divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,pv47)),minus(a_select2(x,pv10),a_select2(mu,pv47))),tptp_minus_2),times(a_select2(sigma,pv47),a_select2(sigma,pv47)))),a_select2(rho,pv47)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,pv47))),pv84) != 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_2]) ).
cnf(c_0_4,negated_conjecture,
pv47 = esk1_0,
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_5,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_2]) ).
cnf(c_0_6,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_3,c_0_4]),c_0_4]),c_0_4]),c_0_4]),c_0_4]),c_0_4]),c_0_5])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV158+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 08:33:13 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.44 % Version: 3.5.1
% 0.13/0.44 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.13/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.44 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.13/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.44 % Starting sh5l with 300s (1) cores
% 0.13/0.44 % new_bool_3 with pid 1327828 completed with status 0
% 0.13/0.44 % Result found by new_bool_3
% 0.13/0.44 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.13/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.44 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.13/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.13/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.13/0.44 % Search class: FGUSM-FFMM31-DFFFFFNN
% 0.13/0.44 % partial match(1): FGHSM-FFMM31-DFFFFFNN
% 0.13/0.44 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.13/0.44 % SubtermCWHack with pid 1327832 completed with status 0
% 0.13/0.44 % Result found by SubtermCWHack
% 0.13/0.44 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.13/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.44 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.13/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.13/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.13/0.44 % Search class: FGUSM-FFMM31-DFFFFFNN
% 0.13/0.44 % partial match(1): FGHSM-FFMM31-DFFFFFNN
% 0.13/0.44 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.13/0.44 % Preprocessing time : 0.002 s
% 0.13/0.44
% 0.13/0.44 % Proof found!
% 0.13/0.44 % SZS status Theorem
% 0.13/0.44 % SZS output start CNFRefutation
% See solution above
% 0.13/0.44 % Parsed axioms : 100
% 0.13/0.44 % Removed by relevancy pruning/SinE : 23
% 0.13/0.44 % Initial clauses : 90
% 0.13/0.44 % Removed in clause preprocessing : 0
% 0.13/0.44 % Initial clauses in saturation : 90
% 0.13/0.44 % Processed clauses : 352
% 0.13/0.44 % ...of these trivial : 3
% 0.13/0.44 % ...subsumed : 116
% 0.13/0.44 % ...remaining for further processing : 232
% 0.13/0.44 % Other redundant clauses eliminated : 0
% 0.13/0.44 % Clauses deleted for lack of memory : 0
% 0.13/0.44 % Backward-subsumed : 1
% 0.13/0.44 % Backward-rewritten : 10
% 0.13/0.44 % Generated clauses : 867
% 0.13/0.44 % ...of the previous two non-redundant : 549
% 0.13/0.44 % ...aggressively subsumed : 0
% 0.13/0.44 % Contextual simplify-reflections : 0
% 0.13/0.44 % Paramodulations : 865
% 0.13/0.44 % Factorizations : 2
% 0.13/0.44 % NegExts : 0
% 0.13/0.44 % Equation resolutions : 0
% 0.13/0.44 % Disequality decompositions : 0
% 0.13/0.44 % Total rewrite steps : 441
% 0.13/0.44 % ...of those cached : 367
% 0.13/0.44 % Propositional unsat checks : 0
% 0.13/0.44 % Propositional check models : 0
% 0.13/0.44 % Propositional check unsatisfiable : 0
% 0.13/0.44 % Propositional clauses : 0
% 0.13/0.44 % Propositional clauses after purity: 0
% 0.13/0.44 % Propositional unsat core size : 0
% 0.13/0.44 % Propositional preprocessing time : 0.000
% 0.13/0.44 % Propositional encoding time : 0.000
% 0.13/0.44 % Propositional solver time : 0.000
% 0.13/0.44 % Success case prop preproc time : 0.000
% 0.13/0.44 % Success case prop encoding time : 0.000
% 0.13/0.44 % Success case prop solver time : 0.000
% 0.13/0.44 % Current number of processed clauses : 221
% 0.13/0.44 % Positive orientable unit clauses : 101
% 0.13/0.44 % Positive unorientable unit clauses: 0
% 0.13/0.44 % Negative unit clauses : 28
% 0.13/0.44 % Non-unit-clauses : 92
% 0.13/0.44 % Current number of unprocessed clauses: 287
% 0.13/0.44 % ...number of literals in the above : 752
% 0.13/0.44 % Current number of archived formulas : 0
% 0.13/0.44 % Current number of archived clauses : 11
% 0.13/0.44 % Clause-clause subsumption calls (NU) : 2476
% 0.13/0.44 % Rec. Clause-clause subsumption calls : 1648
% 0.13/0.44 % Non-unit clause-clause subsumptions : 23
% 0.13/0.44 % Unit Clause-clause subsumption calls : 1073
% 0.13/0.44 % Rewrite failures with RHS unbound : 0
% 0.13/0.44 % BW rewrite match attempts : 12
% 0.13/0.44 % BW rewrite match successes : 7
% 0.13/0.44 % Condensation attempts : 0
% 0.13/0.44 % Condensation successes : 0
% 0.13/0.44 % Termbank termtop insertions : 12362
% 0.13/0.44 % Search garbage collected termcells : 752
% 0.13/0.44
% 0.13/0.44 % -------------------------------------------------
% 0.13/0.44 % User time : 0.016 s
% 0.13/0.44 % System time : 0.005 s
% 0.13/0.44 % Total time : 0.020 s
% 0.13/0.44 % Maximum resident set size: 3760 pages
% 0.13/0.44
% 0.13/0.44 % -------------------------------------------------
% 0.13/0.44 % User time : 0.019 s
% 0.13/0.44 % System time : 0.009 s
% 0.13/0.44 % Total time : 0.028 s
% 0.13/0.44 % Maximum resident set size: 4864 pages
% 0.13/0.45 % E exiting
%------------------------------------------------------------------------------